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55edo: Difference between revisions

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'''55edo''' divides the octave into 55 parts of 21.818{{cent}}. It can be used for a meantone tuning, and is close to [[1-6_Syntonic_Comma_Meantone|1/6 comma meantone]] (and is almost exactly 10/57 comma meantone.) [http://en.wikipedia.org/wiki/Georg_Philipp_Telemann Telemann] suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by [http://en.wikipedia.org/wiki/Leopold_Mozart Leopold] and [http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart Wolfgang Mozart]. It can also be used for [[Meantone_family|mohajira and liese]] temperaments.
'''55edo''' divides the octave into 55 parts of 21.818{{cent}}. It can be used for a meantone tuning, and is close to [[1-6_Syntonic_Comma_Meantone|1/6 comma meantone]] (and is almost exactly 10/57 comma meantone.) [https://en.wikipedia.org/wiki/Georg_Philipp_Telemann Telemann] suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by [https://en.wikipedia.org/wiki/Leopold_Mozart Leopold] and [https://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart Wolfgang Mozart]. It can also be used for [[Meantone_family|mohajira and liese]] temperaments.


== Theory ==
== Theory ==
Line 18: Line 18:
! [[Cent]]s
! [[Cent]]s
! Approximate ratios
! Approximate ratios
! colspan="3" |[[Ups and downs notation|ups and downs]] notation
|-
|-
| 0
| 0
| 0.000
| 0.000
| 1/1
| 1/1
|P1
|perfect 1sn
|D
|-
|-
| 1
| 1
| 21.818
| 21.818
| 128/125, 64/63, 65/64, 78/77, 91/90, 99/98, ''81/80''
| 128/125, 64/63, 65/64, 78/77,
91/90, 99/98, ''81/80''
|^1
|up 1sn
|^D
|-
|-
| 2
| 2
| 43.636
| 43.636
| 36/35
| 36/35
|^^1
|dup 1sn
|^^D
|-
|-
| 3
| 3
| 65.4545
| 65.4545
| 28/27, ''25/24''
| 28/27, ''25/24''
|vvm2
|dudminor 2nd
|vvEb
|-
|-
| 4
| 4
| 87.273
| 87.273
| 25/24, 21/20
| 25/24, 21/20
|vm2
|downminor 2nd
|vEb
|-
|-
| 5
| 5
| 109.091
| 109.091
| 16/15
| 16/15
|m2
|minor 2nd
|Eb
|-
|-
| 6
| 6
| 130.909
| 130.909
| 14/13, ''13/12''
| 14/13, ''13/12''
|^m2
|upminor 2nd
|^Eb
|-
|-
| 7
| 7
| 152.727
| 152.727
| 13/12, 12/11
| 13/12, 12/11
|~2
|mid 2nd
|vvE
|-
|-
| 8
| 8
| 174.5455
| 174.5455
| 11/10, ''10/9''
| 11/10, ''10/9''
|vM2
|downmajor 2nd
|vE
|-
|-
| 9
| 9
| 196.364
| 196.364
| 9/8, 10/9
| 9/8, 10/9
|M2
|major 2nd
|E
|-
|-
| 10
| 10
| 218.182
| 218.182
| 17/15
| 17/15
|^M2
|upmajor 2nd
|^E
|-
|-
| 11
| 11
| 240
| 240
| 8/7, 15/13
| 8/7, 15/13
|^^M2
|dupmajor 2nd
|^^E
|-
|-
| 12
| 12
| 261.818
| 261.818
| 7/6
| 7/6
|vvm3
|dudminor 3rd
|vvF
|-
|-
| 13
| 13
| 283.636
| 283.636
| 13/11
| 13/11
|vm3
|downminor 3rd
|vF
|-
|-
| 14
| 14
| 305.4545
| 305.4545
| 6/5-
| 6/5-
|m3
|minor 3rd
|F
|-
|-
| 15
| 15
| 327.273
| 327.273
| 6/5+
| 6/5+
|^m3
|upminor 3rd
|^F
|-
|-
| 16
| 16
| 349.091
| 349.091
| 11/9, 27/22
| 11/9, 27/22
|~3
|mid 3rd
|^^F
|-
|-
| 17
| 17
| 370.909
| 370.909
| 16/13
| 16/13
|vM3
|downmajor 3rd
|vF#
|-
|-
| 18
| 18
| 392.727
| 392.727
| 5/4
| 5/4
|M3
|major 3rd
|F#
|-
|-
| 19
| 19
| 414.5455
