User:Moremajorthanmajor/16edX: Difference between revisions

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#redirect [[16ed5/2]]
'''16edX''' is the scale which occurs as the dominant reformed Mixolydian mode. It also gives the period of the 16th-decade Roccocavallo branch of the Carrera temperament family.
== Intervals==
{| class="wikitable"
|+
! colspan="4" |Decade
! Period
!Notes
|-
| 6\5
|
|
|
|90
|Intense Aeolian-Subpental Dorian mode begins
|-
|
|17\14
|
|
| 91.071
|
|-
|11\9
|
|
|
|91.{{Overline|6}}
| Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|
|16\13
|
|
| 92.308
|
|-
|5\4
|
|
|
|93.75
|Subpental Dorian mode ends, Pental Dorian mode begins
|-
|
|
|24\19
|
|94.737
|
|-
|
|19\15
|
|
|95
|
|-
|14\11
|
|
|
|95.{{Overline|45}}
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|
| 23\18
|
|
|95.8{{Overline|3}}
|
|-
|9\7
|
|
|
|96.429
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|
|31\24
|
|
|96.875
|
|-
|22\17
|
|
|
|97.059
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|
|35\27
|
|
|97.{{Overline|2}}
|
|-
| 13\10
|
|
|
|97.5
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|
|
|
|98.077
|
|-
|21\16
|
|
|
|98.4375
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|
|25\19
|
|
|98.684
|
|-
|
|
|29\22
|
|98.8{{Overline|63}}
|
|-
|
|
|
|33\25
|99
|
|-
|4\3
|
|
|
|100
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|
| 19\14
|
|
|101.786
|
|-
|15\11
|
|
|
|102.{{Overline|27}}
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|
|26\19
|
|
|102.632
|
|-
|11\8
|
|
|
|103.125
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|
|18\13
|
|
|103.846
|
|-
|
|
|25\18
|
|104.1{{Overline|6}}
|
|-
|7\5
|
|
|
|105
|Mixolydian-Ionian mode ends
|}Relative cents
{| class="wikitable" style="text-align: center"
!Degrees
! colspan="3" |Enneatonic
!Intense Aeolian-Subpental Dorian
!Dorian
|-
|1
|1#/2b
|G#/Jb
|''G#/Ab''
|90.625
|''93.75''
|-
|2
| 2
|J
|''A''
|181.25
|''187.5''
|-
|3
|2#/3b
|J#/Ab
|''A#/Bb''
|271.875
|''281.25''
|-
|4
|3
|J
|''B''
|362.5
|''375''
|-
|5
|3#/4b
|J#/Ab
|B#/Cb
|453.125
|''468.75''
|-
|6
|4
|A
|''C''
|543.75
|''562.5''
|-
|7
|5
|A#/Bb
|''C#/Qb''
|633.375
|''656.25''
|-
|8
|5#/6b
|B
|''Q''
|725
|''750''
|-
|9
|6
|C
|''D''
|815.625
|''843.75''
|-
|10
|6#/7b
| C#/Db
|D#/Sb
|906.25
|''937.5''
|-
|11
|7
|D
|''S''
|996.875
|''1031.25''
|-
|12
| 7#/8b
|D#/Eb
|''S#/Eb''
|1087.5
|''1125''
|-
|13
|8
| colspan="2" | E
|1178.125
|''1218.75''
|-
|14
|8#/9b
| colspan="2" |E#/Fb
|1268.75
|''1312.5''
|-
|15
|9
| colspan="2" |F
|1359.375
|''1406.25''
|-
|16
|1
| colspan="2" |G
|1450
|''1500''
|}
{| class="wikitable" style="text-align: center"
!Degrees
! colspan="3" |Enneatonic
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
| |1
|1#/2b
| colspan="2" |F#/Gb
|''100''
|''103.125''
|-
| |2
|2
| colspan="2" |G
|''200''
|''206.25''
|-
| |3
|2#/3b
|G#/Jb
|''G#/Ab''
|''300''
|''309.375''
|-
| |4
|3
|J
|''A''
|''400''
|''412.5''
|-
| | 5
|3#/4b
|J#/Ab
|''A#/Bb''
|''500''
|''515.625''
|-
| |6
|4
|A
|''B''
|''600''
|''618.75''
|-
| | 7
|5
|B
|''H''
|''700''
|''721.875''
|-
|8
|5#/6b
|B#/Hb
|''H#/Cb''
|''800''
|''825''
|-
|9
|6
|H
|''C''
|''900''
|''928.125''
|-
|10
|6#/7b
|H#/Cb
|''C#/Db''
|''1000''
|''1031.25''
|-
|11
|7
|C
|''D''
|''1100''
|''1134.375''
|-
|12
|7#/8b
|C#/Db
|''D#/Sb''
|''1200''
|''1237.5''
|-
|13
|8
|D
|''S''
|''1300''
|''1340.625''
|-
|14
|8#/9b
| D#/Eb
|''S#/Eb''
|''1400''
|''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==
*[[16ed5/2]] - equal division of the classic major tenth
*[[16ed7/3]] - equal division of the septimal minor tenth
 
