17/16: Difference between revisions

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17/16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], which measures about 99¢. The difference between them is [[289/288]], about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out.

There exists a disagreement in different ~~notation~~ systems on whether 17/16 should be ~~notated as~~ a diatonic semitone or a chromatic semitone. In [[Functional Just System]], it is a diatonic semitone, ~~whereas in~~ [[Helmholtz-Ellis notation]], it is a chromatic semitone.

== Terminology and notation ==

There exists a disagreement in different conceptualization systems on whether 17/16 should be a [[diatonic semitone]] or a [[chromatic semitone]]. In [[Functional Just System]], it is a diatonic semitone, separated by [[4131/4096]] from [[256/243]], the Pythagorean diatonic semitone. In [[Helmholtz-Ellis notation]], it is a [[chromatic semitone]], separated by [[2187/2176]] from [[2187/2048]], the Pythagorean chromatic semitone. The term "large 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 9: / Line 9: @@
 /16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], which measures about 99¢. The difference between them is [[289/288]], about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out.
-There exists a disagreement in different notation systems on whether 17/16 should be notated as a diatonic semitone or a chromatic semitone. In [[Functional Just System]], it is a diatonic semitone, whereas in [[Helmholtz-Ellis notation]], it is a chromatic semitone.
+== Terminology and notation ==
+There exists a disagreement in different conceptualization systems on whether 17/16 should be a [[diatonic semitone]] or a [[chromatic semitone]]. In [[Functional Just System]], it is a diatonic semitone, separated by [[4131/4096]] from [[256/243]], the Pythagorean diatonic semitone. In [[Helmholtz-Ellis notation]], it is a [[chromatic semitone]], separated by [[2187/2176]] from [[2187/2048]], the Pythagorean chromatic semitone. The term "large 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 ==