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

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autopatrolled, emailconfirmed
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BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,276 edits
mNo edit summary
Line 67: Line 67:
|-
|-
! rowspan="2" | EDO  
! rowspan="2" | EDO  
! rowspan="2" |Est. no. of dissonances!! colspan="2" style="background:#d0e8ff;" | Hyperconsonances !! colspan="6" style="background:#c8f0c8;" | Consonances !! colspan="8" style="background:#fff0c8;" | Ambisonances  
! 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;" | 2/1<br /><small>perf oct</small>
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! style="background:#fff0c8;" | 13/1<br /><small>neu 6th^</small>
! style="background:#fff0c8;" | 13/1<br /><small>neu 6th^</small>
! style="background:#fff0c8;" | 8/7<br /><small>supmaj 2nd</small>
! style="background:#fff0c8;" | 8/7<br /><small>supmaj 2nd</small>
! style="background:#fff0c8;" | 13/3<br /><small>lg tri neu 2nd^</small>
|-
|-


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Revision as of 11:35, 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)

DISSONANCES
 9/7 (supmaj 3rd)
13/3 (large tridec neu 2nd^)
15/1 (maj 7th^)
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.

Table of EDOs by general-purpose efficacy (1–53edo)

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Author comments: 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).

*denotes EDOs where an especially high % of their intervals are consonant

EDO Est. no. of dissonances 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
1edo 0 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¢ ✗
2edo 0 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¢ ✗
3edo 1 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¢ ✗
4edo 0 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¢ ✗
5edo 1 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¢ ✓✓
6edo 1 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¢ ✗
7edo 1 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¢ ✗
8edo 4 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¢ ✗
9edo 4 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¢ ✗
10edo 4* 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¢ ✓✓
11edo 6 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¢ ✓✓
12edo 3* 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¢ ✗
13edo 6 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¢ ✗
14edo 8 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¢ ✓
15edo 4* 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¢ ✓✓
16edo 6 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¢ ✓✓
17edo 7 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¢ ✓✓
18edo 8 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¢ ✗
19edo 5* 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¢ ✓
20edo 11 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¢ ✓✓
21edo 10 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¢ ✓✓
22edo 6* 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¢ ✓✓
23edo 15 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¢ ✓
24edo 10* 0.0¢ ✓✓ 2.0¢ ✓✓ 13.7¢ ✓ 2.0¢ ✓✓ 15.7¢ ✓ 18.8¢ ✓ 3.9¢ ✓✓ 16.8¢ ✓ 15.7¢ ✓✓ 1.3¢ ✓✓ 17.5¢ ✓✓ 17.6¢ ✓✓ 0.7¢ ✓✓ 9.5¢ ✓✓ 18.8¢ ✓✓
25edo 14 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¢ ✓✓
26edo 11* 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¢ ✓✓
27edo 12* 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¢ ✓✓
28edo 15 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¢ ✓✓
29edo 14* 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¢ ✓✓
30edo 18 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¢ ✓✓
31edo 16* 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¢ ✓✓
32edo 19 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¢ ✓✓
33edo 21 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¢ ✓✓
34edo 19* 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¢ ✓✓
35edo 21 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¢ ✓✓
36edo 21* 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¢ ✓✓
37edo 23 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¢ ✓✓
38edo 23 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¢ ✓✓
39edo 25 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¢ ✓✓
40edo 26 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¢ ✓✓
41edo 26 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¢ ✓✓
42edo 28 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¢ ✓✓
43edo 28 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¢ ✓✓
44edo 29 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¢ ✓✓
45edo 30 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¢ ✓✓
46edo 31 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¢ ✓✓
47edo 33 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¢ ✓✓
48edo 33 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¢ ✓✓
49edo 34 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¢ ✓✓
50edo 35 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¢ ✓✓
51edo 36 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¢ ✓✓
52edo 37 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¢ ✓✓
53edo 38 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¢ ✓✓

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.

2nd prompt: 

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).
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