User:BudjarnLambeth/The intervals I see as important: Difference between revisions

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== EDO Consonance Ratings (1–53edo) ==
== EDO Consonance Ratings (1–53edo) ==


Table created using Claude, prompt listed below table.
Table created using Claude (I gave it a PDF of the EDO harmonic tables), prompt listed below table.
 
'''Note: major inaccuracy with this table - errors in the same direction should cancel out but they don't, this was my fault for how I wrote the prompt, I'll fix it later.'''


{| class="wikitable sortable" style="text-align:center; font-size:80%;"
{| class="wikitable sortable" style="text-align:center; font-size:80%;"
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! style="background:#fff0c8;" | 13/3<br/><small>lg tri neu 2nd^</small>
! style="background:#fff0c8;" | 13/3<br/><small>lg tri neu 2nd^</small>
|-
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| style="background:#FF9999;" | 204.0¢ ✗
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| style="background:#FF9999;" | 729.0¢ ✗
| style="background:#FF9999;" | 267.0¢ ✗
| style="background:#FF9999;" | 884.0¢ ✗
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| style="background:#FF9999;" | 551.0¢ ✗
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| style="background:#FF9999;" | 617.0¢ ✗
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| style="background:#FF9999;" | 359.0¢ ✗
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| style="background:#FF9999;" | 231.0¢ ✗
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| style="background:#FF9999;" | 857.0¢ ✗
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| style="background:#FF9999;" | 231.0¢ ✗
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| style="background:#FF9999;" | 343.0¢ ✗
| style="background:#FF9999;" | 139.0¢ ✗
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| style="background:#FF9999;" | 210.0¢ ✗
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| style="background:#FF9999;" | 31.4¢ ✗
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| style="background:#FF9999;" | 45.1¢ ✗
| style="background:#FFD700;" | 17.7¢ ✓
| style="background:#FF9999;" | 31.2¢ ✗
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| style="background:#90EE90;" | 3.9¢ ✓✓
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| style="background:#FF9999;" | 62.6¢ ✗
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| style="background:#FF9999;" | 44.9¢ ✗
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| style="background:#FF9999;" | 49.4¢ ✗
| style="background:#FF9999;" | 49.4¢ ✗
| style="background:#FFD700;" | 26.1¢ ✓
| style="background:#FFD700;" | 26.1¢ ✓
| style="background:#FF9999;" | 31.2¢ ✗
| style="background:#FF9999;" | 31.2¢ ✗
| style="background:#FF9999;" | 57.5¢ ✗
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| '''19'''
| '''19'''
Line 410: Line 427:
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| style="background:#FF9999;" | 21.5¢ ✗
| style="background:#FF9999;" | 21.5¢ ✗
| style="background:#FFD700;" | 14.4¢ ✓
| style="background:#FFD700;" | 14.4¢ ✓
| style="background:#FF9999;" | 28.7¢ ✗
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| '''20'''
| '''20'''
Line 434: Line 452:
| style="background:#FF9999;" | 44.3¢ ✗
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| style="background:#FF9999;" | 35.1¢ ✗
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| '''21'''
| '''21'''
Line 452: Line 471:
| style="background:#FFD700;" | 29.9¢ ✓
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| '''22'''
| '''22'''
Line 467: Line 487:
| style="background:#FFD700;" | 13.0¢ ✓
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Line 476: Line 496:
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| style="background:#FFD700;" | 29.4¢ ✓
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| '''23'''
| '''23'''
Line 482: Line 503:
| style="background:#FF9999;" | 21.1¢ ✗
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| style="background:#FF9999;" | 23.7¢ ✗
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| style="background:#FF9999;" | 44.8¢ ✗
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| style="background:#FF9999;" | 46.2¢ ✗
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| style="background:#FFD700;" | 22.6¢ ✓
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| style="background:#FF9999;" | 43.6¢ ✗
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Line 493: Line 514:
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| '''24'''
| '''24'''
Line 503: Line 525:
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| style="background:#FF9999;" | 32.5¢ ✗
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| '''25'''
| '''25'''
Line 524: Line 547:
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| style="background:#90EE90;" | 8.8¢ ✓✓
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| '''26'''
| '''26'''
Line 536: Line 560:
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| '''27'''
| '''27'''
Line 554: Line 579:
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| '''28'''
| '''28'''
Line 572: Line 598:
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| style="background:#FF9999;" | 33.1¢ ✗
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Line 584: Line 610:
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| style="background:#FF9999;" | 32.8¢ ✗
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| '''29'''
| '''29'''
Line 596: Line 623:
| style="background:#90EE90;" | 15.4¢ ✓✓
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| style="background:#FF9999;" | 31.0¢ ✗
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Line 602: Line 629:
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| '''30'''
| '''30'''
Line 608: Line 636:
| style="background:#FFD700;" | 13.7¢ ✓
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| style="background:#FF9999;" | 31.7¢ ✗
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| style="background:#FF9999;" | 26.8¢ ✗
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| '''31'''
| '''31'''
Line 629: Line 658:
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| '''32'''
| '''32'''
Line 647: Line 677:
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| '''33'''
| '''33'''
Line 668: Line 699:
| style="background:#FFD700;" | 24.7¢ ✓
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| '''34'''
| '''34'''
Line 680: Line 712:
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| '''35'''
| '''35'''
Line 698: Line 731:
| style="background:#90EE90;" | 9.2¢ ✓✓
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| style="background:#FF9999;" | 25.4¢ ✗
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| '''36'''
| '''36'''
Line 719: Line 753:
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| style="background:#90EE90;" | 3.9¢ ✓✓
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| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#90EE90;" | 15.7¢ ✓✓
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| style="background:#90EE90;" | 15.3¢ ✓✓
Line 727: Line 761:
| style="background:#90EE90;" | 7.2¢ ✓✓
| style="background:#90EE90;" | 7.2¢ ✓✓
| style="background:#90EE90;" | 2.2¢ ✓✓
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| style="background:#90EE90;" | 9.2¢ ✓✓
| style="background:#90EE90;" | 5.2¢ ✓✓
| style="background:#FF9999;" | 26
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| '''37'''
| '''37'''
Line 734: Line 769:
| style="background:#90EE90;" | 2.9¢ ✓✓
| style="background:#90EE90;" | 2.9¢ ✓✓
| style="background:#FFD700;" | 11.6¢ ✓
