Xenharmonic Wiki

Chromatic pairs: Difference between revisions

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== Starlingtet ==
== Starlingtet ==
Subgroup: 2.5/3.7/3
Svalname: 4&15


Comma: 126/125
Related temperaments: starling; becomes myna


Svalname: 4&15
[[Subgroup]]: 2.5/3.7/3


Related temperaments: starling; becomes myna
[[Comma list]]: 126/125


[[Tp_tuning|POT2 generator]]: ~6/5 = 311.154
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154


[[Gencom|Gencom]]: [2 6/5; 126/125]
[[Gencom|Gencom]]: [2 6/5; 126/125]
Line 763: Line 763:
Mapping: [<1 0 -1|, <0 1 3|]
Mapping: [<1 0 -1|, <0 1 3|]


EDOs: {{EDOs|15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b}}
{{Optimal ET sequence|legend=1| 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.8398 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents


[[starlingtet4|Four note haplotonic scale]]
[[starlingtet4|Four note haplotonic scale]]
Line 774: Line 774:


== Lovecraft ==
== Lovecraft ==
Subgroup: 2.11.13
[[Subgroup]]: 2.11.13


Commas: 1352/1331
[[Comma list]]: 1352/1331


[[Tp_tuning|POT2 generator]]: ~13/11 = 279.318
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318


[[Gencom|Gencom]]: [2 13/11; 1352/1331]
[[Gencom|Gencom]]: [2 13/11; 1352/1331]
Line 786: Line 786:
Mapping: [<1 1 0|, <0 2 3|]
Mapping: [<1 1 0|, <0 2 3|]


EDOS: {{EDOs|13, 30, 43, 73, 116b}}
{{Optimal ET sequence|legend=1| 13, 30, 43, 73, 116b }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.8449 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.8449 cents


[[File:lovecraft_116edo.png|alt=lovecraft_116edo.png|lovecraft_116edo.png]]
[[File:lovecraft_116edo.png|alt=lovecraft_116edo.png|lovecraft_116edo.png]]
Line 799: Line 799:


== Blackbirds ==
== Blackbirds ==
Subgroup: 2.11.13
[[Subgroup]]: 2.11.13


Comma: 29282/28561
[[Comma list]]: 29282/28561


[[Tp_tuning|POT2 generator]]: ~11/8 = 546.660
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 546.660


Gencom: [13/11 11/8; 29282/28561]
Gencom: [13/11 11/8; 29282/28561]
Line 811: Line 811:
Mapping: [<4 0 1|, <0 1 1|]
Mapping: [<4 0 1|, <0 1 1|]


EDOs: {{EDOs|4, 16, 20, 24, 44, 68, 112c, 180bc}}
{{Optimal ET sequence|legend=1| 4, 16, 20, 24, 44, 68, 112c, 180bc }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.8685 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.8685 cents


[[blackbirds8|Eight note albitonic scale]]
[[blackbirds8|Eight note albitonic scale]]
Line 822: Line 822:


== Laz ==
== Laz ==
Subgroup: 2.5.7/3.11/3.13/3
Related temperaments: [[Orwellismic_family#Guanyin-Georgian|georgian]], winston


Commas: 144/143, 176/175, 196/195
[[Subgroup]]: 2.5.7/3.11/3.13/3


Related temperaments: [[Orwellismic_family#Guanyin-Georgian|georgian]], winston
[[Comma list]]: 144/143, 176/175, 196/195


[[Tp_tuning|POT2 generator]]: ~7/6 = 269.300
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300


[[Gencom|Gencom]]: [2 7/6; 144/143 176/175 196/195]
[[Gencom|Gencom]]: [2 7/6; 144/143 176/175 196/195]
Line 836: Line 836:
Mapping: [<1 0 2 -2 6|, <0 3 -1 5 -5|]
Mapping: [<1 0 2 -2 6|, <0 3 -1 5 -5|]


EDOs: {{EDOs|9, 31, 40, 49, 58, 156bde, 205bde}}
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.8790 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents


[[laz5|Five note haplotonic scale]]
[[laz5|Five note haplotonic scale]]
Line 858: Line 858:


== Greeley ==
== Greeley ==
Subgroup: 2.5/3.7/3.11/3
Related temperament: [[Porcupine_family#Opossum|Opossum]], [[Starling_temperaments#Nusecond temperament|Nusecond]]


