Talk:Interval (music)/Archive 2

This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Archive 1

Archive 2

Archive 3

Archiving, and Diatonic and chromatic now established

I have now added a lot of recent material to the archive. A new article has been set up, partly to deal with issues of terminology that have arisen here . Discussion about application of the terms diatonic and chromatic, as applied to intervals or to anything else, is best conducted in the context of that article. I suggest that we now discontinue any such general debate here (and at Talk:Diatonic scale, Talk:Diminished seventh, etc.), and confine it to Talk:Diatonic and chromatic. – Noetica^♬Talk 02:30, 29 March 2007 (UTC)

[A recent question, rescued from the archive (– Noetica^♬Talk 02:30, 29 March 2007 (UTC)):]

I thought an interval was perfect because it used notes that appear only once in the harmonic series or am I misunderstanding something? 68.18.179.218 02:07, 29 March 2007 (UTC)

No, anonymous. The overtones that are responsible for the perfect intervals (in one theory of such intervals) recur at every octave above their first occurrence. (So, in fact, do all overtones.) They may be called perfect for the reason the article gives (and this is connected with their occurrence early in the overtone series); or there may be other reasons.

– Noetica^♬♩ Talk 07:31, 7 May 2007 (UTC)

The intervals table down from C, the image has a mistake, "F5" instead of "P5" i think most people looking at it would realize the mistake, but to some who are not used to this information it may be confusing.

Good point, anonymous. Unfortunately it's a graphic, so it can't be edited within the article itself. Perhaps the editor who made the image will now fix it.

– Noetica^♬♩ Talk 07:31, 7 May 2007 (UTC)

Worldwide view of intervals

How does this article lack a worldwide view? What views should be added? Hyacinth 03:25, 17 June 2007 (UTC)

Usage in chords

Chord:

minor 7th is "m7", not "7". "7" is for dominant 7th. —The preceding unsigned comment was added by 219.71.98.132 (talk) 15:25, August 23, 2007 (UTC)

No, the interval of a minor 7th as part of a chord is indicated by 7 alone. If there is additionally a minor 3rd, the symbol "m" is added as well. −Woodstone 16:26, 23 August 2007 (UTC)

Promotional links

Please see WP:LINKS before re-adding a link intended to promote a website or product. aruffo 05:15, 1 November 2007 (UTC)

I am aware of the way things work with WP links, and I feel mine meets the requirements. It's a free site, no ads, and it gathers useful, scientific data from the users, check it out. Is that not enough? --68.229.94.217 18:09, 2 November 2007 (UTC)

Not usually, no. Read "Links normally to be avoided" and the section immediately following. You also may want to look at WP:NOT for notability guidelines. aruffo 19:09, 2 November 2007 (UTC)

What an interval is

Ask any musician or piano technician to play an interval on the piano, and there's no question of what you mean. Ask for a fifth, a minor third, an augmented unison, a doubly-diminished third, no problem. A minor seventeenth might require some thinking, but everybody knows what it is.

(As for "distances," I thought they were measured in parsecs, nanometers, and the like. Asking for the "distance" of an interval makes no sense to me. I opine that what is meant by "distance" herein is just another sense of the word "interval," one which is measurable in semitones, cents, or octaves, but not in inches.)

To me, an interval, as used in music theory, has an upper note and a lower note, depending on their positions on the musical staff, not on their pitches. In the case of the diminished unison, the upper note is actually lower in pitch ("flatter") than the lower one. In the case of the diminished second, they coincide. The only exception is the perfect unison, in which (conceptually) two notes coincide, and neither is upper nor lower.

Unraveling the complexities of music vocabulary will surely present a challenge! D021317c 03:19, 9 November 2007 (UTC)

Complexities indeed, D. This article is badly written, self-contradictory, and a nest of disputes just waiting to be activated. Otherwise I'd be doing something to fix it! Is the augmented fifth diatonic? Yes, if you count the harmonic and ascending melodic minor scales among diatonic scales; no, if you don't; but hang on: yes, because it's listed in the table at the end of the article as a diatonic interval [Altered since I wrote that.–_⊥^{¡ɐɔıʇǝo}Noetica!^T– 11:24, 2 May 2008 (UTC)]. Because of this sort of entrenched confusion I decided not to persist in editing the Augean Article (here and elsewhere: see Diminished seventh, for example). I initiated Diatonic and chromatic instead. Take a look, sometime.

– Noetica^♬♩ Talk 05:57, 9 November 2007 (UTC)

Quality of Page?

I'm not a musical theory buff, but a Diminished fourth is the same as a major third (NOT technically I'm sure but that's not the point.) Either way it's not in a harmonic minor scale.... Am I missing something?? The third is lowered a half step and 7th raised a half step. An "diminished fourth" is actually in the MAJOR scale? This article (and many music articles) need more defining of terms and less contradictions. It's hard to take these articles as authoritative when there are glaring inaccuracies even to an amateur player.

I appreciate all the contributions, I just wish people like me who are learning and trusting these articles felt more confident of their integrity. --NotDazedbutConfused (talk) 01:16, 2 May 2008 (UTC)

Well ND, I agree that this article is of questionable quality. There are several competing approaches to music theory used in Wikipedia, and together these yield a disgraceful confusion – disheartening and unhelpful to the student. I do not contribute to this page, because there would be too many disputes if I did.

But the statement about the diminished fourth is accurate. Consider the notes B and E♭, and the interval B–E♭. This must be a fourth of some sort, yes? Ignoring flats and sharps, just count the letters: B, C, D, E. Four notes. Now, B–E and B♭–E♭ are perfect fourths; but the interval B–E♭ is one semitone short of a perfect fourth. That makes it a diminished fourth. We are interested in intervals between any pair of notes in a scale, not just intervals involving the keynote. The notes B and E♭ occur in the scale C harmonic minor (...C–D–E♭–F–G–A♭–B–C–D–E♭–F–G...), so the diminished fourth that they make up also occurs in C harmonic minor. (Its inversion E♭–B also occurs in C harmonic minor. E–B and E♭–B♭ are perfect fifths; E♭–B is one semitone larger than either of those, so it is an augmented fifth.)

Yes, in an important sense a diminished fourth is "the same as" a major third (B–D♯, for example): it spans the same number of semitones. But these intervals fit into the conventional scales of Western music theory quite differently. To explain any of this from the ground up so that anyone could follow would take a great deal of time and patience. But I hope what I have said will help.

–_⊥^{¡ɐɔıʇǝo}Noetica!^T– 11:19, 2 May 2008 (UTC)

Yes that does help a lot. I follow the argument, I still don't understand the reason for the different notation (way of looking at it) I guess. I always just think of the root that I'm looking at and then the scale up from there, but thanks for the clarification. I understand that it could be tedious and take a great deal of time and patience to address this all from the ground up, but I feel wikipedia should be that thorough or at least have references to something that thorough. Do you know any site where this can be learned or added to wiki? I have no formal (school) music education and don't have the time to enroll, but am interested. Thanks. NotDazedbutConfused (talk) 23:09, 3 May 2008 (UTC)

It's actually explained on Wikipedia, but the explanation is scattered (most of it appears at enharmonic, albeit in somewhat technical language). This is as simple as I can get it: the major third and diminished fourth happen to be given the same width in the tuning system commonly used today (twelve-tone equal temperament). But in other tuning systems, such as quarter-comma meantone (which was the most common system for the early Baroque), they are not the same: the diminished fourth is actually a little wider. Since the system of naming pitches and intervals was developed at that time, it preserves the distinction, even though in performance it no longer exists. Sort of like how written English preserves spelling distinctions between words that used to sound different but are now homonyms. I hope this helps. — Gwalla | Talk 22:14, 13 June 2008 (UTC)

Compound intervals

The article said:

Intervals larger than a thirteenth seldom need to be spoken of, most often being referred to by their compound names, for example "two octaves plus a fifth" rather than "a 20th".

The reference for that statement was Aikin, Jim (2004). A Player's Guide to Chords and Harmony: Music Theory for Real-World Musicians, p.24. ISBN 0879307986.

An anonymous editor changed the "20th" to "21th" [sic], and then changed back to 20th. That drew my attention.

By my calculation two octaves plus a fifth would work out as a 19th, not a 20th. C to the C above is one octave - an 8th. If we then go to the C above that, it becomes two octaves - a 15th. D is a 16th; E is a 17th; F is an 18th; G is a 19th.

I hesitate to tamper with a quotation. But perhaps the reference is just intended to say that this information (i.e. that we generally talk about two octaves plus a fifth rather than wasting time trying to count exactly how many notes that would be) is found in Aikin, not that those actual examples are given in his book. The quotation marks don't prove that we're quoting Aikin's actual words, as they indicate just that musicians don't normally say "18th", "19th", etc.

I don't have Aikin, but if someone does, it would be good to look it up and see exactly what he says. Rigaudon (talk) 01:43, 30 May 2009 (UTC)

I'm okay with the recent change, which attributes the "two octaves plus a fifth" directly to Aikin's book, but doesn't attribute the "19th" or the "20th" to it. Rigaudon (talk) 19:49, 3 June 2009 (UTC)

Defnition major/minor/perfect

The speculative improved definition was not in line with actual musical definitions and was therefore justly reverted. But it had some merit in explaining the structure. I have now inserted an improved explanation of the definition that keeps the explanatory power, but stays in line with practice. −Woodstone (talk) 04:50, 4 January 2010 (UTC)

It is surprising how difficult it can be to set out in plain English a concept as simple as the definition of interval quality. I'll take a look at your new effort, and see if I can improve on it, or not.—Jerome Kohl (talk) 04:57, 4 January 2010 (UTC)

Explanation for beginners?

I hesitate to try contributing to an article on which I have no expertise, but-- speaking as somebody with no expertise-- I have to say that this article doesn't explain things very well Would it be possible to add a "for beginners" introduction to the beginning to make the article understandable to somebody who doesn't already understand the subject? Geoffrey.landis (talk) 20:58, 25 January 2010 (UTC)

You're absolutely right. In fact you would be perfectly justified in being stronger in your comments about the article. The topic, Interval, is an important cornerstone throughout music, including at a relatively early beginner level. Therefore this article should be written with beginners in mind, particularly at the article's start; likewise the advanced stuff should be left until relatively late. All that stuff near the top about cents and mathematical equations is, from the beginner's perspective, meaningless esoteric geekery. (For some more advanced musicians it can actually be an interesting topic, in the same way that Einstein's General Relativity is interesting to university-level Physics students. But neither is a "beginner start here" topic.) Yes, some mention of it probably belongs in the article, but certainly not at the top. (One wouldn't start an article about wristwatches with Einstein time dilation; one shouldn't start an article about music intervals with cents and commas.) Of course, answering the question "how should the article be structured?" is an interesting challenge. Perhaps you could help. Do a quick skim-read of it, pick out the bits that seem, to you, to shed some light. Then we can consider how we might place those relatively early in the article. (But if you are a Cambridge or Harvard Maths professor, could you temporarily lay aside that day-job in your skim-reading, please!) Feline Hymnic (talk) 17:28, 16 January 2011 (UTC)

Atonality and dissonance

The statement, "In atonal music all intervals (or interval classes) are considered equally consonant melodically and harmonically," is simply incorrect and I will attempt to remove it after typing this. Even in atonal music, a perfect fifth is more consonant than a minor second. This is a matter of acoustics, not compositional treatment. Atonal music uses dissonance differently than tonality does. It doesn't redefine it. —Preceding unsigned comment added by 72.183.235.172 (talk) 08:59, 11 February 2010 (UTC)

Interval Number

The article says: "In Western harmonic theory, intervals are labeled according to the number of staff positions or scale degrees they encompass"

I am not sure that this sentence is accurate. The number of scale steps does not always coincide with the number of staff positions (e.g. if we are using a chromatic scale). I propose to delete the reference to scale steps. Paolo.dL (talk) 23:09, 24 June 2010 (UTC)

Your recent edits have all been very sensible, resulting in nothing but improvements to the clarity of the article, but in this case it appears you are asking for support, which suggests you have some doubts. I think you are right to worry, because this particular definition has a great potential to confuse the beginner. The (usually unspecified) assumption is that "scale degree" refers to diatonic (rather than pentatonic, chromatic, microtonal, etc.) scales, but the same assumption applies (even if with less danger of confusion) to "staff position", since this only has meaning if the reader understands that the conventional staff is based on a diatonic conception of the scale (and that the conventional staff is meant). I find that true beginners also tend to assume that "staff position" might refer only to the lines, or only to the spaces of the staff. Another, more technical factor is that intervals are counted according to scale degree whether they are written down or not, and whether or not the conventional staff is used or even is capable of being used to represent them (for example, in just-intonation systems—even purely diatonic ones—we are accustomed to speak of "large" and "small" minor seconds, etc.). I would suggest keeping "scale step" (or "scale degree"), together with a better explanation of what this term means, perhaps with a comparison to traditional staff notation.—Jerome Kohl (talk) 23:59, 24 June 2010 (UTC)

