Meantone family: Difference between revisions
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Badness: 0.026288 | Badness: 0.026288 | ||
== Migration == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 81/80, 121/120, 126/125 | |||
Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 8 20 5 }}] | |||
Mapping generators: ~2, ~11/9 | |||
POTE generator: ~11/9 = 348.182 | |||
Vals: {{Val list| 7d, 24d, 31, 100de, 131bdee, 162bdee }} | |||
Badness: 0.025516 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 66/65, 81/80, 121/120, 126/125 | |||
Mapping: [{{val| 1 1 0 -3 2 4 }}, {{val| 0 2 8 20 5 -1 }}] | |||
Mapping generators: ~2, ~11/9 | |||
POTE generator: ~11/9 = 348.490 | |||
Vals: {{Val list| 7d, 24d, 31, 55d }} | |||
Badness: 0.028071 | |||
== Bimeantone == | == Bimeantone == | ||
| Line 532: | Line 562: | ||
Scales: [[flattone12]] | Scales: [[flattone12]] | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 551: | Line 581: | ||
Scales: [[flattone12]] | Scales: [[flattone12]] | ||
== Ptolemy == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 81/80, 121/120, 525/512 | |||
Mapping: [{{val| 1 1 0 8 2 }}, {{val| 0 2 8 -18 5 }}] | |||
POTE generator: ~11/9 = 346.922 | |||
Vals: {{Val list| 7, 31dd, 38d, 45e, 83bcddee }} | |||
Badness: 0.058785 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 65/64, 81/80, 105/104, 121/120 | |||
Mapping: [{{val| 1 1 0 8 2 6 }}, {{val| 0 2 8 -18 5 -8 }}] | |||
POTE generator: ~11/9 = 346.910 | |||
Vals: {{Val list| 7, 31ddf, 38df, 45ef, 83bcddeeff }} | |||
Badness: 0.034316 | |||
= Dominant = | = Dominant = | ||
| Line 608: | Line 664: | ||
Vals: {{Val list| 12f, 17c, 29cdef }} | Vals: {{Val list| 12f, 17c, 29cdef }} | ||
Badness: 0. | Badness: 0.024108 | ||
=== Dominion === | === Dominion === | ||
| Line 621: | Line 677: | ||
POTE generator: ~3/2 = 704.905 | POTE generator: ~3/2 = 704.905 | ||
Badness: 0. | Badness: 0.027295 | ||
== Domineering == | == Domineering == | ||
| Line 685: | Line 741: | ||
Vals: {{Val list| 5e, 7, 12f, 19df }} | Vals: {{Val list| 5e, 7, 12f, 19df }} | ||
Badness: 0.018289 | |||
== Domination == | == Domination == | ||
| Line 697: | Line 755: | ||
Vals: {{Val list| 5e, 12e, 17c, 46cd }} | Vals: {{Val list| 5e, 12e, 17c, 46cd }} | ||
Badness: 0. | Badness: 0.036562 | ||
=== 13-limit === | === 13-limit === | ||
| Line 710: | Line 768: | ||
Vals: {{Val list| 5e, 12e, 17c }} | Vals: {{Val list| 5e, 12e, 17c }} | ||
Badness: 0. | Badness: 0.027435 | ||
== Arnold == | == Arnold == | ||
| Line 764: | Line 822: | ||
Badness: 0.021098 | Badness: 0.021098 | ||
= Sharptone = | == Maqamic == | ||
Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo|12EDO]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val. | <span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span> | ||
{{main| Maqamic }} | |||
Maqamic has a hemififth generator (~11/9) and tempers out 36/35 and 121/120. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation. | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 64/63, 121/120 | |||
Mapping: [{{val| 1 1 0 4 2 }}, {{val| 0 2 8 -4 5 }}] | |||
Mapping generators: ~2, ~11/9 | |||
POTE generator: ~11/9 = 350.934 | |||
Vals: {{Val list| 7, 17c, 24d, 41cd }} | |||
Badness: 0.040240 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 36/35, 64/63, 66/65, 121/120 | |||
Mapping: [{{val| 1 1 0 4 2 4 }}, {{val| 0 2 8 -4 5 -1 }}] | |||
Mapping generators: ~2, ~11/9 | |||
POTE generator: ~11/9 = 350.816 | |||
Vals: {{Val list| 7, 17c, 24d, 41cd }} | |||
Badness: 0.027214 | |||
= Sharptone = | |||
Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo|12EDO]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val. | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 779: | Line 872: | ||
{{Val list|legend=1| 5, 7d, 12d }} | {{Val list|legend=1| 5, 7d, 12d }} | ||
[[Badness]]: 0. | [[Badness]]: 0.024848 | ||
== Meanertone == | == Meanertone == | ||
| Line 792: | Line 885: | ||
Vals: {{Val list| 5, 7d, 12de }} | Vals: {{Val list| 5, 7d, 12de }} | ||
Badness: 0. | Badness: 0.025167 | ||
= Plutus = | = Plutus = | ||
| Line 805: | Line 898: | ||
[[POTE generator]]: ~3/2 = 682.895 | [[POTE generator]]: ~3/2 = 682.895 | ||
{{Val list|legend=1| | {{Val list|legend=1| 2cd, 5d, 7 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.045275 | ||
