17/12: Difference between revisions
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{{Infobox Interval | |||
| | | Name = larger septendecimal tritone | ||
| Color name = 17o5, iso 5th | |||
| Sound = jid_17_12_pluck_adu_dr220.mp3 | |||
}} | |||
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 [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion. | |||
17/12 is | 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)]]. | |||
See | 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. | ||
== Approximation == | |||
{{Interval edo approximation|17/12}} | |||
== See also == | |||
* [[24/17]] – its [[octave complement]] | |||
* [[18/17]] – its [[fifth complement]] | |||
* [[Gallery of just intervals]] | |||
[[Category:Tritone]] | |||
Latest revision as of 13:04, 3 November 2025
| 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.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 2 | 1\2 | 600.00 | -3.00 | -0.50 |
| 4 | 2\4 | 600.00 | -3.00 | -1.00 |
| 6 | 3\6 | 600.00 | -3.00 | -1.50 |
| 8 | 4\8 | 600.00 | -3.00 | -2.00 |
| 10 | 5\10 | 600.00 | -3.00 | -2.50 |
| 12 | 6\12 | 600.00 | -3.00 | -3.00 |
| 14 | 7\14 | 600.00 | -3.00 | -3.50 |
| 16 | 8\16 | 600.00 | -3.00 | -4.00 |
| 18 | 9\18 | 600.00 | -3.00 | -4.50 |
| 20 | 10\20 | 600.00 | -3.00 | -5.00 |
| 22 | 11\22 | 600.00 | -3.00 | -5.50 |
| 24 | 12\24 | 600.00 | -3.00 | -6.00 |
| 26 | 13\26 | 600.00 | -3.00 | -6.50 |
| 28 | 14\28 | 600.00 | -3.00 | -7.00 |
| 30 | 15\30 | 600.00 | -3.00 | -7.50 |
| 32 | 16\32 | 600.00 | -3.00 | -8.00 |
| 34 | 17\34 | 600.00 | -3.00 | -8.50 |
| 36 | 18\36 | 600.00 | -3.00 | -9.00 |
| 38 | 19\38 | 600.00 | -3.00 | -9.50 |