| style="background:#FFD700;" | 11.6¢ ✓
| style="background:#FFD700;" | 14.5¢ ✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 4.1¢ ✓✓
| style="background:#90EE90;" | 4.1¢ ✓✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#FFD700;" | 15.7¢ ✓
| style="background:#90EE90;" | 7.5¢ ✓✓
| style="background:#90EE90;" | 14.5¢ ✓✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
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| style="background:#90EE90;" | 7.0¢ ✓✓
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| style="background:#90EE90;" | 11.6¢ ✓✓
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| style="background:#90EE90;" | 2.7¢ ✓✓
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| style="background:#90EE90;" | 14.3¢ ✓✓
| style="background:#90EE90;" | 8.9¢ ✓✓
| style="background:#FF9999;" | 27
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| '''38'''
| '''38'''
Line 752: Line 788:
| style="background:#90EE90;" | 7.4¢ ✓✓
| style="background:#90EE90;" | 7.4¢ ✓✓
| style="background:#90EE90;" | 7.2¢ ✓✓
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| style="background:#FFD700;" | 14.6¢ ✓
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#FFD700;" | 10.1¢ ✓
| style="background:#FFD700;" | 10.1¢ ✓
| style="background:#FFD700;" | 14.4¢ ✓
| style="background:#FFD700;" | 14.4¢ ✓
| style="background:#FFD700;" | 17.3¢ ✓
| style="background:#FFD700;" | 17.3¢ ✓
| style="background:#90EE90;" | 14.6¢ ✓✓
| style="background:#90EE90;" | 0.2¢ ✓✓
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| style="background:#90EE90;" | 17.5¢ ✓✓
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| style="background:#FFD700;" | 21.8¢ ✓
| style="background:#90EE90;" | 7.0¢ ✓✓
| style="background:#FFD700;" | 21.7¢ ✓
| style="background:#90EE90;" | 7.3¢ ✓✓
| style="background:#90EE90;" | 12.1¢ ✓✓
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| style="background:#90EE90;" | 19.3¢ ✓✓
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| style="background:#FF9999;" | 28
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| '''39'''
| '''39'''
Line 770: Line 807:
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#90EE90;" | 5.7¢ ✓✓
| style="background:#90EE90;" | 5.7¢ ✓✓
| style="background:#FFD700;" | 19.4¢ ✓
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#FFD700;" | 15.0¢ ✓
| style="background:#FFD700;" | 15.0¢ ✓
| style="background:#FFD700;" | 11.5¢ ✓
| style="background:#FFD700;" | 11.5¢ ✓
| style="background:#FF9999;" | 20.7¢ ✗
| style="background:#FF9999;" | 20.7¢ ✗
| style="background:#90EE90;" | 19.4¢ ✓✓
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#90EE90;" | 2.5¢ ✓✓
| style="background:#90EE90;" | 2.5¢ ✓✓
| style="background:#FFD700;" | 28.7¢ ✓
| style="background:#FFD700;" | 28.7¢ ✓
| style="background:#FFD700;" | 25.2¢ ✓
| style="background:#90EE90;" | 2.2¢ ✓✓
| style="background:#90EE90;" | 8.2¢ ✓✓
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| style="background:#90EE90;" | 15.0¢ ✓✓
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| style="background:#FF9999;" | 29
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| '''40'''
| '''40'''
Line 791: Line 829:
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 6.1¢ ✓✓
| style="background:#90EE90;" | 6.1¢ ✓✓
| style="background:#FF9999;" | 20.8¢ ✗
| style="background:#90EE90;" | 3.2¢ ✓✓
| style="background:#90EE90;" | 15.7¢ ✓✓
| style="background:#90EE90;" | 15.7¢ ✓✓
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| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 2.4¢ ✓✓
| style="background:#FFD700;" | 23.3¢ ✓
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
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| style="background:#90EE90;" | 12.5¢ ✓✓
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| style="background:#FF9999;" | 30
|-
|-
| '''41'''
| '''41'''
Line 812: Line 851:
| style="background:#90EE90;" | 6.3¢ ✓✓
| style="background:#90EE90;" | 6.3¢ ✓✓
| style="background:#90EE90;" | 4.8¢ ✓✓
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| style="background:#90EE90;" | 8.3¢ ✓✓
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| style="background:#90EE90;" | 3.0¢ ✓✓
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| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 7.8¢ ✓✓
| style="background:#FF9999;" | 31
|-
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| '''42'''
| '''42'''
Line 824: Line 864:
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FFD700;" | 12.3¢ ✓
| style="background:#FFD700;" | 12.3¢ ✓
| style="background:#FF9999;" | 26.0¢ ✗
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
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| style="background:#90EE90;" | 3.9¢ ✓✓
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| style="background:#FFD700;" | 14.9¢ ✓
| style="background:#90EE90;" | 9.7¢ ✓✓
| style="background:#FFD700;" | 26.0¢ ✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 8.5¢ ✓✓
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| style="background:#90EE90;" | 16.3¢ ✓✓
| style="background:#90EE90;" | 11.1¢ ✓✓
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| style="background:#90EE90;" | 17.6¢ ✓✓
| style="background:#FFD700;" | 20.8¢ ✓
| style="background:#FFD700;" | 20.8¢ ✓
Line 836: Line 876:
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#FFD700;" | 24.3¢ ✓
| style="background:#FFD700;" | 24.3¢ ✓
| style="background:#FF9999;" | 32
|-
|-
| '''43'''
| '''43'''
Line 848: Line 889:
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 6.8¢ ✓✓
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| style="background:#90EE90;" | 12.3¢ ✓✓
| style="background:#90EE90;" | 3.5¢ ✓✓
| style="background:#90EE90;" | 13.0¢ ✓✓
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| style="background:#90EE90;" | 3.3¢ ✓✓
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| style="background:#90EE90;" | 7.9¢ ✓✓
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| style="background:#90EE90;" | 1.0¢ ✓✓
| style="background:#FF9999;" | 33
|-
|-
| '''44'''
| '''44'''
Line 863: Line 905:
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FF9999;" | 20.1¢ ✗
| style="background:#90EE90;" | 5.9¢ ✓✓
| style="background:#90EE90;" | 11.6¢ ✓✓
| style="background:#90EE90;" | 11.6¢ ✓✓
| style="background:#90EE90;" | 5.9¢ ✓✓
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| style="background:#90EE90;" | 17.5¢ ✓✓
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| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 8.5¢ ✓✓
| style="background:#90EE90;" | 13.0¢ ✓✓
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| style="background:#90EE90;" | 4.9¢ ✓✓
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| style="background:#90EE90;" | 13.0¢ ✓✓
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| style="background:#90EE90;" | 12.0¢ ✓✓
| style="background:#90EE90;" | 2.2¢ ✓✓
| style="background:#FF9999;" | 34
|-
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| '''45'''
| '''45'''
Line 878: Line 921:
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#90EE90;" | 8.6¢ ✓✓
| style="background:#90EE90;" | 8.6¢ ✓✓
| style="background:#FF9999;" | 21.6¢ ✗
| style="background:#90EE90;" | 4.4¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 9.4¢ ✓✓
| style="background:#90EE90;" | 9.4¢ ✓✓
| style="background:#FFD700;" | 17.4¢ ✓
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#FFD700;" | 21.6¢ ✓
| style="background:#90EE90;" | 4.4¢ ✓✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#FFD700;" | 21.8¢ ✓
| style="background:#90EE90;" | 4.2¢ ✓✓
