Schismic–commatic equivalence continuum: Difference between revisions
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{{Mapping|legend=1| 3 0 64 | 0 1 -12 }} | {{Mapping|legend=1| 3 0 64 | 0 1 -12 }} | ||
: Mapping generators: ~2657205/2097152, ~3 | : Mapping generators: ~2657205/2097152, ~3 | ||
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[[Badness]] (Sintel): 28.4 | [[Badness]] (Sintel): 28.4 | ||
== Quindromeda == | |||
Quindromeda splits the [[4/3|perfect fourth]] into five generators, so its [[ploidacot]] is omega-pentacot. It has an equivalence number {{nowrap| ''n'' {{=}} 5 }}, meaning it equates the Pythagorean comma with a stack of five schismas. | |||
It was named by [[Xenllium]] in 2021 as a portmanteau of ''quintans'' (Latin for "one fifth") and ''[[schismatic family #Garibaldi|andromeda]]'', because the generator is 1/5 of a [[4/3|perfect fourth]] of about 497.6 cents, which can serve as a tuning for andromeda. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| 56 -28 -5 }} | |||
{{Mapping|legend=1| 1 2 0 | 0 -5 28 }} | |||
: mapping generators: ~2, ~4428675/4194304 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.8537{{c}}, ~4428675/4194304 = 99.5137{{c}} | |||
: [[error map]]: {{val| -0.146 +0.184 +0.070 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~4428675/4194304 = 99.5235{{c}} | |||
: error map: {{val| 0.000 +0.428 +0.343 }} | |||
{{Optimal ET sequence|legend=1| 12, … 169, 181, 193, 205, 217, 422 }} | |||
[[Badness]] (Sintel): 9.38 | |||
== Quintaleap == | |||
Quintaleap splits the [[4/3|perfect fourth]] into five generators, each for [[~]][[135/128]], so its [[ploidacot]] is omega-pentacot, the same as [[#Quindromeda|quindromeda]]. It has an equivalence number {{nowrap| ''n'' {{=}} 5/2 }}, meaning it equates a stack of two Pythagorean commas with a stack of five schismas. | |||
It was named by [[Xenllium]] in 2021 as a portmanteau of ''quintans'' (Latin for "one fifth") and ''[[sengic temperaments #Leapday|leapday]]'', because the generator is 1/5 of a [[4/3|perfect fourth]] of about 496.3 cents, which can serve as a tuning for leapday. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 137438953472/134521003125 | |||
{{Mapping|legend=1| 1 2 1 | 0 -5 16 }} | |||
: mapping generators: ~2, ~135/128 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.3592{{c}}, ~135/128 = 99.2137{{c}} | |||
: [[error map]]: {{val| -0.641 +0.695 +0.465 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~135/128 = 99.2556{{c}} | |||
: error map: {{val| 0.000 +1.767 +1.777 }} | |||
{{Optimal ET sequence|legend=1| 12, 73c, 85, 97, 109, 121, 133, 278c, 411bc, 544bc }} | |||
[[Badness]] (Sintel): 10.4 | |||
== Sextile (5-limit) == | == Sextile (5-limit) == | ||
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{{Mapping|legend=1| 6 0 -5 | 0 1 2 }} | {{Mapping|legend=1| 6 0 -5 | 0 1 2 }} | ||
: Mapping generators: ~10/9, ~3 | : Mapping generators: ~10/9, ~3 | ||
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{{Mapping|legend=1| 1 1 6 | 0 7 -44 }} | {{Mapping|legend=1| 1 1 6 | 0 7 -44 }} | ||
: Mapping generators: ~2, ~{{monzo| -37 19 3 }} | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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{{Mapping|legend=1| 4 1 44 | 0 2 -13 }} | {{Mapping|legend=1| 4 1 44 | 0 2 -13 }} | ||
: | : Mapping generators: ~39858075/33554432, ~{{monzo| -37 19 3 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||