Xenharmonic Wiki

Chords of magic: Difference between revisions

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ArrowHead294 (talk | contribs)
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TallKite (talk | contribs)
autopatrolled, Sysops
4,203 edits
fixed 2 errors, added a table of cents for all accidentals, added the vM7 and 7;6;5;4 chords
Line 5: Line 5:
Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.
Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19 and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.


The chord names use ups and downs as described on the pergens page. The generator is vM3 and the enharmonic interval is ^<sup>5</sup>dd2. To simplify the names, lifts and drops are also used. One lift is 41 generators, octave-reduced. (41 because 41edo is a near-optimal tuning of magic.) Thus {{nowrap|/1 {{=}} ^d2 {{=}} 20¢ &minus; 8.2¢}}, i.e. an up minus a tempered pythagorean comma. {{nowrap|/C {{=}} ^Dbb|\C {{=}} vB#|^C {{=}} /B#|and vC {{=}} \Dbb}}.
The chord names use arrows (ups and downs) as described on the [[Pergen|pergens]] page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. The generator is vM3 = 380¢ + c/5, where c = the amount in cents the tempered fifth exceeds 700¢. The enharmonic interval is ^<sup>5</sup>dd2, thus ^<sup>5</sup>C = B##. To simplify the chord names, slashes (lifts and drops) are also used. One lift is -41 generators, octave-reduced. (41 because 41edo is a near-optimal tuning of magic.) Thus {{nowrap|/1 {{=}} ^d2 {{=}} 20¢ &minus; 8.2c}}. Thus a lift equals an up minus a tempered pythagorean comma. {{nowrap|/C {{=}} ^Dbb|\C {{=}} vB#|^C {{=}} /B#|and vC {{=}} \Dbb}}. This notation is "tippy" in the sense that if the fifth is wider than 41edo's fifth, a lift will actually be descending. Furthermore if the fifth is narrower than 19edo's, an up will be descending.
 
{| class="wikitable"
|+Cents values of Magic accidentals
!
!sharp
!up
!lift
!how to convert the score to an edo
|-
!19edo
|1\19 = 61¢
|0\19 = 0¢
|1\19 = 61¢
|ignore the arrows, treat slashes as sharps/flats
|-
!22edo
|3\22 = 164¢
|1\22 = 55¢
| -1\22 = -55¢
|treat lifts as downs and drops as ups
|-
!41edo
|4\41 = 117¢
|1\41 = 29¢
|0\41 = 0¢
|ignore the slashes
|-
!60edo
|5\60 = 100¢
|1\60 = 20¢
|1\60 = 20¢
|treat slashes as arrows
|-
!rank-2
|100¢ + 7c
|20¢ + 3.8c
|20¢ - 8.2c
!
|}
{| class="wikitable center-all"
{| class="wikitable center-all"
|+Magic's genchain
|-
|-
! Genspan
! Genspan
Line 41: Line 79:
| 146
| 146
|-
|-
! Ratios
! Ratio
| 1/1
| 1/1
| 5/4
| 5/4
Line 58: Line 96:
|-
|-
! Interval
! Interval
| P1
| '''P1'''
| vM3
| vM3
| vvA5
| vvA5
Line 65: Line 103:
^/M7
^/M7
| ^m3
| ^m3
| P5
| '''P5'''
| vM7
| vM7
| vvA2
| vvA2
Line 72: Line 110:
^/A4
^/A4
| ^m7
| ^m7
| M2
| '''M2'''
| vA4
| vA4
\d5
\d5
Line 79: Line 117:
| ^^m2
| ^^m2
^/A1
^/A1
|-
!Note
(in C)
|'''C'''
|vE
|vvG#
v\Ab
|^^Cb
^/B
|^Eb
|'''G'''
|vB
|vvD#
v\Eb
|^^Gb
^/F#
|^Bb
|'''D'''
