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== Practical Boundaries of EDOs: [5 ; 112]-EDOs ==
My EDO list (23-limit mapping):
0-4: Joke EDOs


5-6: XXS EDOs
Small EDOs: [[12edo|12fi]], [[14edo|14cf]], [[15edo|15g]], [[17edo|17cgh]], [[19edo|19]], [[22edo|22fh]], [[24edo|24d]], [[26edo|26i]], [[27edo|27eg]], [[29edo|29g]]


7-9: XS EDOs
Medium EDOs: [[31edo|31]], [[34edo|34dh]], [[36edo|36]], [[37edo|37]], [[41edo|41]], [[43edo|43]], [[46edo|46]], [[49edo|49fgh]], [[50edo|50]], [[53edo|53]], [[58edo|58hi]]


10-13: S EDOs
Large EDOs: [[68edo|65d]], [[68edo|68e]], [[72edo|72]], [[77edo|77]], [[80edo|80]], [[87edo|87]], [[94edo|94]], [[99edo|99ef]]


14-19: SM EDOs
Exceptional EDOs: [[111edo|111]], [[171edo|171h]], [[172edo|172f]], [[248edo|248]], [[270edo|270]], [[311edo|311]], [[342edo|342f]], [[684edo|684h]]
 
20-27: M EDOs
 
28-39: ML EDOs
 
40-55: L EDOs
 
56-79: XL EDOs
 
80-112: XXL EDOs
 
113+: Nightmare EDOs
 
171, 270, 311, 342, 684: Joker EDOs.
 
=== Individual pages ===


{| class="wikitable"
{| class="wikitable"
|
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| [[7edo|'''7''']]
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|-
| [[10edo|'''10''']]
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| [[12edo|'''12''']]
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| [[14edo|'''14''']]
| [[15edo|'''15''']]
|
| [[17edo|'''17''']]
|
| [[19edo|'''19''']]
|-
|
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| [[22edo|'''22''']]
|
| [[24edo|'''24''']]
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| [[26edo|'''26''']]
| [[27edo|'''27''']]
|
| [[29edo|'''29''']]
|-
|
| [[31edo|'''31''']]
|
|
| [[34edo|'''34''']]
|
| [[36edo|'''36''']]
| [[37edo|'''37''']]
| [[38edo|'''38''']]
| [[39edo|'''39''']]
|-
|
| [[41edo|'''41''']]
|
| [[43edo|'''43''']]
|
|
| [[46edo|'''46''']]
|
| [[48edo|'''48''']]
| [[49edo|'''49''']]
|-
| [[50edo|'''50''']]
|
|
| [[53edo|'''53''']]
|
|
| [[56edo|'''56''']]
|
| [[58edo|'''58''']]
|
|-
| [[60edo|'''60''']]
|
| [[62edo|'''62''']]
| [[63edo|'''63''']]
|
| [[65edo|'''65''']]
|
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| [[68edo|'''68''']]
|
|-
|
|
| [[72edo|'''72''']]
|
|
|
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| [[77edo|'''77''']]
|
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|-
| [[80edo|'''80''']]
|
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| [[84edo|'''84''']]
|
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| [[87edo|'''87''']]
|
| [[89edo|'''89''']]
|-
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| [[94edo|'''94''']]
|
| [[96edo|'''96''']]
|
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| [[99edo|'''99''']]
|-
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| [[103edo|'''103''']]
|
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| [[106edo|'''106''']]
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|-
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| [[111edo|'''111''']]
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| [[113edo|'''113''']]
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|
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| [[118edo|'''118''']]
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|-
|-
|
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| [[121edo|'''121''']]
|
|
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| [[125edo|'''125''']]
|
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| [[12edo|'''<u>12</u>''']]
|
|
| [[14edo|14]]
| [[15edo|15]]
|
|
| [[17edo|17]]
|
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| [[19edo|'''<u>19</u>''']]
|-
|-
| [[130edo|'''130''']]
|
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| [[22edo|'''<u>22</u>''']]
|
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|[[24edo|24]]
|
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|[[26edo|26]]
|[[27edo|'''27''']]
|
|
|[[29edo|29]]
|-
|-
| [[140edo|'''140''']]
|
|
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| [[31edo|'''<u>31</u>''']]
|
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| [[34edo|'''<u>34</u>''']]
|
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|[[36edo|36]]
| [[37edo|37]]
|
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|-
|-
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| [[41edo|'''<u>41</u>''']]
|
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| [[152edo|'''152''']]
|[[43edo|43]]
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| [[46edo|'''<u>46</u>''']]
|
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| [[159edo|'''159''']]
|[[49edo|49]]
|-
|-
|[[50edo|50]]
|
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| [[53edo|'''<u>53</u>''']]
|
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| [[58edo|'''58''']]
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|-
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| [[171edo|'''171''']]
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Line 221: Line 71:
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| [[65edo|'''65''']]
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| [[68edo|'''68''']]
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|-
|-
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| [[72edo|'''<u>72</u>''']]
| [[183edo|'''183''']]
|
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| [[77edo|'''<u>77</u>''']]
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|-
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| [[80edo|'''80''']]
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Line 242: Line 95:
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| [[87edo|'''<u>87</u>''']]
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Line 251: Line 103:
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| [[94edo|'''<u>94</u>''']]
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| [[99edo|'''99''']]
|
|}
 