== 11-limit == | == 11-limit == | ||
| Line 818: | Line 911: | ||
POTE generator: ~3/2 = 685.234 | POTE generator: ~3/2 = 685.234 | ||
Vals: {{Val list| 5de, 7 }} | Vals: {{Val list| 2cde, 5de, 7 }} | ||
Badness: 0. | Badness: 0.032521 | ||
= Supermean = | = Supermean = | ||
| Line 833: | Line 926: | ||
{{Val list|legend=1| 5d, 12d, 17c, 29c }} | {{Val list|legend=1| 5d, 12d, 17c, 29c }} | ||
[[Badness]]: 0. | [[Badness]]: 0.134204 | ||
== 11-limit == | == 11-limit == | ||
| Line 844: | Line 937: | ||
POTE generator: ~3/2 = 705.096 | POTE generator: ~3/2 = 705.096 | ||
{{Val list | Vals: {{Val list| 5de, 12de, 17c, 29c }} | ||
Badness: 0. | Badness: 0.063262 | ||
== 13-limit == | == 13-limit == | ||
| Line 857: | Line 950: | ||
POTE generator: ~3/2 = 705.094 | POTE generator: ~3/2 = 705.094 | ||
{{Val list | Vals: {{Val list| 5de, 12de, 17c, 29c }} | ||
Badness: 0.040324 | |||
= Godzilla = | = Godzilla = | ||
| Line 885: | Line 980: | ||
{{Val list|legend=1| 5, 14c, 19 }} | {{Val list|legend=1| 5, 14c, 19 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.026747 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 909: | Line 1,003: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 930: | Line 1,023: | ||
== Semafour == | == Semafour == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 946: | Line 1,038: | ||
== Varan == | == Varan == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 962: | Line 1,053: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 978: | Line 1,068: | ||
== Baragon == | == Baragon == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 991: | Line 1,080: | ||
{{Val list|legend=1| 19, 24, 43d }} | {{Val list|legend=1| 19, 24, 43d }} | ||
Badness: 0. | Badness: 0.035673 | ||
= Injera = | = Injera = | ||
Injera has a half-octave period and a generator which can be taken as a fifth or fourth, but also as a 15/14 semitone difference between a half-octave and a perfect fifth. Injera tempers out 50/49, equating 7/5 with 10/7 and giving a tritone of half an octave. A major third up from this tritone is the 7/4. [[38edo]], which is two parallel [[19edo]]s, is an excellent tuning for injera. | Injera has a half-octave period and a generator which can be taken as a fifth or fourth, but also as a 15/14 semitone difference between a half-octave and a perfect fifth. Injera tempers out 50/49, equating 7/5 with 10/7 and giving a tritone of half an octave. A major third up from this tritone is the 7/4. [[38edo]], which is two parallel [[19edo]]s, is an excellent tuning for injera. | ||
| Line 1,024: | Line 1,112: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,045: | Line 1,132: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,066: | Line 1,152: | ||
=== Enjera === | === Enjera === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,082: | Line 1,167: | ||
== Injerous == | == Injerous == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,098: | Line 1,182: | ||
== Lahoh == | == Lahoh == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,133: | Line 1,216: | ||
{{Val list|legend=1| 7, 17c, 24, 31, 100e, 131bee }} | {{Val list|legend=1| 7, 17c, 24, 31, 100e, 131bee }} | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== Mohoho == | == Mohoho == | ||
Subgroup: 2.3.5.11.13 | Subgroup: 2.3.5.11.13 | ||
| Line 1,154: | Line 1,234: | ||
POTE generator: ~11/9 = 348.9155 | POTE generator: ~11/9 = 348.9155 | ||
{{Val list | Vals: {{Val list| 7, 17c, 24, 31, 55, 86ef, 141ceff }} | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
= Mohajira = | = Mohajira = | ||
{{main|Mohajira}} | {{main|Mohajira}} | ||
Mohajira can be viewed as derived from mohaha which maps the interval one quarter tone flat of 16/9 to 7/4, although mohajira really makes more sense as an 11-limit temperament. It tempers out 6144/6125, the porwell comma. [[31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. | Mohajira can be viewed as derived from mohaha which maps the interval one quarter tone flat of 16/9 to 7/4, although mohajira really makes more sense as an 11-limit temperament. It tempers out 6144/6125, the porwell comma. [[31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,194: | Line 1,269: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,271: | Line 1,345: | ||