|vF#
\Gb
|vvA#
v\Bb
|^^Db
^/C#
|}
|}
'''''TODO: complete the tables'''''
'''''TODO: complete the tables'''''
Line 509: Line 571:
! Comments
! Comments
|-
|-
| 1
|1
|0-1-5-6
|1-5/4-3/2-15/8
|Ambitonal
|vM7
|
|-
| 2
| 0-1-2-9
| 0-1-2-9
| 1-5/4-14/9-9/5
| 1-5/4-14/9-9/5
Line 516: Line 585:
|  
|  
|-
|-
| 2
| 3
| 0-2-4-9
| 0-2-4-9
| 1-14/9-6/5-9/5
| 1-14/9-6/5-9/5
Line 523: Line 592:
|  
|  
|-
|-
| 3
| 4
| 0-1-5-9
| 0-1-5-9
| 1-5/4-3/2-9/5
| 1-5/4-3/2-9/5
Line 530: Line 599:
|  
|  
|-
|-
| 4
| 5
| 0-4-5-9
| 0-4-5-9
| 1-6/5-3/2-9/5
| 1-6/5-3/2-9/5
| Ambitonal
| Ambitonal
| ^m7
| ^m7
| <u>or</u> 1-5/4-3/2-5/3 = v6
|<u>or</u> 1-5/4-3/2-5/3 = v6
|-
|-
| 5
| 6
| 0-2-7-9
| 0-2-7-9
| 1-14/9-7/6-9/5
| 1-14/9-7/6-9/5
Line 544: Line 613:
| 1-9/7-3/2-7/3
| 1-9/7-3/2-7/3
|-
|-
| 6
| 7
| 0-5-7-9
| 0-5-7-9
| 1-3/2-7/6-9/5
| 1-3/2-7/6-9/5
Line 551: Line 620:
|  
|  
|-
|-
| 7
| 8
| 0-1-8-9
| 0-1-8-9
| 1-5/4-16/11-9/5
| 1-5/4-16/11-9/5
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|  
|  
|-
|-
| 8
| 9
| 0-4-8-9
| 0-4-8-9
| 1-6/5-16/11-9/5
| 1-6/5-16/11-9/5
Line 565: Line 634:
|  
|  
|-
|-
| 9
| 10
| 0-7-8-9
| 0-7-8-9
| 1-7/6-16/11-9/5
| 1-7/6-16/11-9/5
Line 572: Line 641:
|  
|  
|-
|-
| 10
| 11
| 0-1-2-10
| 0-1-2-10
| 1-5/4-14/9-9/8
| 1-5/4-14/9-9/8
Line 579: Line 648:
|  
|  
|-
|-
| 11
| 12
| 0-1-5-10
| 0-1-5-10
| 1-5/4-3/2-9/8
| 1-5/4-3/2-9/8
Line 586: Line 655:
|  
|  
|-
|-
| 12
| 13
| 0-1-8-10
| 0-1-8-10
| 1-5/4-16/11-9/8
| 1-5/4-16/11-9/8
Line 593: Line 662:
|  
|  
|-
|-
| 13
| 14
| 0-1-9-10
| 0-1-9-10
| 1-5/4-9/5-9/8
| 1-5/4-9/5-9/8
Line 600: Line 669:
| <u>or</u> v9(^7)no5
| <u>or</u> v9(^7)no5
|-
|-
| 14
| 15
| 0-2-9-10
| 0-2-9-10
| 1-14/9-9/5-9/8
| 1-14/9-9/5-9/8
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| <u>or</u> ^7(vv#5)sus2
| <u>or</u> ^7(vv#5)sus2
|-
|-
| 15
| 16
| 0-5-9-10
| 0-5-9-10
| 1-3/2-9/5-9/8
| 1-3/2-9/5-9/8
| Utonal
| Utonal
| ^9no3
| ^9no3
| <u>or</u> ^7sus2 <u>or</u> 2,^7
|<u>or</u> ^7sus2 <u>or</u> 2,^7
|-
|-
| 16
| 17
| 0-8-9-10
| 0-8-9-10
| 1-16/11-9/5-9/8
| 1-16/11-9/5-9/8
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|  
|  
|-
|-
| 17
| 18
| 0-1-2-11
| 0-1-2-11
| 1-5/4-14/9-7/5
| 1-5/4-14/9-7/5
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|  
|  
|-
|-
| 18
| 19
| 0-2-4-11
| 0-2-4-11
| 1-14/9-6/5-7/5
| 1-14/9-6/5-7/5
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|  
|  
|-
|-
| 19
| 20
| 0-2-7-11
| 0-2-7-11
| 1-14/9-7/6-7/5
| 1-14/9-7/6-7/5
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|  
|  
|-
|-
| 20
| 21
| 0-1-9-11
| 0-1-9-11
| 1-5/4-9/5-7/5
| 1-5/4-9/5-7/5
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|  
|  
|-
|-
| 21
| 22
| 0-2-9-11
| 0-2-9-11
| 1-14/9-9/5-7/5
| 1-14/9-9/5-7/5
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|  
|  
|-
|-
| 22
| 23
| 0-4-9-11
| 0-4-9-11
| 1-6/5-9/5-7/5
| 1-6/5-9/5-7/5
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|  
|  
|-
|-
| 23
| 24
| 0-7-9-11
| 0-7-9-11
