Xenharmonic Wiki

Relative errors of small EDOs: Difference between revisions

← Older editNewer edit →
VisualWikitext
No edit summary
No edit summary
Line 433: Line 433:
|356.4
|356.4
|88.7
|88.7
|
|127.9
|
|
|
|
Line 444: Line 444:
| -228.6
| -228.6
| -233.3
| -233.3
|
|320.5
|
|
|
|
Line 455: Line 455:
|186.5
|186.5
|444.8
|444.8
|
| -486.8
|
|
|
|
Line 466: Line 466:
| -398.5
| -398.5
|122.9
|122.9
|
| -294.2
|
|
|
|
Line 477: Line 477:
|16.5
|16.5
| -199.1
| -199.1
|
| -101.6
|
|
|
|
Line 488: Line 488:
|431.6
|431.6
|479.0
|479.0
|
|91.1
|
|
|
|
Line 499: Line 499:
| -153.4
| -153.4
|157.1
|157.1
|
|283.7
|
|
|
|
Line 510: Line 510:
|261.6
|261.6
| -164.8
| -164.8
|
|476.4
|
|
|
|
Line 521: Line 521:
| -323.3
| -323.3
| -486.8
| -486.8
|
| -331.0
|
|
|
|
Line 532: Line 532:
|91.7
|91.7
|191.3
|191.3
|
| -138.3
|
|
|
|
Line 543: Line 543:
| -493.2
| -493.2
| -130.6
| -130.6
|
|54.3
|
|
|
|
Line 554: Line 554:
| -78.2
| -78.2
| -452.5
| -452.5
|
|247.0
|
|
|
|
Line 565: Line 565:
|336.8
|336.8
|225.5
|225.5
|
|439.6
|
|
|
|
Line 576: Line 576:
| -248.1
| -248.1
| -96.4
| -96.4
|
| -367.7
|
|
|
|
Line 587: Line 587:
|166.9
|166.9
| -418.3
| -418.3
|
| -175.1
|
|
|
|
Line 598: Line 598:
| -418.1
| -418.1
|259.7
|259.7
|
|17.5
|
|
|
|
Line 609: Line 609:
| -3.0
| -3.0
| -62.2
| -62.2
|
|210.2
|
|
|
|
Line 620: Line 620:
|412.0
|412.0
| -384.1
| -384.1
|
|402.8
|
|
|
|
Line 631: Line 631:
| -172.9
| -172.9
|294.0
|294.0
|
| -404.5
|
|
|
|
Line 642: Line 642:
|242.1
|242.1
| -28.0
| -28.0
|
| -211.9
|
|
|
|
Line 653: Line 653:
| -342.9
| -342.9
| -349.9
| -349.9
|
| -19.2
|
|
|
|
Line 664: Line 664:
|72.2
|72.2
|328.2
|328.2
|
|173.4
|
|
|
|
Line 675: Line 675:
|487.2
|487.2
|6.2
|6.2
|
|366.1
|
|
|
|
Line 686: Line 686:
| -97.8
| -97.8
| -315.7
| -315.7
|
| -441.3
|
|
|
|
Line 697: Line 697:
|317.3
|317.3
|362.4
|362.4
|
| -248.7
|
|
|
|
Line 708: Line 708:
| -267.4
| -267.4
|40.5
|40.5
|
| -56.0
|
|
|
|
Line 719: Line 719:
|147.4
|147.4
| -281.5
| -281.5
|
|136.6
|
|
|
|
Line 730: Line 730:
| -437.6
| -437.6
|396.6
|396.6
|
|329.3
|
|
|
|
Line 741: Line 741:
| -22.6
| -22.6
|74.7
|74.7
|
| -478.1
|
|
|
|
Line 752: Line 752:
|392.5
|392.5
| -247.3
| -247.3
|
| -285.4
|
|
|
|
Line 763: Line 763:
| -192.5
| -192.5
|430.8
|430.8
|
| -92.8
|
|
|
|
Line 774: Line 774:
|222.5
|222.5
|108.9
|108.9
|
|99.9
|
|
|
|
Line 785: Line 785:
| -362.4
| -362.4
| -213.0
| -213.0
|
|292.5
|
|
|
|
Line 796: Line 796:
|52.6
