Xenharmonic Wiki

Octagar temperaments: Difference between revisions

← Older editNewer edit →

FloraC (talk | contribs)

4 user groups
27,171 edits
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,036 edits
No edit summary
Tags: Mobile edit Mobile web edit
m Units & misc. cleanup. - redundant category
Line 4: Line 4:
Temperaments considered below are slendi and slithy. Discussed elsewhere are:  
Temperaments considered below are slendi and slithy. Discussed elsewhere are:  
* ''[[Sida]]'' (+25/24) → [[Dicot family #Sida|Dicot family]]
* ''[[Sida]]'' (+25/24) → [[Dicot family #Sida|Dicot family]]
* ''[[Ripple]]'' (+36/35) → [[Ripple family #Septimal ripple|Ripple family]]
* ''[[Rip]]'' (+36/35) → [[Ripple family #Rip|Ripple family]]
* ''[[Nautilus]]'' (+49/48) → [[Porcupine family #Nautilus|Porcupine family]]
* ''[[Nautilus]]'' (+49/48) → [[Porcupine family #Nautilus|Porcupine family]]
* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]]
* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]]
Line 11: Line 11:
* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot|Tetracot family]]
* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot|Tetracot family]]
* ''[[Roman]]'' (+525/512) → [[Wesley family #Roman|Wesley family]]
* ''[[Roman]]'' (+525/512) → [[Wesley family #Roman|Wesley family]]
* [[Superkleismic]] (+875/864 or 1029/1024) → [[Gamelismic clan #Superkleismic|Shibboleth family]] and [[Gamelismic clan #Superkleismic|Gamelismic clan]]
* [[Superkleismic]] (+875/864 or 1029/1024) → [[Gamelismic clan #Superkleismic|Gamelismic clan]]
* ''[[Quartonic]]'' (+1728/1715) → [[Quartonic family]]
* ''[[Quartonic]]'' (+1728/1715) → [[Quartonic family]]
* ''[[Bidia]]'' (+2048/2025 or 3136/3125) → [[Diaschismic family #Bidia|Diaschismic family]]
* ''[[Bidia]]'' (+2048/2025 or 3136/3125) → [[Diaschismic family #Bidia|Diaschismic family]]
Line 27: Line 27:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1200.252¢, ~49/48 = 29.187¢
* [[WE]]: ~2 = 1200.252{{c}}, ~49/48 = 29.187{{c}}
* [[CWE]]: ~2 = 1200.000¢, ~49/48 = 29.172¢
* [[CWE]]: ~2 = 1200.000{{c}}, ~49/48 = 29.172{{c}}


{{Optimal ET sequence|legend=1| 41, 206, 247bc, 288bcd, 329bcd }}
{{Optimal ET sequence|legend=1| 41, 206, 247bc, 288bcd, 329bcd }}
Line 42: Line 42:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.803¢, ~49/48 = 29.175¢
* WE: ~2 = 1199.803{{c}}, ~49/48 = 29.175{{c}}
* CWE: ~2 = 1200.000¢, ~49/48 = 29.188¢
* CWE: ~2 = 1200.000{{c}}, ~49/48 = 29.188{{c}}


{{Optimal ET sequence|legend=0| 41, 206e }}
{{Optimal ET sequence|legend=0| 41, 206e }}
Line 57: Line 57:


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.091¢, ~40/39 = 29.103¢
* WE: ~2 = 1199.091{{c}}, ~40/39 = 29.103{{c}}
* CWE: ~2 = 1200.000¢, ~40/39 = 29.158¢
* CWE: ~2 = 1200.000{{c}}, ~40/39 = 29.158{{c}}


{{Optimal ET sequence|legend=0| 41, 124ef, 165ef }}
{{Optimal ET sequence|legend=0| 41, 124ef, 165ef }}
Line 71: Line 71:
{{Mapping|legend=1| 1 3 5 4 | 0 -19 -36 -16 }}
{{Mapping|legend=1| 1 3 5 4 | 0 -19 -36 -16 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~21/20 = 89.282
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/20 = 89.282{{c}}


