Jubilismic clan: Difference between revisions

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Place high-period temperaments down; fix a formatting glitch
Databoxes for diminished to lemba
Line 10: Line 10:
<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


[[POTE generator]]: ~3/2 = 699.523
Mapping: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}]


Mapping: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}]
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


[[POTE generator]]: ~3/2 = 709.109
Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]


Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]
Mapping generators: ~6/5, ~3


{{Val list|legend=1| 4, 8, 12, 44 }}
{{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


POTE generator: ~3/2 = 713.773
Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]


Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]
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


POTE generator: ~3/2 = 689.881
Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]


Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]
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


POTE generator: ~12/11 = 101.679
Mapping: [{{val| 4 1 4 6 6 }}, {{val| 0 2 2 2 3 }}]


Mapping: [{{val| 4 1 4 6 6 }}, {{val| 0 2 2 2 3 }}]
Mapping generators: ~6/5, ~11/7


{{Val list|legend=1| 12, 20b }}
{{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
[[POTE generator]]: ~6/5 = 325.719


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, 26, 48, 70c }}
{{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
[[POTE generator]]: ~6/5 = 325.548


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, 70, 118cd }}
{{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
POTE generator: ~6/5 = 327.038


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, 26e }}
{{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
POTE generator: ~6/5 = 327.841


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, 84bdf }}
{{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
POTE generator: ~6/5 = 323.427


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
POTE generator: ~6/5 = 323.396


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
[[POTE generator]]: ~8/7 = 232.089


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
POTE generator: ~8/7 = 230.974


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
POTE generator: ~8/7 = 230.966


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]]

Template:Val list

Diminished

Deutsch

Period: 1\4

Optimal (POTE) generator: ~3/2 = 699.523

EDO generators: 5\8, 7\12, 9\16

Scales (Scala files): diminished12

Technical data

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

Template:Val list

Badness: 0.0224

11-limit

Period: 1\4

Optimal (POTE) generator: ~3/2 = 709.109

EDO generators: 7\12, 12\20

Scales (Scala files): diminished12

Technical data

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

Template:Val list

Badness: 0.0221

13-limit

Period: 1\4

Optimal (POTE) generator: ~3/2 = 713.773

EDO generators: 7\12, 12\20

Scales (Scala files): diminished12

Technical data

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

Template:Val list

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):

Technical data

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

Template:Val list

Badness: 0.0266

Hemidim

Period: 1\4

Optimal (POTE) generator: ~12/11 = 101.679

EDO generators: 7\12

Scales (Scala files):

Technical data

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

Template:Val list

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):

Technical data

Subgroup: 2.3.5.7

Comma list: 50/49, 875/864

Mapping: [2 1 3 4], 0 4 3 3]]

Template:Val list

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):

Technical data

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]]

Template:Val list

Badness: 0.0321

Fleetwood

Period: 1\2

Optimal (POTE) generator: ~6/5 = 327.038

EDO generators: 6\22, 7\26

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0352

13-limit

Period: 1\2

Optimal (POTE) generator: ~6/5 = 327.841

EDO generators: 5\18, 6\22

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0318

Cavalier

Period: 1\2

Optimal (POTE) generator: ~6/5 = 323.427

EDO generators: 6\22, 7\26

Scales (Scala files):

Technical data

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]]

Template:Val list

Badness: 0.0529

13-limit

Period: 1\2

Optimal (POTE) generator: ~6/5 = 323.396

EDO generators: 6\22, 7\26

Scales (Scala files):

Technical data

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]]

Template:Val list

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):

Technical data

Subgroup: 2.3.5.7

Comma list: 50/49, 525/512

Mapping: [2 2 5 6], 0 3 -1 -1]]

Template:Val list

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):

Technical data

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]]

Template:Val list

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):

Technical data

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]]

Template:Val list

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 ]]

Template:Val list

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]]

Template:Val list

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]]

Template:Val list

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]]

Template:Val list

Badness: 0.0709

Elvis

5-limit

Comma list: 36905625/33554432

POTE generator: ~45/32 = 554.546

Mapping: [2 1 10], 0 2 -5]]

Template:Val list

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 ]]

Template:Val list

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]]

Template:Val list

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]]

Template:Val list

Badness: 0.0440

Comic

5-limit

Comma list: 5120000/4782969

POTE generator: ~81/80 = 55.382

Mapping: [2 1 -3], 0 2 7]]

Template:Val list

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||

Template:Val list

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]]

Template:Val list

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]]

Template:Val list

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]]

Template:Val list

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]]

Template:Val list

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]]

Template:Val list

Badness: 0.0298