|52.6
|465.0
|465.0
|
|485.2
|
|
|
|
Line 807: Line 807:
|467.7
|467.7
|143.1
|143.1
|
| -322.2
|
|
|
|
Line 818: Line 818:
| -117.3
| -117.3
| -178.8
| -178.8
|
| -129.6
|
|
|
|
Line 829: Line 829:
|297.7
|297.7
|499.2
|499.2
|
|63.1
|
|
|
|
Line 840: Line 840:
| -287.2
| -287.2
|143.1
|143.1
|
|255.7
|
|
|
|
Line 851: Line 851:
|127.8
|127.8
| -144.6
| -144.6
|
|448.4
|
|
|
|
Line 862: Line 862:
| -457.2
| -457.2
| -466.5
| -466.5
|
| -359.0
|
|
|
|
Line 873: Line 873:
| -42.1
| -42.1
|211.5
|211.5
|
| -166.3
|
|
|
|
Line 884: Line 884:
|372.9
|372.9
| -110.4
| -110.4
|
|26.3
|
|
|
|
Line 895: Line 895:
| -212.0
| -212.0
| -432.3
| -432.3
|
|219.0
|
|
|
|
Line 906: Line 906:
|203.0
|203.0
|245.8
|245.8
|
|411.6
|
|
|
|
Line 917: Line 917:
| -382.0
| -382.0
| -76.2
| -76.2
|
| -395.7
|
|
|
|
Line 928: Line 928:
|33.1
|33.1
| -398.1
| -398.1
|
| -203.1
|
|
|
|
Line 939: Line 939:
|448.1
|448.1
|280.0
|280.0
|
| -10.5
|
|
|
|
Line 950: Line 950:
| -136.9
| -136.9
| -42.0
| -42.0
|
|182.2
|
|
|
|
Line 961: Line 961:
|278.2
|278.2
| -363.9
| -363.9
|
|374.8
|
|
|
|
Line 972: Line 972:
| -306.8
| -306.8
|314.2
|314.2
|
| -432.5
|
|
|
|
Line 983: Line 983:
|108.3
|108.3
| -7.7
| -7.7
|
| -239.9
|
|
|
|
Line 994: Line 994:
| -476.7
| -476.7
| -329.7
| -329.7
|
| -47.2
|
|
|
|
Line 1,005: Line 1,005:
| -61.7
| -61.7
|348.4
|348.4
|
|145.4
|
|
|
|
Line 1,016: Line 1,016:
|353.4
|353.4
|26.5
|26.5
|
|338.1
|
|
|
|
Line 1,027: Line 1,027:
| -231.6
| -231.6
| -295.5
| -295.5
|
| -469.3
|
|
|
|
Line 1,038: Line 1,038:
|183.4
|183.4
|382.6
|382.6
|
| -276.7
|
|
|
|
Line 1,049: Line 1,049:
| -401.5
| -401.5
|60.7
|60.7
|
| -84.0
|
|
|
|
Line 1,060: Line 1,060:
|13.5
|13.5
| -261.2
| -261.2
|
|108.6
|
|
|
|
Line 1,071: Line 1,071:
|428.6
|428.6
|416.8
|416.8
|
|301.3
|
|
|
|
Line 1,082: Line 1,082:
| -156.4
| -156.4
|94.9
|94.9
|
|493.9
|
|
|
|
Line 1,093: Line 1,093:
|258.6
|258.6
| -227.0
| -227.0
|
| -313.4
|
|
|
|
Line 1,104: Line 1,104:
| -326.3
| -326.3
|451.0
|451.0
|
| -120.8
|
|
|
|
Line 1,115: Line 1,115:
|88.7
|88.7
|129.1
|129.1
|
|71.9
|
|
|
|
Line 1,124: Line 1,124:


== List of RMS Relative Errors of JI Subgroup for Small Edos ==
== List of RMS Relative Errors of JI Subgroup for Small Edos ==
Note: octave equivalence is assumed. For example, the 5-odd-limit takes account of 2/1, 3/1, 5/1, 5/3 and their octave inverses. The 9-odd-limit takes account of 3/2 twice as the [[tonality diamond]] suggests.  
