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55edo: Difference between revisions

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Cleanup on this mostly unmaintained page; move the list of commas to the RTT section
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! [[Degree|#]]
! [[Degree|#]]
! [[Cent]]s
! [[Cent]]s
! Approximate ratios
! Approximate Ratios
! colspan="3" |[[Ups and downs notation|ups and downs]] notation
! colspan="3" | [[Ups and downs notation|Ups and Downs Notation]]
|-
|-
| 0
| 0
| 0.000
| 0.0
| 1/1
| 1/1
|P1
| P1
|perfect 1sn
| perfect 1sn
|D
| D
|-
|-
| 1
| 1
| 21.818
| 21.8
| 128/125, 64/63, 65/64, 78/77,
| 128/125, 64/63, 65/64, 78/77,<br>91/90, 99/98, ''81/80''
91/90, 99/98, ''81/80''
| ^1
|^1
| up 1sn
|up 1sn
| ^D
|^D
|-
|-
| 2
| 2
| 43.636
| 43.6
| 36/35
| 36/35
|^^1
| ^^1
|dup 1sn
| dup 1sn
|^^D
| ^^D
|-
|-
| 3
| 3
| 65.4545
| 65.5
| 28/27, ''25/24''
| 28/27, ''25/24''
|vvm2
| vvm2
|dudminor 2nd
| dudminor 2nd
|vvEb
| vvEb
|-
|-
| 4
| 4
| 87.273
| 87.3
| 25/24, 21/20
| 25/24, 21/20
|vm2
| vm2
|downminor 2nd
| downminor 2nd
|vEb
| vEb
|-
|-
| 5
| 5
| 109.091
| 109.1
| 16/15
| 16/15
|m2
| m2
|minor 2nd
| minor 2nd
|Eb
| Eb
|-
|-
| 6
| 6
| 130.909
| 130.9
| 14/13, ''13/12''
| 14/13, ''13/12''
|^m2
| ^m2
|upminor 2nd
| upminor 2nd
|^Eb
| ^Eb
|-
|-
| 7
| 7
| 152.727
| 152.7
| 13/12, 12/11, ''11/10''
| 13/12, 12/11, ''11/10''
|~2
| ~2
|mid 2nd
| mid 2nd
|vvE
| vvE
|-
|-
| 8
| 8
| 174.5455
| 174.5
| ''10/9''
| ''10/9''
|vM2
| vM2
|downmajor 2nd
| downmajor 2nd
|vE
| vE
|-
|-
| 9
| 9
| 196.364
| 196.4
| 9/8, 10/9
| 9/8, 10/9
|M2
| M2
|major 2nd
| major 2nd
|E
| E
|-
|-
| 10
| 10
| 218.182
| 218.2
| 17/15
| 17/15
|^M2
| ^M2
|upmajor 2nd
| upmajor 2nd
|^E
| ^E
|-
|-
| 11
| 11
| 240
| 240.0
| 8/7, 15/13
| 8/7, 15/13
|^^M2
| ^^M2
|dupmajor 2nd
| dupmajor 2nd
|^^E
| ^^E
|-
|-
| 12
| 12
| 261.818
| 261.8
| 7/6
| 7/6
|vvm3
| vvm3
|dudminor 3rd
| dudminor 3rd
|vvF
| vvF
|-
|-
| 13
| 13
| 283.636
| 283.6
| 13/11
| 13/11
|vm3
| vm3
|downminor 3rd
| downminor 3rd
|vF
| vF
|-
|-
| 14
| 14
| 305.4545
| 305.5
| 6/5-
| 6/5-
|m3
| m3
|minor 3rd
| minor 3rd
|F
| F
|-
|-
| 15
| 15
| 327.273
| 327.3
| 6/5+
| 6/5+
|^m3
| ^m3
|upminor 3rd
| upminor 3rd
|^F
| ^F
|-
|-
| 16
| 16
| 349.091
| 349.1
| 11/9, 27/22
| 11/9, 27/22
|~3
| ~3
|mid 3rd
| mid 3rd
|^^F
| ^^F
|-
|-
| 17
| 17
| 370.909
| 370.9
| 16/13
| 16/13
|vM3
| vM3
|downmajor 3rd
