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

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13/1 (neu 6th^)
13/1 (neu 6th^)
  8/7 (supmaj 2nd)
  8/7 (supmaj 2nd)
13/3 (large tridec neu 2nd^)


DISSONANCES
DISSONANCES
9/7 (supmaj 3rd)
13/3 (large tridec neu 2nd^)
15/1 (maj 7th^)
15/1 (maj 7th^)
9/7 (supmaj 3rd)
11/5 (large undec neu 2nd)
11/5 (large undec neu 2nd)
10/7 (large tritone)
10/7 (large tritone)
Line 53: Line 53:


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.
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.
== Table of EDOs by general-purpose efficacy (1–53edo) ==
{{Editable user page|You may correct factual errors in the table e.g. incorrect numbers}}
This rates EDOs for ''general'' purposes. It doesn't take into account specialist (but still very valid) use cases like inharmonic timbres, dual-fifths usage, subgroup usage, or taking carefully chosen subsets (eg blackjack). EDOs that look bad on this table might still be very good for one or more of those specialist uses.
Table created using Claude (I gave it a PDF of the EDO harmonic tables; my prompt is listed below the table). '''It almost certainly made errors so don't use this as a source for the numbers''' (instead look at the relevant EDO pages directly, they're linked in the left column).
<nowiki>*</nowiki>''denotes EDOs where an especially high % of their intervals are especially consonant''
{| class="wikitable sortable" style="text-align:center; font-size:80%;"
|-
! rowspan="2" | EDO
! rowspan="2" |Est. no. of dissonances!! colspan="2" style="background:#d0e8ff;" | Hyperconsonances !! colspan="6" style="background:#c8f0c8;" | Consonances !! colspan="7" style="background:#fff0c8;" | Ambisonances
|-
! style="background:#d0e8ff;" | 2/1<br /><small>perf oct</small>
! style="background:#d0e8ff;" | 3/1<br /><small>perf 5th^</small>
! style="background:#c8f0c8;" | 5/1<br /><small>maj 3rd^</small>
! style="background:#c8f0c8;" | 4/3<br /><small>perf 4th</small>
! style="background:#c8f0c8;" | 5/3<br /><small>maj 6th</small>
! style="background:#c8f0c8;" | 7/1<br /><small>submin 7th^</small>
! style="background:#c8f0c8;" | 9/1<br /><small>lg maj 2nd^</small>
! style="background:#c8f0c8;" | 7/3<br /><small>submin 3rd^</small>
! style="background:#fff0c8;" | 6/5<br /><small>min 3rd</small>
! style="background:#fff0c8;" | 11/1<br /><small>undec 4th^</small>
! style="background:#fff0c8;" | 7/5<br /><small>sm tritone</small>
! style="background:#fff0c8;" | 9/5<br /><small>min 7th</small>
! style="background:#fff0c8;" | 11/3<br /><small>neu 7th^</small>
! style="background:#fff0c8;" | 13/1<br /><small>neu 6th^</small>
! style="background:#fff0c8;" | 8/7<br /><small>supmaj 2nd</small>
|-
| [[1edo]]
| style="background:#ffffff;" | 0
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 498.0¢ ✗
| style="background:#FF9999;" | 386.0¢ ✗
| style="background:#FF9999;" | 498.0¢ ✗
| style="background:#FF9999;" | 884.0¢ ✗
| style="background:#FF9999;" | 231.0¢ ✗
| style="background:#FF9999;" | 204.0¢ ✗
| style="background:#FF9999;" | 267.0¢ ✗
| style="background:#FF9999;" | 884.0¢ ✗
| style="background:#FF9999;" | 551.0¢ ✗
| style="background:#FF9999;" | 617.0¢ ✗
| style="background:#FF9999;" | 182.0¢ ✗
| style="background:#FF9999;" | 1049.0¢ ✗
| style="background:#FF9999;" | 359.0¢ ✗
| style="background:#FF9999;" | 231.0¢ ✗
|-
| [[2edo]]
| style="background:#ffffff;" | 0
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 102.0¢ ✗
| style="background:#FF9999;" | 214.0¢ ✗
| style="background:#FF9999;" | 102.0¢ ✗
| style="background:#FF9999;" | 316.0¢ ✗
| style="background:#FF9999;" | 231.0¢ ✗
| style="background:#FF9999;" | 204.0¢ ✗
| style="background:#FF9999;" | 333.0¢ ✗
| style="background:#FF9999;" | 316.0¢ ✗
| style="background:#FF9999;" | 49.0¢ ✗
| style="background:#90EE90;" | 17.0¢ ✓✓
| style="background:#FF9999;" | 418.0¢ ✗
| style="background:#FF9999;" | 151.0¢ ✗
| style="background:#FF9999;" | 241.0¢ ✗
| style="background:#FF9999;" | 231.0¢ ✗
|-
| [[3edo]]
| style="background:#ffffff;" | 1
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 98.0¢ ✗
| style="background:#FFD700;" | 14.0¢ ✓
| style="background:#FF9999;" | 98.0¢ ✗
| style="background:#FF9999;" | 84.0¢ ✗
| style="background:#FF9999;" | 169.0¢ ✗
| style="background:#FF9999;" | 196.0¢ ✗
| style="background:#FF9999;" | 267.0¢ ✗
| style="background:#FF9999;" | 84.0¢ ✗
| style="background:#FF9999;" | 151.0¢ ✗
| style="background:#FF9999;" | 183.0¢ ✗
| style="background:#FF9999;" | 182.0¢ ✗
| style="background:#FF9999;" | 249.0¢ ✗
| style="background:#FF9999;" | 41.0¢ ✗