= Mohamaq = | = Mohamaq = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,290: | Line 1,362: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,308: | Line 1,379: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,325: | Line 1,395: | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
= | = Orphic = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 81/80, 5898240/5764801 | |||
[[Mapping]]: [{{val| 2 1 -4 4 }}, {{val|0 4 16 3 }}] | |||
[[Mapping]]: [{{val| 2 1 -4 4 }}, {{val|0 4 16 3 }}] | |||
Mapping generators: ~2401/1728, ~343/288 | Mapping generators: ~2401/1728, ~343/288 | ||
| Line 1,439: | Line 1,413: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,455: | Line 1,428: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,471: | Line 1,443: | ||
= Mothra = | = Mothra = | ||
Mothra splits the fifth into three 8/7 generators. It uses [[1029/1024]], the gamelisma, to accomplish this deed and also tempers out [[1728/1715]], the orwell comma. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra. In the 2.3.7-limit, mothra is identical to [[slendric]]. | Mothra splits the fifth into three 8/7 generators. It uses [[1029/1024]], the gamelisma, to accomplish this deed and also tempers out [[1728/1715]], the orwell comma. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra. In the 2.3.7-limit, mothra is identical to [[slendric]]. | ||
| Line 1,500: | Line 1,471: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,516: | Line 1,486: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,532: | Line 1,501: | ||
== Cynder == | == Cynder == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,548: | Line 1,516: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,564: | Line 1,531: | ||
== Mosura == | == Mosura == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,580: | Line 1,546: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,596: | Line 1,561: | ||
=== Music === | === Music === | ||
* [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ Chris Vaisvil] | * [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ Chris Vaisvil] | ||
= Squares = | = Squares = | ||
Squares splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7]]) intervals, and uses it for a generator. [[31edo]], with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out [[2401/2400]], the breedsma, as well as [[2430/2401]]. | Squares splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7]]) intervals, and uses it for a generator. [[31edo]], with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out [[2401/2400]], the breedsma, as well as [[2430/2401]]. | ||
| Line 1,630: | Line 1,593: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,648: | Line 1,610: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,666: | Line 1,627: | ||
=== Agora === | === Agora === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,684: | Line 1,644: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 1,700: | Line 1,659: | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 1,716: | Line 1,674: | ||
== Cuboctahedra == | == Cuboctahedra == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,760: | Line 1,717: | ||
== Liesel == | == Liesel == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,793: | Line 1,749: | ||
== Elisa == | == Elisa == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,809: | Line 1,764: | ||
== Lisa == | == Lisa == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,825: | Line 1,779: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,860: | Line 1,813: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,876: | Line 1,828: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,892: | Line 1,843: | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 1,908: | Line 1,858: | ||
== 19-limit == | == 19-limit == | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 2,020: | Line 1,969: | ||
= Undevigintone = | = Undevigintone = | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 2,033: | Line 1,981: | ||
{{Val list|legend=1| 19, 38d }} | {{Val list|legend=1| 19, 38d }} | ||
Badness: 0. | Badness: 0.036387 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 2,047: | Line 1,994: | ||
POTE generator: ~11/8 = 537.061 | POTE generator: ~11/8 = 537.061 | ||
{{Val list | Vals: {{Val list| 19, 38df }} | ||
Badness: 0. | Badness: 0.022933 | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||