Commas: 121/120, 126/125
[[Subgroup]]: 2.5/3.7/3.11/3


Related temperament: [[Porcupine_family#Opossum|Opossum]], [[Starling_temperaments#Nusecond temperament|Nusecond]]
[[Comma list]]: 121/120, 126/125


[[Tp_tuning|POT2 generator]]: ~11/10 = 155.776
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~11/10 = 155.776


[[Gencom|Gencom]]: [2 11/10; 121/120 126/125]
[[Gencom|Gencom]]: [2 11/10; 121/120 126/125]
Line 872: Line 872:
Mapping: [<1 1 2 2|, <0 -2 -6 -1|]
Mapping: [<1 1 2 2|, <0 -2 -6 -1|]


EDOs: {{EDOs|8, 15, 23, 54, 77, 100, 131d, 208bd}}
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131d, 208bd }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.034 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents


[[File:greeley_100edo.png|alt=greeley_100edo.png|greeley_100edo.png]]
[[File:greeley_100edo.png|alt=greeley_100edo.png|greeley_100edo.png]]
Line 886: Line 886:


== Semidim ==
== Semidim ==
Subgroup: 2.5/3.7/3.11/3.13/3
Sval name: 8&29


Commas: 121/120, 169/168, 275/273
[[Subgroup]]: 2.5/3.7/3.11/3.13/3


Sval name: 8&29
[[Comma list]]: 121/120, 169/168, 275/273


[[Tp_tuning|POT2 generator]]: ~13/10 = 453.242
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242


[[Gencom|Gencom]]: [2 13/10; 121/120 169/168 275/273]
[[Gencom|Gencom]]: [2 13/10; 121/120 169/168 275/273]
Line 900: Line 900:
Mapping: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
Mapping: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]


EDOs: {{EDOs|5, 8, 13, 21, 29, 37, 44, 45, 188bde}}
{{Optimal ET sequence|legend=1| 5, 8, 13, 21, 29, 37, 44, 45, 188bde }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.052 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents


[[File:semidim_770edo.png|alt=semidim_770edo.png|semidim_770edo.png]]
[[File:semidim_770edo.png|alt=semidim_770edo.png|semidim_770edo.png]]
Line 911: Line 911:


== Mothwelltri ==
== Mothwelltri ==
Subgroup: 2.7/3.11
Svalname: 1&4


Comma: 99/98
Related temperament: Orwell


Svalname: 1&4
[[Subgroup]]: 2.7/3.11


Related temperament: Orwell
[[Comma list]]: 99/98


[[Tp_tuning|POT2 generator]]: ~7/6 = 273.174
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174


[[Gencom|Gencom]]: [2 7/6; 99/98]
[[Gencom|Gencom]]: [2 7/6; 99/98]
Line 927: Line 927:
Mapping: [<1 0 1|, <0 1 2|]
Mapping: [<1 0 1|, <0 1 2|]


EDOs: {{EDOs|9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc}}
{{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.064 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents


[[mothwelltri5|Five note haplotonic scale]]
[[mothwelltri5|Five note haplotonic scale]]
Line 938: Line 938:


== Sulis ==
== Sulis ==
Subgroup: 2.5.9/7.11/9
Related temperament: [[Marvel_family#Minerva|minerva]], würschmidt


Commas: 99/98, 176/175
[[Subgroup]]: 2.5.9/7.11/9


Related temperament: [[Marvel_family#Minerva|minerva]], würschmidt
[[Comma list]]: 99/98, 176/175


[[Tp_tuning|POT2 generator]]: ~5/4 = 386.558
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 386.558


[[Gencom|Gencom]]: [2 5/4; 99/98 176/175]
[[Gencom|Gencom]]: [2 5/4; 99/98 176/175]
Line 952: Line 952:
Mapping: [<1 0 5 -9|, <0 1 -2 4|]
Mapping: [<1 0 5 -9|, <0 1 -2 4|]


EDOs: {{EDOs|22, 25, 28, 31, 59, 90c, 149c}}
{{Optimal ET sequence|legend=1| 22, 25, 28, 31, 59, 90c, 149c }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.074 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents


[[sulis7|Seven note haplotonic scale]]
[[sulis7|Seven note haplotonic scale]]
Line 963: Line 963:


== Skwares ==
== Skwares ==
Subgroup: 2.3.7.11
Related temperament: [[Meantone_family|squares]]


