18/17: Difference between revisions

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== 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.

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 ~~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~~.

For 18/17 specifically:

* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].

* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]].

The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 18/17.

== See also ==

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* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

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

* [[1ed18/17]] – equal multiplication of this interval

[[Category:Second]]

[[Category:Chroma]]

[[Category:Semitone]]

@@ Line 8: / Line 8: @@
 == 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.
+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 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.
+For 18/17 specifically:
+* In the [[Functional Just System]], it is a chromatic semitone, separated by [[4131/4096]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]].
+* In [[Helmholtz-Ellis notation]], it is a diatonic semitone, separated by [[2187/2176]] from the [[256/243|Pythagorean minor second (256/243)]].
+The term ''small septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 18/17.
 == See also ==
@@ Line 17: / Line 21: @@
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
-* [[18/17 equal-step tuning]] – equal multiplication of this interval
+* [[1ed18/17]] – equal multiplication of this interval
 [[Category:Second]]
 [[Category:Chroma]]
 [[Category:Semitone]]