It is indeed a problem that the whole interval terminology is so completely bound to the western diatonic scale. Even the fundamental "octave" does not have a more objective name. However, instead of removing "staff", I would favour removing "scale". Everybody interested in music theory will have at least seen the 5-line staff. We might make explicit that both lines and gaps are counted. −Woodstone (talk) 19:24, 25 June 2010 (UTC)

Thank you for explaining and for your edit. Paolo.dL (talk) 19:11, 26 June 2010 (UTC)

Drifting from interval to tuning

Hi Paolo.dL, with the latest additions, the focus of this article is drifting from "intervals" to "tuning". I wonder if this is the right place to add all these details. Especially mentioning the various sizes of intervals depending on the location in the scale may be confusing here. You added them to the meantone system, but not the 5-limit tuning. This may confuse the readers into thinking the intervals are all the same in 5-limit. −Woodstone (talk) 05:15, 28 June 2010 (UTC)

The recent edits adding variants to 5-limit tuning will be even more confusing to the reader. Originally, the table had the intervals from the tonic of the tuning. Now all internal intervals are added. It muddles the table. I think that if you want to enter all this information, another place for it should be found. Perhaps then, a real table showing which intervals occur where could be given. −Woodstone (talk) 12:23, 28 June 2010 (UTC)

Sorry, I read your comments only now. The section was called "Comparison of different interval naming systems", I changed it to "Comparison between tuning systems", because the focus of the table did not seem to be on the "naming systems". The text referred to methods to compare tuning systems, and methods to obtain "just intonation", not to naming systems. Perhaps I misinterpreted the intention of the author. The table with this comparison was already in the article, and I thought it was very useful, but it was incomplete in my opinion. Do you think we should move it to Tuning systems? The opinion of others is welcome as well. Paolo.dL (talk) 13:42, 28 June 2010 (UTC)

I checked the article about Tuning systems, and there is already a comparison, but there's no comparison which analyses interval sizes, as in the table we are discussing. This comparison focuses on interval sizes. The article about wolf fifth (just one of the intervals) includes a comparison between tuning systems and some insightful information about varied interval sizes. I was inspired by that article. I am not saying that we should keep this section in this article. I am only a guest here. You and the other authors of this beautiful page will decide, and I'll accept your decision. You have a better vision of the whole project. Paolo.dL (talk) 14:21, 28 June 2010 (UTC)

I changed section title to "Size of intervals used in different tuning systems". As far as I know, this information is provided nowhere else in Wikipedia. This table, or a link to it, is probably useful both here and in Tuning systems. Wherever you decide to move it, IMO this title better describes its contents. Paolo.dL (talk) 14:41, 28 June 2010 (UTC)

I read the article with more attention and realized that the first three columns of the table are a comparison of different interval naming systems (that was the original name of the section). I separated these columns from those about interval size, and created a separate table, which I placed into a more appropriate section (created by joining together, and turning into subsections, the two existing sections about alternative naming systems). I also moved the new section next to the "Other names" section, which contains similar terminological information. Paolo.dL (talk) 17:17, 28 June 2010 (UTC)

I slightly simplified the table. Now it focuses only on thirds fourths and fifths. As suggested by Woodstone, I am preparing more complete tables for the articles about specific tuning systems. Paolo.dL (talk) 22:51, 29 June 2010 (UTC)

Interval names and relevant articles

I will edit most of these articles, to make their introductions more consistent with each other:

Number of semitones	Name	Enharmonic notes
0	Perfect Unison	Diminished second
1	Minor second	Augmented unison
2	Major second	Diminished third
3	Minor third	Augmented second
4	Major third	Diminished fourth
5	Perfect fourth	Augmented third
6	Tritone	Diminished fifth Augmented fourth
7	Perfect fifth	Diminished sixth
8	Minor sixth	Augmented fifth
9	Major sixth	Diminished seventh
10	Minor seventh	Augmented sixth
11	Major seventh	Diminished octave
12	Perfect octave	Augmented seventh

In some of these articles, the definition is incomplete. For instance, the perfect fifth was defined as the interval spanning 7 semitones. This is not exactly true. Some intervals composed of 7 semitones are called diminished sixths. Here is what, in my opinion, is a correct definition for a perfect fifth, compared to the previous definition given in Wikipedia:

Previous definition (incomplete)	Correct definition
The perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G; C is a perfect fifth above F.	In Western music, a fifth is a musical interval encompassing five staff positions (see here for more details), and the perfect fifth is a fifth spanning seven semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C, and there are five staff positions from C to G. Diminished and augmented fifths span the same number of staff positions, but consist of a different number of semitones (six and eight).

I will use similar definitions for all the intervals. You might find a more synthetic way to say it, but this is the information needed to gently introduce the article, in my opinion.

− Paolo.dL (talk) 15:27, 23 July 2010 (UTC)

You might want to include words to indicate that both start and end position are counted and that both lines and gaps are counted. −Woodstone (talk) 16:50, 23 July 2010 (UTC)

Yes, I remember your suggestion in a previous section of this talk page. In this case, since introductions should not be too wordy, I used three strategies to address this concern without using too many words (see below) − Paolo.dL (talk) 17:11, 23 July 2010 (UTC)

Important terminological note about interval numbers

A second, third, fourth, fifth, sixth, or seventh can be defined in at least three ways:

a musical interval encompassing/spanning/including 2, 3, 4, 5, 6, or 7 scale degrees (AKA scale steps).
a musical interval encompassing/spanning/including 2, 3, 4, 5, 6, or 7 diatonic scale degrees (AKA scale steps).
a musical interval encompassing/spanning/including 2, 3, 4, 5, 6, or 7 staff positions.

The intervals contained in the table are diatonic to C major. All other intervals are chromatic to C major.

We discussed this in a previous section of this page. We agreed that the first definition is too ambiguous (not valid for chromatic scales), and should not be used. I believe that the second definition should also be avoided, as some seconds, thirds, etc. are not included in a diatonic scale. Namely, no diatonic scale includes augmented and diminished intervals (except for the augmented fourth or diminished fifth). For instance, see the diagram to the right, showing intervals formed by the C major scale. Thus, although the second definition is not ambiguous, it is:

invalid for diminished or augmented seconds, thirds, sixths, or sevenths, and also
invalid for augmented fifths and diminished fourths.

So, the third definition seems to be the only one we can use. However, we shoud always remember that, as Jerome Kohl pointed out in this talk page, the definition of interval number "has a great potential to confuse the beginner." [...] "I find that true beginners also tend to assume that staff position might refer only to the lines, or only to the spaces of the staff." An example of an explanation which might solve this problem was given in this section of the article by Woodstone. In all the above listed articles, to address this concern, I used these strategies:

I provided a link to that section: "(see here for more details)"
I also provided a link to staff position, which now redirects to a section of Staff (music), where you can see this picture
I added an example: "For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C, and there are five staff positions from C to G."

− Paolo.dL (talk) 17:33, 23 July 2010 (UTC)

Quality factor

From section "Cents"
The relationship between the width of a damped oscillator in cents, and its quality factor Q = f / delta f, is 1200 * ln(2) / Q ≈ 832 / Q, since ln(2) (natural log of 2) ≈ 0.693. A tuning fork with a Q of 1000 has bandwidth (intrinsic spreading of tones) of about 1 cent. Most instruments have a much lower Q and hence a higher intrinsic tone width.

This sentence is full of technical expressions which are not explained and that the reader is not supposed to know (e.g. I don't know them, although I perfectly know what an interval ratio and a size in cents is), such as "damped oscillator", "tuning fork", "intrinsic spreading", "intrinsic tone width".

These concepts are not explained in the main article about cents. Why are they in this section, which should be a short summary of that article? Why are they in this article, which should be a generic article (specific details about specific intervals are given elsewhere)? I would completely delete this sentence from this article, or move it in a different section at the end of this article (if you think this is relevant to a generic article about intervals). I don't know in which specific article it belongs, but I don't think it belongs in here.

Wherever it is published, this sentence should be rewritten. As it is, it only serves to confuse the reader.

Paolo.dL (talk) 17:48, 26 August 2010 (UTC)

I agree totally. What's worse, Q factor and Q value appear to have no links to musical sound. Perhaps if it can't be improved, it may have to be removed (rhyming unintended). — Glenn L (talk) 03:25, 27 August 2010 (UTC)

The idea behind this inclusion is certainly valid. I have not checked the background yet, but it implies that for many musical instruments it is not possible to identify a fixed frequency, since inherently the sound produced covers a certain bandwidth. It is badly written, and probably does not need to be in this particular article. But it gives substance to avoiding excessive accuracy in cent values mentioned. −Woodstone (talk) 06:26, 27 August 2010 (UTC)

I understand what you mean, but I would call it "valid" only if there's a source that connects intervals in cents to Q values. Seems like an irrelevant stretch, so I took it out. If someone brings a source, we can reconsider. Dicklyon (talk) 06:33, 27 August 2010 (UTC)

Thank you for answering so quickly, and for deleting the sentence. In Cents (music)#Human perception the just noticeable difference for sound frequency is not only mentioned, but also explained in detail with reference to scientific literature. However, as I already wrote, there's no mention to the Q factor. Paolo.dL (talk) 12:03, 27 August 2010 (UTC)

The Q-factor is not related to human perception, but to the production of the musical sounds. Many instruments are not able to produce a single fundamental frequency, but always a range of frequencies. So the intervals will be not single ratios, but "fuzzy" numbers. −Woodstone (talk) 15:45, 27 August 2010 (UTC)

Interval symbols in chords

Hi Paolo, you have repeatedly confessed in your edit comments that you don't know what the symbols 7, m7 and M7 mean. And it shows in your edits. You keep adding incorrect information. The general rules are:

unless overridden, a major third and perfect fifth are assumed
a single m or M apply to the third
a single + or - or ° apply to the fifth (and if diminished imply a minor third)
a single 7 adds a minor seventh
an M7 adds a major seventh
a single 6 adds a major sixth

So C7 is a major triad plus a minor seventh: C-E-G-Bb. Cm7 is (Cm)7, a C minor triad with added minor seventh. CM7 is C(M7), a major triad with major seventh added.

On another note. There has been discussion in the past if this section belongs in this article, while chords are described extensively elsewhere. It was concluded however that this section focuses on the symbols used not for the chords, but for the intervals occurring in the chords. That's why your shifting the naming triads and chords is a wrong move.

−Woodstone (talk) 08:39, 2 September 2010 (UTC)

Yes, I confirm that I am ignorant about chord signs and chords, but I can read the articles Chord symbols, and Chord (music), and even the example that you added yourself. All of these sources consistently show that C7 is a Cdom7. So, this is what I wrote yesterday in the article (as you can see in the revision history). Then, your correction mixed me up, as I wrote in my latest edit summary, and I confused dom with dim. This is why I thought you were wrong when you wrote that 7 means m7 (interval) + major triad.

However, initially you only wrote that 7 means m7, and did not consider that m7 is ambiguous in this context, because it may mean either m7 interval (correct interpretation) or m7 chord (wrong, but in this context the readers are likely to interpret it this way). There's also another problem in your latest edits. As I wrote in my previous edit summary, the "implied major triad" that you mention in these edits was not mentioned before (readers are neither supposed to know that M3 + P5 are called major triad, nor what a triad is; BTW, I added right now a short gentle introduction explaining what chord and a major triad is). I have no objection about mentioning intervals, rather than just chord names, but the intervals contained in dom7 are already listed in the example! Also, I provided the inernal link for dom7. So, your edit introduced a redundancy in a text that should be brief, because not directly related to intervals. And reduced readability.

Moreover, this is an edit war about nothing. Your help in adjusting this text was absolutely necessary and welcome and precious (as usual), because I did not know the meaning of C7, as I confessed in my first edit summary. You fixed the examples, I fixed the text according to the examples. After that, the text was OK, and many other articles about music are a mess... Let's not lose time fighting about small details in an article that is already almost perfect.

− Paolo.dL (talk) 10:02, 2 September 2010 (UTC)

After adding a short intro, I was able to implement your suggestion. Thanks for being as stubborn as I was. See if you like my implementation.

− Paolo.dL (talk) 11:54, 2 September 2010 (UTC)

I thought about it for a while, but I think moving back to describing not "chords", but "intervals in chords" is better suited for this article. That is how it was till recently and creates less duplication with chord (music). It could be adjusted to explain how the intervals are used to construct the chords, along the lines as shown in the top of this section. More focus on intervals, less on the resulting chords. −Woodstone (talk) 08:09, 3 September 2010 (UTC)

Yes, you are right, in some parts of the list the correct information about intervals was lost due to one of my edits. I restored it, then realized that it was not clear whether "minor seventh" referred to chord or interval, and to make it clear I turned the list into a table. Now everything is clear. Of course, only the main chords and symbols are listed. For more detailed lists, I put the "Main article" links. Feel free to change the order of the columns, if you prefer to put intervals before chords.

