No-fives subgroup temperaments: Difference between revisions
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=== Archy === | === Archy === | ||
See [[Archytas clan #Archy]]. | See [[Archytas clan #Archy]]. | ||
==== Suhajira ==== | ==== Suhajira ==== | ||
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=== Slendroschismic === | === Slendroschismic === | ||
See [[5th-octave temperaments #Slendroschismic]]. | See [[5th-octave temperaments #Slendroschismic]]. | ||
=== Navy === | === Navy === | ||
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=== Purpleheart === | === Purpleheart === | ||
{{ | {{Main| Whitewood }} | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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=== Neutral === | === Neutral === | ||
See [[Rastmic clan #Neutral]]. | See [[Rastmic clan #Neutral]]. | ||
=== Io === | === Io === | ||
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[[Badness]] (Sintel): 0.185 | [[Badness]] (Sintel): 0.185 | ||
=== Alphaxenean === | |||
Alphaxenean tempers out the [[Alpharabian comma]] and equates a stack of four undecimal quartertones with the [[9/8|Pythagorean whole tone]]. It also divides the [[2/1|octave]] into two. | |||
[[Subgroup]]: 2.3.11 | |||
[[Comma list]]: 131769/131072 | |||
{{Mapping|legend=2| 2 1 8 | 0 2 -1 }} | |||
: mapping generators: ~363/256, ~16/11 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~363/256 = 600.1590{{c}}, ~16/11 = 650.8508{{c}} | |||
: [[error map]]: {{val| +0.318 -0.094 -0.897 }} | |||
* [[CWE]]: ~363/256 = 600.0000{{c}}, ~16/11 = 650.7321{{c}} | |||
: error map: {{val| 0.000 -0.491 -2.050 }} | |||
{{Optimal ET sequence|legend=1| 22, 24, 94, 118, 142, 450e, 592e, 1326beeee }} | |||
[[Badness]] (Sintel): 0.395 | |||
=== Infraug === | === Infraug === | ||
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[[Badness]] (Sintel): 0.734 | [[Badness]] (Sintel): 0.734 | ||
==== 2.3.11.13 ==== | ==== 2.3.11.13 subgroup ==== | ||
Subgroup: 2.3.11.13 | Subgroup: 2.3.11.13 | ||
Comma list: 144/143, 729/704 | Comma list: 144/143, 729/704 | ||
Subgroup-val mapping: {{mapping| 1 0 -6 10 | 0 1 6 -4 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 363/361, 729/704 | Comma list: 363/361, 729/704 | ||
Subgroup-val mapping: {{mapping| 1 0 -6 -6 | 0 2 12 13 }} | |||
: mapping generators: ~2, ~19/11 | : mapping generators: ~2, ~19/11 | ||
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Badness (Sintel): 0.415 | Badness (Sintel): 0.415 | ||
=== Profanity === | |||
Profanity identifies [[11/9]] with 2\7. | |||
[[Subgroup]]: 2.3.11 | |||
[[Comma list]]: 19487171/19131876 | |||
{{Mapping|legend=2| 7 0 2 | 0 1 2 }} | |||
: mapping generators: ~1458/1331, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~1458/1331 = 171.4369{{c}}, ~3/2 = 702.9304{{c}} | |||
: [[error map]]: {{val| +0.058 +1.033 -2.467 }} | |||
* [[CWE]]: ~1458/1331 = 171.4286{{c}}, ~3/2 = 702.9442{{c}} | |||
: error map: {{val| 0.000 -0.989 -2.572 }} | |||
{{Optimal ET sequence|legend=1| 7, … 49, 56, 63, 70 }} | |||
[[Badness]] (Sintel): 3.03 | |||
== Temperaments with a 2.3.13 gene == | == Temperaments with a 2.3.13 gene == | ||
=== Tridecapyth === | |||
Sets a stack of 10 (9/8)s equal to 13/4. | |||
[[Subgroup]]: 2.3.13 | |||
[[Comma list]]: 3489660928/3486784401 | |||
See: [[Tridecapyth comma#Temperaments]]. | |||
=== Threedic === | === Threedic === | ||
[[Subgroup]]: 2.3.13 | [[Subgroup]]: 2.3.13 | ||
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Badness (Sintel): 0.135 | Badness (Sintel): 0.135 | ||
==== 2.3.13.23 ==== | ==== 2.3.13.23 subgroup ==== | ||
Subgroup: 2.3.13.23 | Subgroup: 2.3.13.23 | ||