| downmajor 3rd
|vF#
| vF#
|-
|-
| 18
| 18
| 392.727
| 392.7
| 5/4
| 5/4
|M3
| M3
|major 3rd
| major 3rd
|F#
| F#
|-
|-
| 19
| 19
| 414.5455
| 414.5
| 14/11
| 14/11
|^M3
| ^M3
|upmajor 3rd
| upmajor 3rd
|^F#
| ^F#
|-
|-
| 20
| 20
| 436.364
| 436.4
| 9/7
| 9/7
|^^M3
| ^^M3
|dupmajor 3rd
| dupmajor 3rd
|^^F#
| ^^F#
|-
|-
| 21
| 21
| 458.182
| 458.2
| 13/10
| 13/10
|vv4
| vv4
|dud 4th
| dud 4th
|vvG
| vvG
|-
|-
| 22
| 22
| 480
| 480.0
| 21/16
| 21/16
|v4
| v4
|down 4th
| down 4th
|vG
| vG
|-
|-
| 23
| 23
| 501.818
| 501.8
| 4/3, 27/20
| 4/3, 27/20
|P4
| P4
|perfect 4th
| perfect 4th
|G
| G
|-
|-
| 24
| 24
| 523.636
| 523.6
| ''27/20''
| ''27/20''
|^4
| ^4
|up 4th
| up 4th
|^G
| ^G
|-
|-
| 25
| 25
| 545.4545
| 545.5
| 11/8
| 11/8
|~4
| ~4
|mid 4th
| mid 4th
|^^G
| ^^G
|-
|-
| 26
| 26
| 567.273
| 567.3
| 18/13, 25/18
| 18/13, 25/18
|vA4
| vA4
|downaug 4th
| downaug 4th
|vG#
| vG#
|-
|-
| 27
| 27
| 589.091
| 589.1
| 7/5
| 7/5
|A4, vd5
| A4, vd5
|aug 4th, downdim 5th
| aug 4th, downdim 5th
|G#, vAb
| G#, vAb
|-
|-
| 28
| 28
| 610.909
| 610.9
| 10/7
| 10/7
|^A4, d5
| ^A4, d5
|upaug 4th, dim 5th
| upaug 4th, dim 5th
|^G#, Ab
| ^G#, Ab
|-
|-
| 29
| 29
| 632.727
| 632.7
| 13/9, 36/25
| 13/9, 36/25
|^d5
| ^d5
|updim 5th
| updim 5th
|^Ab
| ^Ab
|-
|-
| 30
| 30
| 654.5455
| 654.5
| 16/11
| 16/11
|~5
| ~5
|mid 5th
| mid 5th
|vvA
| vvA
|-
|-
| 31
| 31
| 676.364
| 676.4
| ''40/27''
| ''40/27''
|v5
| v5
|down 5th
| down 5th
|vA
| vA
|-
|-
| 32
| 32
| 698.182
| 698.2
| 3/2, 40/27
| 3/2, 40/27
|P5
| P5
|perfect 5th
| perfect 5th
|A
| A
|-
|-
| 33
| 33
| 720
| 720.0
| 32/21
| 32/21
|^5
| ^5
|up 5th
| up 5th
|^A
| ^A
|-
|-
| 34
| 34
| 741.818
| 741.8
| 20/13
| 20/13
|^^5
| ^^5
|dup 5th
| dup 5th
|^^A
| ^^A
|-
|-
| 35
| 35
| 763.636
| 763.6
| 14/9
| 14/9
|vvm6
| vvm6
|dudminor 6th
| dudminor 6th
|vvBb
| vvBb
|-
|-
| 36
| 36
| 785.4545
| 785.5
| 11/7
| 11/7
|vm6
| vm6
|downminor 6th
| downminor 6th
|vBb
| vBb
|-
|-
| 37
| 37
| 807.273
| 807.3
| 8/5
| 8/5
|m6
| m6
|minor 6th
| minor 6th
|Bb
| Bb
|-
|-
| 38
| 38
| 829.091
| 829.1
| 13/8
| 13/8
|^m6
| ^m6
|upminor 6th
| upminor 6th
|^Bb
| ^Bb
|-
|-
| 39
| 39
| 850.909
| 850.9
| 18/11, 44/27
| 18/11, 44/27
|~6
| ~6
|mid 6th
| mid 6th
|vvB
| vvB
|-
|-
| 40
| 40
| 872.727
| 872.7
| 5/3-
| 5/3-
|vM6
| vM6
|downmajor 6th
| downmajor 6th
|vB
| vB
|-
|-
| 41
| 41
| 894.5455
| 894.5
| 5/3+
| 5/3+
|M6
| M6
|major 6th
| major 6th
|B
| B
|-