{{Optimal ET sequence|legend=1| 27, 94, 121, 215, 336d }}
{{Optimal ET sequence|legend=1| 27, 94, 121, 215, 336d }}


[[Badness]]: 0.107482
[[Badness]] (Smith): 0.107482


=== 11-limit ===
=== 11-limit ===
Line 84: Line 84:
Mapping: {{mapping| 1 3 5 4 8 | 0 -19 -36 -16 -61 }}
Mapping: {{mapping| 1 3 5 4 8 | 0 -19 -36 -16 -61 }}


Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 89.291
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 89.291{{c}}


{{Optimal ET sequence|legend=0| 94, 121, 215, 336de, 551bde }}
{{Optimal ET sequence|legend=0| 94, 121, 215, 336de, 551bde }}


Badness: 0.045895
Badness (Smith): 0.045895


=== 13-limit ===
=== 13-limit ===
Line 97: Line 97:
Mapping: {{mapping| 1 3 5 4 8 4 | 0 -19 -36 -16 -61 -4 }}
Mapping: {{mapping| 1 3 5 4 8 4 | 0 -19 -36 -16 -61 -4 }}


Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 89.286
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 89.286{{c}}


{{Optimal ET sequence|legend=0| 94, 121, 215, 336def }}
{{Optimal ET sequence|legend=0| 94, 121, 215, 336def }}


Badness: 0.028492
Badness (Smith): 0.028492


=== 17-limit ===
=== 17-limit ===
Line 110: Line 110:
Mapping: {{mapping| 1 3 5 4 8 4 9 | 0 -19 -36 -16 -61 -4 -66 }}
Mapping: {{mapping| 1 3 5 4 8 4 9 | 0 -19 -36 -16 -61 -4 -66 }}


Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 89.286
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 89.286{{c}}


{{Optimal ET sequence|legend=0| 94, 121, 215, 336defg }}
{{Optimal ET sequence|legend=0| 94, 121, 215, 336defg }}


Badness: 0.019811
Badness (Smith): 0.019811


=== 19-limit ===
=== 19-limit ===
Line 123: Line 123:
Mapping: {{mapping| 1 3 5 4 8 4 9 7 | 0 -19 -36 -16 -61 -4 -66 -37 }}
Mapping: {{mapping| 1 3 5 4 8 4 9 7 | 0 -19 -36 -16 -61 -4 -66 -37 }}


Optimal tuning (POTE): ~2 = 1200.000, ~19/18 = 89.288
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~19/18 = 89.288{{c}}


{{Optimal ET sequence|legend=0| 94, 121, 215, 336defg }}
{{Optimal ET sequence|legend=0| 94, 121, 215, 336defg }}


Badness: 0.016408
Badness (Smith): 0.016408


=== 23-limit ===
=== 23-limit ===
Line 136: Line 136:
Mapping: {{mapping| 1 3 5 4 8 4 9 7 11 | 0 -19 -36 -16 -61 -4 -66 -37 -87 }}
Mapping: {{mapping| 1 3 5 4 8 4 9 7 11 | 0 -19 -36 -16 -61 -4 -66 -37 -87 }}


Optimal tuning (POTE): ~2 = 1200.000, ~19/18 = 89.297
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~19/18 = 89.297{{c}}


{{Optimal ET sequence|legend=0| 94, 121i, 215 }}
{{Optimal ET sequence|legend=0| 94, 121i, 215 }}


Badness: 0.014946
Badness (Smith): 0.014946


== Tridecatonic ==
== Tridecatonic ==
Line 153: Line 153:
{{Mapping|legend=1| 13 21 31 37 | 0 -1 -2 -1 }}
{{Mapping|legend=1| 13 21 31 37 | 0 -1 -2 -1 }}


