Breedsmic temperaments: Difference between revisions

Revision as of 07:34, 19 July 2021

This page discusses miscellaneous rank-2 temperaments tempering out the breedsma, [-5 -1 -2 4⟩ = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12EDO, for example) which does not possess a neutral third cannot be tempering out the breedsma.

The breedsma is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 × 2401/2400 = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, 25/24. We might note also that 49/40 × 10/7 = 7/4 and 49/40 × (10/7)² = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.

Temperaments discussed elsewhere include:

Hemififths

Main article: Hemififths

Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with 99EDO and 140EDO providing good tunings, and 239EDO an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7- and 9-odd-limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&58 temperament. It requires 25 generator steps to get to the class for the harmonic 5, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS^{[clarification needed]}.

By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. 99EDO is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 5120/5103

Mapping: [⟨1 1 -5 -1], ⟨0 2 25 13]]

Wedgie: ⟨⟨ 2 25 13 35 15 -40 ]]

POTE generator: ~49/40 = 351.477

Minimax tuning:

7- and 9-odd-limit minimax: ~49/40 = [1/5 0 1/25⟩

[[1 0 0 0⟩, [7/5 0 2/25 0⟩, [0 0 1 0⟩, [8/5 0 13/25 0⟩]

Eigenmonzos: 2, 5

Algebraic generator: (2 + sqrt(2))/2

Template:Val list

Badness: 0.022243

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 896/891

Mapping: [⟨1 1 -5 -1 2], ⟨0 2 25 13 5]]