| style="background:#FFD700;" | 22.4¢ ✓
| style="background:#FFD700;" | 22.4¢ ✓
| style="background:#90EE90;" | 17.3¢ ✓✓
| style="background:#90EE90;" | 17.3¢ ✓✓
Line 890: Line 933:
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#FFD700;" | 21.4¢ ✓
| style="background:#FFD700;" | 21.4¢ ✓
| style="background:#FF9999;" | 35
|-
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| '''46'''
| '''46'''
Line 896: Line 940:
| style="background:#90EE90;" | 5.0¢ ✓✓
| style="background:#90EE90;" | 5.0¢ ✓✓
| style="background:#90EE90;" | 2.4¢ ✓✓
| style="background:#90EE90;" | 2.4¢ ✓✓
| style="background:#90EE90;" | 7.4¢ ✓✓
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| style="background:#90EE90;" | 7.4¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | 3.5¢ ✓✓
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| style="background:#90EE90;" | 8.6¢ ✓✓
| style="background:#90EE90;" | 8.6¢ ✓✓
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| style="background:#90EE90;" | 0.2¢ ✓✓
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| style="background:#90EE90;" | 5.7¢ ✓✓
| style="background:#90EE90;" | 3.6¢ ✓✓
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| style="background:#90EE90;" | 8.1¢ ✓✓
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| style="background:#FF9999;" | 36
|-
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| '''47'''
| '''47'''
Line 914: Line 959:
| style="background:#90EE90;" | 3.3¢ ✓✓
| style="background:#90EE90;" | 3.3¢ ✓✓
| style="background:#FFD700;" | 12.6¢ ✓
| style="background:#FFD700;" | 12.6¢ ✓
| style="background:#FFD700;" | 15.9¢ ✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 0.3¢ ✓✓
| style="background:#90EE90;" | 0.3¢ ✓✓
| style="background:#FFD700;" | 14.0¢ ✓
| style="background:#FFD700;" | 14.0¢ ✓
| style="background:#90EE90;" | 15.9¢ ✓✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 10.4¢ ✓✓
| style="background:#90EE90;" | 10.4¢ ✓✓
| style="background:#90EE90;" | 4.7¢ ✓✓
| style="background:#90EE90;" | 4.7¢ ✓✓
Line 926: Line 971:
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 14.6¢ ✓✓
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| style="background:#FF9999;" | 37
|-
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| '''48'''
| '''48'''
Line 932: Line 978:
| style="background:#FFD700;" | 11.3¢ ✓
| style="background:#FFD700;" | 11.3¢ ✓
| style="background:#90EE90;" | 2.0¢ ✓✓
| style="background:#90EE90;" | 2.0¢ ✓✓
| style="background:#FFD700;" | 13.3¢ ✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 6.2¢ ✓✓
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| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
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| style="background:#90EE90;" | 13.3¢ ✓✓
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| style="background:#90EE90;" | 17.5¢ ✓✓
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| style="background:#90EE90;" | 15.2¢ ✓✓
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| style="background:#90EE90;" | 3.3¢ ✓✓
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | 9.5¢ ✓✓
| style="background:#90EE90;" | 9.5¢ ✓✓
| style="background:#90EE90;" | 6.2¢ ✓✓
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| style="background:#90EE90;" | 11.5¢ ✓✓
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| style="background:#FF9999;" | 38
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| '''49'''
| '''49'''
Line 950: Line 997:
| style="background:#90EE90;" | 5.5¢ ✓✓
| style="background:#90EE90;" | 5.5¢ ✓✓
| style="background:#90EE90;" | 8.2¢ ✓✓
| style="background:#90EE90;" | 8.2¢ ✓✓
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#90EE90;" | 2.7¢ ✓✓
| style="background:#FFD700;" | 10.8¢ ✓
| style="background:#FFD700;" | 10.8¢ ✓
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#FFD700;" | 19.0¢ ✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | 13.7¢ ✓✓
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| style="background:#90EE90;" | 16.3¢ ✓✓
| style="background:#90EE90;" | 5.3¢ ✓✓
| style="background:#90EE90;" | 13.5¢ ✓✓
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| style="background:#FFD700;" | 20.1¢ ✓
| style="background:#90EE90;" | 3.7¢ ✓✓
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| style="background:#90EE90;" | 10.8¢ ✓✓
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| style="background:#90EE90;" | 16.1¢ ✓✓
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| style="background:#FF9999;" | 39
|-
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| '''50'''
| '''50'''
Line 968: Line 1,016:
| style="background:#90EE90;" | 2.3¢ ✓✓
| style="background:#90EE90;" | 2.3¢ ✓✓
| style="background:#90EE90;" | 6.0¢ ✓✓
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| style="background:#90EE90;" | 8.3¢ ✓✓
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| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#FFD700;" | 11.9¢ ✓
| style="background:#FFD700;" | 11.9¢ ✓
| style="background:#FFD700;" | 14.8¢ ✓
| style="background:#90EE90;" | 2.8¢ ✓✓
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| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | 0.7¢ ✓✓
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| style="background:#90EE90;" | 6.5¢ ✓✓
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| style="background:#FF9999;" | 40
|-
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| '''51'''
| '''51'''
Line 992: Line 1,041:
| style="background:#90EE90;" | 13.7¢ ✓✓
| style="background:#90EE90;" | 13.7¢ ✓✓
| style="background:#90EE90;" | 10.1¢ ✓✓
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| style="background:#90EE90;" | 13.9¢ ✓✓
| style="background:#90EE90;" | 5.7¢ ✓✓
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| style="background:#90EE90;" | 10.4¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#FF9999;" | 41
|-
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| '''52'''
| '''52'''
Line 1,010: Line 1,060:
| style="background:#90EE90;" | 15.6¢ ✓✓
| style="background:#90EE90;" | 15.6¢ ✓✓
| style="background:#90EE90;" | 2.5¢ ✓✓
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| style="background:#90EE90;" | 19.4¢ ✓✓
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| style="background:#FF9999;" | 42
|-
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| '''53'''
| '''53'''
Line 1,022: Line 1,073:
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 0.1¢ ✓✓
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Line 1,075: Line 1,127:
For 2/1 all pure-octave tunings (eg EDOs) will be excellent. For any interval N/1 you can work it out by reading the absolute error from the Nth harmonic on the tables. For any interval L/M you can figure it out by reading the abs error of L and the abs error of M and then simply adding the two together.
For 2/1 all pure-octave tunings (eg EDOs) will be excellent. For any interval N/1 you can work it out by reading the absolute error from the Nth harmonic on the tables. For any interval L/M you can figure it out by reading the abs error of L and the abs error of M and then simply adding the two together.
Please make a wikitext table which shows how well every hyperconsonance, consonance, and ambisonance is approximated in every EDO from 1edo to 53edo, as well as showing each of their estimated number of dissonances.</pre>
Please make a wikitext table which shows how well every hyperconsonance, consonance, and ambisonance is approximated in every EDO from 1edo to 53edo, as well as showing each of their estimated number of dissonances.</pre>
The PDF I gave Claude was the odd harmonics tables for every EDO 1 to 53,

