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[1] and in Merriam-Webster online[2], 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)
References
- ↑ Willi Apel (1944), Harvard Dictionary of Music, Harvard University Press (text format, retrieved 2025-03-09)
- ↑ Merriam-Webster online: tritone (retrieved 2025-03-09)