Ragismic microtemperaments: Difference between revisions
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* ''[[Unlit]]'' (+{{monzo| 41 -20 -4 }}) → [[Undim family #Unlit|Undim family]] | * ''[[Unlit]]'' (+{{monzo| 41 -20 -4 }}) → [[Undim family #Unlit|Undim family]] | ||
* [[Amity]] (+5120/5103) → [[Amity family #Septimal amity|Amity family]] | * [[Amity]] (+5120/5103) → [[Amity family #Septimal amity|Amity family]] | ||
* [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]] | * [[Catakleismic]] (+225/224) → [[Kleismic family #Catakleismic|Kleismic family]] | ||
* ''[[Zarvo]]'' (+33075/32768) → [[Gravity family #Zarvo|Gravity family]] | * ''[[Zarvo]]'' (+33075/32768) → [[Gravity family #Zarvo|Gravity family]] | ||
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* ''[[Ludizemlic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments #Ludizemlic|37th-octave temperaments]] | * ''[[Ludizemlic]]'' (+{{monzo|-223 47 -11 62}}) → [[37th-octave temperaments #Ludizemlic|37th-octave temperaments]] | ||
Considered below, sorted by increasing [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, and | Considered below, sorted by increasing [[badness]], are supermajor, enneadecal, semidimi, brahmagupta, abigail, gamera, crazy, orga, chlorine, seniority, monzismic, semidimfourth, acrokleismic, quasithird, quincy, deca, keenanose, counterkleismic, sfourth, aluminium, ragitritonic, quatracot, trideci, moulin, palladium, and quindro. | ||
== Supermajor == | == Supermajor == | ||
| Line 1,523: | Line 1,522: | ||
Badness (Sintel): 1.14 | Badness (Sintel): 1.14 | ||
== Quindro == | |||
: ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Quindromeda]].'' | |||
Named by [[Xenllium]] in 2021, quindro may be described as the 205 & 217 temperament. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 4375/4374, {{monzo| 56 -28 -5 }} | |||
{{Mapping|legend=1| 1 2 0 15 | 0 -5 28 -147 }} | |||
: mapping generators: ~2, ~4428675/4194304 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.8431{{c}}, ~4428675/4194304 = 99.5157{{c}} | |||
: [[error map]]: {{val| -0.157 +0.153 +0.125 +0.018 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~4428675/4194304 = 99.5292{{c}} | |||
: error map: {{val| 0.000 +0.399 +0.504 +0.379 }} | |||
{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061 }} | |||
[[Badness]] (Sintel): 8.02 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 4375/4374, 5632/5625, 25165824/25109315 | |||
{{Mapping|legend=0| 1 2 0 15 -5 | 0 -5 28 -147 102 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.8389{{c}}, ~17325/16384 = 99.5152{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~17325/16384 = 99.5286{{c}} | |||
{{Optimal ET sequence|legend=0| 205, 217, 422, 639, 1061e, 2544bccddee, 3605bbccddeee }} | |||
Badness (Sintel): 2.82 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 2080/2079, 4375/4374, 5632/5625, 20480/20449 | |||
{{Mapping|legend=0| 1 2 0 15 -5 11 | 0 -5 28 -147 102 -88 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.8251{{c}}, ~143/135 = 99.5144{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~143/135 = 99.5292{{c}} | |||
{{Optimal ET sequence|legend=0| 205, 217, 422, 639, 1061ef }} | |||
Badness (Sintel): 1.62 | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 1156/1155, 2080/2079, 2431/2430, 4375/4374, 5632/5625 | |||
{{Mapping|legend=0| 1 2 0 15 -5 11 5 | 0 -5 28 -147 102 -88 -11 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.8427{{c}}, ~18/17 = 99.5160{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.5292{{c}} | |||
{{Optimal ET sequence|legend=0| 205, 217, 422, 639, 1061ef }} | |||
Badness (Sintel): 1.23 | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 1156/1155, 1216/1215, 1445/1444, 2080/2079, 2376/2375, 2431/2430 | |||
{{Mapping|legend=0| 1 2 0 15 -5 11 5 4 | 0 -5 28 -147 102 -88 -11 3 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.8301{{c}}, ~18/17 = 99.5148{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.5291{{c}} | |||
{{Optimal ET sequence|legend=0| 205, 217, 422, 639h, 1061efh }} | |||
Badness (Sintel): 1.02 | |||
== References == | == References == | ||