Jubilismic clan: Difference between revisions
Place high-period temperaments down; fix a formatting glitch |
Databoxes for diminished to lemba |
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<span style="display: block; text-align: right;">[[:de:Verminderte_Temperaturen|Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:Verminderte_Temperaturen|Deutsch]]</span> | ||
{{see also|Dimipent family}} | {{see also|Dimipent family}} | ||
Period: 1\4 | |||
Optimal ([[POTE]]) generator: ~3/2 = 699.523 | |||
EDO generators: [[8edo|5\8]], [[12edo|7\12]], [[16edo|9\16]] | |||
Scales (Scala files): [[diminished12]] | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7 | |||
Comma list: 36/35, 50/49 | Comma list: 36/35, 50/49 | ||
[ | Mapping: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}] | ||
Mapping: | Mapping generators: ~6/5, ~3 | ||
{{Val list|legend=1| 4, 12 }} | {{Val list|legend=1| 4, 8d, 12 }} | ||
Badness: 0.0224 | Badness: 0.0224 | ||
</div></div> | |||
== 11-limit == | == 11-limit == | ||
Period: 1\4 | |||
Optimal ([[POTE]]) generator: ~3/2 = 709.109 | |||
EDO generators: [[12edo|7\12]], [[20edo|12\20]] | |||
Scales (Scala files): [[diminished12]] | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 50/49, 56/55 | Comma list: 36/35, 50/49, 56/55 | ||
[ | Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}] | ||
Mapping: | Mapping generators: ~6/5, ~3 | ||
{{Val list|legend=1| 4, | {{Val list|legend=1| 4, 8d, 12, 32cddee, 44cddeee }} | ||
Badness: 0.0221 | Badness: 0.0221 | ||
</div></div> | |||
=== 13-limit === | === 13-limit === | ||
Period: 1\4 | |||
Optimal ([[POTE]]) generator: ~3/2 = 713.773 | |||
EDO generators: [[12edo|7\12]], [[20edo|12\20]] | |||
Scales (Scala files): [[diminished12]] | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 36/35, 40/39, 50/49, 66/65 | Comma list: 36/35, 40/39, 50/49, 66/65 | ||
Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}] | |||
Mapping: | Mapping generators: ~6/5, ~3 | ||
{{Val list|legend=1| 4, 8d, 12f, 20cdef }} | {{Val list|legend=1| 4, 8d, 12f, 20cdef }} | ||
Badness: 0.0195 | Badness: 0.0195 | ||
</div></div> | |||
== Demolished == | == Demolished == | ||
Period: 1\4 | |||
Optimal ([[POTE]]) generator: ~3/2 = 689.881 | |||
EDO generators: [[12edo|7\12]], [[16edo|9\16]], [[28edo|14\28]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 45/44, 50/49 | Comma list: 36/35, 45/44, 50/49 | ||
Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}] | |||
Mapping: | Mapping generators: ~6/5, ~3 | ||
{{Val list|legend=1| 12, 28, 40de }} | {{Val list|legend=1| 12, 28, 40de }} | ||
Badness: 0.0266 | Badness: 0.0266 | ||
</div></div> | |||
== Hemidim == | == Hemidim == | ||
Period: 1\4 | |||
Optimal ([[POTE]]) generator: ~12/11 = 101.679 | |||
EDO generators: [[12edo|7\12]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 50/49, 125/121 | Comma list: 36/35, 50/49, 125/121 | ||
Mapping: [{{val| 4 1 4 6 6 }}, {{val| 0 2 2 2 3 }}] | |||
Mapping: | Mapping generators: ~6/5, ~11/7 | ||
{{Val list|legend=1| 12 | {{Val list|legend=1| 12 }} | ||
Badness: 0.0550 | Badness: 0.0550 | ||
</div></div> | |||
= Doublewide = | = Doublewide = | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~6/5 = 325.719 | |||
EDO generators: [[22edo|6\22]], [[26edo|7\26]], [[48edo|13\48]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7 | |||
Comma list: 50/49, 875/864 | Comma list: 50/49, 875/864 | ||
Mapping: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}] | Mapping: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}] | ||
{{Val list|legend=1| 18, 22 | {{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }} | ||
Badness: 0.0435 | Badness: 0.0435 | ||
</div></div> | |||
== 11-limit == | == 11-limit == | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~6/5 = 325.548 | |||
EDO generators: [[22edo|6\22]], [[26edo|7\26]], [[48edo|13\48]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 50/49, 99/98, 875/864 | Comma list: 50/49, 99/98, 875/864 | ||
Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}] | Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}] | ||
{{Val list|legend=1| 18, 22, 48, | {{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c, 118cd }} | ||