Revision as of 04:41, 27 April 2026

The following are all the 16-integer-limit consonant intervals available in an octave, simplified to their simplest form (by taking them to a higher octave to simplify the fraction), then sorted with most consonant (ie mathematically simplest) first. 

(^in a higher octave)

HYPERCONSONANCES
 2/1 (octave)
 3/1 (perf 5th^)

CONSONANCES
 5/1 (maj 3rd^)
 4/3 (perf 4th)
 5/3 (maj 6th)
 7/1 (submin 7th^)
 9/1 (large maj 2nd^)
 7/3 (submin 3rd^)

AMBISONANCES
 6/5 (min 3rd)
11/1 (undec 4th^)
 7/5 (small tritone)
 9/5 (min 7th)
11/3 (neu 7th^)
13/1 (neu 6th^)
 8/7 (supmaj 2nd)
13/3 (large tridec neu 2nd^)

DISSONANCES
15/1 (maj 7th^)
 9/7 (supmaj 3rd)
11/5 (large undec neu 2nd)
10/7 (large tritone)
10/9 (small maj 2nd)
11/7 (undec submin 6th)
13/5 (tridec maj 3rd^)
12/7 (supmaj 6th)
11/9 (undec neu 3rd)
13/7 (tridec maj 7th)
13/9 (tridec tritone)
15/7 (large minor 2nd^)
14/9 (sept submin 6th)
12/11 (small undec neu 2nd)
13/11 (tridec min 3rd)
14/11 (undec maj 3rd)
16/9 (Pythag min 7th)
15/11 (pentdec 4th)
16/11 (undec sub5th)
14/13 (small tridec neu 2nd)
15/13 (tridec semi4th)
16/13 (tridec neu 3rd)
16/15 (small neu 2nd)

Any general-purpose tuning system should approximate all hyperconsonances within 10 cents or less, all consonances within 20 cents, and all ambisonances within 30 cents. It should also try to have as few notes as possible that do not approximate any of those three categories of interval, because every note that isn't approximating one of them is a wolf interval that adds a 'bitter' taste to the tuning, and a tuning cannot survive very much bitterness.

EDO Consonance Ratings (1–53edo)

Table created using Claude (I gave it a PDF of the EDO harmonic tables), prompt listed below table.

