17/12: Difference between revisions
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In [[17-limit]] [[just intonation]], '''17/12''' is the ''' | In [[17-limit]] [[just intonation]], '''17/12''' is the '''large 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 == | == Terminology and notation == | ||
Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion. | |||
In | For 17/12 specifically: | ||
* In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]]. | |||
* In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from the [[729/512|Pythagorean augmented fourth (729/512)]]. | |||
The term ''large septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17. | |||
== See also == | == See also == | ||
Latest revision as of 08:24, 4 January 2024
| Interval information |
[sound info]
In 17-limit just intonation, 17/12 is the large 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
Conceptualization systems disagree on whether 17/16 should be a diatonic semitone or a chromatic semitone, and as a result the disagreement propagates to all intervals of HC17. See 17-limit for a detailed discussion.
For 17/12 specifically:
- In Functional Just System, it is a diminished fifth, separated by 4131/4096 from the Pythagorean diminished fifth (1024/729).
- In Helmholtz-Ellis notation, it is an augmented fourth, separated by 2187/2176 from the Pythagorean augmented fourth (729/512).
The term large septendecimal tritone omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal tritone of 24/17.