Map of rank-2 temperaments: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
mNo edit summary
Line 1,483: Line 1,483:
|  ||  ||  || 1\60 ||  ||  || 20 ||  
|  ||  ||  || 1\60 ||  ||  || 20 ||  
|-
|-
|  ||  ||  || 1\56 ||  ||  || 21.429 ||
|  ||  ||  || ... ||  ||  || ... ||  
|-
|  ||  ||  || 1\52 ||  ||  || 23.068 ||
|-
|  ||  ||  || 1\48 ||  ||  || 25 ||
|-
|  ||  ||  || 1\44 ||  ||  || 27.273 ||
|-
|  ||  ||  || 1\40 ||  ||  || 30 ||  
|-
|-
|  ||  ||  || 1\36 ||  ||  || 33.333 ||  
|  ||  ||  || 1\36 ||  ||  || 33.333 ||  
Line 2,024: Line 2,016:
|-
|-
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|1\25
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|
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|2\55
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|
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Line 2,032: Line 2,024:
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|43.636
|48
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|-
|-
|1\20
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|1\25
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Line 2,044: Line 2,036:
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|48
|60
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|-
|-
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|2\35
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|3\70
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Line 2,056: Line 2,047:
|
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|51.429
|
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|68.571
|[[Coblack]]
|-
|-
|
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|2\45
|
|
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|5\85
|
|
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|53.3
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|70.588
|Coblack
|-
|-
|
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|3\50
|
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|3\65
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Line 2,080: Line 2,072:
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|55.385
|72
|
|Coblack
|-
|-
|1\20
|
|
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|7\115
|
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|60
|73.043
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|Coblack
|-
|-
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|4\75
|4\65
|
|
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Line 2,104: Line 2,096:
|
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|64
|73.846
|Coblack
|-
| 1\15 ||  ||  ||
|
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| || 80||[[Blackwood]]/[[Blacksmith]]
|-
|-
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|3\55
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|5\70
|
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Line 2,116: Line 2,115:
|
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|65.455
|85.714
|
|Blackwood/Blacksmith
|-
|-
|
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|4\55
|
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|5\90
|
|
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|
Line 2,128: Line 2,127:
|
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|66.667
|87.273
|
|Blackwood/Blacksmith
|-
|-
|
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|2\35
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|7\95
|
|
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Line 2,140: Line 2,139:
|
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|68.571
|88.421
|[[Coblack]]
|Blackwood/Blacksmith
|-
|-
|
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|3\40
|
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|5\85
|
|
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Line 2,152: Line 2,151:
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|70.588
|90
|Coblack
|Blackwood/Blacksmith
|-
|-
|
|
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|3\50
|
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|8\105
|
|
|
|
Line 2,164: Line 2,163:
|
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|72
|91.429
|Coblack
|Blackwood/Blacksmith
|-
|-
|
|
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|5\65
|
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|7\115
|
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|73.043
|92.308
|Coblack
|Blackwood/Blacksmith
|-
|-
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|4\65
|7\90
|
|
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Line 2,188: Line 2,187:
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|73.846
|93.333
|Coblack
|Blackwood/Blacksmith
|-
| 1\15 ||  ||  ||
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| || 80||[[Blackwood]]/[[Blacksmith]]
|-
|-
|2\25
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|5\70
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Line 2,207: Line 2,199:
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|85.714
|96
|Blackwood/Blacksmith
|Blackwood/Blacksmith
|-
|-
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|4\55
|5\60
|
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Line 2,219: Line 2,211:
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|87.273
|100
|Blackwood/Blacksmith
|Blackwood
|-
|-
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|7\95
|8\95
|
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Line 2,231: Line 2,223:
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|88.421
|101.053
|Blackwood/Blacksmith