Notes:
# Patent val mapping is used throughout. 
# Octave equivalence is assumed. For example, the 5-odd-limit takes account of 2/1, 3/1, 5/1, 5/3 and their octave inverses.
# The 9-odd-limit takes account of 3/2 twice as the [[tonality diamond]] suggests. Same goes for other non-prime limits. 
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible"
! rowspan="2" |Edo
! rowspan="2" |Edo
Line 1,144: Line 1,147:
|293.5
|293.5
|452.5
|452.5
|
|408.9
|
|585.0
|
|
|
|
Line 1,157: Line 1,160:
|120.2
|120.2
|328.8
|328.8
|
|356.6
|
|431.1
|
|
|
|
Line 1,170: Line 1,173:
|173.3
|173.3
|162.6
|162.6
|
|365.9
|
|455.1
|
|
|
|
Line 1,183: Line 1,186:
|240.3
|240.3
|224.2
|224.2
|
|196.1
|
|330.7
|
|
|
|
Line 1,196: Line 1,199:
|53.2
|53.2
|253.7
|253.7
|
|254.6
|
|228.5
|
|
|
|
Line 1,209: Line 1,212:
|346.6
|346.6
|325.2
|325.2
|
|284.5
|
|546.1
|
|
|
|
Line 1,222: Line 1,225:
|67.0
|67.0
|156.9
|156.9
|
|333.6
|
|318.7
|
|
|
|
Line 1,235: Line 1,238:
|226.5
|226.5
|271.0
|271.0
|
|519.9
|
|576.8
|
|
|
|
Line 1,248: Line 1,251:
|187.1
|187.1
|232.1
|232.1
|
|245.6
|
|335.9
|
|
|
|
Line 1,261: Line 1,264:
|106.3
|106.3
|227.7
|227.7
|
|201.5
|
|271.0
|
|
|
|
Line 1,274: Line 1,277:
|307.3
|307.3
|547.1
|547.1
|
|483.1
|
|695.3
|
|
|
|
Line 1,287: Line 1,290:
|13.8
|13.8
|104.4
|104.4
|
|200.4
|
|199.3
|
|
|
|
Line 1,300: Line 1,303:
|279.7
|279.7
|363.2
|363.2
|
|487.5
|
|677.8
|
|
|
|
Line 1,313: Line 1,316:
|134.0
|134.0
|431.5
|431.5
|
|460.3
|
|469.9
|
|
|
|
Line 1,326: Line 1,329:
|159.5
|159.5
|144.1
|144.1
|
|202.6
|
|291.6
|
|
|
|
Line 1,339: Line 1,342:
|254.1
|254.1
|221.0
|221.0
|
|254.0
|
|432.9
|
|
|
|
Line 1,352: Line 1,355:
|39.3
|39.3
|355.6
|355.6
|
|412.1
|
|378.0
|
|
|
|
Line 1,365: Line 1,368:
|332.8
|332.8
|289.0
|289.0
|
|298.0
|
|476.3
|
|
|
|
Line 1,378: Line 1,381:
|80.8
|80.8
|81.7
|81.7
|
|186.2
|
|174.0
|
|
|
|
Line 1,391: Line 1,394:
|212.7
|212.7
|455.3
|455.3
|
|402.9
|
|542.0
|
|
|
|
Line 1,404: Line 1,407:
|201.0
|201.0
|321.1
|321.1
|
|283.1
|
|425.8
|
|
|
|
Line 1,417: Line 1,420:
|92.5