POTE generator: ~11/9 = 351.521

@@ Line 1: / Line 1: @@
-'''Breedsmic temperaments''' are rank two temperaments tempering out the [[breedsma]], {{monzo|-5 -1 -2 4}} = [[2401/2400]]. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12EDO, for example) which does not possess a neutral third cannot be tempering out the breedsma.
+This page discusses miscellaneous rank-2 temperaments tempering out the [[breedsma]], {{monzo|-5 -1 -2 4}} = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12EDO, for example) which does not possess a neutral third cannot be tempering out the breedsma.
-It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.
+The breedsma is also the amount by which four stacked [[10/7]] intervals exceed 25/6: 10000/2401 × 2401/2400 = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, [[25/24]]. We might note also that 49/40 × 10/7 = 7/4 and 49/40 × (10/7)<sup>2</sup> = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.
-Temperaments discussed elsewhere include [[Dicot family #Decimal|decimal]], [[Archytas clan #Beatles|beatles]], [[Meantone family #Squares|squares]], [[Starling temperaments #Myna|myna]], [[Keemic temperaments #Quasitemp|quasitemp]], [[Gamelismic clan #Miracle|miracle]], [[Magic family #Quadrimage|quadrimage]], [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], [[Tetracot family #Octacot|octacot]], [[Kleismic family #Quadritikleismic|quadritikleismic]], [[Schismatic family #Sesquiquartififths|sesquiquartififths]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Vulture family #Eagle|eagle]], and [[Gammic family #Neptune|neptune]].
+Temperaments discussed elsewhere include:
+* [[Dicot family #Decimal|Decimal]]
+* [[Archytas clan #Beatles|Beatles]]
+* [[Meantone family #Squares|Squares]]
+* [[Starling temperaments #Myna|Myna]]
+* [[Keemic temperaments #Quasitemp|Quasitemp]]
+* [[Gamelismic clan #Miracle|Miracle]]
+* [[Magic family #Quadrimage|Quadrimage]]
+* [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]]
+* [[Tetracot family #Octacot|Octacot]]
+* [[Kleismic family #Quadritikleismic|Quadritikleismic]]
+* [[Schismatic family #Sesquiquartififths|Sesquiquartififths]]
+* [[Würschmidt family #Hemiwürschmidt|Hemiwürschmidt]]
+* [[Vulture family #Eagle|Eagle]]
+* [[Gammic family #Neptune|Neptune]]
 == Hemififths ==
-{{main|Hemififths}}
+{{Main| Hemififths }}
-Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with [[99edo|99EDO]] and [[140edo|140EDO]] providing good tunings, and [[239edo|239EDO]] an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&amp;58 temperament and has wedgie {{multival|2 25 13 35 15 -40}}, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.
+Hemififths tempers out [[5120/5103]], the hemifamity comma, and [[10976/10935]], hemimage. It has a neutral third as a generator, with [[99edo|99EDO]] and [[140edo|140EDO]] providing good tunings, and [[239edo|239EDO]] an even better one; and other possible tunings are (160)<sup>(1/25)</sup>, giving just 5s, the 7- and 9-odd-limit minimax tuning, or 14<sup>(1/13)</sup>, giving just 7s. It may be called the 41&amp;58 temperament. It requires 25 generator steps to get to the class for the harmonic 5, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS{{clarify}}.
-By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. 99EDO is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.
+By adding [[243/242]] (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. 99EDO is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding [[144/143]] brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be [[16/13]]. 99 remains a good tuning choice.
 Subgroup: 2.3.5.7
