Tridecimal eighth-octave comma: Difference between revisions

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'''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:

'''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]])

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== 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.

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}}.

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, ⁸√{{Overline|([[214990848/214358881]])³·[[815730721/800000000]]}}.

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

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 }}
-'''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:
+'''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]])
@@ Line 17: / Line 17: @@
 == 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.
+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}}.
+/17280's name is derived from the fact that it can coincidentally be expressed as an eighth root of two 8th-octave commas. Specifically, ⁸√{{Overline|([[214990848/214358881]])³·[[815730721/800000000]]}}.
 [[Category:Commas named for their periods per equave]]