Commas: 99/98, 243/242
[[Subgroup]]: 2.3.7.11


Related temperament: [[Meantone_family|squares]]
[[Comma list]]: 99/98, 243/242


[[Tp_tuning|POT2 generator]]: ~9/7 = 425.244
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.244


[[Gencom|Gencom]]: [2 9/7; 99/98 243/242]
[[Gencom|Gencom]]: [2 9/7; 99/98 243/242]
Line 977: Line 977:
Mapping: [<1 3 6 7|, <0 -4 -9 -10|]
Mapping: [<1 3 6 7|, <0 -4 -9 -10|]


EDOs: {{EDOs|5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd}}
{{Optimal ET sequence|legend=1| 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.099 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.099 cents


[[File:skwares_206edo.png|alt=skwares_206edo.png|skwares_206edo.png]]
[[File:skwares_206edo.png|alt=skwares_206edo.png|skwares_206edo.png]]
Line 1,043: Line 1,043:


== Kiribati ==
== Kiribati ==
Subgroup: 2.9/5.7/3.11/9
Related temperament: [[Octagar_family|nakika]], octacot


Commas: 100/99, 245/242
[[Subgroup]]: 2.9/5.7/3.11/9


Related temperament: [[Octagar_family|nakika]], octacot
[[Comma list]]: 100/99, 245/242


[[Tp_tuning|POT2 generator]]: ~21/20 = 87.892
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892


[[Gencom|Gencom]]: [2 21/20; 100/99 245/242]
[[Gencom|Gencom]]: [2 21/20; 100/99 245/242]
Line 1,057: Line 1,057:
Mapping: [<1 1 1 0|, <0 -2 3 4|]
Mapping: [<1 1 1 0|, <0 -2 3 4|]


EDOs: {{EDOs|13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd}}
{{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.245 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents


[[kiribati13|Thirteen note chromatic scale]]
[[kiribati13|Thirteen note chromatic scale]]
Line 1,066: Line 1,066:


== Score ==
== Score ==
Subgroup: 2.7.11.13
[[Subgroup]]: 2.7.11.13


Commas: 343/338, 847/832
[[Comma list]]: 343/338, 847/832


[[Tp_tuning|POT2 generator]]: ~11/8 = 540.099
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099


[[Gencom|Gencom]]: [2 11/8; 343/338 847/832]
[[Gencom|Gencom]]: [2 11/8; 343/338 847/832]
Line 1,078: Line 1,078:
Mapping: [<1 1 3 1|, <0 4 1 6|]
Mapping: [<1 1 3 1|, <0 4 1 6|]


EDOs: {{EDOs|5, 7, 9, 11, 20}}
{{Optimal ET sequence|legend=1| 5, 7, 9, 11, 20 }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.282 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.282 cents


[[File:score_20edo.jpg|alt=score_20edo.jpg|score_20edo.jpg]]
[[File:score_20edo.jpg|alt=score_20edo.jpg|score_20edo.jpg]]
Line 1,144: Line 1,144:


== Joan ==
== Joan ==
Subgroup: 2.9.7.11
Related temperaments: casablanca, orwell


Commas: 99/98, 9317/9216
[[Subgroup]]: 2.9.7.11


Related temperaments: casablanca, orwell
[[Comma list]]: 99/98, 9317/9216


[[Tp_tuning|POT2 generator]]: ~11/8 = 542.672 cents
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents


Gencom: [2 11/8; 99/98 9317/9216]
Gencom: [2 11/8; 99/98 9317/9216]
Line 1,158: Line 1,158:
Mapping: [<1 0 1 3|, <0 7 4 1|]
Mapping: [<1 0 1 3|, <0 7 4 1|]


EDOs: {{EDOs|11, 20, 31, 42, 115bd, 157bd}}
{{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.424 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents


[[joan5|Five note haplotonic scale]]
[[joan5|Five note haplotonic scale]]
Line 1,181: Line 1,181:


== Stacks ==
== Stacks ==
Subgroup: 2.9.15.7.11.13
Related temperament: [[Magic_family#Magic-13-limit|magic]]


Commas: 100/99, 105/104, 144/143, 196/195
Svalname: 11&30


Related temperament: [[Magic_family#Magic-13-limit|magic]]
[[Subgroup]]: 2.9.15.7.11.13


Svalname: 11&30
[[Comma list]]: 100/99, 105/104, 144/143, 196/195


[[Tp_tuning|POT2 generator]]: ~9/7 = 439.146
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 439.146