@@ Line 86: / Line 100: @@
 == Tertiaseptal ==
-{{main|Tertiaseptal}}
+{{Main| Tertiaseptal }}
-Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152, the rainy comma. It can be described as the 31&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo|171EDO]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.
+Aside from the breedsma, tertiaseptal tempers out [[65625/65536]], the horwell comma, [[703125/702464]], the meter, and [[2100875/2097152]], the rainy comma. It can be described as the 31&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo|171EDO]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.
 Subgroup: 2.3.5.7
@@ Line 222: / Line 236: @@
 == Harry ==
-{{main|Harry}}
+{{Main| Harry }}
-{{see also|Gravity family #Harry}}
+{{see also| Gravity family #Harry }}
-Harry adds cataharry, 19683/19600, to the set of commas. It may be described as the 58&amp;72 temperament, with wedgie {{multival|12 34 20 26 -2 -49}}. The period is half an octave, and the generator 21/20, with generator tunings of 9\130 or 14\202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices.
+Harry adds [[cataharry]], 19683/19600, to the set of commas. It may be described as the 58&amp;72 temperament. The period is half an octave, and the generator 21/20, with generator tunings of 9\130 or 14\202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices.
-Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is {{multival|12 34 20 30 ...}}.
+Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is {{multival| 12 34 20 30 …}}.
-Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with {{multival|12 34 20 30 52 ...}} as the octave wedgie. [[130edo|130EDO]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.
+Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with {{multival| 12 34 20 30 52 …}} as the octave wedgie. [[130edo|130EDO]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.
 Subgroup: 2.3.5.7
@@ Line 285: / Line 299: @@
 == Quasiorwell ==
-In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = {{monzo|22 -1 -10 1}}. It has a wedgie {{multival|38 -3 8 -93 -94 27}}. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61\270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.
+In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = {{monzo|22 -1 -10 1}}. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61\270 makes for an excellent tuning choice. Other possibilities are (7/2)<sup>1/8</sup>, giving just 7s, or 384<sup>1/38</sup>, giving pure fifths.
-Adding 3025/3024 extends to the 11-limit and gives {{multival|38 -3 8 64 ...}} for the initial wedgie, and as expected, 270 remains an excellent tuning.
+Adding 3025/3024 extends to the 11-limit and gives {{multival| 38 -3 8 64 …}} for the initial wedgie, and as expected, 270 remains an excellent tuning.
 Subgroup: 2.3.5.7
@@ Line 294: / Line 308: @@
 [[Mapping]]: [{{val|1 31 0 9}}, {{val|0 -38 3 -8}}]
+{{Multival|legend=1| 38 -3 8 -93 -94 27 }}
 [[POTE generator]]: ~1024/875 = 271.107
@@ Line 328: / Line 344: @@
 == Decoid ==
-{{see also|Qintosec family #Decoid}}
+{{see also| Qintosec family #Decoid }}
 Decoid tempers out 2401/2400 and 67108864/66976875, as well as the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}}. Either 8/7 or 16/15 can be used its generator. It may be described as the 130&amp;270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[Qintosec family|qintosec temperament]].
@@ Line 373: / Line 389: @@
 == Neominor ==
-The generator for neominor temperament is tridecimal minor third [[13/11]], also known as "<b>Neo-gothic minor third</b>".