Also, please consider the possibility to move the section somewhere else in the article. It does not need to stay below the "Brief nomenclature" section, because it is about intervals in chords, not only about chord symbols.

Paolo.dL (talk) 08:52, 3 September 2010 (UTC)

Good idea. I flipped a few cases of main vs implied, to make the construction symbolism clear. I think I will move the chord column to the end. −Woodstone (talk) 10:15, 3 September 2010 (UTC)

Nice edit! Ok about moving the chord column, but move to the end both chord names and symbols. This is not anymore a table about symbols alone.

Why Cdim7 is inconsistent? I can't see the inconsistency.

Paolo.dL (talk) 10:19, 3 September 2010 (UTC)

Symbol C7=(C implied M3)7 and Cm7=(Cm)7, both with a minor seventh, but in C°7 the addition to C° is a diminished 7th, not minor; the ° symbol has a double effect. The ^ø symbol prevents the doubling of function. It's (slightly) inconsistent in the real world, not caused by our explanations. I thought to have columns in order: symbol, main, implied, chord name. Don't you think that's the best? It would be strange to start with the intervals without what they apply to. I observed that of the five qualities dim, min, perf, maj, aug, in one chord there can be at most 3 adjacent qualities. That drives some of the implied qualities. Should we mention that? −Woodstone (talk) 10:54, 3 September 2010 (UTC)

I see. But now, you should not anymore look at the table as a list of chord symbols, showing their meaning. The text changed. And with the text, the table also. The text deals with chords (and their definition, their qualities, their names, and eventually, their simbols as well). It is not anymore a subsection of "Brief nomenclature". That's why I believe the list should not start from symbols anymore. I mean, we are showing, first of all, that chord NAMES are given by their main intervals. Your Cm7 = (Cm)7 should be first understood as C minor seventh = (C minor) seventh...

I don't know about the 3 adjacent qualities. I think we should limit details to a minimum. By the way, isn't C7 also called C seventh? At least, in Italian it is always called that way, I did not even know the name "dominant" (and I play guitar).

Paolo.dL (talk) 12:11, 3 September 2010 (UTC)

But that's exactly what I think is wrong. This is not an article about chords, but about intervals. So we should give the meaning of the symbols as showing the intervals that eventually build a chord. The starting point is the symbol conventions for intervals in the context of chords.

The word dominant chord comes from the dominant of the scale, which is the fifth. Its diatonic 7th chord happens to have a minor seventh. In speech it's called G-seven.

By the way, contrary to what is stated, I think I've seen C-5 for a diminished fifth (with implied minor third). Also C6 (added M6), C9 (usually implying an added m7 interval as well) and C-9 are common.

−Woodstone (talk) 15:35, 3 September 2010 (UTC)

Think about it. This section is called "Intervals in chords" (exactly as you suggested in your previous message). Not "Intervals in chord symbols". Moreover, what's more important, the chord or the symbol? In my opinion, the chord! If you don't want to talk about chords, then you should not talk about chord symbols, and delete the entire section. If you read my gentle introduction with attention, you will probably see that you might even safely delete the paragraph and the column table about symbols. The section would be slightly shorter, and this might be desirable. It would not reduce readability (with small adjustments to what would be left). Of course, I am not suggesting to delete the parts about symbols, but I am convinced that chords are more important than chord symbols. So, if you really want to force me to choose only one of them, I choose chords.

− Paolo.dL (talk) 16:45, 3 September 2010 (UTC)

It would be nice if − were used to denote diminished. But in all the examples I can see in the two main articles it is used only as a symbol for minor (although C-(b5) is a diminished triad, it means Cmin(b5), not Cdim(b5), of course). By the way, as I suspected, the Seventh chord is assumed to be, by default, a dom7.

− Paolo.dL (talk) 20:47, 3 September 2010 (UTC)

Hi Paolo, we are not communicating yet. What I have in mind is explaining how to analyse and interpret the symbolism. See proposal below. Perhaps that makes my thinking clear.

Composite symbol	Analysed			Stated	Implied	Chord name
Composite symbol	3rd	5th	add	Stated	Implied	Chord name
C					Major third, perfect fifth	Major triad
CM, Cmaj (rarely CM3, or Cmaj3)	M			Major third	Perfect fifth	Major triad
Cm, Cmin (rarely Cm3, or Cmin3)	m			Minor third	Perfect fifth	Minor triad
C+, or Caug (rarely C+5, or Caug5)		aug		Augmented fifth	Major third	Augmented triad
C°, or Cdim (rarely C°5, or Cdim5)		dim		Diminished fifth	Minor third	Diminished triad
C7, or Cdom7			7	(Minor) seventh	Major third, perfect fifth	Dominant seventh chord
Cm7, or Cmin7	m		7	Minor third, (minor) seventh	Perfect fifth	Minor seventh chord
CM7, or Cmaj7			M7	Major seventh	Major third, perfect fifth	Major seventh chord
C°7, or Cdim7		dim	7	Diminished fifth, (diminished) seventh	Minor third	Diminished seventh chord
C^ø7		dim	7	Diminished fifth, minor seventh	Minor third	Half-diminished seventh chord
C6			6	Major sixth	Major third, perfect fifth	Major add sixth chord]]

Good job. That's a great contribution, but it clearly belongs elsewhere. You said it yourself: this section should only focus on "intervals in chords". This means we should not focus on chord symbols, here. But please, find a way to insert this in Chord notation, or perhaps in Chord (music), in a section with title "Chord notation", referring to the main article Chord notation. Indeed your table is an excellent summary of Chord notation, which clearly belongs in Chord (music)!

− Paolo.dL (talk) 10:16, 4 September 2010 (UTC)

I don't wnat this great contribution to be lost. Your understanding about symbols must be shared. I'll insert this in Chord (music), where a summary section about notation is missing. Paolo.dL (talk) 09:46, 8 September 2010 (UTC)

Structure of section "Intervals in chords"

Let me explain the structure of the section "Intervals in chords". These are its key sentences, and all of them contain the words "intervals" and "chords":

Chords ... are typically defined as the combination of intervals starting from a common note
Sometimes even a single interval (dyad) is considered to be a chord.
Chords are classified based on the quality and number of the intevals which define them.
The symbols used for chord quality are similar to those used for interval quality
The table shows the (1)intervals contained in some of the main (2)chords, and some of the (3)symbols used to denote them.
The main interval is the interval which is used to determine chord name, quality, or number.

This is consistent with Woodstone's suggestion (see above) to focus on "intervals in chords" (notice that these are the first two words in sentence 5, while "symbols" is the last one). In this context, sentence n.4 (the only one with subject "symbols") is just a detail that could be safely deleted. I believe it is nice to keep it there, but I do not believe the focus of the section should be on chord symbols. Compare this with the structure of articles such as Interval (music), or Chord (music). In these articles, the section about shorthand notation comes after the main sections, and takes very little space, relative to the main sections. − Paolo.dL (talk) 11:03, 4 September 2010 (UTC)

Table structure

According to the structure of the section, focusing on chords and intervals (not on chord symbols), this is, in my opinion, the structure that the table should have in this section. Short, simple, readable, and with chords (not symbols) in the first column. I implemented here some of Woodstone's great ideas (see above).

The table shows the intervals contained in some of the main chords (component intervals), and some of the symbols used to denote them. The interval qualities or numbers in boldface font are those conventionally used to name the chord or build its symbol.

Main chords		Component intervals
Name	Symbol (C is used as root)	Third	Fifth	Seventh
Major triad	C	maj3	perf5
Major triad	CM, or Cmaj (rarely CM3, or Cmaj3)	maj3	perf5
Minor triad	Cm, or Cmin (rarely Cm3, or Cmin3)	min3	perf5
Augmented triad	C+, or Caug (rarely C+5, or Caug5)	maj3	aug5
Diminished triad	C°, or Cdim (rarely C°5, or Cdim5)	min3	dim5
Dominant seventh chord	C7, or Cdom7	maj3	perf5	min7
Minor seventh chord	Cm7, or Cmin7	min3	perf5	min7
Major seventh chord	CM7, or Cmaj7	maj3	perf5	maj7
Augmented seventh chord	C+7, or Caug7	maj3	aug5	min7
Diminished seventh chord	C°7, or Cdim7	min3	dim5	dim7
Half-diminished seventh chord	C^ø7	min3	dim5	min7

− Paolo.dL (talk) 11:28, 9 September 2010 (UTC)

Relationship between chord quality and interval quality

In Western music theory, a chord name (e.g. C major seventh), and the corresponding chord symbol (e.g. CM7), are often composed of three parts:

The root note (e.g. C)
The chord quality (e.g. major, or M)
An interval number (e.g. seventh, or 7)

Of course, chord qualities are related with the qualities of the component intervals which define the chord.

The most difficult thing to explain to the readers is: when chord quality is specified, to what component interval(s) does it apply? In short, what is the relationship between chord quality and interval quality?

Only a very limited amount of information is explicitly provided in the chord name or symbol. The root is always specified, but some names or symbols may not include the interval number, the chord quality, or both (e.g., C or CM is typically used instead of CM3). Even when they are all included (e.g. in CM7), the information provided is incomplete. However, it is often necessary to deduce from a chord name or symbol the component intervals which define the chord. The missing information is implied and must be deduced according to some rules.

Comparison with current answer

Here's an example of "inconsistency" in the current approach, created by Woodstone (see his table in the article, and his recent edits):

In CM7, M refers only to 7 (although both 3 and 7 are major).
In Cm7, m refers only to 3 (although both 3 and 7 are major).
In Caug7, aug refers only to 3 (as the added interval is min7).
In Cdim7, dim refers to both 5 and 7.

This is explained by a set of separate specific rules in Woodstone's approach. On the contrary, according to my general rule:

In CM7, M refers to the triad (and it happens to refer also to the added 7th, but this is not a general rule).
In Cm7, m refers to the triad (and it happens to refer also to the added 7th, but this is not a general rule).
In Caug7, aug refers to the triad.
In Cdim7, dim refers to the triad (and it happens to refer also to the added 7th, but this is not a general rule).

Whereas Woodstone listed a series of specific rules, which are inconsistent with respect to each other (i.e., they are almost exceptions, rather than rules), I have found in this notation some consistency which Woodstone had neglected, some order in the apparent chaos, and this makes everything much easier to understand and remember:

The general rule is always valid: chord quality always refers to the basic triad.
Specific rules are needed only to decide whether it also refers to the added interval.
Even these specific rules have a pattern and are easy to remember: in most cases the quality "duplicates", as in major-major, or dim-dim. However, aug does not duplicate in the augmented seventh chord (and min does not duplicate in the minor sixth chord).

So, although this pattern (3) has some exceptions, and that's why the specific rules (2) cannot be grouped into a general rule, the general rule (1) has no exceptions, and that's why it becomes precious (see also footnote 4 in Chord names and symbols (jazz and pop music)#Rules to decode chord names and symbols).

Please compare the two set of rules. I worked hard to explain mine (see "Suggested answer" above). It should be crystal clear. Woodstone's rules are currently explained in the article. We give a different answer to the following question: What is the relationship between chord quality and interval quality? The two answers differ mainly for Cdim7 and CM7. We need to decide:

Are these answers both correct? (I am sure they are)
Provided they are, what is the simplest one?

− Paolo.dL (talk) 13:10, 10 September 2010 (UTC)

What do sources have to say about such rules? Why do we seem to making up our own rules? Dicklyon (talk) 23:14, 13 September 2010 (UTC)

There is unfortunately no universal standard for decoding chord names and symbols. But each set of rules gives of course the same result (see also footnote 4 in Chord names and symbols (jazz and pop music)#Rules to decode chord names and symbols). We do know what the chord symbols, names, and definitions are (see Chord names and symbols (jazz and pop music)), and we are entitled to find the best way to show "patterns" in their relationship. Similarly, for instance, we are entitled to list all symbols used to mean "diminished" (^o, °, dim, or ♭, but not d), even though no source in the literature may give a list as complete as ours.

People from all over the world collected the info in Chord names and symbols (jazz and pop music), and we may have there a collection of data more complete than any other in the literature. So, organizing these data may have never been done before in the literature. That's how we help readers to understand. Otherwise they would need to memorize separately the definitions of each chord. And when they do, they will themselves discover patterns and associations, because that's how our brain manages to remember data. With Woodstone's help, I was seeking the best way to "put together" and organize the huge amount or unrelated information collected by other editors in Chord names and symbols (jazz and pop music), and to facilitate its interpretation.

See also the job we did in building charts showing the interval sizes for Pythagorean tuning, 5-limit tuning, quarter-comma meantone. I computed the values based on the known formulas (from the literature), but I did not copy these values from the literature. Of course, then we checked the results and they were consistent with the literature (except that my table cannot contain typos or rounding errors, because it was built with Microsoft Excel, while tables in the literature may contain typos or rounding errors). Then Woodstone helped me to rearrange the table to reveal a pattern. I rearranged the table not because I found a similar table in the literature, but because Woodstone convinced me that it was useful for the readers to see a pattern. That's how Wikipidia may, sometimes, become better than the sum of its sources.

