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¢).

There exists a disagreement in different ~~notation~~ systems on whether 18/17 should be ~~notated as~~ a diatonic semitone or a chromatic semitone. In the [[Functional Just System]], it is a chromatic semitone, ~~whereas in~~ [[Helmholtz-Ellis notation]], it is a diatonic semitone.

== 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 ==

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* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

* [[18/~~17s~~ equal ~~temperament|AS18/17~~]] ~~- its ambitonal sequence~~

* [[18/17 equal-step tuning]] – equal multiplication of this interval

[[Category:Second]]

[[Category:Chroma]]

[[Category:Semitone]]

@@ Line 7: / Line 7: @@
 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 notation systems on whether 18/17 should be notated as a diatonic semitone or a chromatic semitone. In the [[Functional Just System]], it is a chromatic semitone, whereas in [[Helmholtz-Ellis notation]], it is a diatonic semitone.
+== 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 ==
@@ Line 14: / Line 17: @@
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
-* [[18/17s equal temperament|AS18/17]] - its ambitonal sequence
+* [[18/17 equal-step tuning]] – equal multiplication of this interval
 [[Category:Second]]
 [[Category:Chroma]]
 [[Category:Semitone]]