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In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[ | In [[17-limit]] [[just intonation]], '''17/12''' is the '''larger septendecimal tritone''', measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, [[24/17]], and the interval that separates them is the small [[comma]] [[289/288]], about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered [[edo]] system contains a close approximation to these intervals. | ||
17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]]. | 17/12 is the [[mediant]] between the two septimal tritones [[7/5]] and [[10/7]]. | ||
== Terminology and notation == | |||
There exists a disagreement in different conceptualization systems on whether 17/12 should be an augmented fourth or a diminished fifth. In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from [[1024/729]], the Pythagorean diminished fifth In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from [[729/512]], the Pythagorean augmented fourth. The term "large septendecimal tritone" omits the distinction and only describes its melodic property i.e. the size. | |||
In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded [[circle-of-fifths notation]] is to prepare a [[Pythagorean comma]] accidental so that the interval can be notated in either category. | |||
== See also == | == See also == | ||
Revision as of 09:17, 14 January 2023
| Interval information |
[sound info]
In 17-limit just intonation, 17/12 is the larger septendecimal tritone, measuring very nearly 603¢. Its inversion is the smaller septendecimal tritone, 24/17, and the interval that separates them is the small comma 289/288, about 6¢. This difference is usually negligible, and tempering out this comma allows the 600¢ half-octave to function as both septendecimal tritones. Thus, every even-numbered edo system contains a close approximation to these intervals.
17/12 is the mediant between the two septimal tritones 7/5 and 10/7.
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 17/12 should be an augmented fourth or a diminished fifth. In Functional Just System, it is a diminished fifth, separated by 4131/4096 from 1024/729, the Pythagorean diminished fifth In Helmholtz-Ellis notation, it is an augmented fourth, separated by 2187/2176 from 729/512, the Pythagorean augmented fourth. The term "large septendecimal tritone" omits the distinction and only describes its melodic property i.e. the size.
In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded circle-of-fifths notation is to prepare a Pythagorean comma accidental so that the interval can be notated in either category.