[[Gencom|Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195]
[[Gencom|Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195]
Line 1,197: Line 1,197:
Mapping: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]
Mapping: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]


EDOs: {{EDOs|11, 30, 41, 153cdef, 194cdef, 235cdef}}
{{Optimal ET sequence|legend=1| 11, 30, 41, 153cdef, 194cdef, 235cdef }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.540 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.540 cents


[[stacks5|Five note haplotonic scale]]
[[stacks5|Five note haplotonic scale]]
Line 1,210: Line 1,210:


== Bleu ==
== Bleu ==
Subgroup: 2.3.7.11.13
Sval name: 9&17


Commas: 78/77, 99/98, 144/143
[[Subgroup]]: 2.3.7.11.13


Sval name: 9&17
[[Comma list]]: 78/77, 99/98, 144/143


[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990
[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990
Line 1,226: Line 1,226:
EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]]
EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]]


[[Tp_tuning#T2 tuning|RMS error]]: 1.752 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents


[[File:blue_60edo.png|alt=blue_60edo.png|blue_60edo.png]]
[[File:blue_60edo.png|alt=blue_60edo.png|blue_60edo.png]]
Line 1,239: Line 1,239:


== Sephiroth ==
== Sephiroth ==
Subgroup: 2.5.11.13.17
Related temperament: [[Muggles]]


Commas: 65/64, 170/169, 221/220
[[Subgroup]]: 2.5.11.13.17


Related temperament: [[Muggles]]
[[Comma list]]: 65/64, 170/169, 221/220


[[Tp_tuning|POT2 generator]]: ~5/4 = 372.236
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 372.236


[[Gencom|Gencom]]: [2 5/4; 65/64 170/169 221/220]
[[Gencom|Gencom]]: [2 5/4; 65/64 170/169 221/220]
Line 1,253: Line 1,253:
Mapping: [<1 0 15 6 11|, <0 1 -5 -1 -3|]
Mapping: [<1 0 15 6 11|, <0 1 -5 -1 -3|]


EDOs: {{EDOs|10, 13, 16, 29}}
{{Optimal ET sequence|legend=1| 10, 13, 16, 29 }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.774 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.774 cents


[[sephiroth7|Seven note haplotonic scale]]
[[sephiroth7|Seven note haplotonic scale]]
Line 1,297: Line 1,297:


== Machine ==
== Machine ==
Subgroup: 2.9.7.11
[[Subgroup]]: 2.9.7.11


Commas: 64/63, 99/98
[[Comma list]]: 64/63, 99/98


[[Tp_tuning|POT2 generator]]: ~9/8 = 214.384
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 214.384


[[Gencom|Gencom]]: [2 9/8; 64/63 99/98]
[[Gencom|Gencom]]: [2 9/8; 64/63 99/98]
Line 1,309: Line 1,309:
Mapping: [<1 0 6 13|, <0 1 -1 -3|]
Mapping: [<1 0 6 13|, <0 1 -1 -3|]


EDOs: {{EDOs|5, 6, 11, 17, 28}}
{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}


[[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents


[[File:machine_28edo.png|alt=machine_28edo.png|machine_28edo.png]]
[[File:machine_28edo.png|alt=machine_28edo.png|machine_28edo.png]]
Line 1,322: Line 1,322:


== Deutone ==
== Deutone ==
Subgroup: 2.9.5.7.13
Related temperament: [[Meantone_family|meanpop]]


Commas: 65/64, 81/80, 91/90
[[Subgroup]]: 2.9.5.7.13


Related temperament: [[Meantone_family|meanpop]]
[[Comma list]]: 65/64, 81/80, 91/90


[[Tp_tuning|POT2 generator]]: ~9/8 = 191.059
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 191.059


[[Gencom|Gencom]]: [2 9/8; 65/64 81/80 91/90]
[[Gencom|Gencom]]: [2 9/8; 65/64 81/80 91/90]
Line 1,336: Line 1,336:
Mapping: [<1 0 -4 -13 10|, <0 1 2 5 -2|]
Mapping: [<1 0 -4 -13 10|, <0 1 2 5 -2|]


EDOs: {{EDOs|6, 7, 13, 19, 25e, 44de}}
{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25e, 44de }}


[[Tp_tuning#T2 tuning|RMS error]]: 2.003 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.003 cents