Badness: 0.0321 | Badness: 0.0321 | ||
</div></div> | |||
== Fleetwood == | == Fleetwood == | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~6/5 = 327.038 | |||
EDO generators: [[22edo|6\22]], [[26edo|7\26]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 50/49, 55/54, 176/175 | Comma list: 50/49, 55/54, 176/175 | ||
Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}] | Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}] | ||
{{Val list|legend=1| 22 | {{Val list|legend=1| 22 }} | ||
Badness: 0.0352 | Badness: 0.0352 | ||
</div></div> | |||
=== 13-limit === | === 13-limit === | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~6/5 = 327.841 | |||
EDO generators: [[18edo|5\18]], [[22edo|6\22]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 50/49, 55/54, 65/63, 176/175 | Comma list: 50/49, 55/54, 65/63, 176/175 | ||
Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}] | Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}] | ||
{{Val list|legend=1| 22, | {{Val list|legend=1| 18e, 22, 84bddf }} | ||
Badness: 0.0318 | Badness: 0.0318 | ||
</div></div> | |||
== Cavalier == | == Cavalier == | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~6/5 = 323.427 | |||
EDO generators: [[22edo|6\22]], [[26edo|7\26]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 45/44, 50/49, 875/864 | Comma list: 45/44, 50/49, 875/864 | ||
Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}] | Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}] | ||
{{Val list|legend=1| 26 }} | {{Val list|legend=1| 22e, 26 }} | ||
Badness: 0.0529 | Badness: 0.0529 | ||
</div></div> | |||
=== 13-limit === | === 13-limit === | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~6/5 = 323.396 | |||
EDO generators: [[22edo|6\22]], [[26edo|7\26]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 45/44, 50/49, 78/77, 325/324 | Comma list: 45/44, 50/49, 78/77, 325/324 | ||
Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}] | Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}] | ||
{{Val list|legend=1| 26 }} | {{Val list|legend=1| 22ef, 26 }} | ||
Badness: 0.0350 | Badness: 0.0350 | ||
</div></div> | |||
= Lemba = | = Lemba = | ||
{{see also|Gamelismic clan #Lemba}} | {{see also|Gamelismic clan #Lemba}} | ||
{{see also|Lemba}} | {{see also|Lemba}} | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~8/7 = 232.089 | |||
EDO generator: [[10edo|2\10]], [[16edo|3\16]], [[26edo|5\26]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7 | |||
Comma list: 50/49, 525/512 | Comma list: 50/49, 525/512 | ||
Mapping: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}] | Mapping: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}] | ||
Line 144: | Line 330: | ||
Badness: 0.0622 | Badness: 0.0622 | ||
</div></div> | |||
== 11-limit == | == 11-limit == | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~8/7 = 230.974 | |||
EDO generators: [[10edo|2\10]], [[16edo|3\16]], [[26edo|5\26]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 45/44, 50/49, 385/384 | Comma list: 45/44, 50/49, 385/384 | ||
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}] | Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}] | ||
Line 155: | Line 356: | ||
Badness: 0.0416 | Badness: 0.0416 | ||
</div></div> | |||
== 13-limit == | == 13-limit == | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generator: ~8/7 = 230.966 | |||
EDO generators: [[10edo|2\10]], [[16edo|3\16]], [[26edo|5\26]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 45/44, 50/49, 65/64, 78/77 | Comma list: 45/44, 50/49, 65/64, 78/77 | ||
Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}] | Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}] | ||
Line 166: | Line 382: | ||
Badness: 0.0255 | Badness: 0.0255 | ||
</div></div> | |||
= Crepuscular = | = Crepuscular = |
Revision as of 17:01, 18 March 2021
The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are identified and the octave is divided in two. Doublewide, lemba and diminished are discussed below; others in the clan are pajara, decimal, injera, octokaidecal, hedgehog, bipelog and hexe, which are discussed elsewhere.