|Blackwood
|-
|-
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|3\40
|3\35
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Line 2,243: Line 2,235:
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|90
|102.857
|Blackwood/Blacksmith
|Blackwood
|-
|-
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|8\105
|7\80
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Line 2,255: Line 2,247:
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|91.429
|105
|Blackwood/Blacksmith
|Blackwood
|-
|-
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|5\65
|4\45
|
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Line 2,267: Line 2,259:
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|92.308
|106.667
|Blackwood/Blacksmith
|Blackwood
|-
|-
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|7\90
|5\55
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Line 2,279: Line 2,271:
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|93.333
|109.091
|Blackwood/Blacksmith
|Blackwood
|-
|-
|2\25
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|6\65
|
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|96
|110.769
|Blackwood/Blacksmith
|Blackwood/[[Quintosec]]/[[Sengasec]]
|-
|-
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|5\60
|
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Line 2,303: Line 2,294:
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|100
|25\270
|Blackwood
|111.111
|Blackwood/Quintosec/Sengasec/[[Qintosec]]
|-
|-
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|8\95
|
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|19\205
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|101.053
|111.220
|Blackwood
|Blackwood/Quintosec/SengasecQintosec
|-
|-
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|3\35
|
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Line 2,325: Line 2,316:
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|13\140
|
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|102.857
|111.429
|Blackwood
|Blackwood/Quintosec/Sengasec/Qintosec
|-
|-
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|7\80
|
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|20\215
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|105
|111.628
|Blackwood
|Blackwood/Qintosec
|-
|-
|
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|4\45
|
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|7\75
|
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|106.667
|112
|Blackwood
|Blackwood/[[Qinto]]
|-
|-
|
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|5\55
|
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|15\160
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|109.091
|112.5
|Blackwood
|Blackwood/Qinto
|-
|-
|
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Line 2,370: Line 2,362:
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|6\65
|
|
|
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|8\85
|
|
|
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|110.769
|112.941
|Blackwood/[[Quintosec]]/[[Sengasec]]
|Blackwood/[[Phi as a Generator|Elderthing]]
|-
|-
|
|
Line 2,384: Line 2,376:
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|9\95
|
|
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|25\270
|113.684
|111.111
|Blackwood
|Blackwood/Quintosec/Sengasec/[[Qintosec]]
|-
|-
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Line 2,396: Line 2,388:
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|10\105
|
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|19\205
|
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|111.220
|114.286
|Blackwood/Quintosec/SengasecQintosec
|Blackwood
|-
|-
|1\10
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Line 2,408: Line 2,401:
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|13\140
|
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|111.429
|120
|Blackwood/Quintosec/Sengasec/Qintosec
|Blackwood
|-
|}
 
==Six periods per octave ==
{| class="wikitable"
! colspan="7" |Generator!!Cents !!Comments
|-
|0\6||  || ||
|
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|
|||0||
|-
|
|
|
|
|
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|1\288
|
|
|
|
|
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|20\215
|4.167
|
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|111.628
|Blackwood/Qintosec
|-
|-
|
|
|
|
|
|
|1\282
|
|
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|7\75
|
|
|
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|4.255
|
|
|112
|Blackwood/[[Qinto]]
|-
|-
|
|
|
|
|
|
|1\276
|2\552
|
|
|
|
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|4.348
|
|[[Sextile]]
|15\160
|
|112.5
|Blackwood/Qinto
|-
|-
|
|
Line 2,454: Line 2,450:
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|3\822
|
|4.380
|Sextile
|-
|
|
|
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|8\85
|
|
|
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|112.941
|Blackwood/[[Phi as a Generator|Elderthing]]
|-
|
|
|
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|4\1092
|4.396
|Sextile
|-
|
|
|
|
|
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|1\270
|
|
|9\95
|
|
|
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|113.684
|4.444
|Blackwood
|Sextile
|-
|-
|
|
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|1\264
|
|
|
|
|
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|4.545
|
|
|10\105
|-
|
|
|
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|114.286
|Blackwood
|-
|1\10
|
|
|...
|
|
|
|
|
|
|...
