User:Contribution/Collection of tunings: Difference between revisions

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Line 11: Line 11:
|-
|-
|7ed5/3
|7ed5/3
|9.49840814199706858453236308296456727180164766756424872573514114916072877570
|9.49840814199707
|
|126.336958999921
|Alpha 5/3 analogue
|Alpha 5/3 analogue
|
|
|9.50583353877784930547190333358321934022951981846923290202227451847032504243
|9.50583353877785
|
|126.238272015258
|-
|-
|10edo
|10edo
|10
|10
|
|120.
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 26: Line 26:
|11edo
|11edo
|11
|11
|
|109.090909090909
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 32: Line 32:
|12edo
|12edo
|12
|12
|
|100.
|EDO ≤ 29, Has a strong zeta peak
|EDO ≤ 29, Has a strong zeta peak
|34zpi
|34zpi
Line 39: Line 39:
|-
|-
|9ed5/3
|9ed5/3
|12.2122390397105167515416096780973007780306898582968912188023243346352227116
|12.2122390397105
|
|98.2620792221608
|Beta 5/3 analogue
|Beta 5/3 analogue
|
|
|12.2053823008782061563061181531460480244531636674514886633817351831658567687
|12.2053823008782
|
|98.3172808862904
|-
|-
|13edo
|13edo
|13
|13
|
|92.3076923076923
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 54: Line 54:
|14edo
|14edo
|14
|14
|
|85.7142857142857
|EDO ≤ 29
|EDO ≤ 29
|42zpi
|42zpi
Line 62: Line 62:
|15edo
|15edo
|15
|15
|
|80.
|EDO ≤ 29
|EDO ≤ 29
|47zpi
|47zpi
Line 69: Line 69:
|-
|-
|9ed3/2
|9ed3/2
|15.3856016221630929927857123595661272655350336171249650076700851565894672010
|15.3856016221631
|
|77.9950000961542
|Carlos Alpha 3/2
|Carlos Alpha 3/2
|
|
|15.3915238996927928512944165390898313365314840308651022873979939218067199247
|15.3915238996928
|
|77.9649895501219
|-
|-
|16edo
|16edo
|16
|16
|
|75.
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 84: Line 84:
|17edo
|17edo
|17
|17
|
|70.5882352941176
|EDO ≤ 29
|EDO ≤ 29
|56zpi
|56zpi
Line 92: Line 92:
|18edo
|18edo
|18
|18
|
|66.6666666666667
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
|-
|-
|11ed3/2
|11ed3/2
|18.8046242048660025467380928839141555467650410875971794538189929691649043568
|18.8046242048660
|
|63.8140909877625
|Carlos Beta 3/2
|Carlos Beta 3/2
|
|
|18.7990736394110805048912898911655515976845667285899345790484210796250554266
|18.7990736394111
|
|63.8329325698408
|-
|-
|19edo
|19edo
|19
|19
|
|63.1578947368421
|EDO ≤ 29, Has a strong zeta peak
|EDO ≤ 29, Has a strong zeta peak
|65zpi
|65zpi
Line 114: Line 114:
|20edo
|20edo
|20
|20
|
|60.
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 120: Line 120:
|21edo
|21edo
|21
|21
|
|57.1428571428571
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
|-
|-
|16ed5/3
|16ed5/3
|21.7106471817075853360739727610618680498323375258611399445374654837959514873
|21.7106471817076
|
|55.2724195624655
|Gamma 5/3 analogue
|Gamma 5/3 analogue
|
|
|21.7094399215509101560684062280580414508364638100724154443886464052437918182
|21.7094399215509
|
|55.2754932571412
|-
|-
|22edo
|22edo
|22
|22
|
|54.5454545454545
|EDO ≤ 29, Has a strong zeta peak
|EDO ≤ 29, Has a strong zeta peak
|80zpi
|80zpi
Line 141: Line 141:
|-
|-
|11ed7/5
|11ed7/5
|22.6604698881675975718539343001772210291924199534946609650608950558236849973
|22.6604698881676
|
|52.9556538731173
|Alpha 7/5 analogue
|Alpha 7/5 analogue
|
|
|22.6653911133365613368906944590278143011697888908110193835606068628638720251
|22.6653911133366
|
|52.9441558718088
|-
|-
|23edo
|23edo
|23
|23
|
|52.1739130434783
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 156: Line 156:
|24edo
|24edo
|24
|24
|
|50.