{| class="wikitable"
|[[111edo|111]]
|[[171edo|'''<u>171</u>''']]
|[[172edo|172]]
|[[248edo|248]]
|[[270edo|'''<u>270</u>''']]
|[[311edo|'''<u>311</u>''']]
|[[342edo|'''342''']]
|[[684edo|'''684''']]
|}
 
== Gallery of best ZPIs ==
{|class="wikitable sortable"
!colspan="3"|Tuning
!colspan="3"|Strength
!colspan="2"|Closest EDO
!colspan="2"|Integer limit
|-
!ZPI
!Steps per octave
!Cents
!Height
!Integral
!Gap
!EDO
!Octave
!Consistent
!Distinct
|-
|[[26zpi]]
|10.0084563372591
|119.898609691954
|4.477141
|1.082282
|14.181485
|[[10edo]]
|1198.98609691954
|8
|5
|-
|[[34zpi]]
|12.0231830072926
|99.8071807833375
|5.193290
|1.269599
|15.899282
|[[12edo]]
|1197.68616940005
|10
|6
|-
|[[42zpi]]
|13.9002525327005
|86.3293668353859
|4.592177
|0.984037
|14.097244
|[[14edo]]
|1208.61113569540
|7
|5
|-
|[[47zpi]]
|15.0534898676781
|79.7157343943591
|5.050324
|1.104057
|14.918297
|[[15edo]]
|1195.73601591539
|8
|7
|-
|[[56zpi]]
|17.0445886606675
|70.4035764012981
|5.056957
|1.032175
|14.269437
|[[17edo]]
|1196.86079882207
|4
|4
|-
|[[65zpi]]
|18.9480867166984
|63.3309324546460
|5.980169
|1.313799
|16.699651
|[[19edo]]
|1203.28771663827
|10
|7
|-
|[[80zpi]]
|22.0251467420146
|54.4831784348982
|6.062600
|1.258178
|16.213941
|[[22edo]]
|1198.62992556776
|12
|8
|-
|[[90zpi]]
|24.0057421830853
|49.9880399800983
|5.721613
|1.092055
|14.821136
|[[24edo]]
|1199.71295952236
|6
|6
|-
|[[100zpi]]
|25.9356996537225
|46.2682717652372
|5.545073
|1.031155
|14.793013
|[[26edo]]
|1202.97506589617
|14
|9
|-
|[[106zpi]]
|27.0866140827635
|44.3023257293579
|6.069233
|1.185939
|16.215619
|[[27edo]]
|1196.16279469266
|10
|8
|-
|[[116zpi]]
|28.9399661541990
|41.4651487014917
|5.566209
|1.000619
|14.904418
|[[29edo]]
|1202.48931234326
|8
|7
|-
|[[127zpi]]
|30.9783816349790
|38.7366910944446
|7.003472
|1.403777
|17.739476
|[[31edo]]
|1200.83742392778
|12
|9
|-
|[[144zpi]]
|34.0448410043159
|35.2476312005063
|6.685147
|1.241437
|16.236989
|[[34edo]]
|1198.41946081721
|6
|6
|-
|[[155zpi]]
|35.9823877000425
|33.3496490006021
|6.027497
|1.028887
|14.706508
|[[36edo]]
|1200.58736402167
|8
|8
|-
|[[161zpi]]
|37.0275229191254
|32.4083250889078
|5.287327
|0.891828
|15.095854
|[[37edo]]
|1199.10802828959
|8
|8
|-
|[[166zpi]]
|37.8901105027757