EDO Hyperconsonances Consonances Ambisonances
2/1
perf oct 		3/1
perf 5th^ 		5/1
maj 3rd^ 		4/3
perf 4th 		5/3
maj 6th 		7/1
submin 7th^ 		9/1
lg maj 2nd^ 		7/3
submin 3rd^ 		6/5
min 3rd 		11/1
undec 4th^ 		7/5
sm tritone 		9/5
min 7th 		11/3
neu 7th^ 		13/1
neu 6th^ 		8/7
supmaj 2nd 		13/3
lg tri neu 2nd^
1 0.0¢ ✓✓ 498.0¢ ✗ 386.0¢ ✗ 498.0¢ ✗ 884.0¢ ✗ 231.0¢ ✗ 204.0¢ ✗ 267.0¢ ✗ 884.0¢ ✗ 551.0¢ ✗ 617.0¢ ✗ 182.0¢ ✗ 1049.0¢ ✗ 359.0¢ ✗ 231.0¢ ✗ 139.0¢ ✗ -9
2 0.0¢ ✓✓ 102.0¢ ✗ 214.0¢ ✗ 102.0¢ ✗ 316.0¢ ✗ 231.0¢ ✗ 204.0¢ ✗ 333.0¢ ✗ 316.0¢ ✗ 49.0¢ ✗ 17.0¢ ✓✓ 418.0¢ ✗ 151.0¢ ✗ 241.0¢ ✗ 231.0¢ ✗ 139.0¢ ✗ -8
3 0.0¢ ✓✓ 98.0¢ ✗ 14.0¢ ✓ 98.0¢ ✗ 84.0¢ ✗ 169.0¢ ✗ 196.0¢ ✗ 267.0¢ ✗ 84.0¢ ✗ 151.0¢ ✗ 183.0¢ ✗ 182.0¢ ✗ 249.0¢ ✗ 41.0¢ ✗ 169.0¢ ✗ 139.0¢ ✗ -7
4 0.0¢ ✓✓ 102.0¢ ✗ 86.0¢ ✗ 102.0¢ ✗ 16.0¢ ✓ 69.0¢ ✗ 96.0¢ ✗ 33.0¢ ✗ 16.0¢ ✓✓ 49.0¢ ✗ 17.0¢ ✓✓ 182.0¢ ✗ 151.0¢ ✗ 59.0¢ ✗ 69.0¢ ✗ 161.0¢ ✗ -6
5 0.0¢ ✓✓ 18.0¢ ✗ 94.0¢ ✗ 18.0¢ ✓ 76.0¢ ✗ 9.0¢ ✓✓ 36.0¢ ✗ 27.0¢ ✗ 76.0¢ ✗ 71.0¢ ✗ 103.0¢ ✗ 58.0¢ ✗ 89.0¢ ✗ 119.0¢ ✗ 9.0¢ ✓✓ 101.0¢ ✗ -5
6 0.0¢ ✓✓ 98.0¢ ✗ 13.7¢ ✓ 98.0¢ ✗ 84.3¢ ✗ 31.2¢ ✗ 3.9¢ ✓✓ 66.8¢ ✗ 84.3¢ ✗ 48.7¢ ✗ 17.5¢ ✓✓ 17.6¢ ✓✓ 49.3¢ ✗ 40.5¢ ✗ 31.2¢ ✗ 138.5¢ ✗ -4
7 0.0¢ ✓✓ 16.2¢ ✗ 43.5¢ ✗ 16.2¢ ✓ 27.3¢ ✗ 59.7¢ ✗ 32.5¢ ✗ 75.9¢ ✗ 27.3¢ ✓ 37.0¢ ✗ 103.2¢ ✗ 11.0¢ ✓✓ 20.8¢ ✓ 16.6¢ ✓✓ 59.7¢ ✗ 32.8¢ ✗ -3
8 0.0¢ ✓✓ 48.0¢ ✗ 63.7¢ ✗ 48.0¢ ✗ 15.7¢ ✓ 68.8¢ ✗ 53.9¢ ✗ 116.8¢ ✗ 15.7¢ ✓✓ 48.7¢ ✗ 132.5¢ ✗ 117.6¢ ✗ 0.7¢ ✓✓ 59.5¢ ✗ 68.8¢ ✗ 11.5¢ ✓✓ -2
9 0.0¢ ✓✓ 35.3¢ ✗ 13.7¢ ✓ 35.3¢ ✗ 49.0¢ ✗ 35.5¢ ✗ 62.8¢ ✗ 0.2¢ ✓✓ 49.0¢ ✗ 18.0¢ ✓✓ 49.2¢ ✗ 49.1¢ ✗ 17.3¢ ✓✓ 40.5¢ ✗ 35.5¢ ✗ 5.2¢ ✓✓ -1
10 0.0¢ ✓✓ 18.0¢ ✗ 26.3¢ ✗ 18.0¢ ✓ 44.3¢ ✗ 8.8¢ ✓✓ 36.1¢ ✗ 26.8¢ ✗ 44.3¢ ✗ 48.7¢ ✗ 17.5¢ ✓✓ 62.4¢ ✗ 30.7¢ ✗ 0.5¢ ✓✓ 8.8¢ ✓✓ 18.5¢ ✓✓ 0
11 0.0¢ ✓✓ 47.4¢ ✗ 50.0¢ ✗ 47.4¢ ✗ 97.4¢ ✗ 13.0¢ ✓ 14.3¢ ✓ 60.4¢ ✗ 97.4¢ ✗ 5.9¢ ✓✓ 37.0¢ ✗ 35.7¢ ✗ 41.5¢ ✗ 32.2¢ ✗ 13.0¢ ✓✓ 79.6¢ ✗ 1
12 0.0¢ ✓✓ 2.0¢ ✓✓ 13.7¢ ✓ 2.0¢ ✓✓ 15.7¢ ✓ 31.2¢ ✗ 3.9¢ ✓✓ 33.2¢ ✗ 15.7¢ ✓✓ 48.7¢ ✗ 17.5¢ ✓✓ 17.6¢ ✓✓ 50.7¢ ✗ 40.5¢ ✗ 31.2¢ ✗ 38.5¢ ✗ 2
13 0.0¢ ✓✓ 36.5¢ ✗ 17.1¢ ✓ 36.5¢ ✗ 53.6¢ ✗ 45.7¢ ✗ 19.3¢ ✓ 82.2¢ ✗ 53.6¢ ✗ 2.5¢ ✓✓ 28.6¢ ✓ 2.2¢ ✓✓ 34.0¢ ✗ 9.8¢ ✓✓ 45.7¢ ✗ 46.3¢ ✗ 3
14 0.0¢ ✓✓ 16.2¢ ✗ 42.3¢ ✗ 16.2¢ ✓ 58.5¢ ✗ 26.0¢ ✗ 32.5¢ ✗ 9.8¢ ✓✓ 58.5¢ ✗ 37.0¢ ✗ 68.3¢ ✗ 74.8¢ ✗ 20.8¢ ✓ 16.6¢ ✓✓ 26.0¢ ✓ 32.8¢ ✗ 4
15 0.0¢ ✓✓ 18.0¢ ✗ 13.7¢ ✓ 18.0¢ ✓ 4.3¢ ✓✓ 8.8¢ ✓✓ 36.1¢ ✗ 26.8¢ ✗ 4.3¢ ✓✓ 8.7¢ ✓✓ 22.5¢ ✓ 22.4¢ ✓ 9.3¢ ✓✓ 39.5¢ ✗ 8.8¢ ✓✓ 21.5¢ ✓ 5
16 0.0¢ ✓✓ 27.0¢ ✗ 11.3¢ ✓ 27.0¢ ✗ 15.7¢ ✓ 6.2¢ ✓✓ 21.1¢ ✗ 33.2¢ ✗ 15.7¢ ✓✓ 26.3¢ ✓ 17.5¢ ✓✓ 32.4¢ ✗ 0.7¢ ✓✓ 15.5¢ ✓✓ 6.2¢ ✓✓ 11.5¢ ✓✓ 6