| style="background:#FF9999;" | 169.0¢ ✗
|-
| [[4edo]]
| style="background:#ffffff;" | 0
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 102.0¢ ✗
| style="background:#FF9999;" | 86.0¢ ✗
| style="background:#FF9999;" | 102.0¢ ✗
| style="background:#FFD700;" | 16.0¢ ✓
| style="background:#FF9999;" | 69.0¢ ✗
| style="background:#FF9999;" | 96.0¢ ✗
| style="background:#FF9999;" | 33.0¢ ✗
| style="background:#90EE90;" | 16.0¢ ✓✓
| style="background:#FF9999;" | 49.0¢ ✗
| style="background:#90EE90;" | 17.0¢ ✓✓
| style="background:#FF9999;" | 182.0¢ ✗
| style="background:#FF9999;" | 151.0¢ ✗
| style="background:#FF9999;" | 59.0¢ ✗
| style="background:#FF9999;" | 69.0¢ ✗
|-
| [[5edo]]
| style="background:#ffffff;" | 1
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 18.0¢ ✗
| style="background:#FF9999;" | 94.0¢ ✗
| style="background:#FFD700;" | 18.0¢ ✓
| style="background:#FF9999;" | 76.0¢ ✗
| style="background:#90EE90;" | 9.0¢ ✓✓
| style="background:#FF9999;" | 36.0¢ ✗
| style="background:#FF9999;" | 27.0¢ ✗
| style="background:#FF9999;" | 76.0¢ ✗
| style="background:#FF9999;" | 71.0¢ ✗
| style="background:#FF9999;" | 103.0¢ ✗
| style="background:#FF9999;" | 58.0¢ ✗
| style="background:#FF9999;" | 89.0¢ ✗
| style="background:#FF9999;" | 119.0¢ ✗
| style="background:#90EE90;" | 9.0¢ ✓✓
|-
| [[6edo]]
| style="background:#ffffff;" | 1
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 98.0¢ ✗
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FF9999;" | 98.0¢ ✗
| style="background:#FF9999;" | 84.3¢ ✗
| style="background:#FF9999;" | 31.2¢ ✗
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#FF9999;" | 66.8¢ ✗
| style="background:#FF9999;" | 84.3¢ ✗
| style="background:#FF9999;" | 48.7¢ ✗
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 17.6¢ ✓✓
| style="background:#FF9999;" | 49.3¢ ✗
| style="background:#FF9999;" | 40.5¢ ✗
| style="background:#FF9999;" | 31.2¢ ✗
|-
| [[7edo]]
| style="background:#ffffff;" | 1
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 16.2¢ ✗
| style="background:#FF9999;" | 43.5¢ ✗
| style="background:#FFD700;" | 16.2¢ ✓
| style="background:#FF9999;" | 27.3¢ ✗
| style="background:#FF9999;" | 59.7¢ ✗
| style="background:#FF9999;" | 32.5¢ ✗
| style="background:#FF9999;" | 75.9¢ ✗
| style="background:#FFD700;" | 27.3¢ ✓
| style="background:#FF9999;" | 37.0¢ ✗
| style="background:#FF9999;" | 103.2¢ ✗
| style="background:#90EE90;" | 11.0¢ ✓✓
| style="background:#FFD700;" | 20.8¢ ✓
| style="background:#90EE90;" | 16.6¢ ✓✓
| style="background:#FF9999;" | 59.7¢ ✗
|-
| [[8edo]]
| style="background:#ffffff;" | 4
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 48.0¢ ✗
| style="background:#FF9999;" | 63.7¢ ✗
| style="background:#FF9999;" | 48.0¢ ✗
| style="background:#FFD700;" | 15.7¢ ✓
| style="background:#FF9999;" | 68.8¢ ✗
| style="background:#FF9999;" | 53.9¢ ✗
| style="background:#FF9999;" | 116.8¢ ✗
| style="background:#90EE90;" | 15.7¢ ✓✓
| style="background:#FF9999;" | 48.7¢ ✗
| style="background:#FF9999;" | 132.5¢ ✗
| style="background:#FF9999;" | 117.6¢ ✗
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#FF9999;" | 59.5¢ ✗
| style="background:#FF9999;" | 68.8¢ ✗
|-
| [[9edo]]
| style="background:#ffffff;" | 4
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 35.3¢ ✗
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FF9999;" | 35.3¢ ✗
| style="background:#FF9999;" | 49.0¢ ✗
| style="background:#FF9999;" | 35.5¢ ✗
| style="background:#FF9999;" | 62.8¢ ✗
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#FF9999;" | 49.0¢ ✗
| style="background:#90EE90;" | 18.0¢ ✓✓
| style="background:#FF9999;" | 49.2¢ ✗
| style="background:#FF9999;" | 49.1¢ ✗
| style="background:#90EE90;" | 17.3¢ ✓✓
| style="background:#FF9999;" | 40.5¢ ✗
| style="background:#FF9999;" | 35.5¢ ✗
|-
| '''[[10edo]]'''
| style="background:#ffffff;" | '''4*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#FF9999;" | '''18.0¢ ✗'''
| style="background:#FF9999;" | '''26.3¢ ✗'''
| style="background:#FFD700;" | '''18.0¢ ✓'''
| style="background:#FF9999;" | '''44.3¢ ✗'''
| style="background:#90EE90;" | '''8.8¢ ✓✓'''
| style="background:#FF9999;" | '''36.1¢ ✗'''
| style="background:#FF9999;" | '''26.8¢ ✗'''
| style="background:#FF9999;" | '''44.3¢ ✗'''
| style="background:#FF9999;" | '''48.7¢ ✗'''
| style="background:#90EE90;" | '''17.5¢ ✓✓'''
| style="background:#FF9999;" | '''62.4¢ ✗'''
| style="background:#FF9999;" | '''30.7¢ ✗'''
| style="background:#90EE90;" | '''0.5¢ ✓✓'''
| style="background:#90EE90;" | '''8.8¢ ✓✓'''
|-
| [[11edo]]
| style="background:#ffe0e0;" | 6
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 47.4¢ ✗
