User:Contribution/Collection of tunings: Difference between revisions

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=== Equal divisions of a ratio & optimization ===
=== Equal divisions of a ratio & optimization ===
 
{| class="wikitable"
|+
! colspan="3" |EDRs
! colspan="3" |Optimization
!Comments
|-
!EDR
!Steps per octave
!Cents
!Optimization
!Steps per octave
!Cents
!Why it matters
|-
|7ed5/3
|9.49840814199707
|126.336958999921
|
|9.50583353877785
|126.238272015258
|Alpha 5/3 analogue
|-
|10edo
|10
|120.
| colspan="3" |None
|
|-
|11edo
|11
|109.090909090909
| colspan="3" |None
|
|-
|12edo
|12
|100.
|34zpi
|12.0231830072926
|99.8071807833375
|EDO ≤ 29, Has a strong zeta peak
|-
|9ed5/3
|12.2122390397105
|98.2620792221608
|
|12.2053823008782
|98.3172808862904
|Beta 5/3 analogue
|-
|13edo
|13
|92.3076923076923
| colspan="3" |None
|
|-
|14edo
|14
|85.7142857142857
|42zpi
|13.9002525327005
|86.3293668353859
|EDO ≤ 29
|-
|15edo
|15
|80.
|47zpi
|15.0534898676781
|79.7157343943591
|EDO ≤ 29
|-
|9ed3/2
|15.3856016221631
|77.9950000961542
|
|15.3915238996928
|77.9649895501219
|Carlos Alpha 3/2
|-
|16edo
|16
|75.
| colspan="3" |None
|
|-
|17edo
|17
|70.5882352941176
|56zpi
|17.0445886606675
|70.4035764012981
|EDO ≤ 29
|-
|18edo
|18
|66.6666666666667
| colspan="3" |None
|
|-
|11ed3/2
|18.8046242048660
|63.8140909877625
|
|18.7990736394111
|63.8329325698408
|Carlos Beta 3/2
|-
|19edo
|19
|63.1578947368421
|65zpi
|18.9480867166984
|63.3309324546460
|EDO ≤ 29, Has a strong zeta peak
|-
|20edo
|20
|60.
| colspan="3" |None
|
|-
|21edo
|21
|57.1428571428571
| colspan="3" |None
|
|-
|16ed5/3
|21.7106471817076
|55.2724195624655
|
|21.7094399215509
|55.2754932571412
|Gamma 5/3 analogue
|-
|22edo
|22
|54.5454545454545
|80zpi
|22.0251467420146
|54.4831784348982
|EDO ≤ 29, Has a strong zeta peak
|-
|11ed7/5
|22.6604698881676
|52.9556538731173
|
|22.6653911133366
|52.9441558718088
|Alpha 7/5 analogue
|-
|23edo
|23
|52.1739130434783
| colspan="3" |None
|
|-
|24edo
|24
|50.
|90zpi
|24.0057421830853
|49.9880399800983
|EDO ≤ 29
|-
|39edt
|24.6062603892868
|48.7680769452663
|93zpi no-2 analogue
|24.5738316304204
|48.8324335434323
|Has a strong no-2 zeta peak
|-
|25edo
|25
|48.
