18/17: Difference between revisions
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In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99¢. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢). | In [[17-limit]] [[just intonation]], '''18/17''' is the '''small septendecimal semitone''' of about 99¢. It is very close to [[12edo]]'s "half step" of 100¢, and fairly close to the "large septendecimal semitone" of [[17/16]] (~105¢). | ||
There exists a disagreement in different | == Terminology and notation == | ||
There exists a disagreement in different conceptualization systems on whether 18/17 should be a [[diatonic semitone]] or a [[chromatic semitone]]. In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from [[2187/2048]], the Pythagorean chromatic semitone. In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from [[256/243]], the Pythagorean diatonic semitone. The term "small septendecimal semitone" omits the diatonic/chromatic part 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 == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[18/ | * [[18/17 equal-step tuning]] – equal multiplication of this interval | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
Revision as of 10:00, 12 January 2023
| Interval information |
reduced
[sound info]
In 17-limit just intonation, 18/17 is the small septendecimal semitone of about 99¢. It is very close to 12edo's "half step" of 100¢, and fairly close to the "large septendecimal semitone" of 17/16 (~105¢).
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 18/17 should be a diatonic semitone or a chromatic semitone. In the Functional Just System, it is a chromatic semitone, separated by 4131/4096 from 2187/2048, the Pythagorean chromatic semitone. In Helmholtz-Ellis notation, it is a diatonic semitone, separated by 2187/2176 from 256/243, the Pythagorean diatonic semitone. The term "small septendecimal semitone" omits the diatonic/chromatic part 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
- 17/9 – its octave complement
- 17/12 – its fifth complement
- Gallery of just intervals
- List of superparticular intervals
- 18/17 equal-step tuning – equal multiplication of this interval