So, if we find a set of rules in the literature, that's good, but the very important requirement is that there's no inconsistency between the information collected from the literature and the rules we use to describe and organize that information. That's how we respect the literature and make sure we are not giving a truly original contribution (which is forbidden in Wikipedia).

Also, notice that most of these rules were already given in Chord (music), or Chord names and symbols (jazz and pop music), or Seventh chord, or Sixth chord. And actually, if you compare the two tables you will discover that we only disagree about Cdim7 and CM7, where I believe Woodstone's rules are inconsistent, as explained above. — Paolo.dL (talk) 08:33, 14 September 2010 (UTC)

Perfect versus just

At the beginning of the article it is said that the frequency ratio of a perfect fifth is 3:2. IF this is correct then on a standard piano you can't play a perfect 5th since the interval spacing is 2^(1/12) and 7 semitones gives 2^(7/12) = 1.498, a tad shy of 1.5 . There is a fair bit of ambiguity and internal contradiction in the article that need not be here. 192.12.184.7 (User talk:192.12.184.7) 23:30, 10 February 2012‎

Where is the ambiguity? A "standard piano" (that is, one tuned in 12-equal temperament), by definition does not play "in just intonation", as specified in the passage to which you refer. Do not confuse the expression "perfect fifth", which refers to a musical interval, to any particular tuning of it. The word "perfect" in this context is not synonymous with "just". Can this be made plainer in the article? Perhaps. —Jerome Kohl (talk) 05:06, 11 February 2012 (UTC)

Thanks for your note, 192.12.184.7. You are right: the section Interval (music)#Frequency ratios incorrectly states that the frequency of a perfect fifth is 3:2. This is only true in some tuning systems (e.g. Pythagorean tuning and Just intonation. In other words, only a Pythagorean or just (also called pure) perfect fifth has this size. In general, no interval has a standard size, not even a perfect fourth or a major third. So, the section Interval (music)#Frequency ratios is poorly written and gives misleading information. However, let's not increase too much the complexity of the article at its beginning. A comparison between the terms "perfect" and "just" perhaps belongs in a more specific article or in a more specific section of this article. The definition of the terms just and perfect is correctly given in the relevant articles. I'll try and fix the problem. Paolo.dL (talk) 11:31, 11 February 2012 (UTC)

Thank you for your answer Paolo. Jerome Kohl: it is ambiguous because perfect 5th is attached to the "just intonation". If they are independent concepts then "perfect" should be defined independently of any particular intonation. There are a lot of arguments on this issue scattered through related wikipedia pages on temper, intervals, etc. Some claim that a perfect fifth is a frequency ratio of 3:2 and others claim that it is seven semi-tones no matter what the tuning. I don't have an opinion on the matter but it strikes me that there are three choices: (1)perfect fifth means a 3:2 ratio (2)it means 7 semi-tones, (3)both definitions are used in the music theory literature. If (3) is the case it might be qualified with something like but definition X (where X is either 1 or 2) is used in LIST OF MODERN REFERENCES. Ideally one would define the term "perfect" without reference to a specific interval. — Preceding unsigned comment added by 76.18.82.61 (talk) 15:12, 23 February 2012 (UTC)

I've run into this ambiguity, too – your case 3. In some contexts, "perfect fifth" means exactly the 3:2 ratio, and in other contexts, fourths are fifths are called the "perfect" intervals, however they are tuned. Both are still common in modern music literature, I think. It's unfortunate, but the best we can do is to clarify what we mean when we use the term perfect. Dicklyon (talk) 15:53, 23 February 2012 (UTC)

To Paolo: I do not see any incorrect statement in the section you quote. It begins "The size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, …" (my emphases). To me, this is as plain as it possibly could be: "If and only if just intonation is used to tune intervals, the perfect fifth may be a 3:2 ratio". In fact, even this caution leaves open the possibility that perfect fifths not measured by 3:2 ratios may be found (and they certainly are found) in just-tuning systems.

To Dicklyon: Your experience is doubtless superior to my own. In my own experience as a musician and music theorist interested in tuning theory, I have never come across the word "perfect" used to describe a justly tuned interval, except in compound modifiers such as "perfectly in tune". It is possible, of course, that psychoacousticians (or other experts in fields outside of music theory) use the term that way, and it is easy to see how beginners could confuse the words. I am on the other hand accustomed to seeing "pure fifth" and "pure tuning" used synonymously with "just fifth" and "just tuning". As I said before, perhaps this section needs re-writing for clarity.—Jerome Kohl (talk) 17:17, 23 February 2012 (UTC)

To Jerome: I agree that the sentence does not contain any incorrect statement. Not anymore, because I fixed it :-)

To Dicklyon: I strongly doubt that the term perfect can be safely used in music theory to mean just or pure. In the most common and most widely accepted naming convention (which is described in this article), perfect refers to the quality of the interval, which has got nothing to do with exact size of the interval (expressed in cents or frequency ratio). This naming convention is so commonly used in Western music that it would be rather confusing and inappropriate to use the same term to mean just or pure. The statement that "perfect fifths are 3:2" (or more simply, "fifths are 3:2") may be valid in some contexts (if the writer assumes just intonation), but by no means it implies that perfect is a synonym of just. If accuracy is not required, the expression "about 3:2" or "slightly sharper than 3:2" may be appropriate to describe the size of an equal-tuned perfect fifth. Paolo.dL (talk) 21:11, 23 February 2012 (UTC)

Yes, I understand that meaning in modern western music theory. Yet other reliable sources such as this book contrast "the perfect fifth" with "the equal tempered fifth". They're using the other meaning of perfect, obviously. In some contexts that would be confusing and inappropriate, but in that book it works, because the audience is mostly not expert on modern western music theory. Dicklyon (talk) 00:19, 24 February 2012 (UTC)

Yes, I thought there might be such a source. And I suppose it is about time some mathematician took revenge on music theorists (who are forever misusing mathematical concepts) by deliberately misusing a basic term from music theory!—Jerome Kohl (talk) 05:16, 24 February 2012 (UTC)

I agree with Jerome, and I enjoy his sense of humour :-). This is an example of improper use of widely accepted standard terminology, by an author who is clearly more interested in mathematics than naming conventions in music theory. The book may be reliable in most respects, but not as a source for the definition of the expression "perfect fifth" in music theory. Paolo.dL (talk) 15:34, 24 February 2012 (UTC)

Yes, of course, it's like I said: the definition in standard music theory is one thing, but not all reliable sources (especially those not in standard music theory) use that that definition. That doesn't make them wrong or unreliable, just means there's another meaning outside standard modern western musical theory. Dicklyon (talk) 17:15, 24 February 2012 (UTC)

That book was written by a mathematician (D.J. Benson), but was about music theory as well. I am sure you know there's a lot of math in music theory, and a lot of literature about math in music. The Pythagorean tuning system, which was used for centuries and in which the perfect fifth has a 3:2 frequency ratio, is named after Pythagoras, a phylosopher and mathematician.

In a given context, one might decide to use his own alternative terminology, or his own alternative definition for a standard expression, but in this case I think it was clearly a mistake. D.J. Benson just seems to confuse perfect fifth (P5) with Pithagorean fifth (aka just or pure fifth). He also fails to notice that equally-tempered fifth is not enough to tell the 700 cent fifth (that the rest of the world for centuries has been calling P5) from the 600 cent fifth (diminished fifth). It is unlikely that a reliable author, being perfectly aware of the existance of a widely accepted convention, would try and propose an alternative (and partially overlapping!) convention without warning the readers. There would be no advance in science if scientists did not feel the need to justify and explain inconsistencies with previous literature (which is, in this case, extremely abundant and consistent) and previous widely accepted conventions.

I conclude that D.J. Benson was not aware that his interpretation of the expression perfect fifth was inconsistent with the traditional naming convention. This does not mean he is not a reliable author. Even reliable authors may be wrong somethimes.

Paolo.dL (talk) 18:34, 25 February 2012 (UTC)

The alternative to your persistence in calling him "wrong" would be to admit that there is another usage and meaning of "perfect" besides the one that's standard in western music theory. I can find more examples if you like. For example, here is one that contrasts the "perfect" fifth with the "imperfect" or "Procrustean" fifth that is off a Pythagorean comma. Dicklyon (talk) 19:28, 25 February 2012 (UTC)

There might be another usage, but it would be inappropriate, unless the above mentioned inconsistencies are solved. I am not willing to accept as correct an alternative naming convention which not only is inconsistent with the standard one, which has been widely used worldwide for centuries, but also will fail to take into account that the diminished fifth is greatly dissonant and hence even more "imperfect" than the "non-diminshed" 700 cents fifth. In other words, an alternative convention which is so naive that it fails to tell d5 from P5, when they are equally tempered. Paolo.dL (talk) 00:01, 26 February 2012 (UTC)

Right, it's another usage, as I've been saying. Nobody is asking you to accept it as correct or as a candidate naming convention to replace the more standard usage in western music theory. Dicklyon (talk) 00:10, 26 February 2012 (UTC)

In your previous comment, you considered two alternative options: either "calling him wrong", or admit that there is a non-standard usage of "perfect". My reply was meant to show that I'd rather endorse both options at the same time. Paolo.dL (talk) 01:10, 26 February 2012 (UTC)

Traditional definition of imperfect fifth

Reference: A.L. Leigh Silver (1971), p.354 (suggested above by Dicklyon)

Qualifying the Procrustean fifth (aka wolf fifth) as "imperfect" might be misleading, but is not incompatible with the above mentioned standard naming convention, as the Procrustean fifth is actually not a perfect fifth, but a diminished sixth. The reason why it is often referred to as a fifth is explained in the article Wolf fifth. Indeed, I believe that the expression "imperfect fifth" was traditionally used with that meaning before the 15th century, when Pythagorean tuning was the most commonly adopted tuning system in European classical music. At that time, the only perfect fifth was the Pythagorean one (3:2), which is perfectly consonant, and the term was perfectly appropriate. Nowadays, since the most commonly used tuning system (12-TET) defines a slightly out-of tune (700 cents) perfect fifth, even a perfect fifth is actually, in a way, "imperfect" (i.e. not perfectly consonant). However, the standard naming convention still qualifies it as "perfect", abandoning the original meaning of the term "perfect" (i.e., perfectly consonant). In short, if the standard naming convention is fully adopted, a Procrustean fifth can be safely called "imperfect", although the term might be misleading to those who remember the original meaning of the word "perfect". Paolo.dL (talk) 23:57, 25 February 2012 (UTC)

The expression "imperfect fifth" (or "impure fifth") is also sometimes inappropriately used to refer to a perfect fifth that deviates from the "pure" (3:2) Pythagorean perfect fifth. In other words, to an "impure-perfect" fifth, rather than to a diminished sixth. For instance, in five-limit tuning (see my tables) there exist two kinds of perfect fifths, one of which is impure (40:27) and so severely dissonant that it may be classified as a wolf fifth. This impure-perfect fifth hardly deserves to be qualified as perfect. Thererore, it is sometimes called imperfect fifth. For details and reference, see Wolf fifth#Five-limit tuning. This interpretation of the expression "imperfect fifth" is questionable as it does not take into account that the diminished fifth is an imperfect fifth as well! Indeed, since "imperfect" means non-perfectly consonant (or impure), the expression "imperfect fifth" describes both the "impure-perfect" and the diminished fifth, and cannot be used to indicate only the impure-perfect fifth (for details, see my comment above, posted at 00:01, 26 February 2012). Paolo.dL (talk) 16:31, 27 February 2012 (UTC)

Definition of Perfect

By the way, there's something we have not mentioned yet: this naming convention is awfully complex, as it is linked to the somewhat arbitrary definition of diatonic scale. Even in equal temperament, the notes in a diatonic scale are not equally spaced. The sequence of intervals between adjacent notes has a regular pattern (T-T-S-T-T-T-S-T-T-T-S-T-T-T-S-T...).

The perfect fifth is a fifth as, in that arbitrarily selected scale, it happens to encompass 5 adjacent notes (indeed, it would be called a "seventh" if the scale were chromatic, rather than diatonic). It is perfect because, in this crazy context, there magically happens to be only one kind of fifth. Namely, every possible fifth in a diatonic scale is formed by 1 semitone and 3 tones (4 intervals between 5 adjacent notes). On the contrary, a third is not perfect because in a diatonic scale there are two kinds of thirds: sometimes formed by 2 tones (major third), sometines by 1 tone and 1 semitone (minor third). No wonder that even a mathematician may fail to understand. I wish we could create from scratch a simpler naming convention! Paolo.dL (talk) 16:18, 24 February 2012 (UTC)

I wonder, Paolo, do you have a source for this etymology of "perfect fifth"? It seems suspect to me, of for no better reason than that the description is not accurate: there are only six perfect fifths in a diatonic scale, plus one diminished fifth (semitone + 2 tones + semitone). Wouldn't that mean the correct term should be "very nearly perfect fifth"? ;-)—Jerome Kohl (talk) 16:31, 24 February 2012 (UTC)

Well, you are right. I forgot the tritone (an article which I edited extensively)! Isn't that crazy? A mathematician would say: QED :-) No, I do not have a source, this is my attempt to make sense of something that does not really make sense. Do you have a better explanation for the etimology of the term perfect in this context? Paolo.dL (talk) 16:46, 24 February 2012 (UTC)

The article gives this explanation: Perfect intervals are so-called because of their high levels of consonance, and because the inversion of a perfect interval is also perfect...