| colspan="3" |None
|
|-
|26edo
|26
|46.1538461538462
|100zpi
|25.9356996537225
|46.2682717652372
|EDO ≤ 29
|-
|13ed7/5
|26.7805553223799
|44.8086302003300
|
|26.7758951088566
|44.8164289231577
|Beta 7/5 analogue
|-
|27edo
|27
|44.4444444444444
|106zpi
|27.0866140827635
|44.3023257293579
|EDO ≤ 29, Has a strong zeta peak
|-
|28edo
|28
|42.8571428571429
| colspan="3" |None
|
|-
|29edo
|29
|41.3793103448276
|116zpi
|28.9399661541990
|41.4651487014917
|EDO ≤ 29
|-
|31edo
|31
|38.7096774193548
|127zpi
|30.9783816349790
|38.7366910944446
|Has a strong zeta peak
|-
|13ed4/3
|31.3224709154917
|38.3111537795856
|
|31.3266790320926
|38.3060074376432
|Alpha 4/3 analogue
|-
|34edo
|34
|35.2941176470588
|144zpi
|34.0448410043159
|35.2476312005063
|Has a strong zeta peak
|-
|20ed3/2
|34.1902258270291
|35.0977500432694
|
|34.1894540921914
|35.0985422804417
|Carlos Gamma 3/2
|-
|56edt
|35.3320662000016
|33.9634821583105
|151zpi no-2 analogue
|35.3059427335609
|33.9886123153798
|Has a strong no-2 zeta peak
|-
|36edo
|36
|33.3333333333333
|155zpi no-5 analogue
|35.9775957344990
|33.3540909419168
|Has a strong no-5 zeta peak
|-
|15ed4/3
|36.1413125947981
|33.2029999423075
|
|36.1372975038827
|33.2066890135066
|Beta 4/3 analogue
|-
|37edo
|37
|32.4324324324324
|161zpi no-3 analogue
|37.0117501336435
|32.4221360964286
|Has a strong no-3 zeta peak
|-
|41edo
|41
|29.2682926829268
|184zpi
|40.9880783925993
|29.2768055263764
|Has a strong zeta peak
|-
|96ed5
|41.3449495750457
|29.0241011860920
|186zpi no-2 no-3 analogue
|41.3477989230936
|29.0221010852836
|Has a strong no-2 no-3 zeta peak
|-
|66edt
|41.6413637357162
|28.8175000131119
|188zpi no-2 no-5 analogue
|41.6281274155763
|28.8266629920756
|Has a strong no-2 no-5 zeta peak
|-
|46edo
|46
|26.0869565217391
|214zpi
|46.0089748051542
|26.0818678330031
|Has a strong zeta peak
|-
|24ed7/5
|49.4410252105475
|24.2713413585121
|
|49.4404896216012
|24.2716042900130
|Gamma 7/5 analogue
|-
|53edo
|53
|22.6415094339623
|257zpi
|52.9968291550147
|22.6428640945673
|Has a strong zeta peak
|-
|57edo
|57
|21.0526315789474
|282zpi no-3 no-5 analogue
|56.9949885079207
|21.0544827083040
|Has a strong no-3 no-5 zeta peak
|-
|58edo
|58
|20.6896551724138
|289zpi
|58.0667185533159
|20.6658827964969
|Has a strong zeta peak
|-
|60edo
|60
|20.0000000000000
|301zpi
|59.9201656607655
|20.0266469020418
|Has a strong zeta peak
|-
|65edo
|65
|18.4615384615385
|334zpi
|65.0158450885860
|18.4570391781413
|Has a strong zeta peak
|-
|28ed4/3
|67.4637835102899
|17.7873213976647
|
|67.4633901646646
|17.7874251067289
|Gamma 4/3 analogue
|-
|68edo
|68
|17.6470588235294
|354zpi
|68.0493056282519
|17.6342725163943
|Has a strong zeta peak
|-
|72edo
|72
|16.6666666666667
|380zpi
|71.9506065993786
|16.6781081733140
|Has a strong zeta peak
|-
|77edo
|77
|15.5844155844156
|414zpi
|76.9918536925042
|15.5860645308353
|Has a strong zeta peak
|-
|80edo
|80
|15.0000000000000
|435zpi
|80.0731374302484
|14.9862992572924
|Has a strong zeta peak
|-