| style="background:#FF9999;" | 50.0¢ ✗
| style="background:#FF9999;" | 47.4¢ ✗
| style="background:#FF9999;" | 97.4¢ ✗
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FFD700;" | 14.3¢ ✓
| style="background:#FF9999;" | 60.4¢ ✗
| style="background:#FF9999;" | 97.4¢ ✗
| style="background:#90EE90;" | 5.9¢ ✓✓
| style="background:#FF9999;" | 37.0¢ ✗
| style="background:#FF9999;" | 35.7¢ ✗
| style="background:#FF9999;" | 41.5¢ ✗
| style="background:#FF9999;" | 32.2¢ ✗
| style="background:#90EE90;" | 13.0¢ ✓✓
|-
| '''[[12edo]]'''
| style="background:#ffffff;" | '''3*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''13.7¢ ✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''15.7¢ ✓'''
| style="background:#FF9999;" | '''31.2¢ ✗'''
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#FF9999;" | '''33.2¢ ✗'''
| style="background:#90EE90;" | '''15.7¢ ✓✓'''
| style="background:#FF9999;" | '''48.7¢ ✗'''
| style="background:#90EE90;" | '''17.5¢ ✓✓'''
| style="background:#90EE90;" | '''17.6¢ ✓✓'''
| style="background:#FF9999;" | '''50.7¢ ✗'''
| style="background:#FF9999;" | '''40.5¢ ✗'''
| style="background:#FF9999;" | '''31.2¢ ✗'''
|-
| [[13edo]]
| style="background:#ffe0e0;" | 6
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 36.5¢ ✗
| style="background:#FFD700;" | 17.1¢ ✓
| style="background:#FF9999;" | 36.5¢ ✗
| style="background:#FF9999;" | 53.6¢ ✗
| style="background:#FF9999;" | 45.7¢ ✗
| style="background:#FFD700;" | 19.3¢ ✓
| style="background:#FF9999;" | 82.2¢ ✗
| style="background:#FF9999;" | 53.6¢ ✗
| style="background:#90EE90;" | 2.5¢ ✓✓
| style="background:#FFD700;" | 28.6¢ ✓
| style="background:#90EE90;" | 2.2¢ ✓✓
| style="background:#FF9999;" | 34.0¢ ✗
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#FF9999;" | 45.7¢ ✗
|-
| [[14edo]]
| style="background:#ffe0e0;" | 8
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 16.2¢ ✗
| style="background:#FF9999;" | 42.3¢ ✗
| style="background:#FFD700;" | 16.2¢ ✓
| style="background:#FF9999;" | 58.5¢ ✗
| style="background:#FF9999;" | 26.0¢ ✗
| style="background:#FF9999;" | 32.5¢ ✗
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#FF9999;" | 58.5¢ ✗
| style="background:#FF9999;" | 37.0¢ ✗
| style="background:#FF9999;" | 68.3¢ ✗
| style="background:#FF9999;" | 74.8¢ ✗
| style="background:#FFD700;" | 20.8¢ ✓
| style="background:#90EE90;" | 16.6¢ ✓✓
| style="background:#FFD700;" | 26.0¢ ✓
|-
| '''[[15edo]]'''
| style="background:#ffffff;" | '''4*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#FF9999;" | '''18.0¢ ✗'''
| style="background:#FFD700;" | '''13.7¢ ✓'''
| style="background:#FFD700;" | '''18.0¢ ✓'''
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | '''8.8¢ ✓✓'''
| style="background:#FF9999;" | '''36.1¢ ✗'''
| style="background:#FF9999;" | '''26.8¢ ✗'''
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | '''8.7¢ ✓✓'''
| style="background:#FFD700;" | '''22.5¢ ✓'''
| style="background:#FFD700;" | '''22.4¢ ✓'''
| style="background:#90EE90;" | '''9.3¢ ✓✓'''
| style="background:#FF9999;" | '''39.5¢ ✗'''
| style="background:#90EE90;" | '''8.8¢ ✓✓'''
|-
| [[16edo]]
| style="background:#ffe0e0;" | 6
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 27.0¢ ✗
| style="background:#FFD700;" | 11.3¢ ✓
| style="background:#FF9999;" | 27.0¢ ✗
| style="background:#FFD700;" | 15.7¢ ✓
| style="background:#90EE90;" | 6.2¢ ✓✓
| style="background:#FF9999;" | 21.1¢ ✗
| style="background:#FF9999;" | 33.2¢ ✗
| style="background:#90EE90;" | 15.7¢ ✓✓
| style="background:#FFD700;" | 26.3¢ ✓
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#FF9999;" | 32.4¢ ✗
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | 15.5¢ ✓✓
| style="background:#90EE90;" | 6.2¢ ✓✓
|-
| [[17edo]]
| style="background:#ffe0e0;" | 7
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#FF9999;" | 33.4¢ ✗
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#FF9999;" | 37.3¢ ✗
| style="background:#FFD700;" | 19.4¢ ✓
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#FFD700;" | 15.5¢ ✓
| style="background:#FF9999;" | 37.3¢ ✗
| style="background:#90EE90;" | 13.4¢ ✓✓
| style="background:#FF9999;" | 52.8¢ ✗
| style="background:#FF9999;" | 41.3¢ ✗
| style="background:#90EE90;" | 9.5¢ ✓✓
| style="background:#90EE90;" | 6.5¢ ✓✓
| style="background:#90EE90;" | 19.4¢ ✓✓
|-
| [[18edo]]
| style="background:#ffe0e0;" | 8
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 31.4¢ ✗
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FF9999;" | 31.4¢ ✗
| style="background:#FFD700;" | 17.7¢ ✓
| style="background:#FF9999;" | 31.2¢ ✗