Anyway, I am still convinced that this naming convention is crazy, or at least difficult to understand, as interval qualities such as "minor" and "major" are only needed if you use a diatonic scale. In a chromatic scale, all "thirds" would be formed by 2 semitones, all fourths by 3 semitones, all fifths by 4 semitones, etc. etc. I do realize, however, that it would be extremely difficult (but not impossible) to try and introduce a different terminology. Think about the International System of Units in metrology. It will take centuries, but eventually everybody in the world will accept that convention. Paolo.dL (talk) 17:16, 24 February 2012 (UTC)

Or you could look in a book. Dicklyon (talk) 17:21, 24 February 2012 (UTC)

Thank you, Dicklyon. The definition of "Perfect concord" (i.e. perfect consonance) at page 67 (LXVII) is also insightful. Paolo.dL (talk) 17:38, 24 February 2012 (UTC)

A better explanation, perhaps, but I would have to scramble around to find a reliable source. Speaking from memory, in medieval theory intervals were classed at first into consonances, defined as unisons, octaves, fifths, and fourths, and dissonances (all other intervals). As styles evolved to include thirds and sixths as consonances, a distinction was made between them and the longer-established ones. Because in Pythagorean tuning those established intervals have small superparticular ratios, while the ratios of thirds and sixths are neither small nor superparticular, and because there is a palpable difference in degree of consonance (and so only octaves or fifths could serve as cadential sonorities in two-voice counterpoint, and in textures with more voices, only composite sonorities built of those intervals and fourths between upper voices), the terms "perfect" and "imperfect" were applied to them. Some theorists from this time also distinguished between perfect and imperfect dissonances, the former being "more dissonant" than the latter. When Pythagorean tuning began to give way early in the 16th century to hybrid ("just") tunings in which thirds could be expressed by relatively small superparticular ratios, 5:4 and 6:5, and sixths by their (small superpartient) inversions, 8:5 and 5:3, the same distinction could be made with respect to their limits—that is, "perfect" consonances were formed from numbers 4 or smaller (3-limit), while "imperfect" consonances involved numbers up to 6 (5-limit).—Jerome Kohl (talk) 17:50, 24 February 2012 (UTC)

Thank you, Jerome. Your explanation makes perfectly sense. Please see also my comments about the imperfect fifth above. Let me share another doubt. Godfrey Weber (1841) defines "imperfect concord" (where the word concord seems to mean consonance") as everything except fourth and fifth (which is an over-simplification, as also the unison and octave are perfect). Surprisingly, immediately after he writes that this "term particularly applies" to third and sixth. Why does he exclude the second and seventh? Paolo.dL (talk) 14:54, 27 February 2012 (UTC)

Proposing A-class rating for this article

Somebody changed the rate of this article from A-class to B-class. I think this article is well structured, easily readable, complete, plenty of appropriate and useful references, tables, figures, internal and external links. It is also one of the most useful articles I have ever studied and edited on Wikipedia. Hence, I propose to rate it as an A-class article. Perhaps, it should also be classified as High-importance on the WikiProject-Music-theory's importance scale (about that, I do not have sufficient information to give a reliable judgement). Paolo.dL (talk) 16:42, 11 February 2012 (UTC)

I've restored the A-class rating and marked it top importance. It seems to have been reduced to B-class by User:Tbhotch in this edit, with the summary "No evidence". Unless Tbhotch (or anyone else) can explain what that means and can demonstrate good reason for having reduced the rating, I see no reason for this article not to be A-class. (It's actually the example given for the A-class rating on the Project assessment page). —Mahlerlover1^(converse) 10:30, 7 March 2012 (UTC)

Good job. Thank you for the details. Paolo.dL (talk) 13:39, 9 March 2012 (UTC)

Ti-Fa

Intervals don't change when you move them up or down (C to G is a perfect fifth as is D to A), thus it doesn't matter if its fixed or movable Do solfege. Hyacinth (talk) 08:49, 18 May 2012 (UTC)

Your comment refers to my latest edit summary: "Ti-Fa means little, unless referred to a specific scale or kind of scale. Is it movable Do solfege? Is it fixed Do? Better to refer to example (C-major) and use B-F (as in figure)". Please consider the context.

If you say that Ti-Fa (B-F, or any transposition of it) is a d5, this is not always correct as Ti-Fa, in fixed Do solfege, may mean B-F♯ which is a P5.

Similarly, the statement that Ti-Fa is the only d5 in a diatonic scale is highly questionable. In other words, it is not true that the only d5 in a diatonic scale is always solfaed Ti-Fa:

In fixed Do solfege, this is true only for a specific kind of scale (a scale in which Ti-Fa spans 6 semitones).
In movable Do, this is true for all major scales, for instance, but not for minor scales (in a natural minor scale the d5 interval is called Re-Le).

Most importantly, using a concrete and specific example (B-F in C-major), in which the notes are called with their widely known English name, and for which we even have a complete table, is in my opinion much simpler and more effective than using an abstract concept such as the movable Do solfege, which many people may ignore (in several countries it is not used).

Paolo.dL (talk) 14:34, 18 May 2012 (UTC)

Yes, sorry for the lack of context. Hyacinth (talk) 20:22, 18 May 2012 (UTC)

Interval number

Why is it "crucial to say that G is the "5th step" of a diat. scale starting from C, instead of repeating that C-G "encompasses" 5 steps (or staff positions)"? Hyacinth (talk) 23:03, 24 April 2012 (UTC)

A bit melodramatic to put it that way, but I have answered your question more prosaically by editing the text. For god's sake don't leave it that way, but I can't think how to put it clearly myself, without making a long paragraph out of it.—Jerome Kohl (talk) 00:22, 25 April 2012 (UTC)

After some contemplation, I have modified that passage in an attempt to explain why four steps constitute an interval called a fifth. I am a little uneasy about the explanations of interval-naming conventions throughout this article, but the real answer would probably involve going back to Ancient Greek music theory (which is where our terminology ultimately originates), and that might be just a little too complicated and "scholastic" (in the pejorative sense) for this article. In any case, every musician knows that 2 + 2 = 3, 3 + 3 = 5, etc., and that there is no such thing a zero.—Jerome Kohl (talk) 03:29, 25 April 2012 (UTC)

Yes, the crucial point, which I wanted to make clearer when I first introduced the example, is that, although the interval C-G is actually "four steps wide", it is called a fifth because G is the fifth step (or degree) of a sequence of notes (musical scale) or sequence of staff positions. Everything becomes even clearer, in my opinion, if you mention that this occurs when you call C the first note, or step (as in the C-major diatonic scale), or staff position in that specific sequence. So, G is the fifth element of a sequence starting from C, although of course G is only four positions above C. I read something similar somewhere else, on Wikipedia, and I was surprised to notice that this made everything clearer to me.

To explain this concept, I believe you need to explicitly mention, in an example, the sequence (C-D-E-F-G), which helps to realize that this is something else and something more with respect to the interval (C-G), namely an entire section of the C-major diatonic scale, a scale in which C is called the first step. It is also important that the example in the text refers to the C-major diatonic scale, which is the reference scale in which no accidentals are used. The image, which shows an Ab major diatonic scale, helps the reader to generalize to other diatonic scales (but not all the major diatonic scales include both C and G).

In other words, to move from step 1 to step 5, you need to go 4 steps higher. So, it would be great to be able to call the interval C-G a fourth, rather than a fifth. But the standard naming convention calls it a fifth, as if you started at step zero (which would be, in this case, the B below C), rather than step G. This is because "fifth" does not actually indicate the size of the interval, as we would very much like, but the position of G in a diatonic scale starting from C.

Of course it would be even nicer to be able to call the interval C-G a seventh, alluding to the number of semitones it spans, rather than to the scale step it includes or encompasses... this was made impossible by the history of music. — Preceding unsigned comment added by Paolo.dL (talk • contribs) 04:34, 26 April 2012

All diatonic scales, major, minor, and modal, include [a] C and [a] G, and [an] A, [a] B, [a] D, [a] E, and [a] F. Hyacinth (talk) 02:36, 29 April 2012 (UTC) [08:53, 29 April 2012 (UTC)]

Erm, sorry, Hyacinth, but the B major scale is usually regarded as diatonic, but includes neither C or G, nor A, D, or F, for that matter. What are you trying to say here?—Jerome Kohl (talk) 07:04, 29 April 2012 (UTC)

Disregarding accidentals, every diatonic scale contains every lettered name. A scale having F♯ still contains an F. In that sense the intervals are easy to count. −Woodstone (talk) 09:26, 29 April 2012 (UTC)

The history of music has got a lot to answer for :-D In fact, if we were to erase all that historical distortion and go back to the (European) beginnings, we would have to regard the fifth as a fourteenth, because it contains that number of the quarter tones that were the smallest counting unit in the Greek system of the Harmonicists of the late 5th century BC. Or, less Eurocentrically, we may care to use the sruti system of the Indian subcontinent, which divides the octave into 22 slightly unequal parts and may consider what we call a perfect fifth to be an interval of thirteen srutis, though there are also twelve and fourteen-sruti "perfect fifths". Seriously, though, I think you see that—without indulging in such confusing terminologies—the word "step" is ambiguous, in that it can refer to a degree of the scale, but also may refer to the interval between two adjacent degrees.—Jerome Kohl (talk) 16:52, 26 April 2012 (UTC)

That's interesting. About the term "step", I discovered its ambiguity by reading with attention your edits. Maybe it should be mentioned in the article Scale degree, where scale step is defined as a synonym of scale degree. In this article, I think that we should use only the word "degree", to avoid the ambiguity. Do you agree? Paolo.dL (talk) 17:41, 26 April 2012 (UTC)

Absolutely. No question about it.—Jerome Kohl (talk) 17:44, 26 April 2012 (UTC)

For the millionth time, thank you for your precious advice. I also added reference to Steps and skips, and edited the article Scale degree. Paolo.dL (talk) 20:54, 26 April 2012 (UTC)

It is still not clear to me why you insist on relating the interval C-G to the C major scale. In any diatonic scale that contains C and G, the G is the fifth degree if you start counting upwards from C as one. −Woodstone (talk) 05:19, 27 April 2012 (UTC)

Hyacinth, thank you not only for starting this discussion, but also for creating and inserting this nice image. It is well drawn, pertinent and the details it contains proved to be quite useful. Paolo.dL (talk) 12:17, 27 April 2012 (UTC)

Hi Woodstone, it is a pleasure to meet you again on a talk page. OK, I'll try and explain more thoroughly the reasons why I used the C major scale in my first example. (BTW, notice that I used the A♭ major scale in my second example). I already wrote above that G is the fifth element of any sequence of consecutive notes starting from C, provided that this sequence is taken from a diatonic scale. This is also true for the A♭ major scale, for instance. And I am sure you agree about that.

What you wrote, however, is not exactly the same. It is something more, and I do not completely agree on that. For instance, in the A♭ major scale, G is not and cannot be called the 5th degree, as by definition in that scale the 1st degree (or tonic) is not C, but A♭. Therefore in the A♭ major scale G is, by definition, the 7th degree. The tonic is set by definition, you cannot change it arbitrarily. In other words, in the A♭ major scale C cannot be arbitrarily called the 1st degree (or tonic). If you change the tonic, you change the scale. This is the reason why I need, at least for the first example, a diatonic scale starting from C.

You see, I wanted to show a similarity between two strong terminological conventions: diatonic scale degrees and diatonic interval numbering. So, I am not willing to use the word "degree" arbitarily, I am using it according to a strict convention (for which, BTW, we provided an internal link) which has the same origin and historical strength as the interval naming convention that we are discussing about. The reference to the article Degree (music) is quite important in this context, in my opinion.

There's also another reason for choosing C-major, however. I chose it because it is by all means the reference diatonic scale, the "white key" scale, the only diatonic scale starting from C which does not contains accidentals. Dozens of articles use this scale in their examples. And even in this article, the same scale is used as an example in the next paragraph, about interval quality (see figure). This scale is used so frequently in examples because it is the simplest.

