WikiProject iconMusic theory NA‑class
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I borrowed this format from another template, something like Template:Middle Ages wide 2 (though I vaguely remember a Native American music related template, possibly gone or vertical now), but removed the border as this template is designed to go within a table on each interval page. Hyacinth 18:54, 10 Apr 2005 (UTC)

I think the older (my) horizontal format was easier to read than the jumbled vertical format. Hyacinth 11:31, 23 February 2006 (UTC)[reply]


I replaced "semitone" with "semitone of equal temperament"; in general the diatonic and chromatic semitones differ. Gene Ward Smith 08:29, 11 June 2006 (UTC)[reply]

Diatonic and chromatic[edit]

The table uses the term "diatonic" in a highly idiosyncratic way, but without explanation. This term, along with "chromatic", is the cause of serious uncertainties at several other Wikipedia articles, and in the broader literature. Some of us thought that both terms needed special coverage, so we started up a new article: Diatonic and chromatic. Why not have a look, and join the discussion? Be ready to have comfortable assumptions challenged! – Noetica♬♩Talk 01:40, 4 April 2007 (UTC)[reply]

I left a mssg on Hyacinth's talk page about our proposed change.--Roivas (talk) 00:40, 11 December 2007 (UTC)[reply]

I do not believe that this templates use of diatonic is idiosyncratic in any way. A P4 is the distance between what? According to interval (music): "four diatonic scale degrees". If this is not so, what kind of intervals are on the template? Or, what system of labeling is used to name the intervals on the template? In other words, what is the proposed change? Hyacinth (talk) 04:27, 11 December 2007 (UTC)[reply]

I don't think anyone would argue that the P4 isn't diatonic. The issue is with augmented and diminished intervals being labeled diatonic.--Roivas (talk) 15:51, 11 December 2007 (UTC)[reply]
Those intervals are only augmented or diminished in relation to diatonic intervals and scales. Without that context they are simply the size they are. Hyacinth (talk) 04:46, 13 December 2007 (UTC)[reply]
I would suggest we title the table "Intervals".--Roivas (talk) 15:51, 11 December 2007 (UTC)[reply]
That works for me! Unfortunately, I now really want to know, what is the name for these? Hyacinth (talk) 04:39, 13 December 2007 (UTC)[reply]

If you look at the Goetschius definition on my talk page, you'll see that he defines the augmented and diminished intervals as chromatic. I'm sure this is strange for a lot of folks, but he even considers the minor third a chromatic interval.--Roivas (talk) 15:53, 13 December 2007 (UTC)[reply]

Hyacinth said:

Those intervals are only augmented or diminished in relation to diatonic intervals and scales. Without that context they are simply the size they are. Hyacinth (talk) 04:46, 13 December 2007 (UTC)[reply]

I hate to put it this way, but common sense doesn't seem to apply to music theory. We'll probably be better off avoiding the use of the term "Diatonic" as much as possible.--Roivas (talk) 16:25, 13 December 2007 (UTC)[reply]

The minor 6th and the minor 7th?[edit]

Where are these intervals? I find that they are the only ones missing from the table. What is the reason that they are left out? /Andreas —Preceding unsigned comment added by (talk) 19:59, 30 December 2007 (UTC)[reply]

Non-12-tone intervals[edit]

Should this template be limited to intervals found in Western 12-tone-per-octave meantone tunings? Or should we find room for neutral intervals, subminor and supermajor intervals, commas, etc.? — Gwalla | Talk 21:29, 31 March 2008 (UTC)[reply]

I was bold and added the (7-limit) subminor and supermajor, and the (11-limit/quarter-tone) neutral qualities. I didn't add commas, because while they are technically intervals, they are typically used only in tuning and not as harmonies or melodic steps in their own right. — Gwalla | Talk 20:38, 10 April 2008 (UTC)[reply]

In principle, I'm in favour of including intervals outside the traditional Western twelve semitone system (keyboard, guitar, etc.). That said, the starting point of the majority audience of the English language Wikipedia will be that system. So I suggest that the template contain some sort of dividing line which recognises and acknowledges this. It saves the Western beginner from being confused with non-Western possibilities, and allows the advanced person to explore beyond the confines of Western music. So I'm making an adjustment along those lines. Please feel free to refine it further. Feline Hymnic (talk) 22:45, 13 March 2009 (UTC)[reply]

Supermajor/Subminor vs. Septimal major/minor[edit]

I changed the "Septimal major"/"Septimal minor" tags to "supermajor" and "subminor", which is another commonly used term that more accurately reflects what they are in a diatonic sense. The "septimal minor/major" tags refer specifically to the common just intonation way of tuning these intervals as 7/6 and 9/7, respectively. This is less relevant when it comes to the diatonic function of these intervals -- you don't see a major third referred to here as a "quintal third," for example. The "subminor"/"supermajor" convention more easily explains where these intervals lie compared to the other intervals mentioned. Furthermore, there are more JI subminor and supermajor thirds than just 7/6 and 9/7, and if we're using these words to describe the size of the 250-cent and 450 cent intervals, why tie it down to a specific intonation?