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#90EE90;" | 17.7¢ ✓✓
| style="background:#90EE90;" | 18.0¢ ✓✓
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 17.6¢ ✓✓
| style="background:#FF9999;" | 49.4¢ ✗
| style="background:#FFD700;" | 26.1¢ ✓
| style="background:#FF9999;" | 31.2¢ ✗
|-
| '''[[19edo]]'''
| style="background:#ffe0e0;" | '''5*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#FFD700;" | '''7.2¢ ✓'''
| style="background:#90EE90;" | '''7.4¢ ✓✓'''
| style="background:#90EE90;" | '''7.2¢ ✓✓'''
| style="background:#90EE90;" | '''0.2¢ ✓✓'''
| style="background:#FF9999;" | '''21.5¢ ✗'''
| style="background:#FFD700;" | '''14.4¢ ✓'''
| style="background:#FFD700;" | '''14.3¢ ✓'''
| style="background:#90EE90;" | '''0.2¢ ✓✓'''
| style="background:#90EE90;" | '''17.1¢ ✓✓'''
| style="background:#90EE90;" | '''14.1¢ ✓✓'''
| style="background:#90EE90;" | '''7.0¢ ✓✓'''
| style="background:#FFD700;" | '''24.3¢ ✓'''
| style="background:#90EE90;" | '''19.5¢ ✓✓'''
| style="background:#FFD700;" | '''21.5¢ ✓'''
|-
| [[20edo]]
| style="background:#ffb0b0;" | 11
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 18.0¢ ✗
| style="background:#FF9999;" | 26.3¢ ✗
| style="background:#FFD700;" | 18.0¢ ✓
| style="background:#FF9999;" | 44.3¢ ✗
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#FF9999;" | 23.9¢ ✗
| style="background:#FF9999;" | 26.8¢ ✗
| style="background:#FF9999;" | 44.3¢ ✗
| style="background:#90EE90;" | 11.3¢ ✓✓
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 2.4¢ ✓✓
| style="background:#FFD700;" | 29.3¢ ✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
|-
| [[21edo]]
| style="background:#ffb0b0;" | 10
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 16.2¢ ✗
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FFD700;" | 16.2¢ ✓
| style="background:#FF9999;" | 29.9¢ ✗
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#FF9999;" | 24.7¢ ✗
| style="background:#FFD700;" | 18.8¢ ✓
| style="background:#FFD700;" | 29.9¢ ✓
| style="background:#FFD700;" | 20.1¢ ✓
| style="background:#90EE90;" | 11.1¢ ✓✓
| style="background:#90EE90;" | 11.0¢ ✓✓
| style="background:#FF9999;" | 36.3¢ ✗
| style="background:#90EE90;" | 16.6¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
|-
| '''[[22edo]]'''
| style="background:#ffe0e0;" | '''6*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#FFD700;" | '''7.1¢ ✓'''
| style="background:#90EE90;" | '''4.5¢ ✓✓'''
| style="background:#90EE90;" | '''7.1¢ ✓✓'''
| style="background:#FFD700;" | '''11.6¢ ✓'''
| style="background:#FFD700;" | '''13.0¢ ✓'''
| style="background:#FFD700;" | '''14.3¢ ✓'''
| style="background:#90EE90;" | '''5.9¢ ✓✓'''
| style="background:#90EE90;" | '''11.6¢ ✓✓'''
| style="background:#90EE90;" | '''5.9¢ ✓✓'''
| style="background:#90EE90;" | '''17.5¢ ✓✓'''
| style="background:#90EE90;" | '''18.8¢ ✓✓'''
| style="background:#90EE90;" | '''13.0¢ ✓✓'''
| style="background:#FFD700;" | '''22.3¢ ✓'''
| style="background:#90EE90;" | '''13.0¢ ✓✓'''
|-
| [[23edo]]
| style="background:#ffb0b0;" | 15
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 23.7¢ ✗
| style="background:#FF9999;" | 21.1¢ ✗
| style="background:#FF9999;" | 23.7¢ ✗
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#FF9999;" | 22.5¢ ✗
| style="background:#90EE90;" | 4.8¢ ✓✓
| style="background:#FF9999;" | 46.2¢ ✗
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#FFD700;" | 22.6¢ ✓
| style="background:#FF9999;" | 43.6¢ ✗
| style="background:#FFD700;" | 25.9¢ ✓
| style="background:#FF9999;" | 46.3¢ ✗
| style="background:#90EE90;" | 5.7¢ ✓✓
| style="background:#FFD700;" | 22.5¢ ✓
|-
| '''[[24edo]]'''
| style="background:#ffb0b0;" | '''10*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''13.7¢ ✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''15.7¢ ✓'''
| style="background:#FFD700;" | '''18.8¢ ✓'''
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#FFD700;" | '''16.8¢ ✓'''
| style="background:#90EE90;" | '''15.7¢ ✓✓'''
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | '''17.5¢ ✓✓'''
| style="background:#90EE90;" | '''17.6¢ ✓✓'''
| style="background:#90EE90;" | '''0.7¢ ✓✓'''
| style="background:#90EE90;" | '''9.5¢ ✓✓'''
| style="background:#90EE90;" | '''18.8¢ ✓✓'''
|-
| [[25edo]]
| style="background:#ffb0b0;" | 14
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 18.0¢ ✗
| style="background:#90EE90;" | 2.3¢ ✓✓
| style="background:#FFD700;" | 18.0¢ ✓
| style="background:#FF9999;" | 20.3¢ ✗
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#FFD700;" | 11.9¢ ✓
| style="background:#FF9999;" | 26.8¢ ✗
| style="background:#FFD700;" | 20.3¢ ✓
| style="background:#FFD700;" | 23.3¢ ✓