[[Optimal tuning]] ([[POTE]]): ~21/20 = 92.3077, ~3/2 = 701.9605
[[Optimal tuning]] ([[POTE]]): ~21/20 = 92.3077{{c}}, ~3/2 = 701.9605{{c}}


{{Optimal ET sequence|legend=1| 26, 39d, 65d }}
{{Optimal ET sequence|legend=1| 26, 39d, 65d }}


[[Badness]]: 0.139213
[[Badness]] (Smith): 0.139213


=== 11-limit ===
=== 11-limit ===
Line 166: Line 166:
Mapping: {{mapping| 13 21 31 37 45 | 0 -1 -2 -1 0 }}
Mapping: {{mapping| 13 21 31 37 45 | 0 -1 -2 -1 0 }}


Optimal tuning (POTE): ~21/20 = 92.3077, ~3/2 = 701.7028
Optimal tuning (POTE): ~21/20 = 92.3077{{c}}, ~3/2 = 701.7028{{c}}


{{Optimal ET sequence|legend=0| 26, 39d, 65d }}
{{Optimal ET sequence|legend=0| 26, 39d, 65d }}


Badness: 0.063257
Badness (Smith): 0.063257


=== 13-limit ===
=== 13-limit ===
Line 179: Line 179:
Mapping: {{mapping| 13 21 31 37 45 49 | 0 -1 -2 -1 0 -2 }}
Mapping: {{mapping| 13 21 31 37 45 49 | 0 -1 -2 -1 0 -2 }}


Optimal tuning (POTE): ~21/20 = 92.3077, ~3/2 = 701.3573
Optimal tuning (POTE): ~21/20 = 92.3077{{c}}, ~3/2 = 701.3573{{c}}


{{Optimal ET sequence|legend=0| 26, 39df, 65d }}
{{Optimal ET sequence|legend=0| 26, 39df, 65d }}


Badness: 0.037851
Badness (Smith): 0.037851


== Dhaivatic ==
== Dhaivatic ==
Line 192: Line 192:
{{Mapping|legend=1| 1 -4 -3 6 | 0 21 20 -12 }}
{{Mapping|legend=1| 1 -4 -3 6 | 0 21 20 -12 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~6/5 = 319.198
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~6/5 = 319.198{{c}}


{{Optimal ET sequence|legend=1| 15, 64c, 79, 94, 203, 297 }}
{{Optimal ET sequence|legend=1| 15, 64c, 79, 94, 203, 297 }}


[[Badness]]: 0.168373
[[Badness]] (Smith): 0.168373


=== 11-limit ===
=== 11-limit ===
Line 205: Line 205:
Mapping: {{Mapping| 1 -4 -3 6 0 | 0 21 20 -12 13 }}
Mapping: {{Mapping| 1 -4 -3 6 0 | 0 21 20 -12 13 }}


Optimal tuning (POTE): ~2 = 1200.000, ~6/5 = 319.197
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 319.197{{c}}


{{Optimal ET sequence|legend=0| 15, 64c, 79, 94, 203, 297c }}
{{Optimal ET sequence|legend=0| 15, 64c, 79, 94, 203, 297c }}


Badness: 0.051216
Badness (Smith): 0.051216


=== 13-limit ===
=== 13-limit ===
Line 218: Line 218:
Mapping: {{Mapping| 1 -4 -3 6 0 -8 | 0 21 20 -12 13 44 }}
Mapping: {{Mapping| 1 -4 -3 6 0 -8 | 0 21 20 -12 13 44 }}


Optimal tuning (POTE): ~2 = 1200.000, ~6/5 = 319.165
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~6/5 = 319.165{{c}}


{{Optimal ET sequence|legend=0| 15, 49bceff, 64cf, 79, 94 }}
{{Optimal ET sequence|legend=0| 15, 49bceff, 64cf, 79, 94 }}


Badness: 0.037468
Badness (Smith): 0.037468
   
   
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Octagar temperaments| ]] <!-- main article -->
[[Category:Octagar temperaments| ]] <!-- main article -->
[[Category:Octagar| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Octagar_temperaments"