Tridecimal eighth-octave comma: Difference between revisions

Line 7:

}}

'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma ~~that~~ is the difference between three [[12/11]] ~~neutral seconds~~ and a [[13/10~~]] semisixth, and is also the interval separating [[1331/1296]] from the simpler [[40/39~~]]. ~~It is tempered out in low EDOs that are a multiple~~ of 8, ~~along with [[214990848/214358881]] and [[815730721/800000000]], defining various [[8th-octave temperaments]]. However, that's not all, as~~ it is also ~~tempered out in EDOs such as [[159edo]].~~

'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable 13-limit (specifically no-7 13-limit) comma. As an [[ultraparticular]], it is the difference between a stack of three [[12/11]] and [[13/10]]. In terms of commas, it is also:

* ([[1331/1296]])/([[40/39]])

* ([[24167/24000]])/([[3042/3025]])

* ([[35035/34992]])·([[9801/9800]])

* ([[41503/41472]])·([[1716/1715]])

The latter two expressions are derivable from the fact that an alternate [[S-expression]] is S49·S55·S64·S65·S69.

== Temperaments ==

As its name suggests, it is tempered out in low EDOs that are a multiple of 8 (specifically {{EDOs|8, 16, 24, 32, 40, 56, 64, 72, 80, 96, 120…}}). As its S-expression suggests, it is tempered out in [[gariwizmic]] since all of its constituents are commas of it. It is also tempered out in [[tertiaschis]], [[tritikleismic]], [[Artoneutral (temperament)|artoneutral]], [[Porcupinefowl|''porcupinefowl'']] and [[wizard]] - which means the edos {{EDOs|7, 15, 22f, 87, 94, 159, 166, 253, 270, 364…}} also temper it out by extension.

== Etymology ==

17303/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, <sup>8</sup>√{{Overline|214990848/214358881·815730721/800000000}}.

[[Category:Commas named for their periods per equave]]

@@ Line 7: / Line 7: @@
 }}
-'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] semisixth, and is also the interval separating [[1331/1296]] from the simpler [[40/39]]. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815730721/800000000]], defining various [[8th-octave temperaments]].  However, that's not all, as it is also tempered out in EDOs such as [[159edo]].
+'''17303/17280''', the '''tridecimal eighth-octave comma''', is an unnoticable 13-limit (specifically no-7 13-limit) comma. As an [[ultraparticular]], it is the difference between a stack of three [[12/11]] and [[13/10]]. In terms of commas, it is also:
+* ([[1331/1296]])/([[40/39]])
+* ([[24167/24000]])/([[3042/3025]])
+* ([[35035/34992]])·([[9801/9800]])
+* ([[41503/41472]])·([[1716/1715]])
+The latter two expressions are derivable from the fact that an alternate [[S-expression]] is S49·S55·S64·S65·S69.
+== Temperaments ==
+As its name suggests, it is tempered out in low EDOs that are a multiple of 8 (specifically {{EDOs|8, 16, 24, 32, 40, 56, 64, 72, 80, 96, 120…}}). As its S-expression suggests, it is tempered out in [[gariwizmic]] since all of its constituents are commas of it. It is also tempered out in [[tertiaschis]], [[tritikleismic]], [[Artoneutral (temperament)|artoneutral]], [[Porcupinefowl|''porcupinefowl'']] and [[wizard]] - which means the edos {{EDOs|7, 15, 22f, 87, 94, 159, 166, 253, 270, 364…}} also temper it out by extension.
+== Etymology ==
+/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, <sup>8</sup>√{{Overline|214990848/214358881·815730721/800000000}}.
 [[Category:Commas named for their periods per equave]]