24/17: Difference between revisions
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Simplify the "terminology and notation" section since it's addressed in the 17-limit page |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = small septendecimal tritone | ||
| Color name = 17u4, su 4th | | Color name = 17u4, su 4th | ||
| Sound = jid_24_17_pluck_adu_dr220.mp3 | | Sound = jid_24_17_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[17-limit]] [[just intonation]], '''24/17''' is the ''' | In [[17-limit]] [[just intonation]], '''24/17''' is the '''small septendecimal tritone''', measuring very nearly 597¢. It is the [[mediant]] between [[7/5]] and [[17/12]], the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered [[edo]] systems, including [[12edo]]. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. [[22edo]] is another good edo system for using the half-octave in this way. | ||
== 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 24/17 specifically: | ||
* In [[Functional Just System]], it is an augmented fourth, separated by [[4131/4096]] from the [[729/512|Pythagorean augmented fourth (729/512)]]. | |||
* In [[Helmholtz-Ellis notation]], it is a diminished fifth, separated by [[2187/2176]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]]. | |||
The term ''small septendecimal tritone'' omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of [[17/12]]. | |||
== See also == | == See also == | ||
Latest revision as of 08:22, 4 January 2024
| Interval information |
[sound info]
In 17-limit just intonation, 24/17 is the small septendecimal tritone, measuring very nearly 597¢. It is the mediant between 7/5 and 17/12, the "larger septendecimal tritone". The two septendecimal tritones are each 3¢ away from the 600¢ half-octave, and so they are well-represented in all even-numbered edo systems, including 12edo. Indeed, the latter system, containing good approximations of the 3rd and 17th harmonics, can use the half-octave as 24/17 and 17/12 in close approximations to chords such as 8:12:17 and 16:17:24. 22edo is another good edo system for using the half-octave in this way.
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 24/17 specifically:
- In Functional Just System, it is an augmented fourth, separated by 4131/4096 from the Pythagorean augmented fourth (729/512).
- In Helmholtz-Ellis notation, it is a diminished fifth, separated by 2187/2176 from the Pythagorean diminished fifth (1024/729).
The term small septendecimal tritone omits the distinction and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal tritone of 17/12.