[[File:deutone_44edo.png|alt=deutone_44edo.png|deutone_44edo.png]]
[[File:deutone_44edo.png|alt=deutone_44edo.png|deutone_44edo.png]]
Line 1,362: Line 1,362:


== Skateboard ==
== Skateboard ==
Subgroup: 2.5/3.7/3.11.13/9
Related temperament: [[Starling_family#Thrasher-13-limit|thrasher]]


Commas: 56/55, 91/90, 100/99
[[Subgroup]]: 2.5/3.7/3.11.13/9


Related temperament: [[Starling_family#Thrasher-13-limit|thrasher]]
[[Comma list]]: 56/55, 91/90, 100/99


[[Tp_tuning|POT2 generator]]: ~6/5 = 313.842
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842


[[Gencom|Gencom]]: [2 6/5; 56/55 91/90 100/99]
[[Gencom|Gencom]]: [2 6/5; 56/55 91/90 100/99]
Line 1,376: Line 1,376:
Mapping: [<1 0 -1 2 2|, <0 1 3 2 -2|]
Mapping: [<1 0 -1 2 2|, <0 1 3 2 -2|]


EDOs: {{EDOs|11, 15, 19, 23, 42d, 65d}}
{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}


[[Tp_tuning#T2 tuning|RMS error]]: 2.396 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents


[[skateboard7|Seven note haplotonic scale]]
[[skateboard7|Seven note haplotonic scale]]
Line 1,387: Line 1,387:


== Augment ==
== Augment ==
Subgroup: 2.5.7.11
Related temperament: [[Augmented_family|augmented]]


Commas: 56/55, 128/125
[[Subgroup]]: 2.5.7.11


Related temperament: [[Augmented_family|augmented]]
[[Comma list]]: 56/55, 128/125


[[Tp_tuning|POT2 generator]]: ~8/7 = 228.275
[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~8/7 = 228.275


[[Gencom|Gencom]]: [5/4 8/7; 56/55 128/125]
[[Gencom|Gencom]]: [5/4 8/7; 56/55 128/125]
Line 1,401: Line 1,401:
Mapping: [<3 7 0 2|, <0 0 1 1|]
Mapping: [<3 7 0 2|, <0 0 1 1|]


EDOs: {{EDOs|3, 6, 9, 15, 21}}
{{Optimal ET sequence|legend=1| 3, 6, 9, 15, 21 }}


[[Tp_tuning#T2 tuning|RMS error]]: 2.422 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.422 cents


[[File:augment_21edo.png|alt=augment_21edo.png|augment_21edo.png]]
[[File:augment_21edo.png|alt=augment_21edo.png|augment_21edo.png]]
Line 1,425: Line 1,425:


== Kryptonite ==
== Kryptonite ==
Subgroup: 2.5.7/3.11/3.13/3
Related temperaments: [[Sengic_family|krypton]]


Commas: 56/55, 78/77, 91/90
[[Subgroup]]: 2.5.7/3.11/3.13/3


Related temperaments: [[Sengic_family|krypton]]
[[Comma list]]: 56/55, 78/77, 91/90


[[Tp_tuning|POT2 generator]]: ~13/12 = 132.428
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428


[[Gencom|Gencom]]: [2 13/12; 56/55 78/77 91/90]
[[Gencom|Gencom]]: [2 13/12; 56/55 78/77 91/90]
Line 1,439: Line 1,439:
Mapping: [<1 2 1 2 2|, <0 -3 -2 1 -1|]
Mapping: [<1 2 1 2 2|, <0 -3 -2 1 -1|]


EDOs: {{EDOs|9, 63, 82bd, 91bde}}
{{Optimal ET sequence|legend=1| 9, 63, 82bd, 91bde }}


[[Tp_tuning#T2 tuning|RMS error]]: 2.545 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents


[[kryptonite9|Nine note albitonic scale]]
[[kryptonite9|Nine note albitonic scale]]
Line 1,450: Line 1,450:


== Oregon ==
== Oregon ==
Subgroup: 2.9.15.7.11
[[Subgroup]]: 2.9.15.7.11


Commas: 55/54, 64/63, 100/99
[[Comma list]]: 55/54, 64/63, 100/99


[[Tp_tuning|POT2 generator]]: ~6/5 = 325.495
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495