17 0.0¢ ✓✓ 3.9¢ ✓✓ 33.4¢ ✗ 3.9¢ ✓✓ 37.3¢ ✗ 19.4¢ ✓ 7.9¢ ✓✓ 15.5¢ ✓ 37.3¢ ✗ 13.4¢ ✓✓ 52.8¢ ✗ 41.3¢ ✗ 9.5¢ ✓✓ 6.5¢ ✓✓ 19.4¢ ✓✓ 2.6¢ ✓✓ 7
18 0.0¢ ✓✓ 31.4¢ ✗ 13.7¢ ✓ 31.4¢ ✗ 17.7¢ ✓ 31.2¢ ✗ 3.9¢ ✓✓ 0.2¢ ✓✓ 17.7¢ ✓✓ 18.0¢ ✓✓ 17.5¢ ✓✓ 17.6¢ ✓✓ 49.4¢ ✗ 26.1¢ ✓ 31.2¢ ✗ 5.3¢ ✓✓ 8
19 0.0¢ ✓✓ 7.2¢ ✓ 7.4¢ ✓✓ 7.2¢ ✓✓ 0.2¢ ✓✓ 21.5¢ ✗ 14.4¢ ✓ 14.3¢ ✓ 0.2¢ ✓✓ 17.1¢ ✓✓ 14.1¢ ✓✓ 7.0¢ ✓✓ 24.3¢ ✓ 19.5¢ ✓✓ 21.5¢ ✓ 12.3¢ ✓✓ 9
20 0.0¢ ✓✓ 18.0¢ ✗ 26.3¢ ✗ 18.0¢ ✓ 44.3¢ ✗ 8.8¢ ✓✓ 23.9¢ ✗ 26.8¢ ✗ 44.3¢ ✗ 11.3¢ ✓✓ 17.5¢ ✓✓ 2.4¢ ✓✓ 29.3¢ ✓ 0.5¢ ✓✓ 8.8¢ ✓✓ 18.5¢ ✓✓ 10
21 0.0¢ ✓✓ 16.2¢ ✗ 13.7¢ ✓ 16.2¢ ✓ 29.9¢ ✗ 2.6¢ ✓✓ 24.7¢ ✗ 18.8¢ ✓ 29.9¢ ✓ 20.1¢ ✓ 11.1¢ ✓✓ 11.0¢ ✓✓ 36.3¢ ✗ 16.6¢ ✓✓ 2.6¢ ✓✓ 32.8¢ ✗ 11
22 0.0¢ ✓✓ 7.1¢ ✓ 4.5¢ ✓✓ 7.1¢ ✓✓ 11.6¢ ✓ 13.0¢ ✓ 14.3¢ ✓ 5.9¢ ✓✓ 11.6¢ ✓✓ 5.9¢ ✓✓ 17.5¢ ✓✓ 18.8¢ ✓✓ 13.0¢ ✓✓ 22.3¢ ✓ 13.0¢ ✓✓ 29.4¢ ✓ 12
23 0.0¢ ✓✓ 23.7¢ ✗ 21.1¢ ✗ 23.7¢ ✗ 2.6¢ ✓✓ 22.5¢ ✗ 4.8¢ ✓✓ 46.2¢ ✗ 2.6¢ ✓✓ 22.6¢ ✓ 43.6¢ ✗ 25.9¢ ✓ 46.3¢ ✗ 5.7¢ ✓✓ 22.5¢ ✓ 18.0¢ ✓✓ 13
24 0.0¢ ✓✓ 2.0¢ ✓✓ 13.7¢ ✓ 2.0¢ ✓✓ 15.7¢ ✓ 18.8¢ ✓ 3.9¢ ✓✓ 16.8¢ ✓ 15.7¢ ✓✓ 1.3¢ ✓✓ 32.5¢ ✗ 17.6¢ ✓✓ 0.7¢ ✓✓ 9.5¢ ✓✓ 18.8¢ ✓✓ 11.5¢ ✓✓ 14
25 0.0¢ ✓✓ 18.0¢ ✗ 2.3¢ ✓✓ 18.0¢ ✓ 20.3¢ ✗ 8.8¢ ✓✓ 11.9¢ ✓ 26.8¢ ✗ 20.3¢ ✓ 23.3¢ ✓ 6.5¢ ✓✓ 9.6¢ ✓✓ 41.3¢ ✗ 23.5¢ ✓ 8.8¢ ✓✓ 5.5¢ ✓✓ 15
26 0.0¢ ✓✓ 9.6¢ ✓ 17.1¢ ✓ 9.6¢ ✓✓ 7.5¢ ✓✓ 0.4¢ ✓✓ 19.3¢ ✓ 10.0¢ ✓✓ 7.5¢ ✓✓ 2.5¢ ✓✓ 17.5¢ ✓✓ 2.2¢ ✓✓ 12.1¢ ✓✓ 9.8¢ ✓✓ 0.4¢ ✓✓ 0.2¢ ✓✓ 16
27 0.0¢ ✓✓ 9.2¢ ✓ 13.7¢ ✓ 9.2¢ ✓✓ 4.5¢ ✓✓ 9.0¢ ✓✓ 18.3¢ ✓ 0.2¢ ✓✓ 4.5¢ ✓✓ 18.0¢ ✓✓ 4.7¢ ✓✓ 4.6¢ ✓✓ 27.2¢ ✓ 3.9¢ ✓✓ 9.0¢ ✓✓ 5.3¢ ✓✓ 17
28 0.0¢ ✓✓ 16.2¢ ✗ 0.6¢ ✓✓ 16.2¢ ✓ 15.6¢ ✓ 16.9¢ ✓ 10.4¢ ✓ 33.1¢ ✗ 15.6¢ ✓✓ 5.8¢ ✓✓ 17.5¢ ✓✓ 11.0¢ ✓✓ 22.0¢ ✓ 16.6¢ ✓✓ 16.9¢ ✓✓ 32.8¢ ✗ 18
29 0.0¢ ✓✓ 1.5¢ ✓✓ 13.9¢ ✓ 1.5¢ ✓✓ 15.4¢ ✓ 17.1¢ ✓ 3.0¢ ✓✓ 18.6¢ ✓ 15.4¢ ✓✓ 13.4¢ ✓✓ 3.2¢ ✓✓ 16.9¢ ✓✓ 14.9¢ ✓✓ 12.9¢ ✓✓ 17.1¢ ✓✓ 14.4¢ ✓✓ 19
30 0.0¢ ✓✓ 18.0¢ ✗ 13.7¢ ✓ 18.0¢ ✓ 4.3¢ ✓✓ 8.8¢ ✓✓ 3.9¢ ✓✓ 26.8¢ ✗ 4.3¢ ✓✓ 8.7¢ ✓✓ 22.5¢ ✓ 17.6¢ ✓✓ 9.3¢ ✓✓ 0.5¢ ✓✓ 8.8¢ ✓✓ 18.5¢ ✓✓ 20
31 0.0¢ ✓✓ 5.2¢ ✓ 0.8¢ ✓✓ 5.2¢ ✓✓ 6.0¢ ✓✓ 1.1¢ ✓✓ 10.4¢ ✓ 4.1¢ ✓✓ 6.0¢ ✓✓ 9.4¢ ✓✓ 1.9¢ ✓✓ 11.2¢ ✓✓ 4.2¢ ✓✓ 11.1¢ ✓✓ 1.1¢ ✓✓ 16.3¢ ✓✓ 21
32 0.0¢ ✓✓ 10.5¢ ✗ 11.3¢ ✓ 10.5¢ ✓ 21.8¢ ✗ 6.2¢ ✓✓ 16.4¢ ✓ 4.3¢ ✓✓ 21.8¢ ✓ 11.2¢ ✓✓ 17.5¢ ✓✓ 5.1¢ ✓✓ 0.7¢ ✓✓ 15.5¢ ✓✓ 6.2¢ ✓✓ 26.0¢ ✓ 22
33 0.0¢ ✓✓ 11.0¢ ✗ 13.7¢ ✓ 11.0¢ ✓ 24.7¢ ✗ 13.0¢ ✓ 14.3¢ ✓ 24.0¢ ✗ 24.7¢ ✓ 5.9¢ ✓✓ 0.7¢ ✓✓ 0.6¢ ✓✓ 5.1¢ ✓✓ 4.2¢ ✓✓ 13.0¢ ✓✓ 6.8¢ ✓✓ 23
34 0.0¢ ✓✓ 3.9¢ ✓✓ 1.9¢ ✓✓ 3.9¢ ✓✓ 2.0¢ ✓✓ 15.9¢ ✓ 7.9¢ ✓✓ 19.8¢ ✓ 2.0¢ ✓✓ 13.4¢ ✓✓ 17.8¢ ✓✓ 6.0¢ ✓✓ 9.5¢ ✓✓ 6.5¢ ✓✓ 15.9¢ ✓✓ 2.6¢ ✓✓ 24
35 0.0¢ ✓✓ 16.2¢ ✗ 9.2¢ ✓✓ 16.2¢ ✓ 7.0¢ ✓✓ 8.8¢ ✓✓ 1.8¢ ✓✓ 7.4¢ ✓✓ 7.0¢ ✓✓ 2.7¢ ✓✓ 0.4¢ ✓✓ 11.0¢ ✓✓ 13.5¢ ✓✓ 16.6¢ ✓✓ 8.8¢ ✓✓ 32.8¢ ✗ 25