|83edo
|83
|14.4578313253012
|455zpi no-3 no-5 analogue
|82.9585473728587
|14.4650555970632
|Has a strong no-3 no-5 zeta peak
|-
|84edo
|84
|14.2857142857143
|462zpi
|83.9972142607288
|14.2861880666087
|Has a strong zeta peak
|-
|87edo
|87
|13.7931034482759
|483zpi
|87.0139255957575
|13.7908960178956
|Has a strong zeta peak
|-
|94edo
|94
|12.7659574468085
|532zpi
|93.9836761074943
|12.7681747480009
|Has a strong zeta peak
|-
|99edo
|99
|12.1212121212121
|568zpi
|99.0473345956631
|12.1154194093028
|Has a strong zeta peak
|-
|327ed7
|116.479750184323
|10.3022198974591
|695zpi no-2 no-3 no-5 analogue
|116.481879086492
|10.3020316070705
|Has a strong no-2 no-3 no-5 zeta peak
|-
|171edo
|171
|7.01754385964912
|1114zpi
|170.995891689006
|7.01771246166817
|Exceptionally strong zeta peak
|-
|270edo
|270
|4.44444444444444
|1936zpi
|270.017794631965
|4.44415154799558
|Exceptionally strong zeta peak
|-
|311edo
|311
|3.85852090032154
|2293zpi
|311.004029926555
|3.85847090239759
|Exceptionally strong zeta peak
|-
|342edo
|342
|3.50877192982456
| colspan="3" |None
|
|-
|684edo
|684
|1.75438596491228
| colspan="3" |None
|
|}
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ style="font-size: 105%;" | EDRs collection & optimization
|+ style="font-size: 105%;" | EDRs collection & optimization

Revision as of 14:45, 9 June 2025

Equal-step tunings

Equal divisions of a ratio & optimization

EDRs Optimization Comments
EDR Steps per octave Cents Optimization Steps per octave Cents Why it matters
7ed5/3 9.49840814199707 126.336958999921 9.50583353877785 126.238272015258 Alpha 5/3 analogue
10edo 10 120. None
11edo 11 109.090909090909 None
12edo 12 100. 34zpi 12.0231830072926 99.8071807833375 EDO ≤ 29, Has a strong zeta peak
9ed5/3 12.2122390397105 98.2620792221608 12.2053823008782 98.3172808862904 Beta 5/3 analogue
13edo 13 92.3076923076923 None
14edo 14 85.7142857142857 42zpi 13.9002525327005 86.3293668353859 EDO ≤ 29
15edo 15 80. 47zpi 15.0534898676781 79.7157343943591 EDO ≤ 29
9ed3/2 15.3856016221631 77.9950000961542 15.3915238996928 77.9649895501219 Carlos Alpha 3/2
16edo 16 75. None
17edo 17 70.5882352941176 56zpi 17.0445886606675 70.4035764012981 EDO ≤ 29
18edo 18 66.6666666666667 None
11ed3/2 18.8046242048660 63.8140909877625 18.7990736394111 63.8329325698408 Carlos Beta 3/2
19edo 19 63.1578947368421 65zpi 18.9480867166984 63.3309324546460 EDO ≤ 29, Has a strong zeta peak
20edo 20 60. None
21edo 21 57.1428571428571 None
16ed5/3 21.7106471817076 55.2724195624655 21.7094399215509 55.2754932571412 Gamma 5/3 analogue
22edo 22 54.5454545454545 80zpi 22.0251467420146 54.4831784348982 EDO ≤ 29, Has a strong zeta peak
11ed7/5 22.6604698881676 52.9556538731173 22.6653911133366 52.9441558718088 Alpha 7/5 analogue
23edo 23 52.1739130434783 None
24edo 24 50. 90zpi 24.0057421830853 49.9880399800983 EDO ≤ 29
39edt 24.6062603892868 48.7680769452663 93zpi no-2 analogue 24.5738316304204 48.8324335434323 Has a strong no-2 zeta peak
25edo 25 48. None
