221/220: Difference between revisions

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'''221/220''', the '''minor naiadma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 7.9 [[cent]]s in size. It forms the difference between [[13/10]] (tridecimal semisixth) and [[22/17]] (small septendecimal semisixth). It is also the amount by which ~~a stack of~~ a stack consisting of 13/10 and [[17/10]] exceeds [[11/5]] ([[11/10]] plus an octave). The name ''minor naiadma'' is contrast to the ''major naiadma'', [[170/169]], measuring about 10.2¢, which is the difference between 13/10 and [[17/13]] (large septendecimal semisixth). They are so named because 13/10, 17/13 and 22/17 are naiadic [[interseptimal interval]]s, and 221/220 is smaller than 170/169 by a [[13-limit]] [[unnoticeable comma]], [[2200/2197]] (petrma).

'''221/220''', the '''minor naiadma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 7.9 [[cent]]s in size. It forms the difference between [[13/10]] (tridecimal semisixth) and [[22/17]] (small septendecimal semisixth). It is also the amount by which a stack consisting of 13/10 and [[17/10]] exceeds [[11/5]] ([[11/10]] plus an octave). The name ''minor naiadma'' is contrast to the ''major naiadma'', [[170/169]], measuring about 10.2¢, which is the difference between 13/10 and [[17/13]] (large septendecimal semisixth). They are so named because 13/10, 17/13 and 22/17 are naiadic [[interseptimal interval]]s, and 221/220 is smaller than 170/169 by a [[13-limit]] [[unnoticeable comma]], [[2200/2197]] (petrma).

== Commatic relations ==

This comma identifies itself as the difference between the following superparticular pairs:

* [[34/33]] and [[40/39]]

* [[51/50]] and [[66/65]]

* [[78/77]] and [[120/119]]

* [[91/90]] and [[154/153]]

* [[136/135]] and [[352/351]]

* [[169/168]] and [[715/714]]

It factors into the following superparticular pairs:

* [[225/224]] and [[Flashma|12376/12375]]

* [[243/242]] and [[2431/2430]]

* [[273/272]] and [[1156/1155]]

* [[289/288]] and [[936/935]]

* [[351/350]] and [[595/594]]

* [[364/363]] and [[561/560]]

* [[441/440]] and [[442/441]]

== See also ==

* [[Small comma]]

* [[List of superparticular intervals]]

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-'''221/220''', the '''minor naiadma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 7.9 [[cent]]s in size. It forms the difference between [[13/10]] (tridecimal semisixth) and [[22/17]] (small septendecimal semisixth). It is also the amount by which a stack of a stack consisting of 13/10 and [[17/10]] exceeds [[11/5]] ([[11/10]] plus an octave). The name ''minor naiadma'' is contrast to the ''major naiadma'', [[170/169]], measuring about 10.2¢, which is the difference between 13/10 and [[17/13]] (large septendecimal semisixth). They are so named because 13/10, 17/13 and 22/17 are naiadic [[interseptimal interval]]s, and 221/220 is smaller than 170/169 by a [[13-limit]] [[unnoticeable comma]], [[2200/2197]] (petrma).
+'''221/220''', the '''minor naiadma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 7.9 [[cent]]s in size. It forms the difference between [[13/10]] (tridecimal semisixth) and [[22/17]] (small septendecimal semisixth). It is also the amount by which a stack consisting of 13/10 and [[17/10]] exceeds [[11/5]] ([[11/10]] plus an octave). The name ''minor naiadma'' is contrast to the ''major naiadma'', [[170/169]], measuring about 10.2¢, which is the difference between 13/10 and [[17/13]] (large septendecimal semisixth). They are so named because 13/10, 17/13 and 22/17 are naiadic [[interseptimal interval]]s, and 221/220 is smaller than 170/169 by a [[13-limit]] [[unnoticeable comma]], [[2200/2197]] (petrma).
+== Commatic relations ==
+This comma identifies itself as the difference between the following superparticular pairs:
+* [[34/33]] and [[40/39]]
+* [[51/50]] and [[66/65]]
+* [[78/77]] and [[120/119]]
+* [[91/90]] and [[154/153]]
+* [[136/135]] and [[352/351]]
+* [[169/168]] and [[715/714]]
+It factors into the following superparticular pairs:
+* [[225/224]] and [[Flashma|12376/12375]]
+* [[243/242]] and [[2431/2430]]
+* [[273/272]] and [[1156/1155]]
+* [[289/288]] and [[936/935]]
+* [[351/350]] and [[595/594]]
+* [[364/363]] and [[561/560]]
+* [[441/440]] and [[442/441]]
 == See also ==
 * [[Small comma]]
 * [[List of superparticular intervals]]