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User:FloraC/Sandbox: Difference between revisions

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== 7-Limit Intervals ==
== Proposed temperaments ==
7-limit, 81-odd-limit intervals.
=== A 7-limit rank-3 family (80 & 94 & 118) ===
{| class="wikitable"
Comma: 4802000/4782969
! colspan="2" |Interval Class
 
! colspan="2" |Wa Intervals
=== A 13-limit rank-3 temperament (87 & 94 & 111) ===
! colspan="2" |Yo/Gu Intervals
Comma: 352/351, 847/845, 14641/14580
! colspan="2" |Zo/Ru Intervals
 
! colspan="2" |Ruyo/Zogu Intervals
=== A 13-limit rank-4 temperament (41 & 46 & 53 & 58) ===
! colspan="2" |Yoyo/Gugu Intervals
Comma: 352/351, 847/845
! colspan="2" |Zozo/Ruru Intervals
! colspan="2" |Zoyo/Rugu Intervals
! colspan="2" |Biruyo/Bizogu Intervals
|-
!Traditional Name
!Fifth steps
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
|-
| Negative diminshed 2nd
| +12
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|50/49
|34.976
|-
|Perfect 1sn
|0
|1/1
|0
|81/80
|21.506
|64/63
|27.264
|
|
|
|
|
|
|36/35
|48.770
|
|
|-
|Augmented 1sn
| +7
|
|
|
|
|
|
|15/14
|119.443
|25/24
|70.672
|54/49
|168.213
|
|
|
|
|-
|Minor 2nd
| -5
|
|
|16/15
|111.731
|28/27
|62.961
|21/20
|84.467
|27/25
|133.238
|49/48
|35.697
|
|
|
|
|-
|Major 2nd
| +2
|9/8
|203.910
|10/9
|182.404
|8/7
|231.174
|
|
|
|
|
|
|81/70
|252.680
|
|
|-
|Augmented 2nd
| +9
|
|
|
|
|
|
|
|
|75/64
|274.582
|
|
|
|
|
|
|-
|Minor 3rd
| -3
|32/27
|294.135
|6/5
|315.641
|7/6
|266.871
|
|
|
|
|
|
|
|
|
|
|-
|Major 3rd
| +4
|81/64
|407.820
|5/4
|386.313
|9/7
|435.084
|80/63
|413.578
|
|
|64/49
|462.348
|
|
|
|
|-
|Diminished 4th
| -8
|
|
|
|
|
|
|56/45
|378.602
|32/25
|427.373
|
|
|
|
|
|
|-
|Perfect 4th
| -1
|4/3
|498.045
|27/20
|519.551
|21/16
|470.781
|
|
|
|
|
|
|35/27
|449.275
|
|
|-
|Augmented 4th
| +6
|
|
|45/32
|590.224
|81/56
|638.994
|10/7
|617.488
|
|
|
|
|
|
|
|
|-
|Diminshed 5th
| -6
|
|
|64/45
|609.776
|112/81
|561.006
|7/5
|582.512
|
|
|
|
|
|
|
|
|-
|Perfect 5th
| +1
|3/2
|701.955
|40/27
|680.449
|32/21
|729.219
|
|
|
|
|
|
|54/35
|750.725
|
|
|-
|Augmented 5th
| +8
|
|
|
|
|
|
|45/28
|821.398
|25/16
|772.627
|
|
|
|
|
|
|-
|Minor 6th
| -4
|128/81
|792.180
|8/5
|813.687
|14/9
|764.916
|63/40
|786.422
|
|
|49/32
|737.652
|
|
|
|
|-
|Major 6th
| +3
|27/16
|905.865
|5/3
|884.339
|12/7
|933.129
|
|
|
|
|
|
|
|
|
|
|-
|Diminished 7th
| -9
|
|
|
|
|
|
|
|
|128/75
|925.418
|
|
|
|
|
|
|-
|Minor 7th
| -2
|16/9
|996.090
|9/5
|1017.596
|7/4
|968.826
|
|
|
|
|
|
|140/81
|947.320
|
|
|-
|Major 7th
| +5
|
|
|15/8
|1088.269
|27/14
|1131.039
|40/21
|1115.533
|50/27
|1066.762
|96/49
|1164.303
|
|
|
|
|-
|Diminished 8ve
| -7
|
|
|
|
|
|
|28/15
|1080.557
|48/25
|1129.328
|49/27
|1031.787
|
|
|
|
|-
|Perfect 8ve
|0
|2/1
|1200
|160/81
|1178.494
|63/32
|1172.736
|
|
|
|
|
|
|35/18
|1151.230
|
|
|-
|Diminished 9th
| -12
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|49/25
|1165.028
|}
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