+The generator for neominor temperament is tridecimal minor third [[13/11]], also known as ''Neo-gothic minor third''.
 Subgroup: 2.3.5.7
@@ Line 553: / Line 569: @@
 == Septidiasemi ==
-{{main|Septidiasemi}}
+{{Main| Septidiasemi }}
 Aside from 2401/2400, [[septidiasemi]] tempers out 2152828125/2147483648 in the 7-limit. It is so named because the generator is a "septimal diatonic semitone" (0.15 cents flat of [[15/14]]). It is an excellent tuning for 2.3.5.7.13 and 2.3.5.7.13.17 subgroups rather than full 13- and 17-limit.
@@ Line 560: / Line 576: @@
 [[Comma list]]: 2401/2400, 2152828125/2147483648
-[[Mapping]]: [{{val|1 -1 6 4}}, {{val|0 26 -37 -12}}]
+[[Mapping]]: [{{val| 1 -1 6 4 }}, {{val| 0 26 -37 -12 }}]
 {{Multival|legend=1|26 -37 -12 -119 -92 76}}
@@ Line 577: / Line 593: @@
 Comma list: 243/242, 441/440, 939524096/935859375
-Mapping: [{{val|1 -1 6 4 -3}}, {{val|0 26 -37 -12 65}}]
+Mapping: [{{val| 1 -1 6 4 -3 }}, {{val| 0 26 -37 -12 65 }}]
 POTE generator: ~15/14 = 119.279
@@ Line 590: / Line 606: @@
 Comma list: 243/242, 441/440, 2200/2197, 3584/3575
-Mapping: [{{val|1 -1 6 4 -3 4}}, {{val|0 26 -37 -12 65 -3}}]
+Mapping: [{{val| 1 -1 6 4 -3 4 }}, {{val| 0 26 -37 -12 65 -3 }}]
 POTE generator: ~15/14 = 119.281
@@ Line 603: / Line 619: @@
 Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
-Mapping: [{{val|1 -1 6 4 -3 4 2}}, {{val|0 26 -37 -12 65 -3 21}}]
+Mapping: [{{val| 1 -1 6 4 -3 4 2 }}, {{val| 0 26 -37 -12 65 -3 21 }}]
 POTE generator: ~15/14 = 119.281
@@ Line 618: / Line 634: @@
 [[Comma list]]: 2401/2400, 1224440064/1220703125
-[[Mapping]]: [{{val|1 31 34 26}}, {{val|0 -52 -56 -41}}]
+[[Mapping]]: [{{val| 1 31 34 26 }}, {{val| 0 -52 -56 -41 }}]
 {{Multival|legend=1|52 56 41 -32 -81 -62}}
@@ Line 629: / Line 645: @@
 == Subneutral ==
-{{see also|Luna family}}
+{{See also| Luna family }}
 Subgroup: 2.3.5.7
@@ Line 635: / Line 651: @@
 [[Comma list]]: 2401/2400, 274877906944/274658203125
-[[Mapping]]: [{{val|1 19 0 6}}, {{val|0 -60 8 -11}}]
+[[Mapping]]: [{{val| 1 19 0 6 }}, {{val| 0 -60 8 -11 }}]
 {{Multival|legend=1|60 -8 11 -152 -151 48}}
@@ Line 646: / Line 662: @@
 == Osiris ==
-{{see also|Metric microtemperaments #Geb}}
+{{See also| Metric microtemperaments #Geb }}
 Subgroup: 2.3.5.7
@@ Line 652: / Line 668: @@
 [[Comma list]]: 2401/2400, 31381059609/31360000000
-[[Mapping]]: [{{val|1 13 33 21}}, {{val|0 -32 -86 -51}}]
+[[Mapping]]: [{{val| 1 13 33 21 }}, {{val| 0 -32 -86 -51 }}]
 {{Multival|legend=1|32 86 51 62 -9 -123}}
@@ Line 667: / Line 683: @@
 [[Comma list]]: 2401/2400, 28672/28125
-[[Mapping]]: [{{val|1 5 1 3}}, {{val|0 -18 7 -1}}]
+[[Mapping]]: [{{val| 1 5 1 3 }}, {{val| 0 -18 7 -1 }}]
 {{Multival|legend=1|18 -7 1 -53 -49 22}}
@@ Line 682: / Line 698: @@
 Comma list: 176/175, 2401/2400, 2560/2541
-Mapping: [{{val|1 5 1 3 1}}, {{val|0 -18 7 -1 13}}]
+Mapping: [{{val| 1 5 1 3 1 }}, {{val| 0 -18 7 -1 13 }}]
 POTE generator: ~8/7 = 227.500
@@ Line 695: / Line 711: @@
 Comma list: 176/175, 196/195, 364/363, 512/507
-Mapping: [{{val|1 5 1 3 1 2}}, {{val|0 -18 7 -1 13 9}}]
+Mapping: [{{val| 1 5 1 3 1 2 }}, {{val| 0 -18 7 -1 13 9 }}]
 POTE generator: ~8/7 = 227.493
@@ Line 708: / Line 724: @@
 [[Comma list]]: 2401/2400, 341796875/339738624
-[[Mapping]]: [{{val|1 19 8 10}}, {{val|0 -46 -15 -19}}]
+[[Mapping]]: [{{val| 1 19 8 10 }}, {{val| 0 -46 -15 -19 }}]
 {{Multival|legend=1|46 15 19 -83 -99 2}}
@@ Line 723: / Line 739: @@
 Comma list: 385/384, 1375/1372, 43923/43750
-Mapping: [{{val|1 19 8 10 8}}, {{val|0 -46 -15 -19 -12}}]
+Mapping: [{{val| 1 19 8 10 8 }}, {{val| 0 -46 -15 -19 -12 }}]
 POTE generator: ~100/77 = 454.318
@@ Line 736: / Line 752: @@
 Comma list: 385/384, 625/624, 847/845, 1375/1372
