289/288: Difference between revisions

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'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].

'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[small comma|small]] [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].

== Commatic relations ==

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== Temperaments ==

[[Tempering out]] this comma in the full 17-limit results in the rank-6 '''semitonismic''' temperament, or in the 2.3.17 subgroup, the rank-2 '''semitonic''' temperament. In either case the [[~~2/1|~~octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

[[Tempering out]] this comma in the full 17-limit results in the rank-6 '''semitonismic''' temperament, or in the 2.3.17 subgroup, the rank-2 '''semitonic''' temperament. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

=== Semitonic ===

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== See also ==

* [[Small comma]]

* [[List of superparticular intervals]]

[[Category:Semitonismic]]

[[Category:Commas named for the intervals they stack]]

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-'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].
+'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[small comma|small]] [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].
 == Commatic relations ==
@@ Line 19: / Line 19: @@
 == Temperaments ==
-[[Tempering out]] this comma in the full 17-limit results in the rank-6 '''semitonismic''' temperament, or in the 2.3.17 subgroup, the rank-2 '''semitonic''' temperament. In either case the [[2/1|octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
+[[Tempering out]] this comma in the full 17-limit results in the rank-6 '''semitonismic''' temperament, or in the 2.3.17 subgroup, the rank-2 '''semitonic''' temperament. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
 === Semitonic ===
@@ Line 58: / Line 58: @@
 == See also ==
-* [[Small comma]]
 * [[List of superparticular intervals]]
 [[Category:Semitonismic]]
 [[Category:Commas named for the intervals they stack]]