| 1-7/6-9/5-7/5
| 1-7/6-9/5-7/5
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|  
|  
|-
|-
| 24
| 25
| 0-1-10-11
| 0-1-10-11
| 1-5/4-9/8-7/5
| 1-5/4-9/8-7/5
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|  
|  
|-
|-
| 25
| 26
| 0-2-10-11
| 0-2-10-11
| 1-14/9-9/8-7/5
| 1-14/9-9/8-7/5
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|  
|  
|-
|-
| 26
| 27
| 0-9-10-11
| 0-9-10-11
| 1-9/5-9/8-7/5
| 1-9/5-9/8-7/5
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|  
|  
|-
|-
| 27
| 28
| 0-1-2-12
| 0-1-2-12
| 1-5/4-14/9-7/4
| 1-5/4-14/9-7/4
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|  
|  
|-
|-
| 28
| 29
| 0-2-4-12
| 0-2-4-12
| 1-14/9-6/5-7/4
| 1-14/9-6/5-7/4
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|  
|  
|-
|-
| 29
| 30
| 0-1-5-12
| 0-1-5-12
| 1-5/4-3/2-7/4
| 1-5/4-3/2-7/4
Line 712: Line 781:
|  
|  
|-
|-
| 30
| 31
| 0-4-5-12
| 0-4-5-12
| 1-6/5-3/2-7/4
| 1-6/5-3/2-7/4
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|  
|  
|-
|-
| 31
| 32
| 0-2-7-12
| 0-2-7-12
| 1-14/9-7/6-7/4
| 1-14/9-7/6-7/4
Line 726: Line 795:
|  
|  
|-
|-
| 32
| 33
| 0-5-7-12
| 0-5-7-12
| 1-3/2-7/6-7/4
| 1-3/2-7/6-7/4
Line 733: Line 802:
|  
|  
|-
|-
| 33
| 34
| 0-1-8-12
| 0-1-8-12
| 1-5/4-16/11-7/4
| 1-5/4-16/11-7/4
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|  
|  
|-
|-
| 34
| 35
| 0-4-8-12
| 0-4-8-12
| 1-6/5-16/11-7/4
| 1-6/5-16/11-7/4
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|  
|  
|-
|-
| 35
| 36
| 0-7-8-12
| 0-7-8-12
| 1-7/6-16/11-7/4
| 1-7/6-16/11-7/4
Line 754: Line 823:
|  
|  
|-
|-
| 36
|37
|0-7-11-12
|1-7/6-7/5-7/4
|Otonal
|v\m7(\b5)
|<u>or</u> 1-6/5-3/2-12/7 = ^m^/6
|-
| 38
| 0-1-10-12
| 0-1-10-12
| 1-5/4-9/8-7/4
| 1-5/4-9/8-7/4
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|  
|  
|-
|-
| 37
| 39
| 0-2-10-12
| 0-2-10-12
| 1-14/9-9/8-7/4
| 1-14/9-9/8-7/4
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|  
|  
|-
|-
| 38
| 40
| 0-5-10-12
| 0-5-10-12
| 1-3/2-9/8-7/4
| 1-3/2-9/8-7/4
| Otonal
| Otonal
| v\7sus2
| v\7sus2
| <u>or</u> 2,v\7 <u>or</u> v\9no3
|<u>or</u> 2,v\7 <u>or</u> v\9no3
|-
|-
| 39
| 41
| 0-8-10-12
| 0-8-10-12
| 1-16/11-9/8-7/4
| 1-16/11-9/8-7/4
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|  
|  
|-
|-
| 40
| 42
| 0-1-11-12
| 0-1-11-12
| 1-5/4-7/5-7/4
| 1-5/4-7/5-7/4
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|  
|  
|-
|-
| 41
| 43
| 0-2-11-12
| 0-2-11-12
| 1-14/9-7/5-7/4
| 1-14/9-7/5-7/4
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|  
|  
|-
|-
| 42
| 44
| 0-4-11-12
| 0-4-11-12
| 1-6/5-7/5-7/4
| 1-6/5-7/5-7/4
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|  
|  
|-
|-
| 43
| 45
| 0-7-11-12
| 0-7-11-12
| 1-7/6-7/5-7/4
| 1-7/6-7/5-7/4
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|  
|  
|-
|-
| 44
| 46
| 0-10-11-12
| 0-10-11-12
| 1-9/8-7/5-7/4
| 1-9/8-7/5-7/4
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|  
|  
|-
|-
| 45
| 47
| 0-1-2-13
| 0-1-2-13
