User:Contribution/Collection of tunings: Difference between revisions
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|171*2^n family | |171*2^n family | ||
| | | colspan="3" |None | ||
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|684edo | |684edo | ||
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|171*2^n family | |171*2^n family | ||
| | | colspan="3" |None | ||
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|} | |} | ||
Revision as of 12:39, 9 June 2025
Equal-step tunings
Equal divisions of a ratio & optimization
| EDRs | Optimization | |||||
|---|---|---|---|---|---|---|
| EDR | Steps per octave | Cents | Why it matters | Optimization | Steps per octave | Cents |
| 7ed5/3 | 9.49840814199706858453236308296456727180164766756424872573514114916072877570 | Alpha 5/3 analogue | ||||
| 10edo | 10 | EDO ≤ 29 | None | |||
| 11edo | 11 | EDO ≤ 29 | None | |||
| 12edo | 12 | EDO ≤ 29, Has a strong zeta peak | 34zpi | 12.0231830072926 | 99.8071807833375 | |
| 9ed5/3 | 12.2122390397105167515416096780973007780306898582968912188023243346352227116 | Beta 5/3 analogue | ||||
| 13edo | 13 | EDO ≤ 29 | None | |||
| 14edo | 14 | EDO ≤ 29 | 42zpi | 13.9002525327005 | 86.3293668353859 | |
| 15edo | 15 | EDO ≤ 29 | 47zpi | 15.0534898676781 | 79.7157343943591 | |
| 9ed3/2 | 15.3856016221630929927857123595661272655350336171249650076700851565894672010 | Carlos Alpha 3/2 | ||||
| 16edo | 16 | EDO ≤ 29 | None | |||
| 17edo | 17 | EDO ≤ 29 | 56zpi | 17.0445886606675 | 70.4035764012981 | |
| 18edo | 18 | EDO ≤ 29 | None | |||
| 11ed3/2 | 18.8046242048660025467380928839141555467650410875971794538189929691649043568 | Carlos Beta 3/2 | ||||
| 19edo | 19 | EDO ≤ 29, Has a strong zeta peak | 65zpi | 18.9480867166984 | 63.3309324546460 | |
| 20edo | 20 | EDO ≤ 29 | None | |||
| 21edo | 21 | EDO ≤ 29 | None | |||
| 16ed5/3 | 21.7106471817075853360739727610618680498323375258611399445374654837959514873 | Gamma 5/3 analogue | ||||
| 22edo | 22 | EDO ≤ 29, Has a strong zeta peak | 80zpi | 22.0251467420146 | 54.4831784348982 | |
| 11ed7/5 | 22.6604698881675975718539343001772210291924199534946609650608950558236849973 | Alpha 7/5 analogue | ||||
| 23edo | 23 | EDO ≤ 29 | None | |||
| 24edo | 24 | EDO ≤ 29 | 90zpi | 24.0057421830853 | 49.9880399800983 | |
| 39edt | 24.6062603892868400468815574593676733176838399651433366869555428097087228538 | Has a strong no-2 zeta peak | 93zpi no-2 analogue | 24.5738316304204445883184323365600165414701853056787276394517489970293 | 48.8324335434322607337830293873763777285246843568212813459755275268185837463 | |
| 25edo | 25 | EDO ≤ 29 | None | |||
| 26edo | 26 | EDO ≤ 29 | 100zpi | 25.9356996537225 | 46.2682717652372 | |
| 13ed7/5 | 26.7805553223798880394637405365730793981364963086755084132537850659734459059 | Beta 7/5 analogue | ||||
| 27edo | 27 | EDO ≤ 29, Has a strong zeta peak | 106zpi | 27.0866140827635 | 44.3023257293579 | |
| 28edo | 28 | EDO ≤ 29 | None | |||
| 29edo | 29 | EDO ≤ 29 | 116zpi | 28.9399661541990 | 41.4651487014917 | |
| 31edo | 31 | Has a strong zeta peak | 127zpi | 30.9783816349790 | 38.7366910944446 | |
| 13ed4/3 | 31.3224709154917170595712563005616739301927219730991737328958039656595105508 | Alpha 4/3 analogue | ||||
| 34edo | 34 | Has a strong zeta peak | 144zpi | 34.0448410043159 | 35.2476312005063 | |
| 20ed3/2 | 34.1902258270290955395238052434802828123000747047221444614890781257543715579 | Carlos Gamma 3/2 | ||||
| 56edt | 35.3320662000016164775735184031946078407767958473853039607566768549663712773 | Has a strong no-2 zeta peak | 151zpi no-2 analogue | 35.3059427335608633586867709728239574896988978536248407971925774931920 | 33.9886123153797795726938859938695575674205028551304634432771826217692714955 | |
