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

BudjarnLambeth (talk | contribs)
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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)
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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).
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 consonant''
<nowiki>*</nowiki>''denotes EDOs where an especially high % of their intervals are especially consonant''


{| class="wikitable sortable" style="text-align:center; font-size:80%;"
{| class="wikitable sortable" style="text-align:center; font-size:80%;"
|-
|-
! 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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| style="background:#FFD700;" | 5.7¢ ✓
| style="background:#FFD700;" | 5.7¢ ✓
Line 826: Line 787:
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 15.0¢ ✓✓
| style="background:#90EE90;" | 15.0¢ ✓✓
| style="background:#90EE90;" | 15.5¢ ✓✓
|-
|-
| [[40edo]]
| [[40edo]]
| style="background:#ff8080;" | 25
| style="background:#ff8080;" | 26
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 12.0¢ ✗
| style="background:#FF9999;" | 12.0¢ ✗
Line 845: Line 805:
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 11.5¢ ✓✓
|-
|-
| [[41edo]]
| '''[[41edo]]'''
| style="background:#ff8080;" | 25
| style="background:#ff8080;" | '''26*'''
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | '''0.5¢ ✓✓'''
| style="background:#90EE90;" | 5.8¢ ✓✓
| style="background:#90EE90;" | '''5.8¢ ✓✓'''
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | '''0.5¢ ✓✓'''
| style="background:#90EE90;" | 6.3¢ ✓✓
| style="background:#90EE90;" | '''6.3¢ ✓✓'''
| style="background:#90EE90;" | 3.0¢ ✓✓
| style="background:#90EE90;" | '''3.0¢ ✓✓'''
| style="background:#90EE90;" | 1.0¢ ✓✓
| style="background:#90EE90;" | '''1.0¢ ✓✓'''
| style="background:#90EE90;" | 3.5¢ ✓✓
| style="background:#90EE90;" | '''3.5¢ ✓✓'''
| style="background:#90EE90;" | 6.3¢ ✓✓
| style="background:#90EE90;" | '''6.3¢ ✓✓'''
| style="background:#90EE90;" | 4.8¢ ✓✓
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | 2.8¢ ✓✓
| style="background:#90EE90;" | '''2.8¢ ✓✓'''
| style="background:#90EE90;" | 6.8¢ ✓✓
| style="background:#90EE90;" | '''6.8¢ ✓✓'''
| style="background:#90EE90;" | 4.3¢ ✓✓
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | 8.3¢ ✓✓
| style="background:#90EE90;" | '''8.3¢ ✓✓'''
| style="background:#90EE90;" | 3.0¢ ✓✓
| style="background:#90EE90;" | '''3.0¢ ✓✓'''
| style="background:#90EE90;" | 7.8¢ ✓✓
|-
|-
| [[42edo]]
| [[42edo]]
| style="background:#ff8080;" | 27
| style="background:#ff8080;" | 28
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 12.3¢ ✗
| style="background:#FF9999;" | 12.3¢ ✗
Line 883: Line 841:
| style="background:#90EE90;" | 12.0¢ ✓✓
| style="background:#90EE90;" | 12.0¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#FFD700;" | 24.3¢ ✓
|-
|-
| [[43edo]]
| '''[[43edo]]'''
| style="background:#ff8080;" | 27
| style="background:#ff8080;" | '''28*'''
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | 4.3¢ ✓✓
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | 4.4¢ ✓✓
| style="background:#90EE90;" | '''4.4¢ ✓✓'''
| style="background:#90EE90;" | 4.3¢ ✓✓
| style="background:#90EE90;" | '''4.3¢ ✓✓'''
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | '''8.7¢ ✓✓'''
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#90EE90;" | '''7.9¢ ✓✓'''
| style="background:#90EE90;" | 8.6¢ ✓✓
| style="background:#90EE90;" | '''8.6¢ ✓✓'''
| style="background:#FFD700;" | 12.2¢ ✓
| style="background:#FFD700;" | '''12.2¢ ✓'''
| style="background:#90EE90;" | 8.7¢ ✓✓
| style="background:#90EE90;" | '''8.7¢ ✓✓'''
| style="background:#90EE90;" | 6.8¢ ✓✓