|31.6705331305933
|5.808723
|0.986660
|15.046792
|[[38edo]]
|1203.48025896255
|6
|6
|-
|[[173zpi]]
|39.1237487937926
|30.6719073963176
|5.593908
|0.926356
|14.714802
|[[39edo]]
|1196.20438845639
|7
|7
|-
|[[184zpi]]
|40.9880783925993
|29.2768055263764
|7.570230
|1.423937
|17.722623
|[[41edo]]
|1200.34902658143
|16
|10
|-
|[[196zpi]]
|43.0264994477693
|27.8897892090130
|6.166118
|1.035628
|15.545919
|[[43edo]]
|1199.26093598756
|8
|8
|-
|[[207zpi]]
|44.8397488079316
|26.7619697233392
|5.252141
|0.837163
|14.719415
|[[45edo]]
|1204.28863755026
|7
|7
|-
|[[214zpi]]
|46.0089748051542
|26.0818678330031
|7.495674
|1.356067
|17.747832
|[[46edo]]
|1199.76592031814
|14
|11
|-
|[[226zpi]]
|47.9883202080850
|25.0060847055410
|5.843508
|0.890480
|13.888482
|[[48edo]]
|1200.29206586597
|6
|6
|-
|[[233zpi]]
|49.1412057629230
|24.4194252332612
|5.691547
|0.920677
|15.624024
|[[49edo]]
|1196.55183642980
|7
|7
|-
|[[238zpi]]
|49.9385162652878
|24.0295485277387
|6.655352
|1.111229
|15.942083
|[[50edo]]
|1201.47742638693
|10
|9
|-
|[[257zpi]]
|52.9968291550147
|22.6428640945673
|8.249774
|1.486620
|18.069918
|[[53edo]]
|1200.07179701207
|10
|10
|-
|[[276zpi]]
|56.0083399588546
|21.4253805929895
|6.063216
|0.931117
|14.804703
|[[56edo]]
|1199.82131320741
|8
|8
|-
|[[289zpi]]
|58.0667185533159
|20.6658827964969
|7.814035
|1.358357
|18.056292
|[[58edo]]
|1198.62120219682
|16
|12
|-
|[[301zpi]]
|59.9201656607655
|20.0266469020418
|7.046396
|1.131000
|15.932359
|[[60edo]]
|1201.59881412251
|10
|10
|-
|[[314zpi]]
|61.9380472360525
|19.3741981471691
|6.262952
|0.952068
|15.026453
|[[62edo]]
|1201.20028512448
|8
|8
|-
|[[321zpi]]
|63.0192885705350
|19.0417890652143
|6.768662
|1.049023
|15.412920
|[[63edo]]
|1199.63271110850
|8
|8
|-
|[[334zpi]]
|65.0158450885860
|18.4570391781413
|7.813349
|1.269821
|16.514861
|[[65edo]]
|1199.70754657919
|6
|6
|-
|[[354zpi]]
|68.0493056282519
|17.6342725163943
|7.666604
|1.254592
|17.034505
|[[68edo]]
|1199.13053111481
|10
|10
|-
|[[380zpi]]
|71.9506065993786
|16.6781081733140
|9.157547
|1.625363
|19.964746
|[[72edo]]
|1200.82378847861
|18
|13
|-
|[[414zpi]]
|76.9918536925042
|15.5860645308353
|8.194847
|1.311364
|17.029289
|[[77edo]]
|1200.12696887432
|10
|10
|-
|[[435zpi]]
|80.0731374302484