36 0.0¢ ✓✓ 2.0¢ ✓✓ 13.7¢ ✓ 2.0¢ ✓✓ 15.7¢ ✓ 2.2¢ ✓✓ 3.9¢ ✓✓ 0.2¢ ✓✓ 15.7¢ ✓✓ 15.3¢ ✓✓ 15.9¢ ✓✓ 17.6¢ ✓✓ 17.3¢ ✓✓ 7.2¢ ✓✓ 2.2¢ ✓✓ 5.2¢ ✓✓ 26
37 0.0¢ ✓✓ 11.6¢ ✗ 2.9¢ ✓✓ 11.6¢ ✓ 8.7¢ ✓✓ 4.1¢ ✓✓ 9.3¢ ✓✓ 7.5¢ ✓✓ 8.7¢ ✓✓ 0.0¢ ✓✓ 1.2¢ ✓✓ 12.2¢ ✓✓ 11.6¢ ✓✓ 2.7¢ ✓✓ 4.1¢ ✓✓ 8.9¢ ✓✓ 27
38 0.0¢ ✓✓ 7.2¢ ✓ 7.4¢ ✓✓ 7.2¢ ✓✓ 0.2¢ ✓✓ 10.1¢ ✓ 14.4¢ ✓ 17.3¢ ✓ 0.2¢ ✓✓ 14.5¢ ✓✓ 17.5¢ ✓✓ 7.0¢ ✓✓ 7.3¢ ✓✓ 12.1¢ ✓✓ 10.1¢ ✓✓ 19.3¢ ✓✓ 28
39 0.0¢ ✓✓ 5.7¢ ✓ 13.7¢ ✓ 5.7¢ ✓✓ 8.0¢ ✓✓ 15.0¢ ✓ 11.5¢ ✓ 20.7¢ ✗ 8.0¢ ✓✓ 2.5¢ ✓✓ 28.7¢ ✓ 2.2¢ ✓✓ 3.2¢ ✓✓ 9.8¢ ✓✓ 15.0¢ ✓✓ 15.5¢ ✓✓ 29
40 0.0¢ ✓✓ 12.0¢ ✗ 3.7¢ ✓✓ 12.0¢ ✓ 15.7¢ ✓ 8.8¢ ✓✓ 6.1¢ ✓✓ 3.2¢ ✓✓ 15.7¢ ✓✓ 11.3¢ ✓✓ 12.5¢ ✓✓ 2.4¢ ✓✓ 0.7¢ ✓✓ 0.5¢ ✓✓ 8.8¢ ✓✓ 11.5¢ ✓✓ 30
41 0.0¢ ✓✓ 0.5¢ ✓✓ 5.8¢ ✓✓ 0.5¢ ✓✓ 6.3¢ ✓✓ 3.0¢ ✓✓ 1.0¢ ✓✓ 3.5¢ ✓✓ 6.3¢ ✓✓ 4.8¢ ✓✓ 2.8¢ ✓✓ 6.8¢ ✓✓ 4.3¢ ✓✓ 8.3¢ ✓✓ 3.0¢ ✓✓ 7.8¢ ✓✓ 31
42 0.0¢ ✓✓ 12.3¢ ✗ 13.7¢ ✓ 12.3¢ ✓ 1.4¢ ✓✓ 2.6¢ ✓✓ 3.9¢ ✓✓ 9.7¢ ✓✓ 1.4¢ ✓✓ 8.5¢ ✓✓ 11.1¢ ✓✓ 17.6¢ ✓✓ 20.8¢ ✓ 12.0¢ ✓✓ 2.6¢ ✓✓ 24.3¢ ✓ 32
43 0.0¢ ✓✓ 4.3¢ ✓✓ 4.4¢ ✓✓ 4.3¢ ✓✓ 8.7¢ ✓✓ 7.9¢ ✓✓ 8.6¢ ✓✓ 12.2¢ ✓ 8.7¢ ✓✓ 6.8¢ ✓✓ 3.5¢ ✓✓ 13.0¢ ✓✓ 11.1¢ ✓✓ 3.3¢ ✓✓ 7.9¢ ✓✓ 1.0¢ ✓✓ 33
44 0.0¢ ✓✓ 7.1¢ ✓ 4.5¢ ✓✓ 7.1¢ ✓✓ 11.6¢ ✓ 13.0¢ ✓ 13.0¢ ✓ 5.9¢ ✓✓ 11.6¢ ✓✓ 5.9¢ ✓✓ 17.5¢ ✓✓ 8.5¢ ✓✓ 13.0¢ ✓✓ 4.9¢ ✓✓ 13.0¢ ✓✓ 2.2¢ ✓✓ 34
45 0.0¢ ✓✓ 8.6¢ ✓ 13.0¢ ✓ 8.6¢ ✓✓ 4.4¢ ✓✓ 8.8¢ ✓✓ 9.4¢ ✓✓ 0.2¢ ✓✓ 4.4¢ ✓✓ 8.7¢ ✓✓ 4.2¢ ✓✓ 22.4¢ ✓ 17.3¢ ✓✓ 12.8¢ ✓✓ 8.8¢ ✓✓ 21.4¢ ✓ 35
46 0.0¢ ✓✓ 2.4¢ ✓✓ 5.0¢ ✓✓ 2.4¢ ✓✓ 2.6¢ ✓✓ 3.6¢ ✓✓ 4.8¢ ✓✓ 6.0¢ ✓✓ 2.6¢ ✓✓ 3.5¢ ✓✓ 8.6¢ ✓✓ 0.2¢ ✓✓ 5.9¢ ✓✓ 5.7¢ ✓✓ 3.6¢ ✓✓ 8.1¢ ✓✓ 36
47 0.0¢ ✓✓ 12.6¢ ✗ 3.3¢ ✓✓ 12.6¢ ✓ 9.3¢ ✓✓ 1.4¢ ✓✓ 0.3¢ ✓✓ 14.0¢ ✓ 9.3¢ ✓✓ 10.4¢ ✓✓ 4.7¢ ✓✓ 3.6¢ ✓✓ 23.0¢ ✓ 2.0¢ ✓✓ 1.4¢ ✓✓ 14.6¢ ✓✓ 37
48 0.0¢ ✓✓ 2.0¢ ✓✓ 11.3¢ ✓ 2.0¢ ✓✓ 9.3¢ ✓✓ 6.2¢ ✓✓ 3.9¢ ✓✓ 8.2¢ ✓✓ 9.3¢ ✓✓ 1.3¢ ✓✓ 17.5¢ ✓✓ 7.4¢ ✓✓ 0.7¢ ✓✓ 9.5¢ ✓✓ 6.2¢ ✓✓ 11.5¢ ✓✓ 38
49 0.0¢ ✓✓ 8.2¢ ✓ 5.5¢ ✓✓ 8.2¢ ✓✓ 2.7¢ ✓✓ 10.8¢ ✓ 8.0¢ ✓✓ 2.6¢ ✓✓ 2.7¢ ✓✓ 11.9¢ ✓✓ 5.3¢ ✓✓ 13.5¢ ✓✓ 3.7¢ ✓✓ 7.9¢ ✓✓ 10.8¢ ✓✓ 16.1¢ ✓✓ 39
50 0.0¢ ✓✓ 6.0¢ ✓ 2.3¢ ✓✓ 6.0¢ ✓✓ 3.7¢ ✓✓ 8.8¢ ✓✓ 11.9¢ ✓ 2.8¢ ✓✓ 3.7¢ ✓✓ 0.7¢ ✓✓ 6.5¢ ✓✓ 9.6¢ ✓✓ 6.7¢ ✓✓ 0.5¢ ✓✓ 8.8¢ ✓✓ 5.5¢ ✓✓ 40
51 0.0¢ ✓✓ 3.9¢ ✓✓ 9.8¢ ✓✓ 3.9¢ ✓✓ 13.7¢ ✓ 4.1¢ ✓✓ 7.9¢ ✓✓ 8.0¢ ✓✓ 13.7¢ ✓✓ 10.1¢ ✓✓ 5.7¢ ✓✓ 17.7¢ ✓✓ 14.0¢ ✓✓ 6.5¢ ✓✓ 4.1¢ ✓✓ 2.6¢ ✓✓ 41
52 0.0¢ ✓✓ 9.6¢ ✓ 6.0¢ ✓✓ 9.6¢ ✓✓ 15.6¢ ✓ 0.4¢ ✓✓ 3.8¢ ✓✓ 10.0¢ ✓✓ 15.6¢ ✓✓ 2.5¢ ✓✓ 5.6¢ ✓✓ 2.2¢ ✓✓ 12.1¢ ✓✓ 9.8¢ ✓✓ 0.4¢ ✓✓ 0.2¢ ✓✓ 42
53 0.0¢ ✓✓ 0.1¢ ✓✓ 1.4¢ ✓✓ 0.1¢ ✓✓ 1.3¢ ✓✓ 4.8¢ ✓✓ 0.1¢ ✓✓ 4.8¢ ✓✓ 1.3¢ ✓✓ 7.9¢ ✓✓ 6.2¢ ✓✓ 1.3¢ ✓✓ 7.8¢ ✓✓ 2.8¢ ✓✓ 4.8¢ ✓✓ 2.7¢ ✓✓ 43

