Talk:Tritone

Tritone definitions

We should probably amend the definition section to make clear that tritone has two accepted definitions that do not always agree with each other.

The mathematical definition found in the Harvard Music Dictionary and in Merriam-Webster online, also reflected (and more fully detailed) in [the Wikipedia article] is of a tritone as of three whole tones — 9/8³, which is a (usually tempered) Pythagorean augmented fourth, thereby also implying three whole tones down from the octave, which is a (usually tempered) Pythagorean diminished fifth.

However, the auditory definition of a tritone as being as close to the semioctave as possible or in the region that sounds like a semioctave is reasonable from an auditory point of view, as long as one is aware of the pitfalls that a tritone by this definition may not fit with the harmonic definition, and vice versa; furthermore, the additional stricture in this definition that a tritone be capable of mapping to 12\24 may, depending upon interpretation, cause an interval to be excluded from being a tritone in some tuning systems even if it has the same mapping in a non-24edo system as an interval that maps to 12\24, or cause it to be conditionally a tritone.

For instance, 11/8 maps to 6\13 and thereby to 12\26; 13edo taken as a 2.5.9.11 subgroup tuning also maps a stack of 3 9/8 intervals to 6\13 (thereby meeting the harmonic definition of tritone), which is tied with its octave inverse 7\13 for closest place to the 600 ¢ semioctave (and falls into the outer zone of the melodic tritone region). In contrast, 24edo maps a stack of 3 9/8 intervals to 12\24, but maps 11/8 to 11\24, thereby denying tritone status to 11/8 by both definitions of tritone. Note that the use of mapping (or lack thereof) to 12\24 will not exclude all potential tritones that do not map to the semioctave in even moderately larger tuning systems — for instance, in a mere doubling of 24edo, 48edo has 39/28 mapping to 23\48, even though it maps to 12\24, thereby meeting the auditory definition of a tritone, but not meeting the mathematical definition in 48edo even though it meets both definitions in 24edo.

Lucius Chiaraviglio (talk) 08:57, 9 March 2025 (UTC)

There is some general organization work to do with the interval region pages since they "occupy" page titles that designate concepts which can be treated or not as interval regions. The stricter definitions clearly belong in the lead section, no matter how the rest of the article ends up being structured. And since tritones can be treated as "three whole tones" with a possibly variable size of "whole tone", or as a synonym of semioctave, or as a region capturing intervals in these surroundings, and possibly even other meanings, all of these should be clearly accessible in the same page. I don't think there's a definition that's "more mathematical" than the other, they just attempt to generalize different properties of "tritones" as observed in various tuning systems, and the page should give a good idea of all possible options in their context. --Fredg999 (talk) 03:28, 13 March 2025 (UTC)

I am generally in agreement — I used the terms "methematical" for 3 whole tones and "auditory" for region for lack of better terms. Do you have an idea for better terms? Lucius Chiaraviglio (talk) 07:50, 13 March 2025 (UTC)

Maybe "literal" for tritone = three whole tones. I suppose the "exact semioctave" sense might as well be called the semioctave sense. And similarly the region around these would be the region sense. What do you think? --Fredg999 (talk) 20:24, 13 March 2025 (UTC)

"Literal" sounds okay for tritone = three whole tones. But "semioctave sense" sounds a bit awkward, but I'll admit up-front that I can't think of a better name. Lucius Chiaraviglio (talk) 21:26, 13 March 2025 (UTC)