|92.5
|131.7
|131.7
|
|185.3
|
|201.1
|
|
|
|
Line 1,430: Line 1,433:
|321.1
|321.1
|305.0
|305.0
|
|539.6
|
|682.0
|
|
|
|
Line 1,443: Line 1,446:
|27.6
|27.6
|208.8
|208.8
|
|349.0
|
|312.4
|
|
|
|
Line 1,456: Line 1,459:
|265.8
|265.8
|284.4
|284.4
|313.8
|514.5
|
|
|
|
Line 1,463: Line 1,468:
|
|
|
|
|
|-
|
|-
|26
|26
|147.8
|147.8
|227.3
|227.3
|
|238.4
|
|269.8
|
|
|
|
Line 1,482: Line 1,485:
|145.7
|145.7
|192.1
|192.1
|
|168.9
|
|206.0
|
|
|
|
Line 1,495: Line 1,498:
|268.0
|268.0
|263.2
|263.2
|
|413.4
|
|587.3
|
|
|
|
Line 1,508: Line 1,511:
|25.5
|25.5
|251.3
|251.3
|
|300.3
|
|307.5
|
|
|
|
Line 1,521: Line 1,524:
|319.0
|319.0
|288.3
|288.3
|
|405.2
|
|583.2
|
|
|
|
Line 1,534: Line 1,537:
|94.6
|94.6
|102.5
|102.5
|
|89.7
|
|161.3
|
|
|
|
Line 1,547: Line 1,550:
|198.8
|198.8
|357.0
|357.0
|
|331.2
|
|433.6
|
|
|
|
Line 1,560: Line 1,563:
|214.8
|214.8
|417.3
|417.3
|
|424.5
|
|573.8
|
|
|
|
Line 1,573: Line 1,576:
|78.7
|78.7
|68.1
|68.1
|
|336.1
|
|348.2
|
|
|
|
Line 1,586: Line 1,589:
|334.9
|334.9
|290.9
|290.9
|
|254.0
|
|477.9
|
|
|
|
Line 1,599: Line 1,602:
|41.5
|41.5
|313.1
|313.1
|
|298.2
|
|289.4
|
|
|
|
Line 1,612: Line 1,615:
|252.0
|252.0
|227.2
|227.2
|
|198.8
|
|386.5
|
|
|
|
Line 1,625: Line 1,628:
|161.6
|161.6
|163.3
|163.3
|341.8
|397.0
|
|
|
|
Line 1,632: Line 1,637:
|
|
|
|
|
|-
|
|-
|39
|39
|131.8
|131.8
|273.6
|273.6
|
|515.2
|
|502.3
|
|
|
|
Line 1,651: Line 1,654:
|281.8
|281.8
|333.8
|333.8
|
|320.1
|
|487.1
|
|
|
|
Line 1,664: Line 1,667:
|11.7
|11.7
|146.9
|146.9
|
|131.0
|
|132.6
|
|
|
|
Line 1,677: Line 1,680:
|305.2
|305.2
|323.3
|323.3
|
|314.6
|
|463.9
|
|
|
|
Line 1,690: Line 1,693:
|108.5
|108.5
|190.1
|190.1
|
|248.5
|
|318.2
|
|
|
|
Line 1,703: Line 1,706:
|185.0
|185.0
|263.4
|263.4
|
|370.7
|
|402.2
|
|
|
|
Line 1,716: Line 1,719:
|228.6
|228.6
|303.4
|303.4
|
|267.8
|
|323.3
|
|
|
|
Line 1,729: Line 1,732:
|64.9
|64.9
|117.2
|117.2
|
|183.5
|
|186.2
|
|
|
|
Line 1,742: Line 1,745:
|348.8
|348.8
|313.0
|313.0
|
|322.7
|
|584.7
|
|
|
|
Line 1,755: Line 1,758:
|55.3