|
|
|-
|
|
|
|
|
|
|120
|1\90
|Blackwood
|
|}
|
 
==Six periods per octave ==
{| class="wikitable"
! colspan="7" |Generator!!Cents !!Comments
|-
|0\6||  || ||  
|
|
|13.333
|
|
|||0||
|-
|-
|
|
|
|
|
|
|1\288
|1\84
|
|
|
|
|
|
|4.167
|14.286
|
|
|-
|-
Line 2,521: Line 2,519:
|
|
|
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|1\282
|1\78
|
|
|
|
|
|
|4.255
|15.385
|
|
|-
|-
Line 2,531: Line 2,529:
|
|
|
|
|1\276
|1\72
|2\552
|
|
|
|
|
|4.348
|16.667
|[[Sextile]]
|[[Stearnscape]]
|-
|-
|
|
Line 2,543: Line 2,541:
|
|
|
|
|3\822
|
|
|4.380
|4\282
|Sextile
|17.021
|Stearnscape
|-
|-
|
|
Line 2,553: Line 2,551:
|
|
|
|
|3\210
|
|
|4\1092
|17.143
|4.396
|Stearnscape
|Sextile
|-
|-
|
|
|
|
|
|
|1\270
|
|2\138
|
|
|
|
|17.391
|
|
|4.444
|Sextile
|-
|-
|
|
|
|
|
|
|1\264
|1\66
|
|
|
|
|
|
|4.545
|18.182
|
|
|-
|-
Line 2,581: Line 2,579:
|
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|
|
|...
|1\60
|
|
|
|
|
|
|...
|20
|
|
|-
|-
Line 2,591: Line 2,589:
|
|
|
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|1\90
|1\54
|
|
|
|
|
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|13.333
|22.222
|
|
|-
|-
Line 2,601: Line 2,599:
|
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|
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|1\84
|1\48
|
|
|
|
|
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|14.286
|25
|
|
|-
|-
Line 2,611: Line 2,609:
|
|
|
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|1\78
|1\42
|
|
|
|
|
|
|15.385
|28.571
|
|
|-
|-
Line 2,621: Line 2,619:
|
|
|
|
|1\72
|1\36
|
|
|
|
|
|33.333
|
|
|16.667
|[[Stearnscape]]
|-
|-
|
|
|
|1\30
|
|
|
|
|
|
|
|
|40
|
|
|4\282
|17.021
|Stearnscape
|-
|-
|
|
|1\24
|
|
|
|
|
|
|
|
|3\210
|
|
|17.143
|50
|Stearnscape
|  
|-
|-
|1\18
|
|
|
|
|
|
|
|
|2\138
|
|
|
|
|17.391
| 66.667
|
|
|-
|-
|
|
|2\30
|
|
|
|
|1\66
|
|
|
|
|
|
|18.182
| 80
|
|[[Hexe]]
|-
|-
|
|
|
|
|
|
|1\60
|5\72
|
|
|
|
|
|
|20
|83.333
|
|Hexe
|-
|-
|
|
|
|
|3\42
|
|
|1\54
|
|
|
|
|
|
|22.222
|85.714
|
| Hexe
|-
|-
|
|
|
|
|
|
|1\48
|4\54
|
|
|
|
|
|
|25
|88.889
|
|Hexe
|-
|-
|1\12
|
|
|
|
|
|
|1\42
|
|
|
|
|
|
|28.571
| 100
|
|Hexe
|}
==Seven periods per octave==
{{todo|complete table|comment=add akjaysmic (optimal ETs 140, 224, 301), nitrogen (140, 1407, 1547) and brahmagupta (217, 224, 441, 665)}}
{| class="wikitable"
! colspan="8" |Generator!! Cents!!Comments
|-
|-
| 0\7||  || ||
|
|
|
|
|
|
|1\36
| ||0||
|-
|
|
|
|