26edo 26 46.1538461538462 100zpi 25.9356996537225 46.2682717652372 EDO ≤ 29
13ed7/5 26.7805553223799 44.8086302003300 26.7758951088566 44.8164289231577 Beta 7/5 analogue
27edo 27 44.4444444444444 106zpi 27.0866140827635 44.3023257293579 EDO ≤ 29, Has a strong zeta peak
28edo 28 42.8571428571429 None
29edo 29 41.3793103448276 116zpi 28.9399661541990 41.4651487014917 EDO ≤ 29
31edo 31 38.7096774193548 127zpi 30.9783816349790 38.7366910944446 Has a strong zeta peak
13ed4/3 31.3224709154917 38.3111537795856 31.3266790320926 38.3060074376432 Alpha 4/3 analogue
34edo 34 35.2941176470588 144zpi 34.0448410043159 35.2476312005063 Has a strong zeta peak
20ed3/2 34.1902258270291 35.0977500432694 34.1894540921914 35.0985422804417 Carlos Gamma 3/2
56edt 35.3320662000016 33.9634821583105 151zpi no-2 analogue 35.3059427335609 33.9886123153798 Has a strong no-2 zeta peak
36edo 36 33.3333333333333 155zpi no-5 analogue 35.9775957344990 33.3540909419168 Has a strong no-5 zeta peak
15ed4/3 36.1413125947981 33.2029999423075 36.1372975038827 33.2066890135066 Beta 4/3 analogue
37edo 37 32.4324324324324 161zpi no-3 analogue 37.0117501336435 32.4221360964286 Has a strong no-3 zeta peak
41edo 41 29.2682926829268 184zpi 40.9880783925993 29.2768055263764 Has a strong zeta peak
96ed5 41.3449495750457 29.0241011860920 186zpi no-2 no-3 analogue 41.3477989230936 29.0221010852836 Has a strong no-2 no-3 zeta peak
66edt 41.6413637357162 28.8175000131119 188zpi no-2 no-5 analogue 41.6281274155763 28.8266629920756 Has a strong no-2 no-5 zeta peak
46edo 46 26.0869565217391 214zpi 46.0089748051542 26.0818678330031 Has a strong zeta peak
24ed7/5 49.4410252105475 24.2713413585121 49.4404896216012 24.2716042900130 Gamma 7/5 analogue
53edo 53 22.6415094339623 257zpi 52.9968291550147 22.6428640945673 Has a strong zeta peak
57edo 57 21.0526315789474 282zpi no-3 no-5 analogue 56.9949885079207 21.0544827083040 Has a strong no-3 no-5 zeta peak
58edo 58 20.6896551724138 289zpi 58.0667185533159 20.6658827964969 Has a strong zeta peak
60edo 60 20.0000000000000 301zpi 59.9201656607655 20.0266469020418 Has a strong zeta peak
65edo 65 18.4615384615385 334zpi 65.0158450885860 18.4570391781413 Has a strong zeta peak
28ed4/3 67.4637835102899 17.7873213976647 67.4633901646646 17.7874251067289 Gamma 4/3 analogue
68edo 68 17.6470588235294 354zpi 68.0493056282519 17.6342725163943 Has a strong zeta peak
72edo 72 16.6666666666667 380zpi 71.9506065993786 16.6781081733140 Has a strong zeta peak
77edo 77 15.5844155844156 414zpi 76.9918536925042 15.5860645308353 Has a strong zeta peak
80edo 80 15.0000000000000 435zpi 80.0731374302484 14.9862992572924 Has a strong zeta peak
83edo 83 14.4578313253012 455zpi no-3 no-5 analogue 82.9585473728587 14.4650555970632 Has a strong no-3 no-5 zeta peak
84edo 84 14.2857142857143 462zpi 83.9972142607288 14.2861880666087 Has a strong zeta peak
87edo 87 13.7931034482759 483zpi 87.0139255957575 13.7908960178956 Has a strong zeta peak
