Talk:List of pitch intervals

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Music theory

	Music portal This article is within the scope of WikiProject Music theory, a collaborative effort to improve the coverage of music theory, theory terminology, music theorists, and musical analysis on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.Music theoryWikipedia:WikiProject Music theoryTemplate:WikiProject Music theoryMusic theory
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Tunings, Temperaments, and Scales (defunct)

This article is within the scope of WikiProject Tunings, Temperaments, and Scales, a project which is currently considered to be defunct.Tunings, Temperaments, and ScalesWikipedia:WikiProject Tunings, Temperaments, and ScalesTemplate:WikiProject Tunings, Temperaments, and ScalesTunings, Temperaments, and Scales

Color codes II

I propose the color coding below. Right now the colors are less obtrusive, but more indistinguishable. Hyacinth (talk) 12:04, 16 July 2015 (UTC)[reply]

New Code	Compliant?	Legend (simplified)	Old Code	Compliant?
E	YES	12TET.	E	YES
Q	YES	24TET.	Q	YES
2	YES	2-limit.	2	YES
3	YES	3-limit/Pythagorean.	3	YES
5	YES	5-limit/just.	5	YES
7	YES	7-limit/ septimal.	7	YES
11	YES	11-limit.	11	YES
13	YES	13-limit.	13	YES
17	YES	17-limit.	17	YES
19	YES	19-limit.	19	YES
23	YES	23-limit.
29	YES	29-limit.
M	YES	Meantone temperament.	M	YES
U	YES	Measure/higher ET.	U	YES
S	NA	Superparticular (no code).	S
H	YES	Higher harmonics.	H	YES

As one climbs the limits one progresses through the rainbow.
12TET is made the same color (reddish) as 2-limit, since 2-limit only includes octaves.
24-TET is made a pinkish red.
Meantone is made a brown to match the color (orange) Pythagorean happens to be according to the rainbow pattern.
Units of measurement or equal temperament is made pink (12 is red, 24 is red/pink, > is pink).
Higher harmonics are gray.

Hyacinth (talk) 12:04, 16 July 2015 (UTC)[reply]

One problem is that the text becomes hard to read if the background colors are not soft enough. Especially for people who are color blind. SharkD Talk 06:14, 13 November 2016 (UTC)[reply]

What should soft color and hard color link to? Hyacinth (talk) 23:56, 6 April 2017 (UTC)[reply]

Made a guess. Hyacinth (talk) 00:32, 7 April 2017 (UTC)[reply]

Other tuning images

Is there any interest in me creating more of images like this, but with different tunings? SharkD Talk 01:38, 14 November 2016 (UTC)[reply]

See: WP:BOLD and WP:CAREFUL. Hyacinth (talk) 01:10, 5 February 2020 (UTC)[reply]

Superparticular ratio

There is a column in the table to mark superparticular ratios. The corresponding WP page states they are of importance in music theory, but that page does not mention them. I cannot possibly see any musical relevance of these ratios, except the small ones that naturally occur in limit-tunings. Therefore I propose to eliminate this column. −Woodstone (talk) 14:14, 1 November 2020 (UTC)[reply]

Inconsistency in mathematical data in 2 rows

Hi, I am parsing this wikipedia table for a microtonal project with (Python/Pandas, JavaScript/Mathjs), So I am adding a numerical ratio field (that makes much more sense from the polychromatic/microtonal perspective of my project) after looking the data there are Inconsistencies, things that doesn't match between the cents and the ratio expressed as a formula.

I prefer to just warn about this that change it myself, I am only reporting for the mathemathical inconsistency I don't know if there are other issues or what are the right values. (I am sorry for the format) the end number is the Ratio, also the fractions are represented in a way that Pandas or Python could be get the value with pd.eval or eval

ID Cents
24	23.46	B♯+++	531441/524288	3**(12)/2**(19)	Pythagorean comma,[10][11] ditonic comma	3	1.013643265
316	1223.46	B♯+++	531441/524288	3**(12)/2**(18) Pythagorean augmented seventh	3	1.013643265
531441/524288=1.013643265
3**(12)/2**(18)=2.02728652954102
531441/262144 = 2.02728652954102 <== so this is the right value

237	833.09		5**(1/2)+1/2	φ/1		Golden ratio (833 cents scale)		2.736067977
238	833.11		233/144		233/2**(4)×3**(2)	Golden ratio approximation (833 cents scale)	233	1.618055556
233/144 = 1.61805555555556 = 233/2**(4)×3**(2)
5**(1/2)+1/2 = 2.736067977 = 1742.524889 Cents, this formula maybe wrong, also why two rows pointing to the golden ration?

For the purpose of tuning, notes are conventionally considered octave repeating, and intervals are therefore reduced by factors two to stay under 2. So the second one does not really belong in the table (just as the other few over 2). These seem to be given because they have special name. That is not a good idea, because there is not end to it in view of wider intervals, many of which are common in jazz harmony. They do not add essentially different interval types, only their names.

The golden ratio is (5^1/2+1)/2 or 833.09 cents. You have the brackets wrong. The other one is a rational approximation to the golden ratio. Both are curiosities and have no musical meaning.

−Woodstone (talk) 15:52, 16 July 2021 (UTC)[reply]

Agree, ratios should be given between the octave only.

I don't see any logical reason to have two golden ratios in this list or to have it without the right mathemathical notation as you did mention (5^1/2+1)/2 instead of 5^1/2+1/2 ::-49.230.136.53 (talk) 09:00, 18 July 2021 (UTC)[reply]

2-limit

Unisons and octaves should be 2-limit, not 3-limit, according to http://www.tonalsoft.com/enc/l/limit.aspx — Omegatron (talk) 01:00, 27 December 2022 (UTC)[reply]