|-
| 42
| 42
| 916.364
| 916.4
| 22/13
| 22/13
|^M6
| ^M6
|upmajor 6th
| upmajor 6th
|^B
| ^B
|-
|-
| 43
| 43
| 938.182
| 938.2
| 12/7
| 12/7
|^^M6
| ^^M6
|dupmajor 6th
| dupmajor 6th
|^^B
| ^^B
|-
|-
| 44
| 44
| 960
| 960.0
| 7/4, 26/15
| 7/4, 26/15
|vvm7
| vvm7
|dudminor 7th
| dudminor 7th
|vvC
| vvC
|-
|-
| 45
| 45
| 981.818
| 981.8
| 30/17
| 30/17
|vm7
| vm7
|downminor 7th
| downminor 7th
|vC
| vC
|-
|-
| 46
| 46
| 1003.636
| 1003.6
| 16/9, 9/5
| 16/9, 9/5
|m7
| m7
|minor 7th
| minor 7th
|C
| C
|-
|-
| 47
| 47
| 1025.4545
| 1025.5
| ''9/5''
| ''9/5''
|^m7
| ^m7
|upminor 7th
| upminor 7th
|^C
| ^C
|-
|-
| 48
| 48
| 1047.273
| 1047.3
| ''20/11'', 11/6, 24/13
| ''20/11'', 11/6, 24/13
|~7
| ~7
|mid 7th
| mid 7th
|^^C
| ^^C
|-
|-
| 49
| 49
| 1069.091
| 1069.1
| ''24/13'', 13/7
| ''24/13'', 13/7
|vM7
| vM7
|downmajor 7th
| downmajor 7th
|vC#
| vC#
|-
|-
| 50
| 50
| 1090.909
| 1090.9
| 15/8
| 15/8
|M7
| M7
|major 7th
| major 7th
|C#
| C#
|-
|-
| 51
| 51
| 1112.727
| 1112.7
| 40/21, 48/25
| 40/21, 48/25
|^M7
| ^M7
|upmajor 7th
| upmajor 7th
|^C#
| ^C#
|-
|-
| 52
| 52
| 1134.5455
| 1134.5
| 56/27, ''48/25''
| 56/27, ''48/25''
|^^M7
| ^^M7
|dupmajor 7th
| dupmajor 7th
|^^C#
| ^^C#
|-
|-
| 53
| 53
| 1156.364
| 1156.4
| 35/18
| 35/18
|vv8
| vv8
|dud 8ve
| dud 8ve
|vvD
| vvD
|-
|-
| 54
| 54
| 1178.182
| 1178.2
| 125/64, 63/32, 128/65, 77/39,
| 125/64, 63/32, 128/65, 77/39,<br>180/91, 196/99, ''160/81''
180/91, 196/99, ''160/81''
| v8
|v8
| down 8ve
|down 8ve
| vD
|vD
|-
|-
| 55
| 55
| 1200
| 1200.0
| 2/1
| 2/1
|P8
| P8
|perfect 8ve
| perfect 8ve
|D
| D
|}
|}


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{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Periods<br>per 8ve
! Generator
! Generator
! Temperaments
! Temperaments
|-
|-
|1
| 1
|6\55
| 6\55
|[[Twothirdtonic]]
| [[Twothirdtonic]]
|-
|-
|1
| 1
|16\55
| 16\55
|[[Vicentino]] / [[mohajira]]
| [[Vicentino]] / [[mohajira]]
|-
|-
|1
| 1
|23\55
| 23\55
|[[Meantone]]
| [[Meantone]]
|-
|-
|1
| 1
|26\55
| 26\55
|[[Liese]]
| [[Liese]]
|-
|-
|1
| 1
|27\55
| 27\55
|[[Untriton]] / [[aufo]]
| [[Untriton]] / [[aufo]]
|-
|-
|5
| 5
|6\55
| 6\55
|[[Qintosec]]
| [[Qintosec]]
|-
|-
|11
| 11
|3\55
| 3\55
|[[Hendecatonic]]
| [[Hendecatonic]]
|}
|}


==Instruments==
== Instruments ==
[[Lumatone mapping for 55edo]]
* [[Lumatone mapping for 55edo]]


== Music ==
== Music ==
Retrieved from "https://en.xen.wiki/w/55edo"