| style="background:#90EE90;" | 6.5¢ ✓✓
| style="background:#90EE90;" | 9.6¢ ✓✓
| style="background:#FF9999;" | 41.3¢ ✗
| style="background:#FFD700;" | 23.5¢ ✓
| style="background:#90EE90;" | 8.8¢ ✓✓
|-
| '''[[26edo]]'''
| style="background:#ffb0b0;" | '''11*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#FFD700;" | '''9.6¢ ✓'''
| style="background:#FFD700;" | '''17.1¢ ✓'''
| style="background:#90EE90;" | '''9.6¢ ✓✓'''
| style="background:#90EE90;" | '''7.5¢ ✓✓'''
| style="background:#90EE90;" | '''0.4¢ ✓✓'''
| style="background:#FFD700;" | '''19.3¢ ✓'''
| style="background:#90EE90;" | '''10.0¢ ✓✓'''
| style="background:#90EE90;" | '''7.5¢ ✓✓'''
| style="background:#90EE90;" | '''2.5¢ ✓✓'''
| style="background:#90EE90;" | '''17.5¢ ✓✓'''
| style="background:#90EE90;" | '''2.2¢ ✓✓'''
| style="background:#90EE90;" | '''12.1¢ ✓✓'''
| style="background:#90EE90;" | '''9.8¢ ✓✓'''
| style="background:#90EE90;" | '''0.4¢ ✓✓'''
|-
| '''[[27edo]]'''
| style="background:#ffb0b0;" | '''12*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#FFD700;" | '''9.2¢ ✓'''
| style="background:#FFD700;" | '''13.7¢ ✓'''
| style="background:#90EE90;" | '''9.2¢ ✓✓'''
| style="background:#90EE90;" | '''4.5¢ ✓✓'''
| style="background:#90EE90;" | '''9.0¢ ✓✓'''
| style="background:#FFD700;" | '''18.3¢ ✓'''
| style="background:#90EE90;" | '''0.2¢ ✓✓'''
| style="background:#90EE90;" | '''4.5¢ ✓✓'''
| style="background:#90EE90;" | '''18.0¢ ✓✓'''
| style="background:#90EE90;" | '''4.7¢ ✓✓'''
| style="background:#90EE90;" | '''4.6¢ ✓✓'''
| style="background:#FFD700;" | '''27.2¢ ✓'''
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#90EE90;" | '''9.0¢ ✓✓'''
|-
| [[28edo]]
| style="background:#ffb0b0;" | 15
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 16.2¢ ✗
| style="background:#90EE90;" | 0.6¢ ✓✓
| style="background:#FFD700;" | 16.2¢ ✓
| style="background:#FFD700;" | 15.6¢ ✓
| style="background:#FFD700;" | 16.9¢ ✓
| style="background:#FFD700;" | 10.4¢ ✓
| style="background:#FF9999;" | 33.1¢ ✗
| style="background:#90EE90;" | 15.6¢ ✓✓
| style="background:#90EE90;" | 5.8¢ ✓✓
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 11.0¢ ✓✓
| style="background:#FFD700;" | 22.0¢ ✓
| style="background:#90EE90;" | 16.6¢ ✓✓
| style="background:#90EE90;" | 16.9¢ ✓✓
|-
| '''[[29edo]]'''
| style="background:#ffb0b0;" | '''14*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''1.5¢ ✓✓'''
| style="background:#FFD700;" | '''13.9¢ ✓'''
| style="background:#90EE90;" | '''1.5¢ ✓✓'''
| style="background:#FFD700;" | '''15.4¢ ✓'''
| style="background:#FFD700;" | '''17.1¢ ✓'''
| style="background:#90EE90;" | '''3.0¢ ✓✓'''
| style="background:#FFD700;" | '''18.6¢ ✓'''
| style="background:#90EE90;" | '''15.4¢ ✓✓'''
| style="background:#90EE90;" | '''13.4¢ ✓✓'''
| style="background:#90EE90;" | '''3.2¢ ✓✓'''
| style="background:#90EE90;" | '''16.9¢ ✓✓'''
| style="background:#90EE90;" | '''14.9¢ ✓✓'''
| style="background:#90EE90;" | '''12.9¢ ✓✓'''
| style="background:#90EE90;" | '''17.1¢ ✓✓'''
|-
| [[30edo]]
| style="background:#ff8080;" | 18
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 18.0¢ ✗
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FFD700;" | 18.0¢ ✓
| style="background:#90EE90;" | 4.3¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#FF9999;" | 26.8¢ ✗
| style="background:#90EE90;" | 4.3¢ ✓✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#FFD700;" | 22.5¢ ✓
| style="background:#90EE90;" | 17.6¢ ✓✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
|-
| '''[[31edo]]'''
| style="background:#ffb0b0;" | '''16*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#FFD700;" | '''5.2¢ ✓'''
| style="background:#90EE90;" | '''0.8¢ ✓✓'''
| style="background:#90EE90;" | '''5.2¢ ✓✓'''
| style="background:#90EE90;" | '''6.0¢ ✓✓'''
| style="background:#90EE90;" | '''1.1¢ ✓✓'''
| style="background:#FFD700;" | '''10.4¢ ✓'''
| style="background:#90EE90;" | '''4.1¢ ✓✓'''
| style="background:#90EE90;" | '''6.0¢ ✓✓'''
| style="background:#90EE90;" | '''9.4¢ ✓✓'''
| style="background:#90EE90;" | '''1.9¢ ✓✓'''
| style="background:#90EE90;" | '''11.2¢ ✓✓'''
| style="background:#90EE90;" | '''4.2¢ ✓✓'''
| style="background:#90EE90;" | '''11.1¢ ✓✓'''
| style="background:#90EE90;" | '''1.1¢ ✓✓'''
|-
| [[32edo]]
| style="background:#ff8080;" | 19
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 10.5¢ ✗
| style="background:#FFD700;" | 11.3¢ ✓
| style="background:#FFD700;" | 10.5¢ ✓
| style="background:#FF9999;" | 21.8¢ ✗
| style="background:#90EE90;" | 6.2¢ ✓✓
| style="background:#FFD700;" | 16.4¢ ✓
| style="background:#90EE90;" | 4.3¢ ✓✓
