User:Moremajorthanmajor/8edX: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|+
|+
! colspan="5" | Decade
! colspan="6" | Decade
!Period
!Period
!Notes
!Notes
|-
|-
|6\5
|6\5
|
|
|
|
|
Line 17: Line 18:
|
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|17\14
|17\14
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|
|
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Line 24: Line 26:
|-
|-
|11\9
|11\9
|
|
|
|
|
Line 33: Line 36:
|
|
|16\13
|16\13
|
|
|
|
|
Line 42: Line 46:
|
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|21\17
|21\17
|
|
|
|
|
Line 51: Line 56:
|
|
|26\21
|26\21
|
|
|
|185.714
|185.714
Line 60: Line 66:
|
|
|31\25
|31\25
|
|186
|186
|
|
|-
|-
|5\4
|5\4
|
|
|
|
|
Line 76: Line 84:
|
|
|34\27
|34\27
|
|188.{{Overline|8}}
|188.{{Overline|8}}
|
|
Line 83: Line 92:
|
|
|29\23
|29\23
|
|
|
|189.13
|189.13
Line 90: Line 100:
|
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|24\19
|24\19
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|
|
|
|
Line 97: Line 108:
|
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|19\15
|19\15
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|
|
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|
Line 104: Line 116:
|-
|-
|14\11
|14\11
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|
|
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Line 113: Line 126:
|
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|23\18
|23\18
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|
|
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Line 120: Line 134:
|-
|-
|9\7
|9\7
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|
|
|
|
Line 129: Line 144:
|
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|31\24
|31\24
|
|
|
|
|
Line 136: Line 152:
|-
|-
|22\17
|22\17
|
|
|
|
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Line 145: Line 162:
|
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|35\27
|35\27
|
|
|
|
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Line 152: Line 170:
|-
|-
|13\10
|13\10
|
|
|
|
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Line 160: Line 179:
|-
|-
|17\13
|17\13
|
|
|
|
|
Line 168: Line 188:
|-
|-
|21\16
|21\16
|
|
|
|
|
Line 177: Line 198:
|
|
|25\19
|25\19
|
|
|
|
|
Line 186: Line 208:
|
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|29\22
|29\22
|
|
|
|
|
Line 195: Line 218:
|
|
|33\25
|33\25
|
|
|
|198
|198
Line 205: Line 229:
|37\28
|37\28
|
|
|198.214
|
|-
|
|
|
|
|
|41\31
|198.387
|
|
|-
|-
Line 212: Line 246:
|
|
|
|
|100
|
|200
| Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
| Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|
|
|
|
|
|35\26
|201.923
|
|-
|
|
|
|
|31\23
|
|202.174
|
|-
|
|
|
|27\20
|
|
|202.5
|
|-
|
|
|23\17
|
|
|
|202.941
|
|-
|-
|
|
Line 220: Line 291:
|
|
|
|
|101.786
|
|203.571
|
|
|-
|-
Line 228: Line 300:
|
|
|
|
|102.{{Overline|27}}
|
|204.{{Overline|54}}
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|-
Line 236: Line 309:
|
|
|
|
|102.632
|
|205.263
|
|
|-
|-
Line 244: Line 318:
|
|
|
|
|103.125
|
|206.25
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|-
Line 252: Line 327:
|
|
|
|
|103.846
|
|207.692
|
|
|-
|-
Line 260: Line 336:
|
|
|
|
|104.1{{Overline|6}}
|
|208.{{Overline|3}}
|
|
|-
|-
Line 268: Line 345:
|
|
|
|
|105
|
|210
|Mixolydian-Ionian mode ends
|Mixolydian-Ionian mode ends
|}Relative cents
|}Relative cents
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
!Degrees
!Degrees
! colspan="3" |Enneatonic
!Intense Aeolian-Subpental Dorian
!Intense Aeolian-Subpental Dorian
!Dorian
!Dorian
Line 279: Line 356:
|-
|-
|1
|1
|1#/2b
|G#/Jb
|''G#/Ab''
|''90.625''
|''93.75''
|''96.875''
|-
|2
|2
|J
|''A''
|''181.25''
|''181.25''
|''187.5''
|''187.5''
|''193.75''
|''193.75''
|-
|-
|3
|2
|2#/3b
|J#/Ab
|''A#/Bb''
|''271.875''
|''281.25''
|''290.625''
|-
|4
|3
|J
|''B''
|''362.5''
|''362.5''
|''375''
|''375''
|''387.5''
|''387.5''
|-
|-
|5
|3
|3#/4b
|J#/Ab
|B#/Cb
|''453.125''
|''468.75''
|''484.375''
|-
|6
|4
|A
|''C''
|''543.75''
|''543.75''
|''562.5''
|''562.5''
|''581.25''
|''581.25''
|-
|-
|7
|4
|5
|A#/Bb
|''C#/Qb''
|''633.375''
|''656.25''
|''678.125''
|-
|8
|5#/6b
|B
|''Q''
|''725''
|''725''
|''750''
|''750''
|''775''
|''775''
|-
|-
|9
|5
|6
|C
|''D''
|''815.625''
|''843.75''
|''871.875''
|-
|10
|6#/7b
|C#/Db
|D#/Sb
|''906.25''
|''906.25''
|''937.5''
|''937.5''
|''968.75''
|''968.75''
|-
|-
|11
|6
|7
|D
|''S''
|''996.875''
|''1031.25''
|''1065.625''
|-
|12
|7#/8b
|D#/Eb
|''S#/Eb''
|''1087.5''
|''1087.5''
|''1125''
|''1125''
|''1162.5''
|''1162.5''
|-
|-
| 13
|7
|8
| colspan="2" |E
|''1178.125''
|''1218.75''
|''1259.375''
|-
|14
|8#/9b
| colspan="2" |E#/Fb
|''1268.75''
|''1268.75''
|''1312.5''
|''1312.5''
|''1356.25''
|''1356.25''
|-
|15
|9
| colspan="2" |F
|''1359.375''
|''1406.25''
|''1453.125''
|-
|16
|1
| colspan="2" |G
|''1450''
|''1500''
|''1550''
|}
|}
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
!Degrees
!Degrees
! colspan="3" |Enneatonic
!Subpental-Soft Superpental Mixolydian
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
|-
| | 1
| | 1
|1#/2b
| colspan="2" |F#/Gb
|''100''
|''103.125''
|-
| |2
|2
| colspan="2" |G
|''200''
|''200''
|''206.25''
|''206.25''
|-
|-
| |3
| |2
|2#/3b
|G#/Jb
|''G#/Ab''
|''300''
|''309.375''
|-
| |4
|3
|J
|''A''
|''400''
|''400''
|''412.5''
|''412.5''
|-
|-
| |5
| |3
|3#/4b
|J#/Ab
|''A#/Bb''
|''500''
|''515.625''
|-
| |6
|4
|A
|''B''
|''600''
|''600''
|''618.75''
|''618.75''
|-
|-
| | 7
| |4
|5
|B
|''H''
|''700''
|''721.875''
|-
|8
| 5#/6b
|B#/Hb
|''H#/Cb''
|''800''
|''800''
|''825''
|''825''
|-
|-
|9
| |5
|6
|H
|''C''
|''900''
|''928.125''
|-
|10
|6#/7b
|H#/Cb
|''C#/Db''
|''1000''
|''1000''
|''1031.25''
|''1031.25''
|-
|-
|11
| |6
|7
|C
|''D''
|''1100''
|''1134.375''
|-
|12
|7#/8b
|C#/Db
|''D#/Sb''
|''1200''
|''1200''
|''1237.5''
|''1237.5''
|-
|-
|13
| | 7
|8
|D
|''S''
|''1300''
|''1340.625''
|-
|14
|8#/9b
|D#/Eb
|''S#/Eb''
|''1400''
|''1400''
|''1443.75''
|''1443.75''
|-
|}
|15
|9
| colspan="2" |E
|''1500''
|''1546.875''
|-
|16
|1
| colspan="2" |F
|''1600''
|''1650''
|}By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.686 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of [[110edo]], and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.
==See also==
==See also==
*[[16ed5/2]] - equal division of the classic major tenth
*[[8ed5/2]] - equal division of the classic major tenth
*[[16ed7/3]] - equal division of the septimal minor tenth
*[[8ed7/3]] - equal division of the septimal minor tenth