| style="background:#90EE90;" | '''6.8¢ ✓✓'''
| style="background:#90EE90;" | 3.5¢ ✓✓
| style="background:#90EE90;" | '''3.5¢ ✓✓'''
| style="background:#90EE90;" | 13.0¢ ✓✓
| style="background:#90EE90;" | '''13.0¢ ✓✓'''
| style="background:#90EE90;" | 11.1¢ ✓✓
| style="background:#90EE90;" | '''11.1¢ ✓✓'''
| style="background:#90EE90;" | 3.3¢ ✓✓
| style="background:#90EE90;" | '''3.3¢ ✓✓'''
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#90EE90;" | '''7.9¢ ✓✓'''
| style="background:#90EE90;" | 1.0¢ ✓✓
|-
|-
| [[44edo]]
| [[44edo]]
| style="background:#ff8080;" | 28
| style="background:#ff8080;" | 29
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 7.1¢ ✓
| style="background:#FFD700;" | 7.1¢ ✓
Line 921: Line 877:
| style="background:#90EE90;" | 4.9¢ ✓✓
| style="background:#90EE90;" | 4.9¢ ✓✓
| style="background:#90EE90;" | 13.0¢ ✓✓
| style="background:#90EE90;" | 13.0¢ ✓✓
| style="background:#90EE90;" | 2.2¢ ✓✓
|-
|-
| [[45edo]]
| [[45edo]]
| style="background:#ff8080;" | 29
| style="background:#ff8080;" | 30
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 8.6¢ ✓
| style="background:#FFD700;" | 8.6¢ ✓
Line 940: Line 895:
| style="background:#90EE90;" | 12.8¢ ✓✓
| style="background:#90EE90;" | 12.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#FFD700;" | 21.4¢ ✓
|-
|-
| [[46edo]]
| '''[[46edo]]'''
| style="background:#ff8080;" | 30
| style="background:#ff8080;" | '''31*'''
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | 2.4¢ ✓✓
| style="background:#90EE90;" | '''2.4¢ ✓✓'''
| style="background:#90EE90;" | 5.0¢ ✓✓
| style="background:#90EE90;" | '''5.0¢ ✓✓'''
| style="background:#90EE90;" | 2.4¢ ✓✓
| style="background:#90EE90;" | '''2.4¢ ✓✓'''
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | '''2.6¢ ✓✓'''
| style="background:#90EE90;" | 3.6¢ ✓✓
| style="background:#90EE90;" | '''3.6¢ ✓✓'''
| style="background:#90EE90;" | 4.8¢ ✓✓
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | 6.0¢ ✓✓
| style="background:#90EE90;" | '''6.0¢ ✓✓'''
| style="background:#90EE90;" | 2.6¢ ✓✓
| style="background:#90EE90;" | '''2.6¢ ✓✓'''
| style="background:#90EE90;" | 3.5¢ ✓✓
| style="background:#90EE90;" | '''3.5¢ ✓✓'''
| style="background:#90EE90;" | 8.6¢ ✓✓
| style="background:#90EE90;" | '''8.6¢ ✓✓'''
| style="background:#90EE90;" | 0.2¢ ✓✓
| style="background:#90EE90;" | '''0.2¢ ✓✓'''
| style="background:#90EE90;" | 5.9¢ ✓✓
| style="background:#90EE90;" | '''5.9¢ ✓✓'''
| style="background:#90EE90;" | 5.7¢ ✓✓
| style="background:#90EE90;" | '''5.7¢ ✓✓'''
| style="background:#90EE90;" | 3.6¢ ✓✓
| style="background:#90EE90;" | '''3.6¢ ✓✓'''
| style="background:#90EE90;" | 8.1¢ ✓✓
|-
|-
| [[47edo]]
| [[47edo]]
| style="background:#ff8080;" | 31
| style="background:#ff8080;" | 33
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FF9999;" | 12.6¢ ✗
| style="background:#FF9999;" | 12.6¢ ✗
Line 978: Line 931:
| style="background:#90EE90;" | 2.0¢ ✓✓
| style="background:#90EE90;" | 2.0¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | 14.6¢ ✓✓
|-
|-
| [[48edo]]
| '''[[48edo]]'''
| style="background:#ff8080;" | 31
| style="background:#ff8080;" | '''33*'''
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | 2.0¢ ✓✓
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#FFD700;" | 11.3¢ ✓
| style="background:#FFD700;" | '''11.3¢ ✓'''
| style="background:#90EE90;" | 2.0¢ ✓✓
| style="background:#90EE90;" | '''2.0¢ ✓✓'''
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | '''9.3¢ ✓✓'''
| style="background:#90EE90;" | 6.2¢ ✓✓
| style="background:#90EE90;" | '''6.2¢ ✓✓'''
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#90EE90;" | '''3.9¢ ✓✓'''
| style="background:#90EE90;" | 8.2¢ ✓✓
| style="background:#90EE90;" | '''8.2¢ ✓✓'''
| style="background:#90EE90;" | 9.3¢ ✓✓