| 36edo | 36 | Has a strong no-5 zeta peak | 155zpi no-5 analogue | 35.9775957344990354876843659181629374042162799645238247644819739175425 | 33.3540909419168338960282298282173036675588854165862895775989035929190051321 | |
| 15ed4/3 | 36.1413125947981350687360649621865468425300638151144312302643891911455890971 | Beta 4/3 analogue | ||||
| 37edo | 37 | Has a strong no-3 zeta peak | 161zpi no-3 analogue | 37.0117501336435252522939269985227920601261578745487306336979972897294 | 32.4221360964286053986540281462323756320027885683144327873809896041665053646 | |
| 41edo | 41 | Has a strong zeta peak | 184zpi | 40.9880783925993 | 29.2768055263764 | |
| 96ed5 | 41.3449495750457328643302306013407006787000254796570031349096996442235599236 | Has a strong no-2 no-3 zeta peak | 186zpi no-2 no-3 analogue | 41.3477989230936 | 29.0221010852836 | |
| 66edt | 41.6413637357161908485687895466222163837726522487041082394632262933532232911 | Has a strong no-2 no-5 zeta peak | 188zpi no-2 no-5 analogue | 41.6281274155763001275416027845619755345480144939422820248677372190977 | 28.8266629920755754571831740158108063867663530357929200798818480023767470361 | |
| 46edo | 46 | Has a strong zeta peak | 214zpi | 46.0089748051542 | 26.0818678330031 | |
| 24ed7/5 | 49.4410252105474856113176748367503004273289162621701693783146801217971309033 | Gamma 7/5 analogue | ||||
| 53edo | 53 | Has a strong zeta peak | 257zpi | 52.9968291550147 | 22.6428640945673 | |
| 57edo | 57 | Has a strong no-3 no-5 zeta peak | 282zpi no-3 no-5 analogue | 56.9949885079206769176514037038198357725273287855611008976484058072516 | 21.0544827083039808806917479490481104480956786904618314090632684997207904034 | |
| 58edo | 58 | Has a strong zeta peak | 289zpi | 58.0667185533159 | 20.6658827964969 | |
| 60edo | 60 | Has a strong zeta peak | 301zpi | 59.9201656607655 | 20.0266469020418 | |
| 65edo | 65 | Has a strong zeta peak | 334zpi | 65.0158450885860 | 18.4570391781413 | |
| 28ed4/3 | 67.4637835102898521283073212627482207727227857882136049631601931568050996480 | Gamma 4/3 analogue | ||||
| 68edo | 68 | Has a strong zeta peak | 354zpi | 68.0493056282519 | 17.6342725163943 | |
| 72edo | 72 | Has a strong zeta peak | 380zpi | 71.9506065993786 | 16.6781081733140 | |
| 77edo | 77 | Has a strong zeta peak | 414zpi | 76.9918536925042 | 15.5860645308353 | |
| 80edo | 80 | Has a strong zeta peak | 435zpi | 80.0731374302484 | 14.9862992572924 | |
| 83edo | 83 | Has a strong no-3 no-5 zeta peak | 455zpi no-3 no-5 analogue | 82.9585473728587401934282446836610895074185494886540503684148508037660 | 14.4650555970631644892614919440394905869155594072293855522604093941309631517 | |
| 84edo | 84 | Has a strong zeta peak | 462zpi | 83.9972142607288 | 14.2861880666087 | |
| 87edo | 87 | Has a strong zeta peak | 483zpi | 87.0139255957575 | 13.7908960178956 | |
| 94edo | 94 | Has a strong zeta peak | 532zpi | 93.9836761074943 | 12.7681747480009 | |
| 99edo | 99 | Has a strong zeta peak | 568zpi | 99.0473345956631 | 12.1154194093028 | |
| 327ed7 | 116.479750184323251720135904506422003080366592226710079912941501697613698777 | Has a strong no-2 no-3 no-5 zeta peak | 695zpi no-2 no-3 no-5 analogue | 116.481879086491562246584713240674074197523436163157572853694264779074 | 10.3020316070704971370763940790472253291607124811459581948058543261473166559 | |
| 171edo | 171 | Exceptionally strong zeta peak | 1114zpi | 170.995891689006 | 7.01771246166817 | |
| 270edo | 270 | Exceptionally strong zeta peak | 1936zpi | 270.017794631965 | 4.44415154799558 | |
| 311edo | 311 | Exceptionally strong zeta peak | 2293zpi | 311.004029926555 | 3.85847090239759 | |
| 342edo | 342 | 171*2^n family | None | |||
| 684edo | 684 | 171*2^n family | None | |||