[[Category:16-tone scales]]
[[Category:EdX]]

Revision as of 00:33, 23 May 2023

16edX is the scale which occurs as the dominant reformed Mixolydian mode. It also gives the period of the 16th-decade Roccocavallo branch of the Carrera temperament family.

Intervals

Decade Period Notes
6\5 90 Intense Aeolian-Subpental Dorian mode begins
17\14 91.071
11\9 91.6 Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
16\13 92.308
5\4 93.75 Subpental Dorian mode ends, Pental Dorian mode begins
24\19 94.737
19\15 95
14\11 95.45 Pental Dorian mode ends, Superpental Dorian mode begins
23\18 95.83
9\7 96.429 Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
31\24 96.875
22\17 97.059 Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
35\27 97.2
13\10 97.5 Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13 98.077
21\16 98.4375 Subpental Mixolydian mode ends, Pental Mixolydian mode begins
25\19 98.684
29\22 98.863
33\25 99
4\3 100 Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
19\14 101.786
15\11 102.27 Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
26\19 102.632
11\8 103.125 Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
18\13 103.846
25\18 104.16
7\5 105 Mixolydian-Ionian mode ends

Relative cents

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
1 1#/2b G#/Jb G#/Ab 90.625 93.75
2 2 J A 181.25 187.5
3 2#/3b J#/Ab A#/Bb 271.875 281.25
4 3 J B 362.5 375
5 3#/4b J#/Ab B#/Cb 453.125 468.75
6 4 A C 543.75 562.5
7 5 A#/Bb C#/Qb 633.375 656.25
8 5#/6b B Q 725 750
9 6 C D 815.625 843.75
10 6#/7b C#/Db D#/Sb 906.25 937.5
11 7 D S 996.875 1031.25
12 7#/8b D#/Eb S#/Eb 1087.5 1125
13 8 E 1178.125 1218.75
14 8#/9b E#/Fb 1268.75 1312.5
15 9 F 1359.375 1406.25
16 1 G 1450 1500
Degrees Enneatonic Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 1#/2b F#/Gb 100 103.125
2 2 G 200 206.25
3 2#/3b G#/Jb G#/Ab 300 309.375
4 3 J A 400 412.5
5 3#/4b J#/Ab A#/Bb 500 515.625
6 4 A B 600 618.75
7 5 B H 700 721.875
8 5#/6b B#/Hb H#/Cb 800 825
9 6 H C 900 928.125
10 6#/7b H#/Cb C#/Db 1000 1031.25
11 7 C D 1100 1134.375
12 7#/8b C#/Db D#/Sb 1200 1237.5
13 8 D S 1300 1340.625
14 8#/9b D#/Eb S#/Eb 1400 1443.75
15 9 E 1500 1546.875
16 1 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

  • 16ed5/2 - equal division of the classic major tenth
  • 16ed7/3 - equal division of the septimal minor tenth
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