| style="background:#90EE90;" | '''9.3¢ ✓✓'''
| style="background:#90EE90;" | 1.3¢ ✓✓
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | 17.5¢ ✓✓
| style="background:#90EE90;" | '''17.5¢ ✓✓'''
| style="background:#90EE90;" | 7.4¢ ✓✓
| style="background:#90EE90;" | '''7.4¢ ✓✓'''
| style="background:#90EE90;" | 0.7¢ ✓✓
| style="background:#90EE90;" | '''0.7¢ ✓✓'''
| style="background:#90EE90;" | 9.5¢ ✓✓
| style="background:#90EE90;" | '''9.5¢ ✓✓'''
| style="background:#90EE90;" | 6.2¢ ✓✓
| style="background:#90EE90;" | '''6.2¢ ✓✓'''
| style="background:#90EE90;" | 11.5¢ ✓✓
|-
|-
| [[49edo]]
| [[49edo]]
| style="background:#ff8080;" | 32
| style="background:#ff8080;" | 34
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 8.2¢ ✓
| style="background:#FFD700;" | 8.2¢ ✓
Line 1,016: Line 967:
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#90EE90;" | 10.8¢ ✓✓
| style="background:#90EE90;" | 10.8¢ ✓✓
| style="background:#90EE90;" | 16.1¢ ✓✓
|-
|-
| [[50edo]]
| [[50edo]]
| style="background:#ff8080;" | 33
| style="background:#ff8080;" | 35
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 6.0¢ ✓
| style="background:#FFD700;" | 6.0¢ ✓
Line 1,035: Line 985:
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 0.5¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 8.8¢ ✓✓
| style="background:#90EE90;" | 5.5¢ ✓✓
|-
|-
| [[51edo]]
| [[51edo]]
| style="background:#ff8080;" | 34
| style="background:#ff8080;" | 36
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
| style="background:#90EE90;" | 3.9¢ ✓✓
Line 1,054: Line 1,003:
| style="background:#90EE90;" | 6.5¢ ✓✓
| style="background:#90EE90;" | 6.5¢ ✓✓
| style="background:#90EE90;" | 4.1¢ ✓✓
| style="background:#90EE90;" | 4.1¢ ✓✓
| style="background:#90EE90;" | 2.6¢ ✓✓
|-
|-
| [[52edo]]
| [[52edo]]
| style="background:#ff8080;" | 35
| style="background:#ff8080;" | 37
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#FFD700;" | 9.6¢ ✓
| style="background:#FFD700;" | 9.6¢ ✓
Line 1,073: Line 1,021:
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 9.8¢ ✓✓
| style="background:#90EE90;" | 0.4¢ ✓✓
| style="background:#90EE90;" | 0.4¢ ✓✓
| style="background:#90EE90;" | 0.2¢ ✓✓
|-
|-
| [[53edo]]
| '''[[53edo]]'''
| style="background:#ff8080;" | 36
| style="background:#ff8080;" | 38^
| style="background:#90EE90;" | 0.0¢ ✓✓
| style="background:#90EE90;" | '''0.0¢ ✓✓'''
| style="background:#90EE90;" | 0.1¢ ✓✓
| style="background:#90EE90;" | '''0.1¢ ✓✓'''
| style="background:#90EE90;" | 1.4¢ ✓✓
| style="background:#90EE90;" | '''1.4¢ ✓✓'''
| style="background:#90EE90;" | 0.1¢ ✓✓
| style="background:#90EE90;" | '''0.1¢ ✓✓'''
| style="background:#90EE90;" | 1.3¢ ✓✓
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | 4.8¢ ✓✓
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | 0.1¢ ✓✓
| style="background:#90EE90;" | '''0.1¢ ✓✓'''
| style="background:#90EE90;" | 4.8¢ ✓✓
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | 1.3¢ ✓✓
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | 7.9¢ ✓✓
| style="background:#90EE90;" | '''7.9¢ ✓✓'''
| style="background:#90EE90;" | 6.2¢ ✓✓
| style="background:#90EE90;" | '''6.2¢ ✓✓'''
| style="background:#90EE90;" | 1.3¢ ✓✓
| style="background:#90EE90;" | '''1.3¢ ✓✓'''
| style="background:#90EE90;" | 7.8¢ ✓✓
| style="background:#90EE90;" | '''7.8¢ ✓✓'''
| style="background:#90EE90;" | 2.8¢ ✓✓
| style="background:#90EE90;" | '''2.8¢ ✓✓'''
| style="background:#90EE90;" | 4.8¢ ✓✓
| style="background:#90EE90;" | '''4.8¢ ✓✓'''
| style="background:#90EE90;" | 2.7¢ ✓✓
|}
|}


Line 1,125: Line 1,071:
13/1 (neu 6th^)
13/1 (neu 6th^)
  8/7 (supmaj 2nd)
  8/7 (supmaj 2nd)
13/3 (large tridec neu 2nd^)
DISSONANCES
DISSONANCES
Any note not within range of one of the above.
Any note not within range of one of the above.