Template talk:Infobox musical interval

Inverse & complement

I don't see the point of distinguishing between "inverse" and "complement". It wastes space. Also, some intervals correspond to more than one just interval, for example the major second can be 9/8 or 10/9. —Keenan Pepper 13:32, 15 March 2006 (UTC)

I don't have particularly strong feelings on the first point, except that they differ for Unison and Octave and are theoretically distinct concepts. On the second point, the individual pages which call this template should be changed so that they read "just_interval = 9:8 or 10:9" for example. Is 'or' the right word? Andeggs 07:49, 16 March 2006 (UTC)

"9:8 or 10:9" works for me. —Keenan Pepper 01:09, 17 March 2006 (UTC)

Pythagorean tuning

​​​ I propose that new parameters for Pythagorean tuning be added under "size" and "cents". Currently, these intervals are entered under the just intonation parameters, but this is inaccurate, since Pythagorean tuning does not always match up with just intonation. Additionally, it might be helpful to create parameters for other sizes of the interval, such as the septimal minor sixth. Any thoughts on this? -Ezhao02 (talk) 22:41, 19 February 2020 (UTC)

Could you clarify in what way Pythagorean tuning does not match with just intonation? I think I know what you mean but, after some back-and-forth recently at the Just intonation article, it would appear that any whole-number ratio now qualifies, even when the factors are very large.—Jerome Kohl (talk) 23:23, 19 February 2020 (UTC)

@Jerome Kohl: I'd say that just intonation is intended to sound consonant (at least for consonant intervals) or derived from consonant intervals. For instance, a Pythagorean major third (81:64) quite obviously sounds too wide due to the "beating", especially when compared to a just major third (5:4). An example of the second type would be that the just interval for a minor second (16:15) is derived from the interval between a just major third (5:4) and a perfect fourth (4:3). -Ezhao02 (talk) 23:53, 19 February 2020 (UTC)

That's what I thought you meant. Yet there is nothing in the current version of template to prevent using ratios such as 81:64 or even 531441:524288 to describe intervals, is there?—Jerome Kohl (talk) 01:58, 20 February 2020 (UTC)

@Jerome Kohl: I'm arguing that there's currently no good place to put ratios like 81:64. Currently, it's placed in the parameters for just intervals, but it doesn't fit there and would work better in a new parameter. Ezhao02 (talk) 20:42, 20 February 2020 (UTC)

Maybe the problem is not with the parameter so much as the way "just interval" is being construed. While I take your point that just intonation was originally designed to optimize a small number of consonant intervals (despite inevitably leaving behind a lot of detritus), I'm not so sure that this is any longer the case. Many 20th-century composers of microtonal music (e.g., Ben Johnston) refer to higher-limit tuning systems as "just". Is there a more inclusive term for all intervals expressed as whole-number ratios? It seems to me that making separate classifications for "just" and "Pythagorean" might open up the possibility of yet a third category (fourth, fifth, ... categories) for non-Pythagorean and non-just intervals, such as a 43:33 "perfect fourth".—Jerome Kohl (talk) 21:32, 20 February 2020 (UTC)

@Jerome Kohl: Do you know if any scholars define just intonation as any system that uses whole-number ratios? Ezhao02 (talk) 02:44, 21 February 2020 (UTC)

I agree that adding pythagorean tuning is just one of many tunings, which all could be added. But the infobox if supposed to be a short summary, so only the most common parameters should be added. If someone is looking for pythagorean tuning there's very good overview of the intervals on that page, so no need to put it in the infobox. The 24TET size is also out of place in that sense, I was just removing values where 24TET and 12TET are equal. (and FYI: Pythagorean tuning would be 3-limit just intonation) Ptt (talk) 09:31, 21 February 2020 (UTC)

Hello. As far as I know "Just Intonation" in the 20th/21st centuries is used in the context of rational-number intervals, for example in Extended Helmholtz-Ellis Just Intonation Pitch Notation. This is in contrast to intervals of $n$-TET tunings which are based on irrational numbers of the form $2^{k/n}$. However, the term "just intonation" has been used traditionally to refer to 5-limit just intonation tuning, which is based on major and minor triads containing major (5:4) and minor (6:5) thirds respectively. kupirijo (talk) 16:21, 22 February 2020 (UTC)