| 1-5/4-14/9-12/11
| 1-5/4-14/9-12/11
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|  
|  
|-
|-
| 46
| 48
| 0-2-4-13
| 0-2-4-13
| 1-14/9-6/5-12/11
| 1-14/9-6/5-12/11
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|  
|  
|-
|-
| 47
| 49
| 0-1-5-13
| 0-1-5-13
| 1-5/4-3/2-12/11
| 1-5/4-3/2-12/11
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|  
|  
|-
|-
| 48
| 50
| 0-4-5-13
| 0-4-5-13
| 1-6/5-3/2-12/11
| 1-6/5-3/2-12/11
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|  
|  
|-
|-
| 49
| 51
| 0-1-8-13
| 0-1-8-13
| 1-5/4-16/11-12/11
| 1-5/4-16/11-12/11
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|  
|  
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|-
| 50
| 52
| 0-4-8-13
| 0-4-8-13
| 1-6/5-16/11-12/11
| 1-6/5-16/11-12/11
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|  
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| 51
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| 0-1-9-13
| 0-1-9-13
| 1-5/4-9/5-12/11
| 1-5/4-9/5-12/11
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| 52
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| 0-2-9-13
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| 1-14/9-9/5-12/11
| 1-14/9-9/5-12/11
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| 53
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| 0-4-9-13
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| 1-6/5-9/5-12/11
| 1-6/5-9/5-12/11
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| 54
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| 0-5-9-13
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| 1-3/2-9/5-12/11
| 1-3/2-9/5-12/11
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|  
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| 55
| 57
| 0-8-9-13
| 0-8-9-13
| 1-16/11-20/11-12/11
| 1-16/11-20/11-12/11
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|  
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| 0-1-11-13
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| 1-5/4-7/5-12/11
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| 0-4-11-13
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| 76
| 78
| 0-10-11-18
| 0-10-11-18
| 1-9/8-7/5-18/11
| 1-9/8-7/5-18/11
Line 1,041: Line 1,117:
|  
|  
|-
|-
| 77
| 79
| 0-5-13-18
| 0-5-13-18
| 1-3/2-12/11-18/11
| 1-3/2-12/11-18/11
Line 1,048: Line 1,124:
|  
|  
|-
|-
| 78
| 80
| 0-8-13-18
| 0-8-13-18
| 1-16/11-12/11-18/11
| 1-16/11-12/11-18/11
Line 1,055: Line 1,131:
|  
|  
|-
|-
| 79
| 81
| 0-9-13-18
| 0-9-13-18
| 1-20/11-12/11-18/11
| 1-20/11-12/11-18/11
Line 1,062: Line 1,138:
|  
|  
|-
|-
| 80
| 82
| 0-11-13-18
| 0-11-13-18
| 1-7/5-12/11-18/11
| 1-7/5-12/11-18/11
Line 1,069: Line 1,145:
|  
|  
|-
|-
| 81
| 83
| 0-2-7-20
| 0-2-7-20
| 1-14/9-7/6-14/11
| 1-14/9-7/6-14/11
Line 1,076: Line 1,152:
|  
|  
|-
|-
| 82
| 84
| 0-7-8-20
| 0-7-8-20
| 1-7/6-16/11-14/11
| 1-7/6-16/11-14/11
Line 1,083: Line 1,159:
|  
|  
|-
|-
| 83
| 85