Furthermore, the use of the "septimal" name is inconsistent with the step sizes given: an actual septimal 7/6 subminor third would not be 2 1/2 steps, as listed, but closer to 2 2/3; a septimal 9/7 supermajor third would be almost exactly 4 1/3 steps. The logic behind the listing of these intervals in terms of equal-tempered "step" sizes is presumably to explain what they are in a way that is familiar to the average reader, who will be more easily able to grasp step sizes in terms of quarter-tones rather than integer ratios such as 7/6. Thus, to simply refer to the 250 cent interval for what it is -- a "subminor" third -- rather than tie it down to a specific intonation, such as 7/6, makes more sense all around than the way it was before.

On the other hand, if we want the "subminor third" link down there to refer specifically to the subminor 7/6 third, then perhaps we should change the step size to 2 2/3, which 7/6 is nearly equivalent to, rather than 2 1/2 -- this would allow us to distinguish between the subminor third and the supermajor second (which is 2 1/3); both are currently rounded off to 2 1/2, which might be confusing. ---- Battaglia01 (talk) 03:26, 27 June 2009 (UTC)[reply]

This edit was reverted, as the page for "supermajor second" was blank. As a compromise, I've put the "supermajor" and "subminor" names back, and created those pages. For now, they just redirect to the corresponding "septimal interval" moniker, although if anyone else wants to set up a page on supermajor and subminor intervals in general, and outside of any specific septimal intonation, be my guest. ---- Battaglia01 (talk) 19:14, 19 July 2009 (UTC)[reply]


I expanded this to include the various commas, the wolf, quarter tone etc. There are probably others that should be here too. I also corrected some of the links and created a few articles that actually did not exist eg Augmented seventh which originally redirected to the unrelated chord on a minor seventh... I hope I haven't gone too over the top! --Jubilee♫clipman 01:22, 23 December 2009 (UTC)[reply]

It's getting a bit large. Alas, my template-fu is not strong enough to make the "other intervals" subgroup start collapsed. — Gwalla | Talk 22:15, 23 December 2009 (UTC)[reply]
I don't think we need to add any more. Some of the "other invervals" could be removed if they are only discussed by acousticians, but things like the wolf interval, microtone, cent etc probably ought to stay. I'll have another think soon. --Jubilee♫clipman 02:41, 24 December 2009 (UTC)[reply]


Is a thirteenth 18 or 19 semitones? or should it be 20 or 21? (talk) 23:41, 17 December 2010 (UTC)[reply]

Cleaned up microtonal intervals[edit]

I thought it more prudent to use the 72-tet based naming rather than 24-tet. For instance, the only subminor seventh that most people care about is 7/4, and to represent 7/4 with the crappy 24-tet based 950 cent approximation is a little silly and will probably place people astray. There's no need to place such importance on 24-tet, especially when 7/4 is the first microtonal interval most people ever learn.

The names for these intervals were originally names like "septimal minor third" and "septimal major third," but with cents values like 250 cents and 450 cents. I suggested changing them because it's more proper to refer to them as "subminor thirds" and "supermajor thirds." If one were going to use the septimal moniker it would be more common to hear it referred to as a "septimal supermajor third" than a "septimal major third."

So I at the time advocated changing the changing of the intervals from "septimal minor" to "subminor," which is more common, proper, and for the purposes of this template, easier for the average reader to grasp. However, to leave the cents values at 2 1/2 steps and 4 1/2 steps seemed to me to be a little bit silly, so I changed them to their almost-perfect 72-tet approximations: 2 2/3 steps and 4 1/3 step. This is the whole reason that people use 72-tet at all, because it makes the conceptualizing and mapping of intervals, as well as relating them to 12-tet, incredibly intuitive and simple. The fact that subminor intervals work out to x 2/3 steps, and supermajor intervals work out to x 1/3 steps is no coincidence - it's because 72-tet also tempers out the Pythagorean comma and maps 64/63 to 2/3's of a step. So this leads to a really intuitive pattern.

The neutral intervals in 72-tet are generally mapped to x 1/2 step intervals. The one exception is the neutral sixth - although there are lots of neutral sixths, the most consonant in that vicinity is generally 13/8. 13/8, in 72-tet, falls right between 8 1/3 and 8 1/2 steps. Both mappings represent it about equally as well. Since it doesn't a difference tuning wise, and either mapping would be fine for the purposes of this template, I thought it best to represent it with 8 1/2, since for the purposes of coherence to the reader it continues the "neutral intervals = 1/2 step alteration" pattern.

I also was bold and put the frequency ratios next to each interval. Although there are other supermajor thirds in the area, like 13/10, they aren't as notable as 9/7, so it makes more sense to emphasize, for each general interval class, the most notable one in the vicinity. If this comes off as too cluttered, we can get rid of them, but I don't think we should ever go back to the 24-tet based convention - no point. — Preceding unsigned comment added by Battaglia01 (talkcontribs) 05:45, 24 January 2011 (UTC)[reply]