Horwell temperaments: Difference between revisions
mNo edit summary |
mNo edit summary |
||
| Line 3: | Line 3: | ||
Discussed elsewhere are [[Hemimage temperaments|bisupermajor]], [[Kleismic family|countercata]], [[Mirkwai clan|eris]], [[Escapade family|escaped]], [[Hemimean clan|hemithirds]], [[Diaschismic family|keen]], [[Semicomma family|orwell]], [[Amity family|paramity]], [[Schismatic family|pontiac]], [[Breedsmic temperaments|tertiaseptal]], and [[Würschmidt family|worschmidt]]. | Discussed elsewhere are [[Hemimage temperaments|bisupermajor]], [[Kleismic family|countercata]], [[Mirkwai clan|eris]], [[Escapade family|escaped]], [[Hemimean clan|hemithirds]], [[Diaschismic family|keen]], [[Semicomma family|orwell]], [[Amity family|paramity]], [[Schismatic family|pontiac]], [[Breedsmic temperaments|tertiaseptal]], and [[Würschmidt family|worschmidt]]. | ||
= Mutt = | == Mutt == | ||
{{Main|Mutt temperament}} | {{Main|Mutt temperament}} | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: {{monzo| -44 -3 21 }} | [[Comma list]]: {{monzo| -44 -3 21 }} | ||
| Line 16: | Line 18: | ||
[[Badness]]: 0.162467 | [[Badness]]: 0.162467 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | |||
Comma list: 65625/65536, 250047/250000 | Comma list: 65625/65536, 250047/250000 | ||
| Line 29: | Line 33: | ||
Badness: 0.028406 | Badness: 0.028406 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 4375/4356, 16384/16335 | Comma list: 441/440, 4375/4356, 16384/16335 | ||
| Line 40: | Line 46: | ||
Badness: 0.058344 | Badness: 0.058344 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 364/363, 441/440, 625/624, 2200/2197 | Comma list: 364/363, 441/440, 625/624, 2200/2197 | ||
| Line 51: | Line 59: | ||
Badness: 0.029089 | Badness: 0.029089 | ||
= Fifthplus = | == Fifthplus == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 420175/419904 | [[Comma list]]: 65625/65536, 420175/419904 | ||
| Line 64: | Line 74: | ||
[[Badness]]: 0.025840 | [[Badness]]: 0.025840 | ||
= Emkay = | == Emkay == | ||
Emkay (87&224) tempers out the same 5-limit comma as the [[Hemimean clan #Emka|emka temperament]] (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out. | Emkay (87&224) tempers out the same 5-limit comma as the [[Hemimean clan #Emka|emka temperament]] (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out. | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 244140625/243045684 | [[Comma list]]: 65625/65536, 244140625/243045684 | ||
| Line 79: | Line 91: | ||
[[Badness]]: 0.135696 | [[Badness]]: 0.135696 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3025/3024, 4000/3993, 65625/65536 | Comma list: 3025/3024, 4000/3993, 65625/65536 | ||
| Line 90: | Line 104: | ||
Badness: 0.035586 | Badness: 0.035586 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197 | Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197 | ||
| Line 101: | Line 117: | ||
Badness: 0.017853 | Badness: 0.017853 | ||
= Oquatonic = | == Oquatonic == | ||
The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28. | The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28. | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 390625/388962 | [[Comma list]]: 65625/65536, 390625/388962 | ||
Revision as of 03:43, 2 June 2021
Horwell temperaments temper out the horwell comma, [-16 1 5 1⟩ = 65625/65536.
Discussed elsewhere are bisupermajor, countercata, eris, escaped, hemithirds, keen, orwell, paramity, pontiac, tertiaseptal, and worschmidt.
Mutt
Subgroup: 2.3.5
Comma list: [-44 -3 21⟩
Mapping: [⟨3 5 7], ⟨0 -7 -1]]
POTE generator: ~5/4 = 385.980
Badness: 0.162467
7-limit
Subgroup: 2.3.5.7
Comma list: 65625/65536, 250047/250000
Mapping: [⟨3 5 7 8], ⟨0 -7 -1 12]]
Wedgie: ⟨⟨ 21 3 -36 -44 -116 -92 ]]
POTE generator: ~5/4 = 385.964
Vals: Template:Val list
Badness: 0.028406
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4356, 16384/16335
Mapping: [⟨3 5 7 8 10], ⟨0 -7 -1 12 11]]
POTE generator: ~5/4 = 386.020
Vals: Template:Val list
Badness: 0.058344
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 625/624, 2200/2197
Mapping: [⟨3 5 7 8 10 11], ⟨0 -7 -1 12 11 3]]
POTE generator: ~5/4 = 386.022
Vals: Template:Val list
Badness: 0.029089
Fifthplus
Subgroup: 2.3.5.7
Comma list: 65625/65536, 420175/419904
Mapping: [⟨1 11 -3 20], ⟨0 -23 13 -42]]
Wedgie: ⟨⟨ 23 -13 42 -74 2 134 ]]
POTE generator: ~5488/3645 = 708.774
Badness: 0.025840
Emkay
Emkay (87&224) tempers out the same 5-limit comma as the emka temperament (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out.
Subgroup: 2.3.5.7
Comma list: 65625/65536, 244140625/243045684
Mapping: [⟨1 14 6 -28], ⟨0 -27 -8 67]]
Wedgie: ⟨⟨ 27 8 -67 -50 -182 -178 ]]
POTE generator: ~3125/2268 = 551.7745
Badness: 0.135696
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 65625/65536
Mapping: [⟨1 14 6 -28 3], ⟨0 -27 -8 67 1]]
POTE generator: ~11/8 = 551.7746
Vals: Template:Val list
Badness: 0.035586
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197
Mapping: [⟨1 14 6 -28 3 6], ⟨0 -27 -8 67 1 -5]]
POTE generator: ~11/8 = 551.7749
Vals: Template:Val list
Badness: 0.017853
Oquatonic
The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the hemfiness (4096000/4084101, saquinru-atriyo). In this temperament, major third of 5/4 is mapped into 9\28.
Subgroup: 2.3.5.7
Comma list: 65625/65536, 390625/388962
Mapping: [⟨28 44 65 79], ⟨0 1 0 -1]]
Wedgie: ⟨⟨ 28 0 -28 -65 -123 -65 ]]
POTE generator: ~126/125 = 16.3994
Badness: 0.088286