|55.3
|296.2
|296.2
|
|379.3
|
|342.2
|
|
|
|
Line 1,768: Line 1,771:
|238.2
|238.2
|210.2
|210.2
|
|246.8
|
|337.0
|
|
|
|
Line 1,781: Line 1,784:
|175.5
|175.5
|153.2
|153.2
|
|212.8
|
|269.9
|
|
|
|
Line 1,794: Line 1,797:
|118.0
|118.0
|369.2
|369.2
|327.8
|395.0
|
|
|
|
Line 1,801: Line 1,806:
|
|
|
|
|
|-
|
|-
|52
|52
|295.6
|295.6
|418.8
|418.8
|
|368.5
|
|584.2
|
|
|
|
Line 1,820: Line 1,823:
|2.1
|2.1
|42.9
|42.9
|
|156.4
|
|141.8
|
|
|
|
Line 1,833: Line 1,836:
|291.3
|291.3
|487.6
|487.6
|
|497.5
|
|619.3
|
|
|
|
Line 1,846: Line 1,849:
|122.3
|122.3
|289.1
|289.1
|
|385.3
|
|381.6
|
|
|
|
Line 1,859: Line 1,862:
|171.2
|171.2
|181.9
|181.9
|
|244.1
|
|363.9
|
|
|
|
Line 1,872: Line 1,875:
|242.4
|242.4
|245.0
|245.0
|
|254.8
|
|381.3
|
|
|
|
Line 1,885: Line 1,888:
|51.0
|51.0
|211.2
|211.2
|
|186.2
|
|166.1
|
|
|
|
Line 1,898: Line 1,901:
|344.5
|344.5
|342.3
|342.3
|
|326.6
|
|542.8
|
|
|
|
Line 1,911: Line 1,914:
|69.1
|69.1
|197.9
|197.9
|
|263.3
|
|235.1
|
|
|
|
Line 1,924: Line 1,927:
|224.4
|224.4
|241.9
|241.9
|
|376.0
|
|461.9
|
|
|
|
Line 1,937: Line 1,940:
|189.3
|189.3
|205.1
|205.1
|
|179.5
|
|322.6
|
|
|
|
Line 1,950: Line 1,953:
|104.2
|104.2
|266.9
|266.9
|
|261.4
|
|292.9
|
|
|
|
Line 1,963: Line 1,966:
|309.4
|309.4
|511.0
|511.0
|499.4
|724.3
|
|
|
|
Line 1,970: Line 1,975:
|
|
|
|
|
|-
|
|-
|65
|65
|16.0
|16.0
|62.3
|62.3
|
|328.9
|
|295.6
|
|
|
|
Line 1,989: Line 1,992:
|277.5
|277.5
|395.1
|395.1
|
|408.3
|
|614.1
|
|
|
|
Line 2,002: Line 2,005:
|136.1
|136.1
|390.9
|390.9
|
|359.3
|
|409.0
|
|
|
|
Line 2,015: Line 2,018:
|157.4
|157.4
|136.3
|136.3
|
|119.2
|
|229.5
|
|
|
|
Line 2,028: Line 2,031:
|256.3
|256.3
|223.1
|223.1
|
|372.1
|
|515.5
|
|
|
|
Line 2,041: Line 2,044:
|37.2
|37.2
|311.9
|311.9
|
|340.6
|
|316.2
|
|
|
|
Line 2,054: Line 2,057:
|330.7
|330.7
|293.5
|293.5
|
|429.1
|
|646.1
|
|
|
|
Line 2,067: Line 2,070:
|82.9
|82.9
|111.3
|111.3
|
|99.2
|
|117.5
|
|
|
|
Line 2,080: Line 2,083:
|210.5
|210.5
|307.6
|307.6
|
|299.5
|
|352.1
|
|
|
|
Line 2,093: Line 2,096:
|203.1
