User:FloraC/Sandbox: Difference between revisions

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== 7-Limit Intervals ==
7-limit, 81-odd-limit intervals.
{| class="wikitable"
! colspan="2" |Interval Class
! colspan="2" |Wa Intervals
! colspan="2" |Yo/Gu Intervals
! colspan="2" |Zo/Ru Intervals
! colspan="2" |Ruyo/Zogu Intervals
! colspan="2" |Yoyo/Gugu Intervals
! colspan="2" |Zozo/Ruru Intervals
! colspan="2" |Zoyo/Rugu Intervals
! colspan="2" |Biruyo/Bizogu Intervals
|-
!Traditional Name
!Fifthspan
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
|-
| ?
| +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
|
|
|
|
|
|
|
|
|
|
|-
|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
|
|
|
|
|
|
|
|
|
|
|-
|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
|}
== Intervals of 87edo ==
== Intervals of 87edo ==
{| class="wikitable"
{| class="wikitable right-2 right-4"
!
!#
!Cents
!Cents
!Approximated Ratios
!Approximated Ratios
Line 182: Line 633:
|-
|-
|29
|29
|400
|400.000
|63/50, 44/35
|63/50, 44/35
|vF#
|vF#

Revision as of 13:02, 2 June 2020

7-Limit Intervals

7-limit, 81-odd-limit intervals.

Interval Class Wa Intervals Yo/Gu Intervals Zo/Ru Intervals Ruyo/Zogu Intervals Yoyo/Gugu Intervals Zozo/Ruru Intervals Zoyo/Rugu Intervals Biruyo/Bizogu Intervals
Traditional Name Fifthspan Ratio Cent Ratio Cent Ratio Cent Ratio Cent Ratio Cent Ratio Cent Ratio Cent Ratio Cent
? +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
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
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

Intervals of 87edo

# Cents Approximated Ratios Ups and Downs Notation Solfege
0 0.000 1/1 D
1 13.793 126/125, 100/99, 91/90 ^D
2 27.586 81/80, 64/63, 49/48, 55/54, 65/64 ^^D
3 41.379 50/49, 45/44 ^^^D/vvvEb
4 55.172 28/27, 36/35, 33/32 vvEb
5 68.966 25/24, 27/26, 26/25 vEb
6 82.759 21/20, 22/21 Eb
7 96.552 35/33 ^Eb
8 110.345 16/15 ^^Eb
9 124.138 15/14, 14/13 ^^^Eb
10 137.931 13/12 ^^^^Eb
11 151.724 12/11 vvvvE
12 165.517 11/10 vvvE
13 179.310 10/9 vvE
14 193.103 28/25 vE
15 206.897 9/8 E
16 220.690 25/22 ^E
17 234.483 8/7 ^^E
18 248.276 15/13 ^^^E/vvvF
19 262.089 7/6 vvF
20 275.862 75/64 vF
21 289.655 33/28, 13/11 F
22 303.448 25/21, 105/88 ^F
23 317.241 6/5 ^^F
24 331.034 63/52 ^^^F
25 344.828 11/9, 39/32 ^^^^F
26 358.621 27/22, 16/13 vvvvF#
27 372.414 26/21 vvvF#
28 386.207 5/4 vvF#
29 400.000 63/50, 44/35 vF#
30 413.793 14/11, 33/26 F#
31 427.586 32/25 ^F#
32 441.379 9/7 ^^F#
33 455.172 13/10 ^^^F#/vvvG
34 468.966 21/16 vvG
35 482.759 33/25 vG
36 496.552 4/3 G
37 510.345 75/56 ^G
38 524.138 27/20 ^^G
39 537.931 15/11 ^^^G
40 551.724 11/8 ^^^^G
41 565.517 18/13 vvvvG#, vAb
42 579.310 7/5, 39/28 vvvG#, Ab
43 593.103 45/32 vvG#, ^Ab
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