|
|
|33.333
|
|1\91
|
|
|
|13.187
|
|
|-
|-
|
|
|
|
|1\30
|
|
|
|
|1\84
|
|
|
|
|40
|
|
|14.286
|[[Absurdity]]
|-
|-
|
|
|
|
|
|
|2\54
|
|
|
|
|
|
|44.444
|
|
|4\329
|14.59
|Absurdity
|-
|-
|
|
|1\24
|
|
|
|
Line 2,745: Line 2,756:
|
|
|
|
|50
|3\245
|  
|
|14.69
|
|-
|-
|
|
|
|
|
|
|3\66
|
|
|
|2\161
|
|
|
|
|54.545
|14.907
|
|
|-
|-
|
|
|
|
|2\42
|
|
|
|
|1\77
|
|
|
|
| 57.143
|
|
|15.584
|[[Septant]]
|-
|-
|
|
|
|
|
|
|3\60
|
|
|
|
|
|
|60
|
|
|4\301
|15.947
|Septant
|-
|-
|1\18
|
|
|
|
Line 2,785: Line 2,800:
|
|
|
|
| 66.667
|3\224
|
|
|16.071
|Septant
|-
|-
|
|
|
|
|
|
|4\66
|
|
|
|
|2\147
|
|
|72.727
|
|
|16.327
|Septant
|-
|-
|
|
|
|
|3\48
|
|
|1\70
|
|
|
|
|
|
|17.143
|
|
| 75
|
|-
|-
|
|
|
|
|
|
|5\78
|
|
|1\63
|
|
|
|
|76.923
|
|
|19.048
|[[Sevond]]
|-
|-
|
|
|2\30
|
|
|
|
|
|
|
|2\119
|
|
|
|
| 80
|20.168
|[[Hexe]]
|Sevond
|-
|-
|
|
|
|
|
|
|5\72
|
|1\56
|
|
|
|
|
|
|83.333
|21.429
|Hexe
|Sevond
|-
|-
|
|
|
|
|3\42
|
|
|
|1\49
|
|
|
|
|
|
|85.714
|24.49
| Hexe
|
|-
|-
|
|
|
|
|
|
|4\54
|1\42
|
|
|
|
|
|
|
|88.889
|28.571
|Hexe
|[[Mistismic temperaments#Neutron|Neutron]]
|-
|-
|1\12
|
|
|
|
|
|
|
|
|
|3\119
|
|
|
|
| 100
|30.252
|Hexe
|Neutron
|}
==Seven periods per octave==
{{todo|complete table|comment=add akjaysmic (optimal ETs 140, 224, 301), nitrogen (140, 1407, 1547) and brahmagupta (217, 224, 441, 665)}}
{| class="wikitable"
! colspan="8" |Generator!! Cents!!Comments
|-
|-
| 0\7||  || ||
|
|
|
|
|
|
| ||0||
|-
|
|
|
|
|
|
|5\196
|
|
|1\91
|30.612
|Neutron
|-
|
|
|
|
|
|
|13.187
|
|
|
|
|
|7\273
|30.769
|Neutron
|-
|-
|
|
Line 2,894: Line 2,919:
|
|
|
|
|1\84
|2\77
|
|
|
|
|
|
|14.286
|31.169
|[[Absurdity]]
|Neutron
|-
|-
|
|
|
|
|1\35
|
|
|
|
Line 2,908: Line 2,934:
|
|
|
|
|4\329
|34.286
|14.59
|[[Whitewood family#Redwood|Redwood]]
|Absurdity
|-
|-
|
|
|
|
|
|
| 2\63
|
|
|
|
|
|
|3\245
|
|14.69
|
|
|38.095
|Redwood
|-
|-
|
|
| 1\28
|
|
|
|
|
|
|
|
|2\161
|
|
|
|
|14.907
|42.857
|
|Redwood/[[Whitewood]]
|-
|-
|
|
|
|
|
|
| 3\77
|
|
|1\77
|
|
|
|
|
|
|15.584
| 46.753
|[[Septant]]
|Whitewood
|-
|-
|
|
|
|
|2\49
|
|
|
|
Line 2,952: Line 2,978:
|
|
|
|
|4\301
|48.980
|15.947
|Whitewood
|Septant
|-
|-
|
|
|
|
|
|
|3\70
|
|
|
|
|
|
|3\224
|
|
|16.071
| 51.429
|Septant
|Whitewood
|-
|-
|1\21
|
|
|
|
Line 2,972: Line 2,998:
|
|
|
|
|2\147
|
|
|
|
|16.327
|57.143
|Septant
|Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
|-
|-
|
|
|
|
|
|
|
| 4\77
|1\70