No-threes POTE generator: ~5/4 = 380.840
No-threes mapping: [⟨2 0 1 1], ⟨0 0 1 1]]
Diminished
Period: 1\4
Optimal (POTE) generator: ~3/2 = 699.523
EDO generators: 5\8, 7\12, 9\16
Scales (Scala files): diminished12
Subgroup: 2.3.5.7
Comma list: 36/35, 50/49
Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]
Mapping generators: ~6/5, ~3
Badness: 0.0224
11-limit
Period: 1\4
Optimal (POTE) generator: ~3/2 = 709.109
Scales (Scala files): diminished12
Subgroup: 2.3.5.7.11
Comma list: 36/35, 50/49, 56/55
Mapping: [⟨4 0 3 5 14], ⟨0 1 1 1 0]]
Mapping generators: ~6/5, ~3
Badness: 0.0221
13-limit
Period: 1\4
Optimal (POTE) generator: ~3/2 = 713.773
Scales (Scala files): diminished12
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 40/39, 50/49, 66/65
Mapping: [⟨4 0 3 5 14 15], ⟨0 1 1 1 0 0]]
Mapping generators: ~6/5, ~3
Badness: 0.0195
Demolished
Period: 1\4
Optimal (POTE) generator: ~3/2 = 689.881
EDO generators: 7\12, 9\16, 14\28
Scales (Scala files):
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 50/49
Mapping: [⟨4 0 3 5 -5], ⟨0 1 1 1 3]]
Mapping generators: ~6/5, ~3
Badness: 0.0266
Hemidim
Period: 1\4
Optimal (POTE) generator: ~12/11 = 101.679
EDO generators: 7\12
Scales (Scala files):
Subgroup: 2.3.5.7.11
Comma list: 36/35, 50/49, 125/121
Mapping: [⟨4 1 4 6 6], ⟨0 2 2 2 3]]
Mapping generators: ~6/5, ~11/7
Badness: 0.0550
Doublewide
Period: 1\2
Optimal (POTE) generator: ~6/5 = 325.719
EDO generators: 6\22, 7\26, 13\48
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 50/49, 875/864
Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]
Badness: 0.0435
11-limit
Period: 1\2
Optimal (POTE) generator: ~6/5 = 325.548
EDO generators: 6\22, 7\26, 13\48
Scales (Scala files):
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98, 875/864
Mapping: [⟨2 1 3 4 8], ⟨0 4 3 3 -2]]
Badness: 0.0321
Fleetwood
Period: 1\2
Optimal (POTE) generator: ~6/5 = 327.038
Scales (Scala files):
Subgroup: 2.3.5.7.11
Comma list: 50/49, 55/54, 176/175
Mapping: [⟨2 1 3 4 2], ⟨0 4 3 3 9]]
Badness: 0.0352
13-limit
Period: 1\2
Optimal (POTE) generator: ~6/5 = 327.841
Scales (Scala files):
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 55/54, 65/63, 176/175
Mapping: [⟨2 1 3 4 2 3], ⟨0 4 3 3 9 8]]
Badness: 0.0318
Cavalier
Period: 1\2
Optimal (POTE) generator: ~6/5 = 323.427
Scales (Scala files):
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 875/864
Mapping: [⟨2 1 3 4 1], ⟨0 4 3 3 11]]
Badness: 0.0529
13-limit
Period: 1\2
Optimal (POTE) generator: ~6/5 = 323.396
Scales (Scala files):
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 50/49, 78/77, 325/324
Mapping: [⟨2 1 3 4 1 2], ⟨0 4 3 3 11 10]]
Badness: 0.0350
Lemba
Period: 1\2
Optimal (POTE) generator: ~8/7 = 232.089
EDO generator: 2\10, 3\16, 5\26
Scales (Scala files):
Subgroup: 2.3.5.7
Comma list: 50/49, 525/512
Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]
Badness: 0.0622
11-limit
Period: 1\2
Optimal (POTE) generator: ~8/7 = 230.974
EDO generators: 2\10, 3\16, 5\26
Scales (Scala files):
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 385/384
Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]
Badness: 0.0416
13-limit
Period: 1\2
Optimal (POTE) generator: ~8/7 = 230.966
EDO generators: 2\10, 3\16, 5\26
Scales (Scala files):
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 50/49, 65/64, 78/77
Mapping: [⟨2 2 5 6 5 7], ⟨0 3 -1 -1 5 1]]
Badness: 0.0255
Crepuscular
Comma list: 50/49, 4375/4374
POTE generator: ~27/25 = 140.349
Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]
Wedgie: ⟨⟨ 10 14 14 -1 -6 -7 ]]
Badness: 0.0867
11-limit
Comma list: 50/49, 99/98, 1944/1925
POTE generator: ~12/11 = 140.587
Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]
Badness: 0.0408
13-limit
Comma list: 50/49, 78/77, 99/98, 144/143
POTE generator: ~12/11 = 140.554
Mapping: [⟨2 2 3 4 6 6], ⟨0 5 7 7 4 6]]
Badness: 0.0244
Bipyth
Comma list: 50/49, 20480/19683
POTE generator: ~3/2 = 709.437
Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]
Wedgie: ⟨⟨ 2 18 18 24 23 -9 ]]
Badness: 0.1650
11-limit
Comma list: 50/49, 121/120, 896/891
POTE generator: ~3/2 = 709.310
Mapping: [⟨2 0 -24 -23 -9], ⟨0 1 9 9 5]]
Badness: 0.0709
Elvis
5-limit
Comma list: 36905625/33554432
POTE generator: ~45/32 = 554.546
Mapping: [⟨2 1 10], ⟨0 2 -5]]
Badness: 0.8840
7-limit
Comma list: 50/49, 8505/8192
POTE generator: ~45/32 = 553.721
Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]
Wedgie: ⟨⟨ 4 -10 -10 -25 -27 5 ]]
Badness: 0.1415
11-limit
Comma list: 45/44, 50/49, 1344/1331
POTE generator: ~11/8 = 553.882
Mapping: [⟨2 1 10 11 8], ⟨0 2 -5 -5 -1]]
Badness: 0.0632
13-limit
Comma list: 45/44, 50/49, 78/77, 1053/1024
POTE generator: ~11/8 = 553.892
Mapping: [⟨2 1 10 11 8 16], ⟨0 2 -5 -5 -1 -8]]
Badness: 0.0440
Comic
5-limit
Comma list: 5120000/4782969
POTE generator: ~81/80 = 55.382
Mapping: [⟨2 1 -3], ⟨0 2 7]]
Badness: 0.4912
7-limit
Comma list: 50/49, 2240/2187
POTE generator: ~81/80 = 54.699
Mapping: [⟨2 1 -3 -2], ⟨0 2 7 7]]
Wedgie: <<4 14 14 13 11 -7||
Badness: 0.0844
11-limit
Comma list: 50/49, 99/98, 2662/2625
POTE generator: ~81/80 = 55.184
Mapping: [⟨2 1 -3 -2 -4], ⟨0 2 7 7 10]]
Badness: 0.0451
13-limit
Comma list: 50/49, 65/63, 99/98, 968/945
POTE generator: ~81/80 = 54.435
Mapping: [⟨2 1 -3 -2 -4 3], ⟨0 2 7 7 10 4]]
Badness: 0.0415
Duodecim
Comma list: 36/35, 50/49, 64/63
POTE generator: ~11/8 = 565.023
Mapping: [⟨12 19 28 34 0], ⟨0 0 0 0 1]]
Badness: 0.030536
Vigintiduo
Comma list: 50/49, 64/63, 245/243
POTE generator: ~11/8 = 557.563
Mapping: [⟨22 35 51 62 0], ⟨0 0 0 0 1]]
Badness: 0.0484
Vigin
Comma list: 50/49, 55/54, 64/63, 99/98
POTE generator: ~13/8 = 844.624
Mapping: [⟨22 35 51 62 76 0], ⟨0 0 0 0 0 1]]
Badness: 0.0298