There are three possible options:

"the C major diatonic scale" (very specific example, simplest possible)
"any diatonic scale starting from C" (as I explained in one of my edit summaries, this generalization would not allow me to indicate the exact sequence C-D-E-F-G, which makes the example more complete, more grounded, more concrete, more easily understandable)
"any diatonic scale" (this generalization would invalidate the example, as I explained above, as in 6 out of 7 diatonic scales G is not typically called the 5th degree)

I chose the first option because it is the simpest, and in my opinion in this example a generalization is not useful. In most cases, examples need to be simple and specific to be clear. Their purpose is to reduce abstraction to a minimum. A second example can be used, as I did, to show that the concept can be generalized (see the example about the A♭ major scale, and the relevant figure). But even the second example needs to be specific! Otherwise, it would become a generic statement which might not be grasped by everybody.

Paolo.dL (talk) 12:21, 27 April 2012 (UTC)

Hyacinth, before introducing more mistakes in the article (see recent edit summaries by Jerome Kohl and me), you should participate in this discussion constructively. I exhaustively explained my edits in this talk page. Before reverting them you should explain your rationale. You can't just ignore my explanations.

When I reverted your latest edit, in my edit summary I had to repeat something that I had already explained in this discussion (which you started, by the way): the sequence C-D-E-F-G is not contained in all diatonic scales. Also, you were warned repeatedly by Jerome Kohl and me about the fact that G is not simply the fifth note or degree from C. About that, there's even a sentence in the article: "the interval C-G is called a fifth, although G is only four notes, or scale degrees, or staff positions above C". However, you inserted again the sentence: "G is the fifth scale degree from C."

If consensus if reached about not using the C-major scale as an example, we'll do it. In the meantime, I suggest to keep the examples as I wrote them. They are correct and there's no hurry to change them. Moreover, I am the author of the examples we are discussing about and I think that, as far as we discuss matters of personal preference, my personal preference should be respected.

Paolo.dL (talk) 11:05, 29 April 2012 (UTC)

In the current status, the explanation is repetitive and circuitous. We can keep the start by defining correctly the count as related to the staff positions (including both notes). The staff positions correspond to a cyclic map to the first letters of the alphabet. Accidentals in the staff have no effect on the named size of the interval. From either D, D♭ or D♯ to any of A, A♭ or A♯ is always a fifth. No need to limit to a particular scale. I suppose we can work on a version focusing on this. −Woodstone (talk) 11:51, 29 April 2012 (UTC)

Yes, accidentals do not change the staff position of a note, hence they have no effect on the interval number. That's already explained in the article. Yes, there's no need to limit to a particular diatonic scale, although in an example it is easier to use a scale without accidentals.

We decided, long ago, to count staff positions instead of diatonic scale degreees to introduce the concept of interval number. However, I believe we also need reference to diatonic scales, as staff positions are just a way to represent diatonic scales (or more generally 7-tone scales) and I believe the reader should be well aware of that. Actually, the staff without key signature represents natural notes, i.e. A, B, C, D, E, F, G.

You are right about the fact that the text is now somewhat repetitive and circuitous. I have an idea to simplify, which might be welcome by Hyacinth as well. In one or two days I will propose a simpler version.

Paolo.dL (talk) 23:37, 29 April 2012 (UTC)

Paolo.dL, perhaps you confuse an insult with an invitation. If you are going to accuse someone of making an an error you should describe it (or point specifically to it) rather than just asserting one occurred. Just because I haven't been adding reams of text doesn't mean I haven't been participating in this discussion all along. One hint is that rather than simply reverting your edits to the article I have edited it differently each time. Hyacinth (talk) 00:38, 30 April 2012 (UTC)

In which case, in your opinion, I confused an insult with an invitation? Was that an insult or an invitation, in your opionion? By whom?

Your mistakes (more than one) have been corrected, and the history page keeps record of the relevant edit summaries. E.g. on the 25th of april Jerome Kohl corrected a mistake of yours and explained very clearly: "C to D is one step, D to E is one step, C to E is therefore two steps, etc., C to G is four, not five steps". He also explained the same concept in the talk page. More recently, in a single edit you did the same mistake again (!), together with another one. I corrected them, and in my edit summary I explained: "Not all diat. scales contain C-G. Not all contain C-D-E-F-G. G is not the 5th scale deg from C (it is the 4th)". Your edits were written with too little care. You seemed not to have read with attention the previous edit summaries and the talk page, although I am 100 sure that your intention was to improve the page. This is my opinion. It is not an insult. It is not about you, but about your recent behaviour.

Participating in a discussion means explaining your rationale, i.e. the reason why you propose a change, and the reason why you don't like what others did. You keep avoiding this. We need to reach consensus in this page. The topic is complex. Edit summaries are too short to thoroughly explain an approach.

Paolo.dL (talk) 10:30, 1 May 2012 (UTC)

I edited, taking into account with great care the excellent suggestions by other editors in this talk page. I hope that this is enough to reach consensus. It is very hard to make everybody happy, but I believe the section improved a lot. Paolo.dL (talk) 11:24, 1 May 2012 (UTC)

I guess you accepted my edits. Thank you. In my opinion, this discussion might be made more useful as a reference for future editors if you somehow conclude it by explicitly showing some consensus, even with a short sentence, for instance by endorsing my final edits, or at least the parts of them you like. Otherwise our work will appear as a collection of different opinions, and will not be taken seriously into account in the future. Paolo.dL (talk) 17:47, 3 May 2012 (UTC)

Well, I've been looking in at the article from time to time, and glancing at discussion. I do not think the article is clear and concise, or always accurate. As one who has been concerned about strange equivocations on the terms diatonic and chromatic, I find this particularly likely to cause confusion (my underlining and numbering):

In a diatonic scale, [1] the number of staff positions always coincides with the number of notes, and hence with the number of scale degrees. In other words, C-G is a fifth as in any diatonic scale that contains C and G, the sequence from C to G includes five notes, and these notes occupy five consecutive staff positions. For instance, in the A♭-major diatonic scale, the five notes are C-D♭-E♭-F-G (see figure). [2] This is true only for diatonic scales. For instance, in a chromatic scale, the notes from C to G are eight (C-C♯-D-D♯-E-F-F♯-G), although they still occupy only five staff positions. This is the reason why interval numbers are also called diatonic numbers, and this convention is called diatonic numbering.

Concerning each underlined portion:

"Coincides with" suggests something mysterious; but it is so basic as to be almost a matter of definition. Surely the staff is set up as it is just because it fits the system of scales that we conventionally use. In any case, what "number of staff positions"? We know that this means "the number of staff positions occupied by and intermediate between the notes forming the interval", right? But newcomers may not get that. Yes, an explanation follows; but why make a statement that then demands such an explanation? Why not this, from the start: "Positions on the staff correspond with the letter names of notes, so that counting through the positions from one note of an interval to the other gives the number of the interval."
"This is true only for diatonic scales." Well, what about the harmonic minor scale – or indeed less common heptatonic scales with notes named on the diatonic scheme? The statement is indeterminate for the harmonic minor scale (is that included as diatonic, for the purposes of this article?), and false for some less common scales. (Note also that the linked article for scale degrees does not mention chromatic scales, and gives the impression that only diatonic scales – or rather, "major and minor scales" – have steps; so how is the beginner to make sense of the contrast here, which assumes that this notion at least is common to all types of scales?)

Noetica^Tea? 23:38, 3 May 2012 (UTC)

NOTE: With Noetica's consent, and according to the guideline WP:Refactoring talk pages, I moved the second part of the previous comment into the next section (subsection #Contributions posted in 2012). Although the text was related to point 2, it deserved to be moved into a separate section as it started a new, more general, discussion about Diatonic and chromatic intervals. Paolo.dL (talk) 09:41, 13 May 2012 (UTC)

You wrote several interesting comments, so this is not yet a conclusion as I hoped. I edited again, taking into account your points 1 and 2. Paolo.dL (talk) 13:58, 4 May 2012 (UTC)

Diatonic and chromatic

Noetica opened above a discussion about the meaning of the term diatonic and chromatic in this context. This is a new topic, not directly related to the topic discussed in the previous section. I believe it deserves a separate section. With Noetica's consent, I moved the relevant text below. At the beginning of this section, I also moved previous contributions posted in 2007 and 2010 about the same topic. Some other discussions in this talk page about the same topic were archived here. See also Diatonic and chromatic, and Talk:Diatonic and chromatic. Paolo.dL (talk) 12:09, 6 May 2012 (UTC)

The Tritone is a diatonic Interval? (discussed in 2007)

In the process of creating the Diatonic and chromatic article, we have found that the tritone is not held to be diatonic in some sources. Should we make the article reflect our research?--Roivas 16:16, 20 September 2007 (UTC)

A tritone is a musical interval in one sense of the word, but not in others. What I mean is that a tritone is sounded by two notes separated by an interval of six semitones (which are themselves intervals in yet another sense of the word!), a conceptualization which differs from that of thirds, fourths, octaves, etc.

The latter are based, in one sense, on the notes (or degrees) of the diatonic scale, and in another, by an abstraction related to the positions of notes (represented by the familiar symbols seen in sheet music) on a staff.

Two intervals are said to be "enharmonic" (IIRC) if they sound the same, but have different names. For example, playing a B and the F above it gives the sound of a tritone, as does C-flat with the E-sharp above it. They sound alike and are played alike, but the former is a diminished fifth, while the latter is a doubly-augmented third. They are written and thought of differently.

Piano technicians refer to middle C as "C-4" or "key (number) 40." If you play key 39 ("B-3", without considering how it is written) and key 45 ("F-4"), you get the sound of a tritone. That combination of keys can also be called a tritone.

Note that 45 minus 39 is six. Because the interval separating the pitches is six semitones, it is a tritone, in one sense of the word. But to call it a diminished fifth or augmented fourth is technically a mistake, albeit a common one, without a richer context. D021317c 03:19, 9 November 2007 (UTC)

My concern has nothing to do with the confusion of terms you mention (diminished fifth, augmented fourth, or tritone) or what you regard a tritone to be in the abstract sense.

There are easy-to-find sources specifying that the tritone is not a diatonic interval.

Goetschius' The Theory and Practice of Tone-Relations has this definition of DIATONIC INTERVALS: 16. All those intervals which agree with the natural major scale (i.e., where the upper tone corresponds exactly to the scale-step of the lower tone as tonic), are called natural or diatonic intervals.

This musicological text refutes your claim that the tritone is diatonic, no matter what your reasoning is.--Roivas (talk) 16:33, 28 November 2007 (UTC)

I think that this text does not exclude the tritones F-B and B-F. Let me explain. I assume that natural major scale means C-major scale (composed of the natural notes C-D-E-F-G-A-B). The text has two interpretations:

Strict interpretation: you can call diatonic only the intervals C-D, C-E, C-F, C-G, C-A, C-B, C-C, as they use the tonic of the C-major scale (i.e., C) as the lower tone. In the figure below (first column), you can see that these intervals do not include a tritone (TT), but also they do not include minor intervals (m2, m3, m6, m7)! So, this interpretation is absurd (the natural minor scale is a diatonic scale, why shouldn't we call diatonic or natural the minor intervals formed by this scale?).

Other interpretation: You can call diatonic all the intervals formed by natural notes (see figure below), which include both tritones (F-B and B-F) and minor intervals. This is the correct interpretation, in my opinion.

Paolo.dL (talk) 19:52, 14 May 2012 (UTC)

Contributions posted in 2010

The latest edit by Woodstone in the main table implies that A4 and d5 are at the same time diatonic and chromatic intervals. This is not consistent with the definition given in this article:

Text	"A diatonic interval is an interval formed by two notes of a diatonic scale. The table on the right depicts all diatonic intervals for C major."
Figure caption	"All other intervals are chromatic to C-major".

It seems that the two sets (chromatic and diatonic) are not supposed to overlap. Please, make the article consistent. Either go back to previous version of table, or change the definition of diatonic interval.

− Paolo.dL (talk) 14:08, 29 August 2010 (UTC)

There are several definitions of diatonic. Especially the status of the tritone varies. So I see no problem in leaving it undetermined in the table. −Woodstone (talk) 17:26, 29 August 2010 (UTC)

Well, then fix the definition, please. There's no mention in the definition about the undetermined status of the tritone. Paolo.dL (talk) 18:16, 29 August 2010 (UTC)

The subsection about diatonic and chromatic intervals is a very poor summary of Diatonic and chromatic#Diatonic and chromatic intervals. I believe this is the only part of the article that does not deserve the "A class" rating. Is there anyone who feels like to improve this subsection? I am not an expert in this topic, which is not as simple as it seems. For instance, I recently discovered that tritones are both diatonic and chromatic..., so the two cathegories seem not to be mutually exclusive. Possibly, just a few more words will suffice. The subsection should be as concise as possible. — Paolo.dL (talk) 17:11, 20 September 2010 (UTC)

I added two short sentences, one of which copied from Diatonic and chromatic#Diatonic and chromatic intervals. Now the definition is complete, but this is not the only possible definition. Perhaps, this is enough. Perhaps not. I leave the decision to other editors.

