Tridecimal eighth-octave comma: Difference between revisions

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|Ratio = 17303/17280

|Monzo = -7 -3 -1 0 3 1

~~|Name =~~

|Color name = 3o1o<sup>3</sup>g1 <br> thotrilo-agu unison

|Name = Tridecimal eighth-octave comma

|Comma = yes

}}

17303/17280 is an unnoticable comma ~~that~~ is the difference between three [[12/11]] ~~neutral seconds~~ and a [[13/10]] ~~supermajor third~~. It is tempered out in low EDOs that are a multiple of 8, ~~along with~~ [[~~214990848/214358881~~]] ~~and~~ [[~~815830271/800000000~~]], ~~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, ⁸√{{Overline|([[214990848/214358881]])³·[[815730721/800000000]]}}.

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

@@ Line 2: / Line 2: @@
 |Ratio = 17303/17280
 |Monzo = -7 -3 -1 0 3 1
-|Name =
 |Color name = 3o1o<sup>3</sup>g1 <br> thotrilo-agu unison
+|Name = Tridecimal eighth-octave comma
 |Comma = yes
 }}
-/17280 is an unnoticable comma that is the difference between three [[12/11]] neutral seconds and a [[13/10]] supermajor third. It is tempered out in low EDOs that are a multiple of 8, along with [[214990848/214358881]] and [[815830271/800000000]], 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, ⁸√{{Overline|([[214990848/214358881]])³·[[815730721/800000000]]}}.
+[[Category:Commas named for their periods per equave]]