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Garischismic clan: Difference between revisions

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m Units & misc. cleanup
Switch to Sintel's badness, WE & CWE tunings
Line 11: Line 11:
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.2079{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9155{{c}}, ~3/2 = 702.1584{{c}}
: [[error map]]: {{val| -0.085 +0.119 +0.027 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2124{{c}}
: error map: {{val| 0.000 +0.257 +0.201 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2079{{c}} -->


{{Optimal ET sequence|legend=1| 12, 29, 41, 94, 135, 364, 499, 634, 3035bd, 3669bd, 4303bd, 4937bbdd, 5571bbdd }}
{{Optimal ET sequence|legend=1| 12, 29, 41, 94, 135, 364, 499, 634, 3035bd, 3669bd, 4303bd, 4937bbdd, 5571bbdd }}


[[Badness]] (Smith): 0.0135
[[Badness]] (Sintel): 0.463


=== Overview to extensions ===
=== Overview to extensions ===
Line 43: Line 48:
Subgroup-val mapping: {{mapping| 1 0 25 -33 | 0 1 -14 23 }}
Subgroup-val mapping: {{mapping| 1 0 25 -33 | 0 1 -14 23 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.2292{{c}}
Optimal tunings:
* WE: ~2 = 1199.9631{{c}}, ~3/2 = 702.2077{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2290{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2292{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}
{{Optimal ET sequence|legend=0| 12e, 41, 94, 135, 716, 851, 986, 1121, 1256 }}


Badness (Smith): 0.00731
Badness (Sintel): 0.276


== Cotoneum ==
== Cotoneum ==
Line 60: Line 68:
{{Mapping|legend=1| 1 0 80 25 | 0 1 -49 -14 }}
{{Mapping|legend=1| 1 0 80 25 | 0 1 -49 -14 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.317{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0386{{c}}, ~3/2 = 702.3396{{c}}
: [[error map]]: {{val| +0.039 +0.423 +0.244 -1.155 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.3164{{c}}
: error map: {{val| 0.000 +0.361 +0.182 -1.256 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.317{{c}} -->


{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 258, 475 }}
{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 258, 475 }}


[[Badness]] (Smith): 0.105632
[[Badness]] (Sintel): 2.67


=== 11-limit ===
=== 11-limit ===
Line 73: Line 86:
Mapping: {{mapping| 1 0 80 25 -33 | 0 1 -49 -14 23 }}
Mapping: {{mapping| 1 0 80 25 -33 | 0 1 -49 -14 23 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.303{{c}}
Optimal tunings:
* WE: ~2 = 1199.8629{{c}}, ~3/2 = 702.2224{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3036{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.303{{c}} -->


{{Optimal ET sequence|legend=0| 41, 135c, 176, 217 }}
{{Optimal ET sequence|legend=0| 41, 135c, 176, 217 }}


Badness (Smith): 0.050966
Badness (Sintel): 1.68


=== 13-limit ===
=== 13-limit ===
Line 86: Line 102:
Mapping: {{mapping| 1 0 80 25 -33 -93 | 0 1 -49 -14 23 61 }}
Mapping: {{mapping| 1 0 80 25 -33 -93 | 0 1 -49 -14 23 61 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.306{{c}}
Optimal tunings:
* WE: ~2 = 1199.8897{{c}}, ~3/2 = 702.2415{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3061{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.306{{c}} -->


{{Optimal ET sequence|legend=0| 41, 176, 217 }}
{{Optimal ET sequence|legend=0| 41, 176, 217 }}


Badness (Smith): 0.036951
Badness (Sintel): 1.53


=== 17-limit ===
=== 17-limit ===
Line 99: Line 118:
Mapping: {{mapping| 1 0 80 25 -33 -93 -137 | 0 1 -49 -14 23 61 89 }}
Mapping: {{mapping| 1 0 80 25 -33 -93 -137 | 0 1 -49 -14 23 61 89 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.307{{c}}
Optimal tunings:
* WE: ~2 = 1199.8939{{c}}, ~3/2 = 702.2445{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3064{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.307{{c}} -->


{{Optimal ET sequence|legend=0| 41, 176, 217 }}
{{Optimal ET sequence|legend=0| 41, 176, 217 }}