— Paolo.dL (talk) 17:33, 20 September 2010 (UTC)

Oh my giddy aunt! I hadn't seen "Diatonic and chromatic" until now (I think I've been afraid to look, and not without reason, it turns out). I think what you have done here is reasonable, but I agree it is not the only possible definition. Part of the problem is persistent sloppy usage. In a twelve-tone context, for example, all semitones are called "chromatic" intervals and all other intervals "diatonic" (twelve-tone thinking disregards the distinction between, e.g., a diminished fourth and a major third). I'm a bit puzzled, though, by your statement about tritones being both chromatic and diatonic. Where did you find this? One other definition (which I am unable to find in the murk of the "Diatonic and chromatic" article) is that "chromatic" may apply to inflected tones in a diatonic context, for example, an F natural within the key of G major is a "chromatic" note. This is impossibly contextual, of course, and probably best stayed away from in this article. You have been doing splendid work here, Paolo. Are you sure you can't be tempted to turn your attention to "Diatonic and chromatic"?—Jerome Kohl (talk) 18:03, 20 September 2010 (UTC)

Correction: I had seen "Diatonic and chromatic" before (the evidence is on the Talk:Diatonic and chromatic page), but had repressed all memories of it. Was that article the source of the confusion about tritones? It is a rambling, incoherent mess—and that is one of its better features! We really do urgently need your help over there, Paolo!—Jerome Kohl (talk) 19:14, 20 September 2010 (UTC)

Thank you for your kind words about my edits. It is good sometimes to feel the friendship of other editors. I moved at the beginning of this section a previous discussion about the same topic. All I know comes from that discussion and Diatonic and chromatic#Diatonic and chromatic intervals. I am also familiar on the definition of diatonic scale and chromatic scale, or diatonic and chromatic semitone. That's it.

Explaining the rules for decoding chord names and symbols was a tough job. Fortunately, Woodstone greatly helped me with his edits and his contributions in this page. And there was Chord names and symbols (jazz and pop music), which did not contain rules, but at least listed a huge amount of equivalent symbols for each chord, from which, with Woodstone's help, I was able to deduce the two general rules. But it took too much time, because initially I was not familiar at all with that topic. It would take even more time to fix Diatonic and chromatic. Logic is not enough to fix that article. This is a job which requires an expert.

— Paolo.dL (talk) 21:24, 20 September 2010 (UTC)

Contributions posted in 2012 - Part 1

The scope of the term diatonic remains unsettled in many Wikipedia articles. Often this besetting quirk in music theory is simply sidestepped or glossed over. But it is still present as a difficulty for newcomers, whose view of the terrain may be less filtered by theory than the expert's view. We have a chart of the intervals in the article for the C major scale; and we say things like this: "The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone." Easy and comfortable. But newcomers will wonder about the harmonic minor, with its augmented second. We say: "The diminished fourth is an interval found between the seventh and third degrees of the harmonic minor scale, while the doubly augmented second only occurs in entirely chromatic contexts." OK, so the reader must read between the lines. This suggests that the harmonic minor is not a "chromatic context"; but we must assume that it is a "non-diatonic context", from the passage that I quote indented, above. So exactly what does the reader find, between the lines? No determinate ruling on the harmonic minor scale – though it is given a place in this article. The problem first manifests in the article with this text:

Intervals may be also classified as: / Diatonic intervals, between the notes of a diatonic scale, or / Chromatic intervals, non-diatonic intervals between the notes of a chromatic scale.

This gives the appearance of an exhaustive partitioning of the domain: every interval is either diatonic or chromatic. Later in the article this appearance is qualified or dispelled, but the augmented second is left in theoretical limbo. Not much use telling readers that the doubly augmented second is chromatic, if we leave things uncertain for the plain vanilla augmented second. Both diatonic and chromatic are linked to the article Diatonic and chromatic, which for either would be correct, but it inefficiently has the reader loading the same large article twice. Better if things could be made clearer right at this point. I worked hard on the article Diatonic and chromatic, to exhibit clearly some of these embarrassing uncertainties in how intervals and scales are discussed. That article evolved in an extraordinarily difficult climate, and this is reflected in much of its structure and detail. But the lessons from it are important. They have not been attended to here, or at similar articles. Still, a good effort, guys! I would write this whole article again, making a fresh attempt at clarity and certainty for the newcomer – but honestly acknowledging those areas where standard theorising is itself vague and uncertain. Noetica^Tea? 23:38, 3 May 2012 (UTC)

Noetica, is it correct, in your opinion, to state that typically diatonic scales are defined as a transposition of the white note scale, and hence they never contain steps larger than a whole tone? In other words, they never contain augmented seconds, such as the interval between the sixth and seventh degree of the harmonic minor scale. This is what I deduce from the intro of the article Diatonic scale, which by the way does not warn readers about other possible interpretations of the term diatonic in this context... Paolo.dL (talk) 16:50, 4 May 2012 (UTC)

Your question is rather careful and indirect, Paolo. I appreciate that! I will answer carefully but indirectly. The article Diatonic scale works with one widely used definition, and ignores others that have been used, that are still used, and that indeed still underlie many assertions made about scales, steps, intervals, chords, harmony, and so on. That article does not situate the harmonic minor in the scheme of things; but the harmonic minor exists, and must be accounted for in any useful discussion of scales, steps, intervals, etc. Myself, I think this a major flaw in modern theory, and it affects many of our articles. Any thoughtful beginner might feel confused. She would be right to feel confused! Now, is the complexity-ignoring definition that I refer to "typical"? Yes. See relevant sections of Diatonic and chromatic for a survey of the issues and of alternative definitions that do covertly get used in our discussions of intervals and the like, including in this article, where as I have suggested it is sometimes assumed that every standard scale is either diatonic or chromatic, and sometimes not. Noetica^Tea? 23:41, 4 May 2012 (UTC)

Although I highly value your work, I am not very interested in the messy subject of the alternative definitions of "diatonic scale". I would be glad if we could agree that the definition given in the current version of Diatonic scale is the main-stream definition, so that we can fix this article accordingly. This of course implies that the harmonic minor scale is not diatonic, which does not worry me at all. Paolo.dL (talk) 12:09, 6 May 2012 (UTC)

I am interested in that topic because some of us have to be! Like it or not, the terms are very often used imprecisely and with equivocation, even among specialists who should know better. Of course it would be fine if this article were revised with a single, clear understanding of diatonic in mind, and of chromatic. But that choice would have to be made explicit early, and the overall task might not be as simple as you appear to assume. Many points would have to be adjusted for strict accuracy, and it would be unwise and unhelpful simply to remain silent on the difficult issues such as accounting lucidly and rationally for the intervals of the harmonic minor. Consider also precisely how the forms of the melodic minor are to be fitted into the scheme of things, especially given that business of intervals being "diatonic in" or "diatonic to" some scales or keys but not others.

Related issues: Why are the diminished fifth and augmented fourth not uniformly considered diatonic in the article? Why are so many diverse theoretical perspectives and their associated points all pressed together in the article? I think it would be far less confusing for readers if a kind of dominant "received view" (in as much as it can be isolated; see my concerns above!) were presented first, without complications from perspectives beyond, as it were, "common practice" broadly construed. Get some well-defined and pragmatically important core right first; then move on to the extensions, exceptions, quibbles, and caveats.

I think everyone participating here is well motivated, and much good work has been done. It is a large and theoretically heterogeneous topic, and those are of course among the most controversial and resistant from which to produce a top-notch encyclopedic article. Let's see what we can do. Myself, I have reasons to hold back for a while.

Noetica^Tea? 17:20, 8 May 2012 (UTC)

I don't think that in this article we should explain the different meanings of "diatonic" (is this what you mean when you write "the extensions, exceptions, quibbles, and caveats"? I am not sure I understand everything you wrote). We may specify very briefly, when needed, that we refer to the transpositions of the "white note" scale.

Would you mind to tell us in which section are the A4 and d5 classified as non-diatonic intervals? Paolo.dL (talk) 22:09, 8 May 2012 (UTC)

In these sections it is not made clear that the augmented fourth and the diminished fifth are diatonic:

A. Main intervals (see the table)

B. Diatonic and chromatic "Aside from tritones, all intervals that are either augmented or diminished are chromatic, and the rest are diatonic."

In B, the wording is very strange. What does it mean, about tritones? Could be 1, 2, 3, or 4, working from what we are told in the rest of the article:

All these intervals are diatonic: perfect, major, and minor intervals, and tritones. All other intervals are chromatic.
All these intervals are diatonic: perfect, major, and minor intervals. All other intervals are chromatic, except tritones which are neither chromatic nor diatonic.
All these intervals are diatonic: perfect, major, and minor intervals. All other intervals are chromatic, except tritones which are sometimes chromatic and sometimes diatonic.
All these intervals are diatonic: perfect, major, and minor intervals. All other intervals are chromatic, except tritones which are neither.

It is not clear to what the statement in B is limited. Is it just about intervals in a chromatic scale? Well, which chromatic scale? (Is that a relevant or well-formed question, even?) In the chromatic scale presumed to begin on C (which we appear, perhaps, to be invited to consider), is the tritone between D-flat and G diatonic, or chromatic? How about the same interval considered in the context of the chromatic scale beginning on A-flat? The context does appear to affect our approach to this interval, right?

Now, how about the augmented second? Is it a chromatic interval? Apparently, from B above (however it is interpreted). How about the major second between C# and D# in the ascending melodic, in E minor? (Is it diatonic? Is it chromatic? Is it "diatonic to" E minor? Is it "chromatic to" E minor?) How about the major third between B and D# in E minor? (Is it diatonic? Is it chromatic? Is it "diatonic to" E minor? Is it "chromatic to" E minor?) How about that same major third in various other contexts? Always diatonic? Sometimes chromatic? Sometimes chromatic "to" some key?

These are questions readers might reasonably ask, given the present content of this article. But will they be able to find answers to them?

In short, you do not need to be interested in the uncertainties that are exposed in Diatonic and chromatic. There are enough uncertainties and confusions in the present article as it stands.

Noetica^Tea? 00:25, 11 May 2012 (UTC)

Intervals formed by the notes of a C major diatonic scale.

This is quite interesting. A previous discussion on this talk page, that I moved at the beginning of this discussion (as it has exactly the same title), may help us to understand why the table in "Main intervals" shows tritones as indeterminate (diatonic and chromatic at the same time, or either diatonic or chromatic, or neither). I have doubts as well. Is it so important to distinguish between chromatic and diatonic intervals? Can this be done only if you first decide what diatonic scale you are using? Does this distinction deserve to be mentioned in the introduction? In the most specific case, that is if you are working within a specific diatonic scale (or, more generally, a specific non-chromatic 7-note scale), as represented in my figure:

some major intervals are "chromatic" (do not appear in the figure),
some minor intervals are "chromatic",
a few perfect intervals are "chromatic",
most tritones are "chromatic",
most augmented or diminished intervals are "chromatic".

With this in mind, I realize now that the two column labels "diatonic" and "chromatic" in the main table make no sense and are totally misleading, although I may be the editor responsible for naming the colums that way. Paolo.dL (talk) 09:53, 11 May 2012 (UTC)

Paolo, please be cautious when moving sections of a talkpage around. It can make the course of the larger discussion on the talkpage unintelligible. Also do not use the same heading exactly for two sections; this disables reliable linking. (I fixed that earlier; let's not do it again.) Do not alter another editor's contributions without signalling that you have done so. I have repaired a useful link that you supplied in my preceding contribution here.

Now, I am glad that you are seeing some of the difficulties on this page. There are more, of course. You said this earlier concerning Diatonic and chromatic: "Logic is not enough to fix that article." Logic is a limited but essential resource. What will be enough to fix the present article? Many resources will be needed. As it stands it is no useful guide for beginners. Is it useful for anyone?

At D&C, a few editors came in late and attempted to tidy up. They did not come to terms with the theoretical issues there (sometimes falling victim to the very confusions that were treated in what that they sought to amend). Many of the same issues affect this article. In fact, D&C was started in an effort to deal comprehensively with confusions at articles including this one, some years ago.

For now I will address only one question that you pose: "Is it so important to distinguish between chromatic and diatonic intervals?" Excellent question! Well, people do attempt that distinction all the time, and get into contradictions and absurdities, and rarely ever notice that they have done so. I agree with you that we should work from a single well-settled and overt definition. If we stray from that definition, we should first be aware that we are doing so; and second, we should say that we are doing so. Good luck!