|14.9862992572924
|7.873146
|1.247325
|17.087322
|[[80edo]]
|1198.90394058339
|12
|12
|-
|[[448zpi]]
|81.9541455954050
|14.6423343356444
|6.653983
|0.941321
|14.718732
|[[82edo]]
|1200.67141552284
|8
|8
|-
|[[462zpi]]
|83.9972142607288
|14.2861880666087
|8.020965
|1.241945
|16.733121
|[[84edo]]
|1200.03979759513
|10
|10
|-
|[[483zpi]]
|87.0139255957575
|13.7908960178956
|8.869041
|1.439474
|18.061741
|[[87edo]]
|1199.80795355692
|16
|14
|-
|[[497zpi]]
|89.0229355804124
|13.4796723133902
|7.567368
|1.124501
|16.042570
|[[89edo]]
|1199.69083589172
|12
|12
|-
|[[532zpi]]
|93.9836761074943
|12.7681747480009
|8.806201
|1.394050
|17.832744
|[[94edo]]
|1200.20842631208
|24
|15
|-
|[[546zpi]]
|95.9543940692998
|12.5059410946136
|7.327322
|1.045052
|15.480737
|[[96edo]]
|1200.57034508290
|6
|6
|-
|[[568zpi]]
|99.0473345956631
|12.1154194093028
|9.406495
|1.510412
|18.536483
|[[99edo]]
|1199.42652152097
|12
|12
|-
|[[596zpi]]
|102.936629522070
|11.6576577800491
|8.543510
|1.340775
|18.270998
|[[103edo]]
|1200.73875134506
|15
|15
|-
|[[655zpi]]
|111.059577998833
|10.8050113427643
|9.038544
|1.394739
|18.041165
|[[111edo]]
|1199.35625904684
|22
|16
|-
|[[706zpi]]
|117.969513574257
|10.1721195895637
|9.850823
|1.544280
|18.861062
|[[118edo]]
|1200.31011156852
|12
|12
|-
|[[796zpi]]
|130.003910460506
|9.23049157328654
|10.355108
|1.634018
|19.594551
|[[130edo]]
|1199.96390452725
|16
|16
|-
|[[872zpi]]
|139.990541024216
|8.57200773152536
|10.076688
|1.548424
|19.514765
|[[140edo]]
|1200.08108241355
|10
|10
|-
|[[965zpi]]
|152.052848107925
|7.89199291517551
|10.468420
|1.593855
|19.487224
|[[152edo]]
|1199.58292310668
|15
|15
|-
|[[1019zpi]]
|158.953545367059
|7.54937549350618
|9.845175
|1.436994
|18.334134
|[[159edo]]
|1200.35070346748
|16
|16
|-
|[[1114zpi]]
|170.995891689006
|7.01771246166817
|11.076998
|1.652856
|19.091741
|[[171edo]]
|1200.02883094526
|14
|14
|-
|[[1210zpi]]
|182.999728466810
|6.55738677895164
|11.020824
|1.643410
|19.731996
|[[183edo]]
|1200.00178054815
|18
|18
|-
|[[1266zpi]]
|189.933554886685
|6.31799894818965
|10.475446
|1.520966
|19.002922
|[[190edo]]
|1200.41980015603
|16
|16
|-
|-
|
|[[1291zpi]]
|
|193.021683290400
|
|6.21691811792258
|
|10.257644
|
|1.453742
|
|18.344849
|