|EDO ≤ 29
|EDO ≤ 29
|90zpi
|90zpi
Line 163: Line 163:
|-
|-
|39edt
|39edt
|24.6062603892868400468815574593676733176838399651433366869555428097087228538
|24.6062603892868
|
|48.7680769452663
|Has a strong no-2 zeta peak
|Has a strong no-2 zeta peak
|93zpi no-2 analogue
|93zpi no-2 analogue
|24.5738316304204445883184323365600165414701853056787276394517489970293
|24.5738316304204
|48.8324335434322607337830293873763777285246843568212813459755275268185837463
|48.8324335434323
|-
|-
|25edo
|25edo
|25
|25
|
|48.
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 178: Line 178:
|26edo
|26edo
|26
|26
|
|46.1538461538462
|EDO ≤ 29
|EDO ≤ 29
|100zpi
|100zpi
Line 185: Line 185:
|-
|-
|13ed7/5
|13ed7/5
|26.7805553223798880394637405365730793981364963086755084132537850659734459059
|26.7805553223799
|
|44.8086302003300
|Beta 7/5 analogue
|Beta 7/5 analogue
|
|
|26.7758951088566298880936792337104829942053519649764791577134427848906306935
|26.7758951088566
|
|44.8164289231577
|-
|-
|27edo
|27edo
|27
|27
|
|44.4444444444444
|EDO ≤ 29, Has a strong zeta peak
|EDO ≤ 29, Has a strong zeta peak
|106zpi
|106zpi
Line 202: Line 202:
|28edo
|28edo
|28
|28
|
|42.8571428571429
|EDO ≤ 29
|EDO ≤ 29
| colspan="3" |None
| colspan="3" |None
Line 208: Line 208:
|29edo
|29edo
|29
|29
|
|41.3793103448276
|EDO ≤ 29
|EDO ≤ 29
|116zpi
|116zpi
Line 216: Line 216:
|31edo
|31edo
|31
|31
|
|38.7096774193548
|Has a strong zeta peak
|Has a strong zeta peak
|127zpi
|127zpi
Line 223: Line 223:
|-
|-
|13ed4/3
|13ed4/3
|31.3224709154917170595712563005616739301927219730991737328958039656595105508
|31.3224709154917
|
|38.3111537795856
|Alpha 4/3 analogue
|Alpha 4/3 analogue
|
|
|31.3266790320925769568440621347599177997268649586304206236224098328788901126
|31.3266790320926
|
|38.3060074376432
|-
|-
|34edo
|34edo
|34
|34
|
|35.2941176470588
|Has a strong zeta peak
|Has a strong zeta peak
|144zpi
|144zpi
Line 239: Line 239:
|-
|-
|20ed3/2
|20ed3/2
|34.1902258270290955395238052434802828123000747047221444614890781257543715579
|34.1902258270291
|
|35.0977500432694
|Carlos Gamma 3/2
|Carlos Gamma 3/2
|
|
|34.1894540921913877696909378855859519354721286088761026127617141568017474368
|34.1894540921914
|
|35.0985422804417
|-
|-
|56edt
|56edt
|35.3320662000016164775735184031946078407767958473853039607566768549663712773
|35.3320662000016
|
|33.9634821583105
|Has a strong no-2 zeta peak
|Has a strong no-2 zeta peak
|151zpi no-2 analogue
|151zpi no-2 analogue
|35.3059427335608633586867709728239574896988978536248407971925774931920
|35.3059427335609
|33.9886123153797795726938859938695575674205028551304634432771826217692714955
|33.9886123153798
|-
|-
|36edo
|36edo
|36
|36
|
|33.3333333333333
|Has a strong no-5 zeta peak
|Has a strong no-5 zeta peak
|155zpi no-5 analogue
|155zpi no-5 analogue
|35.9775957344990354876843659181629374042162799645238247644819739175425
|35.9775957344990
|33.3540909419168338960282298282173036675588854165862895775989035929190051321