| style="background:#FFD700;" | 21.8¢ ✓
| style="background:#90EE90;" | 11.2¢ ✓✓
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 5.1¢ ✓✓
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | 15.5¢ ✓✓
| style="background:#90EE90;" | 6.2¢ ✓✓
|-
| [[33edo]]
| style="background:#ff8080;" | 21
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 11.0¢ ✗
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FFD700;" | 11.0¢ ✓
| style="background:#FF9999;" | 24.7¢ ✗
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FFD700;" | 14.3¢ ✓
| style="background:#FF9999;" | 24.0¢ ✗
| style="background:#FFD700;" | 24.7¢ ✓
| style="background:#90EE90;" | 5.9¢ ✓✓
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | 0.6¢ ✓✓
| style="background:#90EE90;" | 5.1¢ ✓✓
| style="background:#90EE90;" | 4.2¢ ✓✓
| style="background:#90EE90;" | 13.0¢ ✓✓
|-
| '''[[34edo]]'''
| style="background:#ff8080;" | '''19*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#90EE90;" | '''1.9¢ ✓✓'''
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''15.9¢ ✓'''
| style="background:#90EE90;" | '''7.9¢ ✓✓'''
| style="background:#FFD700;" | '''19.8¢ ✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#90EE90;" | '''13.4¢ ✓✓'''
| style="background:#90EE90;" | '''17.8¢ ✓✓'''
| style="background:#90EE90;" | '''6.0¢ ✓✓'''
| style="background:#90EE90;" | '''9.5¢ ✓✓'''
| style="background:#90EE90;" | '''6.5¢ ✓✓'''
| style="background:#90EE90;" | '''15.9¢ ✓✓'''
|-
| [[35edo]]
| style="background:#ff8080;" | 21
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 16.2¢ ✗
| style="background:#90EE90;" | 9.2¢ ✓✓
| style="background:#FFD700;" | 16.2¢ ✓
| style="background:#90EE90;" | 7.0¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 1.8¢ ✓✓
| style="background:#90EE90;" | 7.4¢ ✓✓
| style="background:#90EE90;" | 7.0¢ ✓✓
| style="background:#90EE90;" | 2.7¢ ✓✓
| style="background:#90EE90;" | 0.4¢ ✓✓
| style="background:#90EE90;" | 11.0¢ ✓✓
| style="background:#90EE90;" | 13.5¢ ✓✓
| style="background:#90EE90;" | 16.6¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
|-
| '''[[36edo]]'''
| style="background:#ff8080;" | '''21*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''13.7¢ ✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''15.7¢ ✓'''
| style="background:#90EE90;" | '''2.2¢ ✓✓'''
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#90EE90;" | '''0.2¢ ✓✓'''
| style="background:#90EE90;" | '''15.7¢ ✓✓'''
| style="background:#90EE90;" | '''15.3¢ ✓✓'''
| style="background:#90EE90;" | '''15.9¢ ✓✓'''
| style="background:#90EE90;" | '''17.6¢ ✓✓'''
| style="background:#90EE90;" | '''17.3¢ ✓✓'''
| style="background:#90EE90;" | '''7.2¢ ✓✓'''
| style="background:#90EE90;" | '''2.2¢ ✓✓'''
|-
| [[37edo]]
| style="background:#ff8080;" | 23
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 11.6¢ ✗
| style="background:#90EE90;" | 2.9¢ ✓✓
| style="background:#FFD700;" | 11.6¢ ✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 4.1¢ ✓✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 7.5¢ ✓✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 1.2¢ ✓✓
| style="background:#90EE90;" | 12.2¢ ✓✓
| style="background:#90EE90;" | 11.6¢ ✓✓
| style="background:#90EE90;" | 2.7¢ ✓✓
| style="background:#90EE90;" | 4.1¢ ✓✓
|-
| [[38edo]]
| style="background:#ff8080;" | 23
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 7.2¢ ✓
| style="background:#90EE90;" | 7.4¢ ✓✓
| style="background:#90EE90;" | 7.2¢ ✓✓
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#FFD700;" | 10.1¢ ✓
| style="background:#FFD700;" | 14.4¢ ✓
| style="background:#FFD700;" | 17.3¢ ✓
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#90EE90;" | 14.5¢ ✓✓
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 7.0¢ ✓✓
| style="background:#90EE90;" | 7.3¢ ✓✓
| style="background:#90EE90;" | 12.1¢ ✓✓
| style="background:#90EE90;" | 10.1¢ ✓✓
|-
| [[39edo]]
| style="background:#ff8080;" | 25
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 5.7¢ ✓
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#90EE90;" | 5.7¢ ✓✓
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#FFD700;" | 15.0¢ ✓
| style="background:#FFD700;" | 11.5¢ ✓
| style="background:#FF9999;" | 20.7¢ ✗
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#90EE90;" | 2.5¢ ✓✓
| style="background:#FFD700;" | 28.7¢ ✓
| style="background:#90EE90;" | 2.2¢ ✓✓
| style="background:#90EE90;" | 3.2¢ ✓✓
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 15.0¢ ✓✓
|-
| [[40edo]]
| style="background:#ff8080;" | 26
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 12.0¢ ✗
| style="background:#90EE90;" | 3.7¢ ✓✓