|[[193edo]]
|
|1199.86519675906
|
|12
|
|12
|-
|-
|
|[[1332zpi]]
|
|198.058774452480
|
|6.05880756011603
|
|10.278915
| [[224edo|'''224''']]
|1.464293
|
|18.655774
|
|[[198edo]]
|
|1199.64389690297
|
|16
|
|16
|-
|-
|
|[[1488zpi]]
|
|217.024704123598
|
|5.52932443726124
|
|11.270977
|
|1.627018
|
|19.515371
|
|[[217edo]]
|
|1199.86340288569
|
|13
|
|13
|-
|-
|
|[[1546zpi]]
|
|224.002551156014
|
|5.35708184485908
|
|11.730463
|
|1.700865
|
|19.715639
|
|[[224edo]]
|
|1199.98633324843
|
|16
|
|16
|-
|-
|
|[[1705zpi]]
|
|242.934231195669
|
|4.93960852735271
|
|11.384629
|
|1.631497
|
|19.962157
|
|[[243edo]]
|
|1200.32487214671
|
|10
|
|10
|-
|-
|
|[[1936zpi]]
|
|270.017794631965
|
|4.44415154799558
|
|13.370691
|
|1.998595
|
|22.286976
|
|[[270edo]]
|
|1199.92091795881
|
|22
|
|22
|-
|-
|[[270edo|'''270''']]
|[[2040zpi]]
|
|282.066063876742
|
|4.25432249277737
|
|11.026514
|
|1.491063
|
|18.869628
|
|[[282edo]]
|
|1199.71894296322
|
|28
|
|24
|-
|-
|
|[[2100zpi]]
|
|288.959426104593
|
|4.15283216809007
|
|10.631610
|
|1.359133
|
|17.289237
|
|[[289edo]]
|
|1200.16849657803
|
|10
|
|10
|-
|-
|
|[[2205zpi]]
|
|300.987043913283
|
|3.98688257274532
|
|11.722438
|
|1.566848
|
|18.581196
|
|[[301edo]]
|
|1200.05165439634
|
|18
|
|18
|-
|-
|
|[[2293zpi]]
|
|311.004029926555
|
|3.85847090239759
|
|13.066467
|
|1.895394
|
|22.370880
|
|[[311edo]]
|
|1199.98445064565
|
|42
|
|25
|-
|-
|
|[[2372zpi]]
| [[311edo|'''311''']]
|319.948565035409
|
|3.75060285039002
|
|10.740787
|
|1.403356
|
|18.462665
|
|[[320edo]]
|
|1200.19291212481
|
|20
|
|20
|-
|-
|
|[[2399zpi]]
|
|322.991983375731
|
|3.71526248874128
|
|11.323352
|
|1.479976
|
|18.943004
|
|[[323edo]]
|
|1200.02978386343
|
|10
|
|10
|-
|-
|
|[[2444zpi]]
|
|328.074125897684
|
|3.65770996635754
|
|11.115173
|
|1.494672
|
|19.606922
|
|[[328edo]]
|
|1199.72886896527
|
|15
|
|15
|-
|-
|
|[[2568zpi]]
|
|341.974850913987
| [[342edo|'''342''']]
|3.50902996753355
|
|13.478611
|
|1.890555
|
|20.767404
|
|[[342edo]]
|
|1200.08824889647
|
|12
|
|12
|-
|-
|
|[[5818zpi]]
|
|683.938934890938
|
|1.75454260429165
|
|14.267321
|[[684edo|'''684''']]
|1.773752
|
|20.109967
|
|[[684edo]]
|
|1200.10714133549
|
|18
|
|18
|}
|}


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