| 414.5455
| 14/11
| 14/11
|^M3
|upmajor 3rd
|^F#
|-
|-
| 20
| 20
| 436.364
| 436.364
| 9/7
| 9/7
|^^M3
|dupmajor 3rd
|^^F#
|-
|-
| 21
| 21
| 458.182
| 458.182
| 13/10
| 13/10
|vv4
|dud 4th
|vvG
|-
|-
| 22
| 22
| 480
| 480
| 21/16
| 21/16
|v4
|down 4th
|vG
|-
|-
| 23
| 23
| 501.818
| 501.818
| 4/3, 27/20
| 4/3, 27/20
|P4
|perfect 4th
|G
|-
|-
| 24
| 24
| 523.636
| 523.636
| ''27/20''
| ''27/20''
|^4
|up 4th
|^G
|-
|-
| 25
| 25
| 545.4545
| 545.4545
| 11/8
| 11/8
|~4
|mid 4th
|^^G
|-
|-
| 26
| 26
| 567.273
| 567.273
| 18/13, 25/18
| 18/13, 25/18
|vA4
|downaug 4th
|vG#
|-
|-
| 27
| 27
| 589.091
| 589.091
| 7/5
| 7/5
|A4, vd5
|aug 4th, downdim 5th
|G#, vAb
|-
|-
| 28
| 28
| 610.909
| 610.909
| 10/7
| 10/7
|^A4, d5
|upaug 4th, dim 5th
|^G#, Ab
|-
|-
| 29
| 29
| 632.727
| 632.727
| 13/9, 36/25
| 13/9, 36/25
|^d5
|updim 5th
|^Ab
|-
|-
| 30
| 30
| 654.5455
| 654.5455
| 16/11
| 16/11
|~5
|mid 5th
|vvA
|-
|-
| 31
| 31
| 676.364
| 676.364
| ''40/27''
| ''40/27''
|v5
|down 5th
|vA
|-
|-
| 32
| 32
| 698.182
| 698.182
| 3/2, 40/27
| 3/2, 40/27
|P5
|perfect 5th
|A
|-
|-
| 33
| 33
| 720
| 720
| 32/21
| 32/21
|^5
|up 5th
|^A
|-
|-
| 34
| 34
| 741.818
| 741.818
| 20/13
| 20/13
|^^5
|dup 5th
|^^A
|-
|-
| 35
| 35
| 763.636
| 763.636
| 14/9
| 14/9
|vvm6
|dudminor 6th
|vvBb
|-
|-
| 36
| 36
| 785.4545
| 785.4545
| 11/7
| 11/7
|vm6
|downminor 6th
|vBb
|-
|-
| 37
| 37
| 807.273
| 807.273
| 8/5
| 8/5
|m6
|minor 6th
|Bb
|-
|-
| 38
| 38
| 829.091
| 829.091
| 13/8
| 13/8
|^m6
|upminor 6th
|^Bb
|-
|-
| 39
| 39
| 850.909
| 850.909
| 18/11, 44/27
| 18/11, 44/27
|~6
|mid 6th
|vvB
|-
|-
| 40
| 40
| 872.727
| 872.727
| 5/3-
| 5/3-
|vM6
|downmajor 6th
|vB
|-
|-
| 41
| 41
| 894.5455
| 894.5455
| 5/3+
| 5/3+
|M6
|major 6th
|B
|-
|-
| 42
| 42
| 916.364
| 916.364
| 22/13
| 22/13
|^M6
|upmajor 6th
|^B
|-
|-
| 43
| 43
| 938.182
| 938.182
| 12/7
| 12/7
|^^M6
|dupmajor 6th
|^^B
|-
|-
| 44
| 44
| 960
| 960
| 7/4, 26/15
| 7/4, 26/15
|vvm7
|dudminor 7th
|vvC
|-
|-
| 45
| 45
| 981.818
| 981.818
| 30/17
| 30/17
|vm7
|downminor 7th
|vC
|-
|-
| 46
| 46
| 1003.636
| 1003.636
| 16/9, 9/5
| 16/9, 9/5
|m7
|minor 7th
|C
|-
|-
| 47
| 47
| 1025.4545
| 1025.4545
| ''9/5'', 20/11
| ''9/5'', 20/11
|^m7
|upminor 7th
|^C
|-
|-
| 48
| 48
| 1047.273
| 1047.273
| 11/6, 24/13
| 11/6, 24/13
|~7
|mid 7th
|^^C
|-
|-
| 49
| 49
| 1069.091
| 1069.091
| ''24/13'', 13/7
| ''24/13'', 13/7
|vM7
|downmajor 7th
|vC#
|-
|-
| 50
| 50
| 1090.909
| 1090.909
| 15/8
| 15/8
|M7
|major 7th
|C#
|-
|-
| 51
| 51
| 1112.727
| 1112.727
| 40/21, 48/25
| 40/21, 48/25
|^M7
|upmajor 7th
|^C#
|-
|-
| 52
| 52
| 1134.5455
| 1134.5455
| 56/27, ''48/25''
| 56/27, ''48/25''
|^^M7
|dupmajor 7th
|^^C#
|-
|-
| 53
| 53
| 1156.364
| 1156.364
| 35/18
| 35/18
|vv8
|dud 8ve
|vvD
|-
|-
| 54
| 54
| 1178.182
| 1178.182
| 125/64, 63/32, 128/65, 77/39, 180/91, 196/99, ''160/81''
| 125/64, 63/32, 128/65, 77/39,
180/91, 196/99, ''160/81''
|v8
|down 8ve
|vD
|-
|-
| 55
| 55
| 1200
| 1200
| 2/1
| 2/1
|P8
|perfect 8ve
|D
|}
|}


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