94edo 94 12.7659574468085 532zpi 93.9836761074943 12.7681747480009 Has a strong zeta peak
99edo 99 12.1212121212121 568zpi 99.0473345956631 12.1154194093028 Has a strong zeta peak
327ed7 116.479750184323 10.3022198974591 695zpi no-2 no-3 no-5 analogue 116.481879086492 10.3020316070705 Has a strong no-2 no-3 no-5 zeta peak
171edo 171 7.01754385964912 1114zpi 170.995891689006 7.01771246166817 Exceptionally strong zeta peak
270edo 270 4.44444444444444 1936zpi 270.017794631965 4.44415154799558 Exceptionally strong zeta peak
311edo 311 3.85852090032154 2293zpi 311.004029926555 3.85847090239759 Exceptionally strong zeta peak
342edo 342 3.50877192982456 None
684edo 684 1.75438596491228 None
EDRs collection & optimization
EDRs Optimization Comments
EDR Steps per octave Cents Optimization Steps per octave Cents Why it matters
7ed5/3 9.49840814199707 126.336958999921 9.50583353877785 126.238272015258 Alpha 5/3 analogue
10edo 10 120. None
11edo 11 109.090909090909 None
12edo 12 100. 34zpi 12.0231830072926 99.8071807833375 EDO ≤ 29, Has a strong zeta peak
9ed5/3 12.2122390397105 98.2620792221608 12.2053823008782 98.3172808862904 Beta 5/3 analogue
13edo 13 92.3076923076923 None
14edo 14 85.7142857142857 42zpi 13.9002525327005 86.3293668353859 EDO ≤ 29
15edo 15 80. 47zpi 15.0534898676781 79.7157343943591 EDO ≤ 29
9ed3/2 15.3856016221631 77.9950000961542 15.3915238996928 77.9649895501219 Carlos Alpha 3/2
16edo 16 75. None
17edo 17 70.5882352941176 56zpi 17.0445886606675 70.4035764012981 EDO ≤ 29
18edo 18 66.6666666666667 None
11ed3/2 18.8046242048660 63.8140909877625 18.7990736394111 63.8329325698408 Carlos Beta 3/2
19edo 19 63.1578947368421 65zpi 18.9480867166984 63.3309324546460 EDO ≤ 29, Has a strong zeta peak
20edo 20 60. None
21edo 21 57.1428571428571 None
16ed5/3 21.7106471817076 55.2724195624655 21.7094399215509 55.2754932571412 Gamma 5/3 analogue
22edo 22 54.5454545454545 80zpi 22.0251467420146 54.4831784348982 EDO ≤ 29, Has a strong zeta peak
11ed7/5 22.6604698881676 52.9556538731173 22.6653911133366 52.9441558718088 Alpha 7/5 analogue
23edo 23 52.1739130434783 None
24edo 24 50. 90zpi 24.0057421830853 49.9880399800983 EDO ≤ 29
39edt 24.6062603892868 48.7680769452663 93zpi no-2 analogue 24.5738316304204 48.8324335434323 Has a strong no-2 zeta peak
25edo 25 48. None
26edo 26 46.1538461538462 100zpi 25.9356996537225 46.2682717652372 EDO ≤ 29
13ed7/5 26.7805553223799 44.8086302003300 26.7758951088566 44.8164289231577 Beta 7/5 analogue
27edo 27 44.4444444444444 106zpi 27.0866140827635 44.3023257293579 EDO ≤ 29, Has a strong zeta peak
28edo 28 42.8571428571429 None
29edo 29 41.3793103448276 116zpi 28.9399661541990 41.4651487014917 EDO ≤ 29
31edo 31 38.7096774193548 127zpi 30.9783816349790 38.7366910944446 Has a strong zeta peak
13ed4/3 31.3224709154917 38.3111537795856 31.3266790320926 38.3060074376432 Alpha 4/3 analogue
34edo 34 35.2941176470588 144zpi 34.0448410043159 35.2476312005063 Has a strong zeta peak
20ed3/2 34.1902258270291 35.0977500432694 34.1894540921914 35.0985422804417 Carlos Gamma 3/2