|
|
|
|
|
|
|17.143
|
|
|62.338
|Jamesbond/Septimal
|-
|-
|
|
|
|
|3\56
|
|
|
|
|1\63
|
|
|
|
|
|
|19.048
|64.286
|[[Sevond]]
| Jamesbond/Septimal
|-
|-
|
|
|
|
|
|
|5\91
|
|
|
|
|2\119
|
|
|
|
|20.168
|65.934
|Sevond
|Jamesbond/Septimal
|-
|-
|
|
|2\35
|
|
|
|
|
|
|1\56
|
|
|
|
|
|
|21.429
| 68.571
|Sevond
|Jamesbond/Septimal/[[Greenwood]]
|-
|-
|
|
|
|
|
|
|
|5\84
|1\49
|
|
|
|
|
|
|24.49
|
|
|71.429
|Jamesbond/Septimal/Greenwood
|-
|-
|
|
|
|
|3\49
|
|
|1\42
|
|
|
|
|
|
|
|
|28.571
| 73.469
|[[Mistismic temperaments#Neutron|Neutron]]
|Jamesbond/Septimal/Greenwood
|-
|-
|
|
|
|
|
|
|4\63
|
|
|
|
|3\119
|
|
|
|
|30.252
|76.190
|Neutron
|Jamesbond/Septimal/Greenwood
|-
|-
| 1\14
|
|
|
|
Line 3,061: Line 3,087:
|
|
|
|
|5\196
|
|
|30.612
|85.714
|Neutron
|Jamesbond/Septimal/Greenwood
|}
 
==Eight periods per octave==
{{todo|complete table|comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable"
! colspan="9" |Generator!!Cents!!Comments
|-
|-
|0\8||  ||
|
|
|
|
Line 3,071: Line 3,103:
|
|
|
|
| ||0||
|-
|
|
|
|
|7\273
|30.769
|Neutron
|-
|
|
|
|
|
|
|
|
|2\77
|1\80
|
|
|
|
|15
|
|
|31.169
|Neutron
|-
|-
|
|
|
|
|1\35
|
|
|
|
Line 3,096: Line 3,124:
|
|
|
|
|34.286
|2\152
|[[Whitewood family#Redwood|Redwood]]
|
|15.789
|[[Octoid]]
|-
|-
|
|
|
|
|
|
| 2\63
|
|
|
|
|
|
|
|
|38.095
|
|Redwood
|3\224
|16.071
|Octoid
|-
|-
|
|
| 1\28
|
|
|
|
|
|
|
|1\72
|
|
|
|
|
|
|42.857
|16.667
|Redwood/[[Whitewood]]
|Octoid
|-
|-
|
|
|
|
|
|
| 3\77
|
|1\64
|
|
|
|
|
|
|
|18.75
|
|
| 46.753
|Whitewood
|-
|-
|
|
|
|
|2\49
|
|1\56
|
|
|
|
|
|
|
|
|
|21.429
|
|
|48.980
|Whitewood
|-
|-
|
|
|
|1\48
|
|
|
|
|3\70
|
|
|
|
|
|
|
|
| 51.429
|25
|Whitewood
|
|-
|-
|1\21
|
| 1\40
|
|
|
|
|
Line 3,161: Line 3,198:
|
|
|
|
|30
|
|
|57.143
|Whitewood/[[Jamesbond]]/[[7th-octave temperaments#Septimal|Septimal]]
|-
|-
|
|
|2\72
|
|
|
|
|
|
| 4\77
|
|
|
|
|
|
|33.333
|
|
|62.338
|Jamesbond/Septimal
|-
|-
|1\32
|
|
|
|
|
|3\56
|
|
|
|
Line 3,184: Line 3,222:
|
|
|
|
|64.286
|37.5
| Jamesbond/Septimal
|[[Semidim]]
|-
|-
|
|
|
|3\88
|
|
|
|
|5\91
|
|
|
|
|
|
|
|
|65.934
|40.909
|Jamesbond/Septimal
|Semidim
|-
|-
|
|
|2\35
|2\56
|
|
|
|
Line 3,206: Line 3,245:
|
|
|
|
| 68.571
|
|Jamesbond/Septimal/[[Greenwood]]
|42.857
|Semidim
|-
|-
|
|
|
|3\80
|
|
|
|
|5\84
|
|
|
|
|
|
|
|
|71.429
|45
|Jamesbond/Septimal/Greenwood
|Semidim
|-
|-
|
|
|
|
|3\49
|
|4\104
|
|
|
|
Line 3,228: Line 3,270:
|
|
|
|
| 73.469
