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'''2500/2499''', the '''sperasma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] with a size of about 0.693 [[cent]]s. Among other things, it is the difference between the small septimal sixth-tone of [[50/49]] and the large septendecimal sixth-tone of [[51/50]]. It also represents the little gap between [[17/12]] and a stack of two [[25/21]]'s. | |||
== Commatic relations == | == Commatic relations == | ||
This comma is the difference between the following superparticular pairs: | This comma is the difference between the following superparticular pairs: | ||
* [[120/119]] and [[126/125]] | * [[120/119]] and [[126/125]] | ||
* [[375/374]] and [[441/440]] | * [[375/374]] and [[441/440]] | ||
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== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit results in the rank-6 '''sperasmic | Tempering out this comma in the 17-limit results in the rank-6 '''sperasmic''' temperament, or in the the 2.3.5.7.17 subgroup, the rank-4 '''speric''' temperament. You may find a list of good equal temperaments that support these temperaments below. | ||
=== Speric === | |||
[[Subgroup]]: 2.3.5.7.17 | |||
{{Mapping|legend=2| 1 0 0 0 2 | 0 1 0 0 -1 | 0 0 1 0 4 | 0 0 0 1 -2 }} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}} | |||
{{Optimal ET sequence|legend=1| 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648 }} | |||
[[Badness]] (Sintel): 0.122 | |||
=== Sperasmic === | === Sperasmic === | ||
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| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}}, ~11/8 = 551.3474{{c}}, ~13/8 = 840.5571{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}}, ~11/8 = 551.3352{{c}}, ~13/8 = 840.5461{{c}} | |||
{{Optimal ET sequence|legend=1| 19, 24d, 27eg, 29g, 31, 41g, 43, 53g, 58g, 60e, 68, 72, 103, 111, 140, 171, 183, 239f, 243e, 270, 311, 354, 414, 422, 494, 581, 764, 935, 1075, 1106, 1178, 1672, 1942, 2113, 2253, 2535, 2805g, 3299d, 3713, 3983g, 4477 }} | {{Optimal ET sequence|legend=1| 19, 24d, 27eg, 29g, 31, 41g, 43, 53g, 58g, 60e, 68, 72, 103, 111, 140, 171, 183, 239f, 243e, 270, 311, 354, 414, 422, 494, 581, 764, 935, 1075, 1106, 1178, 1672, 1942, 2113, 2253, 2535, 2805g, 3299d, 3713, 3983g, 4477 }} | ||
[[Badness]] (Sintel): 1.13 | |||
[[ | |||
== Etymology == | == Etymology == | ||
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== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== References == | == References == | ||
<references/> | <references/> | ||
[[Category:Sperasmic]] | |||
[[Category:Commas named by translating something into another language]] | |||