[[Category:16-tone scales]]
[[Category:8-tone scales]]
[[Category:EdX]]
[[Category:EdX]]

Revision as of 03:13, 8 June 2023

This is the neutral scale of the Vesuvius temperament family. It also gives every other period of the 16th-decade Roccocavallo branch of the Carrera temperament family.

Intervals

Decade Period Notes
6\5 180 Intense Aeolian-Subpental Dorian mode begins
17\14 182.143
11\9 183.3 Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
16\13 184.615
21\17 185.294
26\21 185.714
31\25 186
5\4 187,5 Subpental Dorian mode ends, Pental Dorian mode begins
34\27 188.8
29\23 189.13
24\19 189.474
19\15 190
14\11 190.90 Pental Dorian mode ends, Superpental Dorian mode begins
23\18 191.6
9\7 192.857 Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
31\24 193
22\17 194.118 Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
35\27 194.4
13\10 195 Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13 196.154
21\16 196.875 Subpental Mixolydian mode ends, Pental Mixolydian mode begins
25\19 197.37
29\22 197.72
33\25 198
37\28 198.214
41\31 198.387
4\3 200 Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
35\26 201.923
31\23 202.174
27\20 202.5
23\17 202.941
19\14 203.571
15\11 204.54 Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
26\19 205.263
11\8 206.25 Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
18\13 207.692
25\18 208.3
7\5 210 Mixolydian-Ionian mode ends

Relative cents

Degrees Intense Aeolian-Subpental Dorian Dorian Dorian-Mixolydian
1 181.25 187.5 193.75
2 362.5 375 387.5
3 543.75 562.5 581.25
4 725 750 775
5 906.25 937.5 968.75
6 1087.5 1125 1162.5
7 1268.75 1312.5 1356.25
Degrees Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 200 206.25
2 400 412.5
3 600 618.75
4 800 825
5 1000 1031.25
6 1200 1237.5
7 1400 1443.75

See also

  • 8ed5/2 - equal division of the classic major tenth
  • 8ed7/3 - equal division of the septimal minor tenth
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