|33.3540909419168
|-
|-
|15ed4/3
|15ed4/3
|36.1413125947981350687360649621865468425300638151144312302643891911455890971
|36.1413125947981
|
|33.2029999423075
|Beta 4/3 analogue
|Beta 4/3 analogue
|
|
|36.1372975038827189126955782616010667080444649149049203398769171912866739333
|36.1372975038827
|
|33.2066890135066
|-
|-
|37edo
|37edo
|37
|37
|
|32.4324324324324
|Has a strong no-3 zeta peak
|Has a strong no-3 zeta peak
|161zpi no-3 analogue
|161zpi no-3 analogue
|37.0117501336435252522939269985227920601261578745487306336979972897294
|37.0117501336435
|32.4221360964286053986540281462323756320027885683144327873809896041665053646
|32.4221360964286
|-
|-
|41edo
|41edo
|41
|41
|
|29.2682926829268
|Has a strong zeta peak
|Has a strong zeta peak
|184zpi
|184zpi
Line 287: Line 287:
|-
|-
|96ed5
|96ed5
|41.3449495750457328643302306013407006787000254796570031349096996442235599236
|41.3449495750457
|
|29.0241011860920
|Has a strong no-2 no-3 zeta peak
|Has a strong no-2 no-3 zeta peak
|186zpi no-2 no-3 analogue
|186zpi no-2 no-3 analogue
Line 295: Line 295:
|-
|-
|66edt
|66edt
|41.6413637357161908485687895466222163837726522487041082394632262933532232911
|41.6413637357162
|
|28.8175000131119
|Has a strong no-2 no-5 zeta peak
|Has a strong no-2 no-5 zeta peak
|188zpi no-2 no-5 analogue
|188zpi no-2 no-5 analogue
|41.6281274155763001275416027845619755345480144939422820248677372190977
|41.6281274155763
|28.8266629920755754571831740158108063867663530357929200798818480023767470361
|28.8266629920756
|-
|-
|46edo
|46edo
|46
|46
|
|26.0869565217391
|Has a strong zeta peak
|Has a strong zeta peak
|214zpi
|214zpi
Line 311: Line 311:
|-
|-
|24ed7/5
|24ed7/5
|49.4410252105474856113176748367503004273289162621701693783146801217971309033
|49.4410252105475
|
|24.2713413585121
|Gamma 7/5 analogue
|Gamma 7/5 analogue
|
|
|49.4404896216012431820279531253051214534813134522812930224375745518827463625
|49.4404896216012
|
|24.2716042900130
|-
|-
|53edo
|53edo
|53
|53
|
|22.6415094339623
|Has a strong zeta peak
|Has a strong zeta peak
|257zpi
|257zpi
Line 328: Line 328:
|57edo
|57edo
|57
|57
|
|21.0526315789474
|Has a strong no-3 no-5 zeta peak
|Has a strong no-3 no-5 zeta peak
|282zpi no-3 no-5 analogue
|282zpi no-3 no-5 analogue
|56.9949885079206769176514037038198357725273287855611008976484058072516
|56.9949885079207
|21.0544827083039808806917479490481104480956786904618314090632684997207904034
|21.0544827083040
|-
|-
|58edo
|58edo
|58
|58
|
|20.6896551724138
|Has a strong zeta peak
|Has a strong zeta peak
|289zpi
|289zpi
Line 344: Line 344:
|60edo
|60edo
|60
|60
|
|20.0000000000000
|Has a strong zeta peak
|Has a strong zeta peak
|301zpi
|301zpi
Line 352: Line 352:
|65edo
|65edo
|65
|65
|
|18.4615384615385
|Has a strong zeta peak
|Has a strong zeta peak
|334zpi
|334zpi
Line 359: Line 359:
|-
|-
|28ed4/3
|28ed4/3
|67.4637835102898521283073212627482207727227857882136049631601931568050996480