|46.154
|Jamesbond/Septimal/Greenwood
|Semidim
|-
|-
|
|
|
|
|
|
|4\63
|
|5\128
|
|
|
|
|
|
|
|
|76.190
|46.875
|Jamesbond/Septimal/Greenwood
|Semidim
|-
|-
| 1\14
|
|
|
|
|
|
|
|
|
|6\152
|
|
|
|
|
|
|85.714
|47.368
|Jamesbond/Septimal/Greenwood
|Semidim
|}
 
==Eight periods per octave==
{{todo|complete table|comment=Add Twilight temperament (optimal ETs 152, 328, 480, 808) and Octium temperament (472, 1400, 1872)}}
{| class="wikitable"
! colspan="9" |Generator!!Cents!!Comments
|-
|-
|0\8||  ||
|
|
|
|
Line 3,265: Line 3,302:
|
|
|
|
| ||0||
|
|7\176
|
|
|47.727
|Semidim
|-
|-
|
|
Line 3,273: Line 3,315:
|
|
|
|
|1\80
|8\200
|
|
|
|
|15
|48
|
|Semidim
|-
|-
|
|
Line 3,285: Line 3,327:
|
|
|
|
|9\224
|
|
|2\152
|
|
|15.789
|48.214
|[[Octoid]]
|Semidim/[[Octant]]
|-
|-
|
|
Line 3,299: Line 3,341:
|
|
|
|
|3\224
|28\696
|16.071
|48.276
|Octoid
|Semidim/Octant
|-
|-
|
|
Line 3,308: Line 3,350:
|
|
|
|
|1\72
|
|
|
|
|19\472
|
|
|16.667
|48.305
|Octoid
|Semidim/Octant
|-
|-
|
|
|
|
|
|
|
|1\64
|
|
|
|
|
|
|10\248
|
|
|18.75
|
|
|48.387
|Semidim
|-
|-
|1\24
|
|
|
|
|
|
|1\56
|
|
|
|
Line 3,336: Line 3,378:
|
|
|
|
|21.429
|50
|
|Semidim
|-
|-
|2\40
|
|
|
|
|1\48
|
|
|
|
Line 3,348: Line 3,390:
|
|
|
|
|25
| 60
|
|-
|
| 1\40
|
|
|
|
|
|
|
|30
|
|-
|
|
|2\72
|
|
|
|
|
|
|33.333
|
|-
|1\32
|
|
|
|
|
|
|
|
|37.5
|[[Semidim]]
|-
|
|
|3\88
|
|
|
|
|
|
|40.909
|Semidim
|-
|
|2\56
|
|
|
|
|
|
|
|42.857
|Semidim
|-
|
|
|3\80
|
|
|
|
|
|
|45
|Semidim
|-
|
|
|
|4\104
|
|
|
|
|
|46.154
|Semidim
|-
|
|
|
|
|5\128
|
|
|
|
|46.875
|Semidim
|-
|
|
|
|
|
|6\152
|
|
|
|47.368
|Semidim
|-
|
|
|
|
|
|
|7\176
|
|
|47.727
|Semidim
|-
|
|
|
|
|
|
|8\200
|
|
|48
|Semidim
|-
|
|
|
|
|
|
|9\224
|
|
|48.214
|Semidim/[[Octant]]
|-
|
|
|
|
|
|
|
|
|28\696
|48.276
|Semidim/Octant
|-
|
|
|
|
|
|
|
|19\472
|
|48.305
|Semidim/Octant
|-
|
|
|
|
|
|
|10\248
|
|
|48.387
|Semidim
|-
|1\24
|
|
|
|
|
|
|
|
|50
|Semidim
|-
|
|
|4\88
|
|
|
|
|
|
|54.545
|
|-
|
| 3\64
|
|
|
|
|
|
|
| 56.250
|
|-
|
|
|5\104
|
|
|
|
|
|
|57.692
|
|-
|2\40
|
|
|
|
|
|
|
|
| 60
|
|-
|
|
|5\96
|
|
|
|
|
|
|62.5
|
|-
|
|3\56
|
|
|
|
|
|
|
|64.286
|
|-
|
|
|4\72
|
|
|
|
|
|
|66.667
|
|
|-
|-
Line 3,725: Line 3,491:
|
|
|26.667
|26.667
|
|-
|
|
|2\81
|
|
|
|
|
|29.63
|
|
|-
|-
Line 3,913: Line 3,668:
|53.333
|53.333
|  
|  
|-
|
|
|5\108
|
|
|
|
|
|55.556
|
|-
|
|3\63
|
|
|
|
|
|
|57.143
|
|-
|
|
|4\81
|
|
|
|
|
|59.259
|
|-
|-
|1\18
|1\18