| style="background:#FFD700;" | 12.0¢ ✓
| style="background:#FFD700;" | 15.7¢ ✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 6.1¢ ✓✓
| style="background:#90EE90;" | 3.2¢ ✓✓
| style="background:#90EE90;" | 15.7¢ ✓✓
| style="background:#90EE90;" | 11.3¢ ✓✓
| style="background:#90EE90;" | 12.5¢ ✓✓
| style="background:#90EE90;" | 2.4¢ ✓✓
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
|-
| '''[[41edo]]'''
| style="background:#ff8080;" | '''26*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''0.5¢ ✓✓'''
| style="background:#90EE90;" | '''5.8¢ ✓✓'''
| style="background:#90EE90;" | '''0.5¢ ✓✓'''
| style="background:#90EE90;" | '''6.3¢ ✓✓'''
| style="background:#90EE90;" | '''3.0¢ ✓✓'''
| style="background:#90EE90;" | '''1.0¢ ✓✓'''
| style="background:#90EE90;" | '''3.5¢ ✓✓'''
| style="background:#90EE90;" | '''6.3¢ ✓✓'''
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | '''2.8¢ ✓✓'''
| style="background:#90EE90;" | '''6.8¢ ✓✓'''
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | '''8.3¢ ✓✓'''
| style="background:#90EE90;" | '''3.0¢ ✓✓'''
|-
| [[42edo]]
| style="background:#ff8080;" | 28
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 12.3¢ ✗
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#FFD700;" | 12.3¢ ✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#90EE90;" | 9.7¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 8.5¢ ✓✓
| style="background:#90EE90;" | 11.1¢ ✓✓
| style="background:#90EE90;" | 17.6¢ ✓✓
| style="background:#FFD700;" | 20.8¢ ✓
| style="background:#90EE90;" | 12.0¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
|-
| '''[[43edo]]'''
| style="background:#ff8080;" | '''28*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | '''4.4¢ ✓✓'''
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | '''8.7¢ ✓✓'''
| style="background:#90EE90;" | '''7.9¢ ✓✓'''
| style="background:#90EE90;" | '''8.6¢ ✓✓'''
| style="background:#FFD700;" | '''12.2¢ ✓'''
| style="background:#90EE90;" | '''8.7¢ ✓✓'''
| style="background:#90EE90;" | '''6.8¢ ✓✓'''
| style="background:#90EE90;" | '''3.5¢ ✓✓'''
| style="background:#90EE90;" | '''13.0¢ ✓✓'''
| style="background:#90EE90;" | '''11.1¢ ✓✓'''
| style="background:#90EE90;" | '''3.3¢ ✓✓'''
| style="background:#90EE90;" | '''7.9¢ ✓✓'''
|-
| [[44edo]]
| style="background:#ff8080;" | 29
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 7.1¢ ✓
| style="background:#90EE90;" | 4.5¢ ✓✓
| style="background:#90EE90;" | 7.1¢ ✓✓
| style="background:#FFD700;" | 11.6¢ ✓
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#90EE90;" | 5.9¢ ✓✓
| style="background:#90EE90;" | 11.6¢ ✓✓
| style="background:#90EE90;" | 5.9¢ ✓✓
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | 8.5¢ ✓✓
| style="background:#90EE90;" | 13.0¢ ✓✓
| style="background:#90EE90;" | 4.9¢ ✓✓
| style="background:#90EE90;" | 13.0¢ ✓✓
|-
| [[45edo]]
| style="background:#ff8080;" | 30
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 8.6¢ ✓
| style="background:#FFD700;" | 13.0¢ ✓
| style="background:#90EE90;" | 8.6¢ ✓✓
| style="background:#90EE90;" | 4.4¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 9.4¢ ✓✓
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#90EE90;" | 4.4¢ ✓✓
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | 4.2¢ ✓✓
| style="background:#FFD700;" | 22.4¢ ✓
| style="background:#90EE90;" | 17.3¢ ✓✓
| style="background:#90EE90;" | 12.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
|-
| '''[[46edo]]'''
| style="background:#ff8080;" | '''31*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''2.4¢ ✓✓'''
| style="background:#90EE90;" | '''5.0¢ ✓✓'''
| style="background:#90EE90;" | '''2.4¢ ✓✓'''
| style="background:#90EE90;" | '''2.6¢ ✓✓'''
| style="background:#90EE90;" | '''3.6¢ ✓✓'''
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | '''6.0¢ ✓✓'''
| style="background:#90EE90;" | '''2.6¢ ✓✓'''
| style="background:#90EE90;" | '''3.5¢ ✓✓'''
| style="background:#90EE90;" | '''8.6¢ ✓✓'''
| style="background:#90EE90;" | '''0.2¢ ✓✓'''
| style="background:#90EE90;" | '''5.9¢ ✓✓'''
| style="background:#90EE90;" | '''5.7¢ ✓✓'''
| style="background:#90EE90;" | '''3.6¢ ✓✓'''
|-
| [[47edo]]
| style="background:#ff8080;" | 33
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 12.6¢ ✗
| style="background:#90EE90;" | 3.3¢ ✓✓
| style="background:#FFD700;" | 12.6¢ ✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 0.3¢ ✓✓
| style="background:#FFD700;" | 14.0¢ ✓
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | 10.4¢ ✓✓
| style="background:#90EE90;" | 4.7¢ ✓✓
| style="background:#90EE90;" | 3.6¢ ✓✓
| style="background:#FFD700;" | 23.0¢ ✓
