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]]) | * ([[1331/1296]])/([[40/39]]) | ||
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== Temperaments == | == 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 == | == 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, | 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]] | [[Category:Commas named for their periods per equave]] | ||
Latest revision as of 01:25, 30 September 2026
| Interval information |
thotrilo-agu unison
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 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, porcupinefowl and wizard - which means the 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√(214990848/214358881)³·815730721/800000000.