[[Gencom|Gencom]]: [2 6/5; 55/54 64/63 100/99]
[[Gencom|Gencom]]: [2 6/5; 55/54 64/63 100/99]
Line 1,462: Line 1,462:
Mapping: [<1 1 1 5 2|, <0 3 4 -3 2|]
Mapping: [<1 1 1 5 2|, <0 3 4 -3 2|]


EDOs: {{EDOs|7, 11, 37b, 48b, 59b}}
{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }}


[[Tp_tuning#T2 tuning|RMS error]]: 2.550 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents


[[oregon7|Seven note haplotonic scale]]
[[oregon7|Seven note haplotonic scale]]
Line 1,473: Line 1,473:


== Antikythera ==
== Antikythera ==
Subgroup: 2.9.5.7
Related temperament: [[pajara|pajara]]


Commas: 50/49, 64/63
[[Subgroup]]: 2.9.5.7


Related temperament: [[pajara|pajara]]
[[Comma list]]: 50/49, 64/63


[[Tp_tuning|POT2 generator]]: ~8/7 = 214.095
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 214.095


[[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63]
[[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63]
Line 1,487: Line 1,487:
Mapping: [<2 0 11 12|, <0 1 -1 -1|]
Mapping: [<2 0 11 12|, <0 1 -1 -1|]


EDOS: {{EDOs|4, 6, 10, 16, 22, 28}}
{{Optimal ET sequence|legend=1| 4, 6, 10, 16, 22, 28 }}


[[Tp_tuning#T2 tuning|RMS error]]: 2.572 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.572 cents


[[File:antikythera_28edo.png|alt=antikythera_28edo.png|antikythera_28edo.png]]
[[File:antikythera_28edo.png|alt=antikythera_28edo.png|antikythera_28edo.png]]
Line 1,500: Line 1,500:


== Glacial ==
== Glacial ==
Subgroup: 2.9.5.11.13
[[Subgroup]]: 2.9.5.11.13


Commas: 45/44, 65/64, 81/80
[[Comma list]]: 45/44, 65/64, 81/80


[[Tp_tuning|POT2 generator]]: ~9/8 = 186.151
[[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151


[[Gencom|Gencom]]: [2 9/8; 45/44 65/64 81/80]
[[Gencom|Gencom]]: [2 9/8; 45/44 65/64 81/80]
Line 1,512: Line 1,512:
Mapping: [<1 0 -4 -6 10|, <0 1 2 3 -2|]
Mapping: [<1 0 -4 -6 10|, <0 1 2 3 -2|]


EDOs: {{EDOs|6, 13, 45be, 58bce, 71bce, 84bce}}
{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}


[[Tp_tuning#T2 tuning|RMS error]]: 2.887 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents


[[glacial6|Six note haplotonic scale]]
[[glacial6|Six note haplotonic scale]]
Line 1,523: Line 1,523:


== Leantone ==
== Leantone ==
Subgroup: 2.9.5.7.11
Related temperament: [[Meanenneadecal|meanenneadecal]]


Commas: 45/44, 56/55, 81/80
[[Subgroup]]: 2.9.5.7.11


Related temperament: [[Meanenneadecal|meanenneadecal]]
[[Comma list]]: 45/44, 56/55, 81/80


[[Tp_tuning|POT2 generator]]: ~9/8 = 192.500
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.500


[[Gencom|Gencom]]: [2 9/8; 45/44 56/55 81/80]
[[Gencom|Gencom]]: [2 9/8; 45/44 56/55 81/80]
Line 1,537: Line 1,537:
Mapping: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
Mapping: [<1 0 -4 -13 -6|, <0 1 2 5 3|]


EDOs: {{EDOs|6, 7, 13, 19, 25, 31, 56, 81}}
{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25, 31, 56, 81 }}


[[Tp_tuning#T2 tuning|RMS error]]: 3.882 cents
[[Tp tuning #T2 tuning|RMS error]]: 3.882 cents


[[File:leantone_81edo.png|alt=leantone_81edo.png|leantone_81edo.png]]
[[File:leantone_81edo.png|alt=leantone_81edo.png|leantone_81edo.png]]
Line 1,546: Line 1,546:
* [[leantone7|Seven note albitonic scale]]
* [[leantone7|Seven note albitonic scale]]
* [[leantone13|Thirteen note chromatic scale]]
* [[leantone13|Thirteen note chromatic scale]]
== Notes ==


[[Category:Lists of scales]]
[[Category:Lists of scales]]
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