|203.1
|287.1
|287.1
|
|315.3
|
|463.5
|
|
|
|
Line 2,106: Line 2,109:
|90.4
|90.4
|166.9
|166.9
|
|331.0
|
|308.4
|
|
|
|
Line 2,119: Line 2,122:
|323.3
|323.3
|326.6
|326.6
|
|287.1
|
|440.1
|
|
|
|
Line 2,132: Line 2,135:
|29.8
|29.8
|166.5
|166.5
|
|205.9
|
|190.6
|
|
|
|
Line 2,145: Line 2,148:
|263.7
|263.7
|310.2
|310.2
|
|273.7
|
|473.9
|
|
|
|
Line 2,158: Line 2,161:
|149.9
|149.9
|264.8
|264.8
|
|366.1
|
|378.6
|
|
|
|
Line 2,171: Line 2,174:
|143.5
|143.5
|160.8
|160.8
|
|221.6
|
|228.8
|
|
|
|
Line 2,184: Line 2,187:
|270.1
|270.1
|247.6
|247.6
|
|268.4
|
|409.2
|
|
|
|
Line 2,197: Line 2,200:
|23.4
|23.4
|293.9
|293.9
|
|262.0
|
|265.3
|
|
|
|
Line 2,210: Line 2,213:
|346.9
|346.9
|277.2
|277.2
|
|293.3
|
|505.3
|
|
|
|
Line 2,223: Line 2,226:
|96.8
|96.8
|85.9
|85.9
|
|175.1
|
|227.6
|
|
|
|
Line 2,236: Line 2,239:
|196.7
|196.7
|394.4
|394.4
|
|433.9
|
|484.7
|
|
|
|
Line 2,249: Line 2,252:
|216.9
|216.9
|380.3
|380.3
|
|437.3
|
|495.7
|
|
|
|
Line 2,262: Line 2,265:
|76.6
|76.6
|79.4
|79.4
|
|191.9
|
|228.6
|
|
|
|
Line 2,275: Line 2,278:
|337.1
|337.1
|299.0
|299.0
|
|298.6
|
|519.6
|
|
|
|
Line 2,288: Line 2,291:
|43.6
|43.6
|270.8
|270.8
|
|238.6
|
|254.5
|
|
|
|
Line 2,301: Line 2,304:
|249.9
|249.9
|241.1
|241.1
|
|251.9
|
|389.3
|
|
|
|
Line 2,314: Line 2,317:
|163.8
|163.8
|190.4
|190.4
|
|254.1
|
|260.8
|
|
|
|
Line 2,327: Line 2,330:
|129.7
|129.7
|234.4
|234.4
|
|367.0
|
|372.4
|
|
|
|
Line 2,340: Line 2,343:
|283.9
|283.9
|307.6
|307.6
|
|269.2
|
|484.0
|
|
|
|
Line 2,353: Line 2,356:
|9.6
|9.6
|189.7
|189.7
|
|207.6
|
|188.8
|
|
|
|
Line 2,366: Line 2,369:
|303.0
|303.0
|299.0
|299.0
|
|261.3
|
|415.5
|
|
|
|
Line 2,379: Line 2,382:
|110.6
|110.6
|155.4
|155.4
|
|363.1
|
|411.4
|
|
|
|
Line 2,390: Line 2,393:
|-
|-
|97
|97
|18209
|182.9
|297.6
|297.6
|
|335.4
|
|463.8
|
|
|
|
Line 2,405: Line 2,408:
|230.7
|230.7
|478.1
|478.1
|
|430.6
|
|550.3
|
|
|
|
Line 2,418: Line 2,421:
|62.7
|62.7
|80.9
|80.9
|
|70.6
|
|89.3
|
|
|
|
Retrieved from "https://en.xen.wiki/w/Relative_errors_of_small_EDOs"