Prompt: 

Use the attached PDF to fulfil this request: The following are all the 16-integer-limit consonant intervals available in an octave, simplified to their simplest form (by taking them to a higher octave to simplify the fraction), then sorted with most consonant (ie mathematically simplest) first.
(^in a higher octave)
HYPERCONSONANCES
Within 5 cents error = excellent
Within 10 cents = good enough
More than 10 cents = poor
 2/1 (octave)
 3/1 (perf 5th^)
CONSONANCES
Within 10 cents = excellent
Within 20 cents = good enough
More than 20 cents = poor
 5/1 (maj 3rd^)
 4/3 (perf 4th)
 5/3 (maj 6th)
 7/1 (submin 7th^)
 9/1 (large maj 2nd^)
 7/3 (submin 3rd^)
AMBISONANCES
Within 20 cents = excellent
Within 30 cents = good enough
More than 30 cents = poor
 6/5 (min 3rd)
11/1 (undec 4th^)
 7/5 (small tritone)
 9/5 (min 7th)
11/3 (neu 7th^)
13/1 (neu 6th^)
 8/7 (supmaj 2nd)
13/3 (large tridec neu 2nd^)
DISSONANCES
Any note not within range of one of the above.
The total number of notes in a tuning minus 10 is a good heuristic to estimate how many of these there are.
Less than 5 of these = excellent
5 to 15 of these = good enough
More than 15 of these = poor
For 2/1 all pure-octave tunings (eg EDOs) will be excellent. For any interval N/1 you can work it out by reading the absolute error from the Nth harmonic on the tables. For any interval L/M you can figure it out by reading the abs error of L and the abs error of M and then simply adding the two together.
Please make a wikitext table which shows how well every hyperconsonance, consonance, and ambisonance is approximated in every EDO from 1edo to 53edo, as well as showing each of their estimated number of dissonances.
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