| 0-2-9-20
| 0-2-9-20
| 1-14/9-9/5-14/11
| 1-14/9-9/5-14/11
Line 1,090: Line 1,166:
|  
|  
|-
|-
| 84
| 86
| 0-7-9-20
| 0-7-9-20
| 1-7/6-9/5-14/11
| 1-7/6-9/5-14/11
Line 1,097: Line 1,173:
|  
|  
|-
|-
| 85
| 87
| 0-8-9-20
| 0-8-9-20
| 1-16/11-20/11-14/11
| 1-16/11-20/11-14/11
Line 1,104: Line 1,180:
|  
|  
|-
|-
| 86
| 88
| 0-2-10-20
| 0-2-10-20
| 1-14/9-9/8-14/11
| 1-14/9-9/8-14/11
Line 1,111: Line 1,187:
|  
|  
|-
|-
| 87
| 89
| 0-8-10-20
| 0-8-10-20
| 1-16/11-9/8-14/11
| 1-16/11-9/8-14/11
Line 1,118: Line 1,194:
|  
|  
|-
|-
| 88
| 90
| 0-9-10-20
| 0-9-10-20
| 1-9/5-9/8-14/11
| 1-9/5-9/8-14/11
Line 1,125: Line 1,201:
|  
|  
|-
|-
| 89
| 91
| 0-2-11-20
| 0-2-11-20
| 1-14/9-7/5-14/11
| 1-14/9-7/5-14/11
Line 1,132: Line 1,208:
|  
|  
|-
|-
| 90
| 92
| 0-7-11-20
| 0-7-11-20
| 1-7/6-7/5-14/11
| 1-7/6-7/5-14/11
Line 1,139: Line 1,215:
|  
|  
|-
|-
| 91
| 93
| 0-9-11-20
| 0-9-11-20
| 1-9/5-7/5-14/11
| 1-9/5-7/5-14/11
Line 1,146: Line 1,222:
|  
|  
|-
|-
| 92
| 94
| 0-10-11-20
| 0-10-11-20
| 1-9/8-7/5-14/11
| 1-9/8-7/5-14/11
Line 1,153: Line 1,229:
|  
|  
|-
|-
| 93
| 95
| 0-2-12-20
| 0-2-12-20
| 1-14/9-7/4-14/11
| 1-14/9-7/4-14/11
Line 1,160: Line 1,236:
|  
|  
|-
|-
| 94
| 96
| 0-7-12-20
| 0-7-12-20
| 1-7/6-7/4-14/11
| 1-7/6-7/4-14/11
Line 1,167: Line 1,243:
|  
|  
|-
|-
| 95
| 97
| 0-8-12-20
| 0-8-12-20
| 1-16/11-7/4-14/11
| 1-16/11-7/4-14/11
Line 1,174: Line 1,250:
|  
|  
|-
|-
| 96
| 98
| 0-10-12-20
| 0-10-12-20
| 1-9/8-7/4-14/11
| 1-9/8-7/4-14/11
Line 1,181: Line 1,257:
|  
|  
|-
|-
| 97
| 99
| 0-11-12-20
| 0-11-12-20
| 1-7/5-7/4-14/11
| 1-7/5-7/4-14/11
Line 1,188: Line 1,264:
|  
|  
|-
|-
| 98
| 100
| 0-2-13-20
| 0-2-13-20
| 1-14/9-12/11-14/11
| 1-14/9-12/11-14/11
Line 1,195: Line 1,271:
|  
|  
|-
|-
| 99
| 101
| 0-8-13-20
| 0-8-13-20
| 1-16/11-12/11-14/11
| 1-16/11-12/11-14/11
Line 1,202: Line 1,278:
|  
|  
|-
|-
| 100
| 102
| 0-9-13-20
| 0-9-13-20
| 1-20/11-12/11-14/11
| 1-20/11-12/11-14/11
Line 1,209: Line 1,285:
|  
|  
|-
|-
| 101
| 103
| 0-11-13-20
| 0-11-13-20
| 1-7/5-12/11-14/11
| 1-7/5-12/11-14/11
Line 1,216: Line 1,292:
|  
|  
|-
|-
| 102
| 104
| 0-12-13-20
| 0-12-13-20
| 1-7/4-12/11-14/11
| 1-7/4-12/11-14/11
Line 1,223: Line 1,299:
|  
|  
|-
|-
| 103
| 105
| 0-7-18-20
| 0-7-18-20
| 1-7/6-18/11-14/11
| 1-7/6-18/11-14/11
Line 1,230: Line 1,306:
|  
|  
|-
|-
| 104
| 106
| 0-8-18-20
| 0-8-18-20
| 1-16/11-18/11-14/11
| 1-16/11-18/11-14/11
Line 1,237: Line 1,313:
|  
|  
|-
|-
| 105
| 107
| 0-9-18-20
| 0-9-18-20
| 1-20/11-18/11-14/11
| 1-20/11-18/11-14/11
Line 1,244: Line 1,320:
|  
|  
|-
|-
| 106
| 108
| 0-10-18-20
| 0-10-18-20
| 1-9/8-18/11-14/11
| 1-9/8-18/11-14/11
Line 1,251: Line 1,327:
|  
|  
|-
|-
| 107
| 109
| 0-11-18-20
| 0-11-18-20
| 1-7/5-18/11-14/11
| 1-7/5-18/11-14/11
Line 1,258: Line 1,334:
|  
|  
|-
|-
| 108
| 110
| 0-13-18-20
| 0-13-18-20
| 1-12/11-18/11-14/11
| 1-12/11-18/11-14/11
Retrieved from "https://en.xen.wiki/w/Chords_of_magic"