User:Contribution/Collection of tunings: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Contribution (talk | contribs)
3,308 edits
No edit summary
Contribution (talk | contribs)
3,308 edits
No edit summary
Line 1: Line 1:
== Equal-step tunings ==
== Equal-step tunings ==
{| class="wikitable"
 
|+
=== Equal divisions of a ratio & optimization ===
!Name
 
!Steps per octave
{| class="wikitable sortable"
!Step size (cents)
|+ style="font-size: 105%;" | EDRs collection & optimization
!Why it matters
|- style="white-space: nowrap;"
! colspan="4" | EDRs !! colspan="3" | Optimization
|- style="white-space: nowrap;"
! EDR !! Steps per octave !! Cents !! Why it matters !! Optimization !! Steps per octave !! Cents
|-
|
|
|
|
|
|
|
|}
 
 
{| class="wikitable sortable"
|+ style="font-size: 105%;" | EDRs collection & optimization
|- style="white-space: nowrap;"
! colspan="4" | EDRs !! colspan="3" | Optimization
|- style="white-space: nowrap;"
! EDR !! Steps per octave !! Cents !! Why it matters !! Optimization !! Steps per octave !! Cents
|-
|-
|5edo
|5edo

Revision as of 09:27, 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


EDRs collection & optimization
EDRs Optimization
EDR Steps per octave Cents Why it matters Optimization Steps per octave Cents
5edo 5 EDO ≤ 29, Alpha 2/1 analogue
6edo 6 EDO ≤ 29
7edo 7 EDO ≤ 29, Beta 2/1 analogue
8edo 8 EDO ≤ 29
9edo 9 EDO ≤ 29
7ed5/3 9.49840814199706858453236308296456727180164766756424872573514114916072877570 Alpha 5/3 analogue
10edo 10 EDO ≤ 29
26zpi 10.0084563372591 119.898609691954
11edo 11 EDO ≤ 29
12edo 12 EDO ≤ 29, Has a strong zeta peak, Gamma 2/1 analogue
34zpi 12.0231830072926 99.8071807833375
9ed5/3 12.2122390397105167515416096780973007780306898582968912188023243346352227116 Beta 5/3 analogue
13edo 13 EDO ≤ 29
42zpi 13.9002525327005 86.3293668353859
14edo 14 EDO ≤ 29
15edo 15 EDO ≤ 29
47zpi 15.0534898676781 79.7157343943591
9ed3/2 15.3856016221630929927857123595661272655350336171249650076700851565894672010 Carlos Alpha 3/2
51zpi 15.9443732426877 75.2616601314409
16edo 16 EDO ≤ 29
17edo 17 EDO ≤ 29
56zpi no-5 analogue 17.0347927675362037047409871190907115584257359751871828691074626558313
56zpi 17.0445886606675 70.4035764012981
18edo 18 EDO ≤ 29
11ed3/2 18.8046242048660025467380928839141555467650410875971794538189929691649043568 Carlos Beta 3/2
65zpi 18.9480867166984 63.3309324546460
19edo 19 EDO ≤ 29, Has a strong zeta peak
20edo 20 EDO ≤ 29
21edo 21 EDO ≤ 29
75zpi 21.0279383259393 57.0669354931351
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
24edo 24 EDO ≤ 29
90zpi 24.0057421830853 49.9880399800983
93zpi no-2 analogue 24.5738316304204445883184323365600165414701853056787276394517489970293 48.8324335434322607337830293873763777285246843568212813459755275268185837463
93zpi 24.5782550666850 48.8236449961234
39edt 24.6062603892868400468815574593676733176838399651433366869555428097087228538 Has a strong no-2 zeta peak
25edo 25 EDO ≤ 29
100zpi 25.9356996537225 46.2682717652372
26edo 26 EDO ≤ 29
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
116zpi 28.9399661541990 41.4651487014917
29edo 29 EDO ≤ 29
127zpi 30.9783816349790 38.7366910944446
31edo 31 Has a strong zeta peak
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
151zpi 35.2948974160593 33.9992488391253
151zpi no-2 analogue 35.3059427335608633586867709728239574896988978536248407971925774931920 33.9886123153797795726938859938695575674205028551304634432771826217692714955
56edt 35.3320662000016164775735184031946078407767958473853039607566768549663712773 Has a strong no-2 zeta peak
155zpi no-5 analogue 35.9775957344990354876843659181629374042162799645238247644819739175425 33.3540909419168338960282298282173036675588854165862895775989035929190051321
155zpi 35.9823877000425 33.3496490006021
36edo 36 Has a strong no-5 zeta peak
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
161zpi 37.0275229191254 32.4083250889078
184zpi 40.9880783925993 29.2768055263764
41edo 41 Has a strong zeta peak
186zpi 41.3438354846780 29.0248832971658
96ed5 41.3449495750457328643302306013407006787000254796570031349096996442235599236 Has a strong no-2 no-3 zeta peak
186zpi no-2 no-3 analogue 41.3477989230936 29.0221010852836
188zpi no-2 no-5 analogue 41.6281274155763001275416027845619755345480144939422820248677372190977 28.8266629920755754571831740158108063867663530357929200798818480023767470361
66edt 41.6413637357161908485687895466222163837726522487041082394632262933532232911 Has a strong no-2 no-5 zeta peak
188zpi 41.6477381898475 28.8130893094339
46edo 46 Has a strong zeta peak
214zpi 46.0089748051542 26.0818678330031
24ed7/5 49.4410252105474856113176748367503004273289162621701693783146801217971309033 Gamma 7/5 analogue
257zpi 52.9968291550147 22.6428640945673
53edo 53 Has a strong zeta peak
282zpi 56.9682909142655 21.0643496713977
282zpi no-3 no-5 analogue 56.9949885079206769176514037038198357725273287855611008976484058072516 21.0544827083039808806917479490481104480956786904618314090632684997207904034
57edo 57 Has a strong no-3 no-5 zeta peak
58edo 58 Has a strong zeta peak
289zpi 58.0667185533159 20.6658827964969
301zpi 59.9201656607655 20.0266469020418
60edo 60 Has a strong zeta peak
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
380zpi 71.9506065993786 16.6781081733140
72edo 72 Has a strong zeta peak
414zpi 76.9918536925042 15.5860645308353
77edo 77 Has a strong zeta peak
80edo 80 Has a strong zeta peak
435zpi 80.0731374302484 14.9862992572924
455zpi no-3 no-5 analogue 82.9585473728587401934282446836610895074185494886540503684148508037660 14.4650555970631644892614919440394905869155594072293855522604093941309631517
455zpi 82.9665108106434 14.4636671866169
83edo 83 Has a strong no-3 no-5 zeta peak
462zpi 83.9972142607288 14.2861880666087
84edo 84 Has a strong zeta peak
87edo 87 Has a strong zeta peak
483zpi 87.0139255957575 13.7908960178956
532zpi 93.9836761074943 12.7681747480009
94edo 94 Has a strong zeta peak
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
695zpi 116.484048333840 10.3018397554387
1114zpi 170.995891689006 7.01771246166817
171edo 171 Exceptionally strong zeta peak
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
684edo 684 171*2^n family
Retrieved from "https://en.xen.wiki/index.php?title=User:Contribution/Collection_of_tunings&oldid=199003"