56edt 35.3320662000016 33.9634821583105 151zpi no-2 analogue 35.3059427335609 33.9886123153798 Has a strong no-2 zeta peak
36edo 36 33.3333333333333 155zpi no-5 analogue 35.9775957344990 33.3540909419168 Has a strong no-5 zeta peak
15ed4/3 36.1413125947981 33.2029999423075 36.1372975038827 33.2066890135066 Beta 4/3 analogue
37edo 37 32.4324324324324 161zpi no-3 analogue 37.0117501336435 32.4221360964286 Has a strong no-3 zeta peak
41edo 41 29.2682926829268 184zpi 40.9880783925993 29.2768055263764 Has a strong zeta peak
96ed5 41.3449495750457 29.0241011860920 186zpi no-2 no-3 analogue 41.3477989230936 29.0221010852836 Has a strong no-2 no-3 zeta peak
66edt 41.6413637357162 28.8175000131119 188zpi no-2 no-5 analogue 41.6281274155763 28.8266629920756 Has a strong no-2 no-5 zeta peak
46edo 46 26.0869565217391 214zpi 46.0089748051542 26.0818678330031 Has a strong zeta peak
24ed7/5 49.4410252105475 24.2713413585121 49.4404896216012 24.2716042900130 Gamma 7/5 analogue
53edo 53 22.6415094339623 257zpi 52.9968291550147 22.6428640945673 Has a strong zeta peak
57edo 57 21.0526315789474 282zpi no-3 no-5 analogue 56.9949885079207 21.0544827083040 Has a strong no-3 no-5 zeta peak
58edo 58 20.6896551724138 289zpi 58.0667185533159 20.6658827964969 Has a strong zeta peak
60edo 60 20.0000000000000 301zpi 59.9201656607655 20.0266469020418 Has a strong zeta peak
65edo 65 18.4615384615385 334zpi 65.0158450885860 18.4570391781413 Has a strong zeta peak
28ed4/3 67.4637835102899 17.7873213976647 67.4633901646646 17.7874251067289 Gamma 4/3 analogue
68edo 68 17.6470588235294 354zpi 68.0493056282519 17.6342725163943 Has a strong zeta peak
72edo 72 16.6666666666667 380zpi 71.9506065993786 16.6781081733140 Has a strong zeta peak
77edo 77 15.5844155844156 414zpi 76.9918536925042 15.5860645308353 Has a strong zeta peak
80edo 80 15.0000000000000 435zpi 80.0731374302484 14.9862992572924 Has a strong zeta peak
83edo 83 14.4578313253012 455zpi no-3 no-5 analogue 82.9585473728587 14.4650555970632 Has a strong no-3 no-5 zeta peak
84edo 84 14.2857142857143 462zpi 83.9972142607288 14.2861880666087 Has a strong zeta peak
87edo 87 13.7931034482759 483zpi 87.0139255957575 13.7908960178956 Has a strong zeta peak
94edo 94 12.7659574468085 532zpi 93.9836761074943 12.7681747480009 Has a strong zeta peak
99edo 99 12.1212121212121 568zpi 99.0473345956631 12.1154194093028 Has a strong zeta peak
327ed7 116.479750184323 10.3022198974591 695zpi no-2 no-3 no-5 analogue 116.481879086492 10.3020316070705 Has a strong no-2 no-3 no-5 zeta peak
171edo 171 7.01754385964912 1114zpi 170.995891689006 7.01771246166817 Exceptionally strong zeta peak
270edo 270 4.44444444444444 1936zpi 270.017794631965 4.44415154799558 Exceptionally strong zeta peak
311edo 311 3.85852090032154 2293zpi 311.004029926555 3.85847090239759 Exceptionally strong zeta peak
342edo 342 3.50877192982456 None
684edo 684 1.75438596491228 None
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