|67.4637835102899
|
|17.7873213976647
|Gamma 4/3 analogue
|Gamma 4/3 analogue
|
|
|67.4633901646646229125509837448674678686996796942776788677245523727102699760
|67.4633901646646
|
|17.7874251067289
|-
|-
|68edo
|68edo
|68
|68
|
|17.6470588235294
|Has a strong zeta peak
|Has a strong zeta peak
|354zpi
|354zpi
Line 376: Line 376:
|72edo
|72edo
|72
|72
|
|16.6666666666667
|Has a strong zeta peak
|Has a strong zeta peak
|380zpi
|380zpi
Line 384: Line 384:
|77edo
|77edo
|77
|77
|
|15.5844155844156
|Has a strong zeta peak
|Has a strong zeta peak
|414zpi
|414zpi
Line 392: Line 392:
|80edo
|80edo
|80
|80
|
|15.0000000000000
|Has a strong zeta peak
|Has a strong zeta peak
|435zpi
|435zpi
Line 400: Line 400:
|83edo
|83edo
|83
|83
|
|14.4578313253012
|Has a strong no-3 no-5 zeta peak
|Has a strong no-3 no-5 zeta peak
|455zpi no-3 no-5 analogue
|455zpi no-3 no-5 analogue
|82.9585473728587401934282446836610895074185494886540503684148508037660
|82.9585473728587
|14.4650555970631644892614919440394905869155594072293855522604093941309631517
|14.4650555970632
|-
|-
|84edo
|84edo
|84
|84
|
|14.2857142857143
|Has a strong zeta peak
|Has a strong zeta peak
|462zpi
|462zpi
Line 416: Line 416:
|87edo
|87edo
|87
|87
|
|13.7931034482759
|Has a strong zeta peak
|Has a strong zeta peak
|483zpi
|483zpi
Line 424: Line 424:
|94edo
|94edo
|94
|94
|
|12.7659574468085
|Has a strong zeta peak
|Has a strong zeta peak
|532zpi
|532zpi
Line 432: Line 432:
|99edo
|99edo
|99
|99
|
|12.1212121212121
|Has a strong zeta peak
|Has a strong zeta peak
|568zpi
|568zpi
Line 439: Line 439:
|-
|-
|327ed7
|327ed7
|116.479750184323251720135904506422003080366592226710079912941501697613698777
|116.479750184323
|
|10.3022198974591
|Has a strong no-2 no-3 no-5 zeta peak
|Has a strong no-2 no-3 no-5 zeta peak
|695zpi no-2 no-3 no-5 analogue
|695zpi no-2 no-3 no-5 analogue
|116.481879086491562246584713240674074197523436163157572853694264779074
|116.481879086492
|10.3020316070704971370763940790472253291607124811459581948058543261473166559
|10.3020316070705
|-
|-
|171edo
|171edo
|171
|171
|
|7.01754385964912
|Exceptionally strong zeta peak
|Exceptionally strong zeta peak
|1114zpi
|1114zpi
Line 456: Line 456:
|270edo
|270edo
|270
|270
|
|4.44444444444444
|Exceptionally strong zeta peak
|Exceptionally strong zeta peak
|1936zpi
|1936zpi
Line 464: Line 464:
|311edo
|311edo
|311
|311
|
|3.85852090032154
|Exceptionally strong zeta peak
|Exceptionally strong zeta peak
|2293zpi
|2293zpi
Line 472: Line 472:
|342edo
|342edo
|342
|342
|
|3.50877192982456
|171*2^n family
|171*2^n family
| colspan="3" |None
| colspan="3" |None
Line 478: Line 478:
|684edo
|684edo
|684
|684
|
|1.75438596491228
|171*2^n family
|171*2^n family
| colspan="3" |None
| colspan="3" |None
|}
|}

Revision as of 14:36, 9 June 2025

Equal-step tunings

Equal divisions of a ratio & optimization

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