| style="background:#90EE90;" | 2.0¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
|-
| '''[[48edo]]'''
| style="background:#ff8080;" | '''33*'''
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | '''11.3¢ ✓'''
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#90EE90;" | '''9.3¢ ✓✓'''
| style="background:#90EE90;" | '''6.2¢ ✓✓'''
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#90EE90;" | '''8.2¢ ✓✓'''
| style="background:#90EE90;" | '''9.3¢ ✓✓'''
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | '''17.5¢ ✓✓'''
| style="background:#90EE90;" | '''7.4¢ ✓✓'''
| style="background:#90EE90;" | '''0.7¢ ✓✓'''
| style="background:#90EE90;" | '''9.5¢ ✓✓'''
| style="background:#90EE90;" | '''6.2¢ ✓✓'''
|-
| [[49edo]]
| style="background:#ff8080;" | 34
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 8.2¢ ✓
| style="background:#90EE90;" | 5.5¢ ✓✓
| style="background:#90EE90;" | 8.2¢ ✓✓
| style="background:#90EE90;" | 2.7¢ ✓✓
| style="background:#FFD700;" | 10.8¢ ✓
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | 2.7¢ ✓✓
| style="background:#90EE90;" | 11.9¢ ✓✓
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| style="background:#90EE90;" | 3.7¢ ✓✓
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#90EE90;" | 10.8¢ ✓✓
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| [[50edo]]
| style="background:#ff8080;" | 35
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 6.0¢ ✓
| style="background:#90EE90;" | 2.3¢ ✓✓
| style="background:#90EE90;" | 6.0¢ ✓✓
| style="background:#90EE90;" | 3.7¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#FFD700;" | 11.9¢ ✓
| style="background:#90EE90;" | 2.8¢ ✓✓
| style="background:#90EE90;" | 3.7¢ ✓✓
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| style="background:#90EE90;" | 6.5¢ ✓✓
| style="background:#90EE90;" | 9.6¢ ✓✓
| style="background:#90EE90;" | 6.7¢ ✓✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
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| [[51edo]]
| style="background:#ff8080;" | 36
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#FFD700;" | 13.7¢ ✓
| style="background:#90EE90;" | 4.1¢ ✓✓
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#90EE90;" | 8.0¢ ✓✓
| style="background:#90EE90;" | 13.7¢ ✓✓
| style="background:#90EE90;" | 10.1¢ ✓✓
| style="background:#90EE90;" | 5.7¢ ✓✓
| style="background:#90EE90;" | 17.7¢ ✓✓
| style="background:#90EE90;" | 14.0¢ ✓✓
| style="background:#90EE90;" | 6.5¢ ✓✓
| style="background:#90EE90;" | 4.1¢ ✓✓
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| [[52edo]]
| style="background:#ff8080;" | 37
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 9.6¢ ✓
| style="background:#90EE90;" | 6.0¢ ✓✓
| style="background:#90EE90;" | 9.6¢ ✓✓
| style="background:#FFD700;" | 15.6¢ ✓
| style="background:#90EE90;" | 0.4¢ ✓✓
| style="background:#90EE90;" | 3.8¢ ✓✓
| style="background:#90EE90;" | 10.0¢ ✓✓
| style="background:#90EE90;" | 15.6¢ ✓✓
| style="background:#90EE90;" | 2.5¢ ✓✓
| style="background:#90EE90;" | 5.6¢ ✓✓
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| style="background:#90EE90;" | 12.1¢ ✓✓
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 0.4¢ ✓✓
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| '''[[53edo]]'''
| style="background:#ff8080;" | 38^
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | '''0.1¢ ✓✓'''
| style="background:#90EE90;" | '''1.4¢ ✓✓'''
| style="background:#90EE90;" | '''0.1¢ ✓✓'''
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | '''0.1¢ ✓✓'''
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | '''7.9¢ ✓✓'''
| style="background:#90EE90;" | '''6.2¢ ✓✓'''
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | '''7.8¢ ✓✓'''
| style="background:#90EE90;" | '''2.8¢ ✓✓'''
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
|}
Prompt:
<pre>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)
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.</pre>
2nd prompt:
<pre>Correct the numbers provided in the wikitext table.
Use the attached PDF to calculate the correct numbers.
All the columns N/1 (eg 2/1, 3/1) are already correct. For the other columns, some cells are correct and some not. What you need to do is subtract the error (in cents (¢)) of the two harmonics involved, but don't disregard their direction. For example if harmonic 5 has +10¢ error and harmonic 3 has -9¢ error, then the total error of interval 5/3 is 19¢ (opposite errors add). If harmonic 5 has +10¢ error and harmonic 3 has +9¢ error, then the total error of interval 5/3 is 1¢ (same-direction errors subtract).</pre>
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