Noetica^Tea? 12:37, 11 May 2012 (UTC)

Hi Paolo, good work on the article. You surely never give up. As you can see from the interval table reproduced in this section, the set perfect/major/minor/tt can rightly be called diatonic in the now explicit meaning. I adapted the table in the article accordingly, making it more concise as well. What about "enharmonic" for the diminished/augmented column? −Woodstone (talk) 12:03, 13 May 2012 (UTC)

I think that the column label "diatonic intervals" is totally misleading. I already explained this above (09:53, 11 May 2012), confirming and amplifying the previous enlightening contribution by Noetica (00:25, 11 May 2012), which I beg you to read again. Moreover, in your version of the table, you use the name "tritone", failing to notice that it is a Latin name, and that d5 and A4 are tritones, as shown in the figure which you refer to. Your edit misleadingly implies that d5 and A4 are not tritones and most importantly, that they do not appear in a diatonic scale, contrary to what is shown in the figure. Moreover, I think that mentioning the alternative names (Latin names) "Semitone", "Tone" and "Tritone" in a separate column is quite important, for two reasons:

they are widely and frequently used, in some contexts even more frequently than the corresponding diatonic names.
This article is not about the diatonic naming convention for intervals, but about intervals.

I cannot imagine an article about Intervals in which the terms semitone, tone, and tritone are not mentioned early, and do not appear in the table listing the main intervals.

There's no need to use in the table the distinction between diatonic and non-diatonic. If we use it (and I strongly advice not to use it), then we need to consider d5 and A4 as diatonic intervals, unless we reach consensus in this talk page about a different operational definition of the expression "diatonic interval", which is quite unlikely in my opinion. However, the topic is too complex to be discussed in this article and in this talk page. So, I hope we can accept that there's another article (Diatonic and chromatic), which is linked in this article, which gives details that cannot be easily summarized here.

Paolo.dL (talk) 16:40, 13 May 2012 (UTC)

Proposing featured article status

This article has been used for a long time as an example of A-class article (see Wikipedia:WikiProject Music theory/Assessment). Recently, we fixed some problems in sections #Interval number and quality and #Interval width, making it even more accurate and easy to read. In my opinion, this makes the article mature for the Featured article status. This simply means that the editors agree that the article is well written and exhaustive, according to Wikipedia standards and guidelines, and they feel that it does not need further edits, unless there is new published information. For details, please see Wikipedia:Featured article criteria. Paolo.dL (talk) 16:58, 20 May 2012 (UTC)

Contributions posted in 2012 - Part 2

Paolo, I certainly appreciate your dedication to this important article. But I think it is nowhere near the standard required of a featured article. I would have spent more time on it myself (and may yet do so), but I have an aversion to it because of past experience. Too many different perspectives are jumbled together, and that helps no one – least of all those who are new to music theory, whom we ought to be thinking of first of all. But just to stick with matter of diatonic and chromatic intervals, which is by no means sorted out, let's look at the most relevant section in its entirety:

Diatonic and chromatic

A diatonic interval is an interval formed by two notes of a diatonic scale.
A chromatic interval is a non-diatonic interval formed by two notes of a chromatic scale.

The A♭-major scale.

Since a chromatic scale includes the notes of all diatonic scales, the intervals formed by the notes of a chromatic scale may be both diatonic or chromatic.

The table above depicts all diatonic intervals formed by the notes of the C major diatonic scale (also called intervals diatonic to C major). All other intervals (for instance from C to C♯) are called chromatic to C major. For instance, the perfect fifth A♭-E♭ is chromatic to C major, because A♭ and E♭ are not contained in the C major scale. However, it is diatonic to other diatonic scales, such as the A♭ major one.

Bit by bit:

A diatonic interval is an interval formed by two notes of a diatonic scale.
A chromatic interval is a non-diatonic interval formed by two notes of a chromatic scale.

Does this mean by any two notes of a diatonic scale, as defined in the current note 3 (which is self-contradictory as it stands because, because no natural minor scale is a transposition of the C major scale!)? If so, let that be said. Does it mean that if two notes occur in any diatonic scale, then the interval that they form must be considered diatonic in any context whatsoever? This is contradicted in what follows, and not in a way that will help anyone. To be clear: According to the section as it stands, the interval formed by E and F (a minor second) is diatonic simpliciter, but chromatic to G major. That will confuse people; and if G natural minor is a diatonic scale (see note 3), is the interval formed by E and F# chromatic to G natural minor? That seems to be entailed; but are we happy with that? Then consider the interval formed by F# and G; are we happy to say it is chromatic to G natural minor? Are we, for that matter, happy to say it is "chromatic to G minor"? Can we make sense of "chromatic to G harmonic minor"? That seems like a fair question, and one avoided here. Note that those links for "diatonic" and "chromatic" both end up at the same long article, which means that many readers would unwittingly load it twice. Now, a chromatic scale can be spelt in various ways. The intervals formed by its notes are perhaps not usefully characterised as chromatic or diatonic at all. The melodic interval formed by G and G# is effectively the same as that formed by G and A♭, in the middle of an ascending chromatic run. How does it help, or even make sense, to call the former chromatic and the latter diatonic? How does it make sense, in the context of a chromatic scale, to say that the interval D–A# is chromatic, while the interval D–B♭ is diatonic? (Or E♭–F# versus D#–F#? See Chromatic_scale#Notation, and note also how notation may vary ascending and descending.) Does it matter which chromatic scale we are talking about (if that makes sense, which in some contexts it certainly does)? The next bit:

Since a chromatic scale includes the notes of all diatonic scales, the intervals formed by the notes of a chromatic scale may be both diatonic or chromatic.

Only true if we consider a chromatic scale as consisting of an ascending portion and a descending portion, with sharps on the way up and flats on the way down! Then see uncertainties that I raise immediately above. They are not resolved here. And "may be both diatonic or chromatic" is ungrammatical, compounding the uncertainty of meaning: "may be both diatonic and chromatic" (severally or jointly? how, when, and why? simultaneously? indeterminately?); or "may be diatonic or chromatic" (how, when, and why?).

The table above depicts all diatonic intervals formed by the notes of the C major diatonic scale (also called intervals diatonic to C major).

The beginner might well be confused by the qualifier "diatonic" in "all diatonic intervals formed by the notes", because all the intervals formed by the notes of the C major scale are diatonic! We seem to be narrowing something down; but we cannot be. And then, why "C major diatonic scale"? This seems, again, to make a distinction: but none is possible – because there is no non-diatonic C major scale. And then, "also called intervals diatonic to C major", which highlights a besetting conceptual equivocation (and therefore a besetting expository issue): is "an interval" strictly identified as an ordered pair of two named pitches or notes (like C and the G above it)? Alternatively, is "an interval" something abstracted from a set of ordered pairs that share some feature (so that C–G and F#–C# are "the same interval", or more strictly "instances of the same interval")? Both are right in their ways, of course. But let me illustrate the confusion. By the portion of text we have under the microscope right now, and by the table it refers to, it could be meant that "C–G is diatonic to" C major; or it could be meant that the "perfect fifth is diatonic to" C major. The latter would be true in a more trivial sense than the former; but it needs to be clear to the beginner. Make no mistake: beginners wrestle intelligently with questions that experienced theorists glide over stupidly, especially when explaining things to beginners. That's half the problem, in fact. All of that might be considered as clarified by what follows:

All other intervals (for instance from C to C♯) are called chromatic to C major.

But no. The example C–C# is ill-chosen, because it is chromatic regardless of context. Better to omit that example; for all the close-reading beginner knows, it picks out the more abstract entity augmented unison, and makes the statement that it is not chromatic to C major. Only in the next bit is the matter settled:

For instance, the perfect fifth A♭-E♭ is chromatic to C major, because A♭ and E♭ are not contained in the C major scale.

But for the smart beginner (and I stress that, again) who is concerned to get this absolutely right, that comes late and indirectly. More could be said about the distinction between diatonic and chromatic in this article, before we even look beyond to other issues. But that should do for now. Getting all of this right and useful as theory is hard enough; getting it right as a matter of exposition is a nightmare. Very few sources do a good job of it, and we should not be surprised that Wikipedia's offering is not yet optimal. But it has the potential to be, since so many eyes can be focused intently on its development.

Noetica^Tea? 02:09, 21 May 2012 (UTC)

That's interesting. Let's start with the note. How do you like this version?

Strict definition of diatonic scale (version 1)
The expression diatonic scale is herein strictly defined as a 7-tone scale which is either a sequence of successive natural notes (such as the C-major scale, C-D-E-F-G-A-B, or the A-minor scale, A-B-C-D-E-F-G) or any transposition thereof. This includes, for instance, the major and the natural minor scales, but does not include some other 7-tone scales, such as the melodic minor and the harmonic minor scales (see also Diatonic and chromatic).

Is there a simple way to indicate the seven possible heptatonic scales composed of natural notes ordered in their correct sequence?

A, B, C, D, E, F, G
B, C, D, E, F, G, A
C, D, E, F, G, A, B
D, E, F, G, A, B, C
E, F, G, A, B, C, D
F, G, A, B, C, D, E
G, A, B, C, D, E, F

Paolo.dL (talk) 09:04, 21 May 2012 (UTC)

How about: a strict diatonic scale is one that can be written on a staff without using any accidentals except for the signature. In the article this would need to be explained in more reader friendly phrasing and terms. −Woodstone (talk) 10:37, 21 May 2012 (UTC)

This is a smart approach, but it works only if you use standard key signatures. In other words, the 14 key signatures (with up to 7 sharps or 7 flats) defined by the Circle of fifth. Let's not forget that it is theoretically possible to write a non-strictly-diatonic scale, such as the melodic minor scale, by using notes without accidentals on a staff with a non-standard key signature. As a consequence, this definition is easy to grasp only for those who are very familiar with the standard key signatures. Since the definition of the standard key signatures is not simple (except for those who know it already), it seems to me that this approach is less direct that the one I suggested above. Therefore it does not work, in my opinion, as the main definition, but it might be added as an alternative definition. Here is an example (I think that the previous version 1 is clear enough, though; alternative definitions should be given in the article diatonic scale; here, we should select only one definition).

Strict definition of diatonic scale (version 2)
The expression diatonic scale is herein strictly defined as a 7-tone scale which is either a sequence of successive natural notes (such as the C-major scale, C-D-E-F-G-A-B, or the A-minor scale, A-B-C-D-E-F-G) or any transposition thereof. In other words, a scale that can be can be written using seven consecutive notes without accidentals on a staff with a conventional key signature, or with no signature. This includes, for instance, the major and the natural minor scales, but does not include some other 7-tone scales, such as the melodic minor and the harmonic minor scales (see also Diatonic and chromatic).

Paolo.dL (talk) 15:50, 21 May 2012 (UTC)

One of the advantages of using the signature, is that it implicitly makes clear that diatonic intervals are relative to a scale. Notes that need accidentals are chromatic to that scale. An objection to both boxed proposals is that it uses the term transposition, which is well defined, but may be misunderstood by the average reader. The signature is easier to explain and details can be referred to key signature. −Woodstone (talk) 16:42, 21 May 2012 (UTC)

In this case, I find it hard to agree with you. The concept of transposition (i.e. raise or lower all notes by the same number of semitones) is so simple, compared to the definition of "standard key signature" (in turn based on the Circle of fifths), that a definition of diatonic scale based on transposition is likely to be understood correctly by much more people than one based on "standard key signature". In both cases, you refer to a separate article (Transposition (music) or Key signature) for details. Paolo.dL (talk) 18:14, 21 May 2012 (UTC)

While waiting for other comments, since the currently published version of note 3 is misleading (as explained by Noetica), I will insert into the article the version 2 proposed above, as that version is a compromise between my proposal (version 1) and Woodstone's one. Paolo.dL (talk) 15:48, 25 May 2012 (UTC)

Non-standard key signatures are a total red herring. When you say "key signature" it's assumed you mean normal ones, just like you don't have to say "biological tree" or "internal-combustion car". But it seems like the discussion has veered into the best way to define "diatonic", which doesn't really belong in this article. —Wahoofive (talk) 16:48, 25 May 2012 (UTC)

Actually, the discussion is currently about a note (note 3) which describes just one of the possible definitions of diatonic scale. Namely, the "strict" definition operationally adopted by this article. We are also discussing about the subsection "Diatonic and chromatic", which is part of this article, although it is supposed to be a summary of the main article, which provides more complete information and references (mainly, in section Diatonic and chromatic#Intervals). Paolo.dL (talk) 17:07, 25 May 2012 (UTC)

Non-standard key signatures may be a total red herring for someone who knows both rules and exceptions. Most readers may not even know the rules. I know the rule, for instance, but I am not sure about the exceptions. I strongly doubt that there exist no exceptions in the literature, especially when the harmonic minor and melodic minor scales are used. This is what I would do if I were a composer, and I wanted to use the harmonic A-minor scale (A B C D E F G♯ A): I would write a diesis as a key signature for G, instead of adding it to each G that I write on the staff. And even if you might be able to convince me that I am wrong, and that there exist no exceptions in the literature, you should consider that I am just one of the many readers that are smart enough to regard as reasonable and convenient, and hence possible, to use unconventional key signatures to represent unconventional scales. And many others may not even know the rule! Paolo.dL (talk) 09:04, 26 May 2012 (UTC)