-Mapping: [{{val|1 19 8 10 8 9}}, {{val|0 -46 -15 -19 -12 -14}}]
+Mapping: [{{val| 1 19 8 10 8 9 }}, {{val| 0 -46 -15 -19 -12 -14 }}]
 POTE generator: ~13/10 = 454.316
@@ Line 751: / Line 767: @@
 [[Comma list]]: 2401/2400, 177147/175000
-[[Mapping]]: [{{val|1 5 9 7}}, {{val|0 -22 -43 -27}}]
+[[Mapping]]: [{{val| 1 5 9 7 }}, {{val| 0 -22 -43 -27 }}]
 {{Multival|legend=1|22 43 27 17 -19 -58}}
@@ Line 766: / Line 782: @@
 Comma list: 243/242, 441/440, 43923/43750
-Mapping: [{{val|1 5 9 7 12}}, {{val|0 -22 -43 -27 -55}}]
+Mapping: [{{val| 1 5 9 7 12 }}, {{val| 0 -22 -43 -27 -55 }}]
 POTE generator: ~10/9 = 186.345
@@ Line 779: / Line 795: @@
 Comma list: 243/242, 351/350, 441/440, 847/845
-Mapping: [{{val|1 5 9 7 12 11}}, {{val|0 -22 -43 -27 -55 -47}}]
+Mapping: [{{val| 1 5 9 7 12 11 }}, {{val| 0 -22 -43 -27 -55 -47 }}]
 POTE generator: ~10/9 = 186.347
@@ Line 792: / Line 808: @@
 Comma list: 243/242, 351/350, 441/440, 561/560, 847/845
-Mapping: [{{val|1 5 9 7 12 11 3}}, {{val|0 -22 -43 -27 -55 -47 7}}]
+Mapping: [{{val| 1 5 9 7 12 11 3 }}, {{val| 0 -22 -43 -27 -55 -47 7 }}]
 POTE generator: ~10/9 = 186.348
@@ Line 807: / Line 823: @@
 [[Comma list]]: 2401/2400, 78732/78125
-[[Mapping]]: [{{val|1 13 17 13}}, {{val|0 -28 -36 -25}}]
+[[Mapping]]: [{{val| 1 13 17 13 }}, {{val| 0 -28 -36 -25 }}]
-{{Multival|legend=1|28 36 25 -8 -39 -43}}
+{{Multival|legend=1| 28 36 25 -8 -39 -43 }}
 [[POTE generator]]: ~250/189 = 489.235
@@ Line 822: / Line 838: @@
 Comma list: 243/242, 441/440, 78408/78125
-Mapping: [{{val|1 13 17 13 32}}, {{val|0 -28 -36 -25 -70}}]
+Mapping: [{{val| 1 13 17 13 32 }}, {{val| 0 -28 -36 -25 -70 }}]
 POTE generator: ~250/189 = 489.252
@@ Line 835: / Line 851: @@
 Comma list: 243/242, 351/350, 441/440, 10985/10976
-Mapping:  [{{val|1 13 17 13 32 9}}, {{val|0 -28 -36 -25 -70 -13}}]
+Mapping:  [{{val| 1 13 17 13 32 9 }}, {{val| 0 -28 -36 -25 -70 -13 }}]
 POTE generator: ~65/49 = 489.256
@@ Line 848: / Line 864: @@
 [[Comma list]]: 2401/2400, 390625/387072
-[[Mapping]]: [{{val|1 -13 -4 -4}}, {{val|0 30 13 14}}]
+[[Mapping]]: [{{val| 1 -13 -4 -4 }}, {{val| 0 30 13 14 }}]
 {{Multival|legend=1|30 13 14 -49 -62 -4}}
@@ Line 863: / Line 879: @@
 Comma list: 385/384, 1375/1372, 4000/3993
-Mapping: [{{val|1 -13 -4 -4 2}}, {{val|0 30 13 14 3}}]
+Mapping: [{{val| 1 -13 -4 -4 2 }}, {{val| 0 30 13 14 3 }}]
 POTE generator: ~7/5 = 583.387
@@ Line 876: / Line 892: @@
 Comma list: 169/168, 364/363, 385/384, 625/624
-Mapping: [{{val|1 -13 -4 -4 2 -7}}, {{val|0 30 13 14 3 22}}]
+Mapping: [{{val| 1 -13 -4 -4 2 -7 }}, {{val| 0 30 13 14 3 22 }}]
 POTE generator: ~7/5 = 583.387
@@ Line 884: / Line 900: @@
 Badness: 0.028683
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
-[[Category:Temperament]]
 [[Category:Temperament collection]]
-[[Category:Breed]]
+[[Category:Breedsmic temperaments| ]] <!-- main article -->
 [[Category:Rank 2]]

Breedsmic temperaments: Difference between revisions

Revision as of 07:34, 19 July 2021

Hemififths

11-limit

13-limit

Semihemi

13-limit

Tertiaseptal

11-limit

13-limit

17-limit

Tertia

13-limit

17-limit

Hemitert

13-limit

17-limit

Harry

11-limit

13-limit

17-limit

Quasiorwell

11-limit

13-limit

Decoid

11-limit

13-limit

Neominor

11-limit

13-limit

Emmthird

Quinmite

Unthirds

11-limit

13-limit

Newt

11-limit

13-limit

Amicable

Septidiasemi

Sedia

13-limit

17-limit

Maviloid

Subneutral

Osiris

Gorgik

11-limit

13-limit

Fibo

11-limit

13-limit

Mintone

11-limit

13-limit

17-limit

Catafourth

11-limit

13-limit

Cotritone

11-limit

13-limit

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