Badness (Smith): 0.029495
Badness (Sintel): 1.50


=== 19-limit ===
=== 19-limit ===
Line 112: Line 134:
Mapping: {{mapping| 1 0 80 25 -33 -93 -137 74 | 0 1 -49 -14 23 61 89 -44 }}
Mapping: {{mapping| 1 0 80 25 -33 -93 -137 74 | 0 1 -49 -14 23 61 89 -44 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.308{{c}}
Optimal tunings:
* WE: ~2 = 1199.8766{{c}}, ~3/2 = 702.2355{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3077{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.308{{c}} -->


{{Optimal ET sequence|legend=0| 41, 176, 217 }}
{{Optimal ET sequence|legend=0| 41, 176, 217 }}


Badness (Smith): 0.021811
Badness (Sintel): 1.33


== World calendar ==
== World calendar ==
World calendar tempers out the [[dimcomp comma]] and the garischisma, and can be described as the {{nowrap| 12 & 364 }} temperament. The name derives from a [[wikipedia: World Calendar|certain calendar layout]] by the same name.  
World calendar tempers out the [[dimcomp comma]] and the garischisma, and can be described as the {{nowrap| 12 & 364 }} temperament. The name derives from a {{w|World Calendar|certain calendar layout}} by the same name.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 128: Line 153:
: mapping generators: ~25/21, ~91125/57344
: mapping generators: ~25/21, ~91125/57344


[[Optimal tuning]] ([[POTE]]): ~25/21 = 300.0000{{c}}, ~91125/57344 = 801.0947{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~25/21 = 299.9938{{c}}, ~91125/57344 = 801.0780{{c}}
: [[error map]]: {{val| -0.025 +0.195 -0.603 +0.452 }}
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~91125/57344 = 801.0955{{c}}
: error map: {{val| 0.000 +0.236 -0.555 +0.501 }}
<!-- * [[POTE]]: ~25/21 = 300.0000{{c}}, ~91125/57344 = 801.0947{{c}} -->


{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}
{{Optimal ET sequence|legend=1| 12, …, 352, 364 }}


[[Badness]] (Smith): 0.292
[[Badness]] (Sintel): 7.39


=== 2.3.5.7.17 subgroup ===
=== 2.3.5.7.17 subgroup ===
Line 141: Line 171:
Subgroup-val mapping: {{mapping| 4 1 -44 86 3 | 0 2 -13 -28 5 }}
Subgroup-val mapping: {{mapping| 4 1 -44 86 3 | 0 2 -13 -28 5 }}


Optimal tuning (POTE): ~25/21 = 300.0000{{c}}, ~27/17 = 801.0908{{c}}
Optimal tunings:
* WE: ~25/21 = 299.9861{{c}}, ~27/17 = 801.0536{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~27/17 = 801.0919{{c}}
<!-- * POTE: ~25/21 = 300.0000{{c}}, ~27/17 = 801.0908{{c}} -->


{{Optimal ET sequence|legend=0| 12, …, 352, 364 }}
{{Optimal ET sequence|legend=0| 12, …, 352, 364 }}


Badness (Smith): 0.0743
Badness (Sintel): 2.74


=== 2.3.5.7.17.19 subgroup ===
=== 2.3.5.7.17.19 subgroup ===
Line 152: Line 185:
Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000
Comma list: 1216/1215, 2025/2023, 8075/8064, 48013/48000


Sval mapping: {{mapping| 4 1 -44 86 3 25 | 0 2 -13 -28 5 -3 }}
Subgroup-val mapping: {{mapping| 4 1 -44 86 3 25 | 0 2 -13 -28 5 -3 }}


Optimal tuning (POTE): ~25/21 = 300.0000{{c}}, ~27/17 = 801.0945{{c}}
Optimal tunings:
* WE: ~25/21 = 299.9982{{c}}, ~27/17 = 801.0898{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~27/17 = 801.0946{{c}}
<!-- * POTE: ~25/21 = 300.0000{{c}}, ~27/17 = 801.0945{{c}} -->


{{Optimal ET sequence|legend=0| 12, …, 352, 364 }}
{{Optimal ET sequence|legend=0| 12, …, 352, 364 }}


Badness (Smith): 0.0378
Badness (Sintel): 1.82


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Garischismic clan| ]] <!-- main article -->
[[Category:Garischismic clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Garischismic_clan"