Xenharmonic Wiki

55edo: Difference between revisions

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{{interwiki
{{interwiki
| de =  
| de = 55-EDO
| en = 55edo
| en = 55edo
| es = 55 EDO
| es = 55 EDO
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}}
}}
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|55}}
{{ED intro}}


== Theory ==
== Theory ==
55edo can be used for a [[meantone]] tuning, and is close to [[1/6-comma meantone]] (and is almost exactly 10/57-comma meantone.) {{w|Georg Philipp Telemann|Telemann}} suggested it as a theoretical basis for analyzing the [[meantone intervals|intervals of meantone]], in which he was followed by {{w|Leopold Mozart|Leopold}} and {{w|Wolfgang Amadeus Mozart|Wolfgang Mozart}}. It can also be used for [[Meantone family|mohajira and liese]] temperaments.
55edo can be used for a [[meantone]] tuning, and is close to [[1/6-comma meantone]] (and is almost exactly 10/57-comma meantone). {{w|Georg Philipp Telemann|Telemann}} suggested it as a theoretical basis for analyzing the [[meantone intervals|intervals of meantone]]. {{w|Leopold Mozart|Leopold}} and {{w|Wolfgang Amadeus Mozart|Wolfgang Mozart}} recommended 55edo or something close to it, with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref> It can also be used for [[Meantone_family#Mohajira|Mohajira]] and [[Meantone_family#Liese|Liese]] temperaments. It also supports an extremely sharp tuning of [[huygens|Huygens/undecimal meantone]] using the 55de [[val]], meaning that primes 7 and 11 are mapped very sharply to their second-best mapping.


=== Odd harmonics ===
=== Odd harmonics ===
Line 15: Line 15:


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 55 factors into {{factorization|55}}, 55edo contains [[5edo]] and [[11edo]] as its subsets.  
Since 55 factors into {{factorization|55}}, 55edo contains [[5edo]] and [[11edo]] as its subsets.


== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2 left-3"
{| class="wikitable center-1 right-2 left-3"
|-
|-
! [[Degree|#]]
! [[Degree|&#35;]]
! [[Cent]]s
! [[Cent]]s
! Approximate Ratios
! Approximate ratios
! colspan="3" | [[Ups and downs notation|Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
| 0
| 0
Line 34: Line 34:
| 1
| 1
| 21.8
| 21.8
| 128/125, 64/63, 65/64, 78/77,<br>91/90, 99/98, ''81/80''
| 65/64, 78/77, 99/98, ''128/125''
| ^1
| ^1
| up 1sn
| up 1sn
Line 41: Line 41:
| 2
| 2
| 43.6
| 43.6
| 36/35
| 36/35, ''64/63''
| ^^1
| ^^1
| dup 1sn
| dup 1sn
Line 48: Line 48:
| 3
| 3
| 65.5
| 65.5
| 28/27, ''25/24''
| 28/27
| vvm2
| vvm2
| dudminor 2nd
| dudminor 2nd
Line 55: Line 55:
| 4
| 4
| 87.3
| 87.3
| 25/24, 21/20
| 21/20, ''18/17'', ''25/24''
| vm2
| vm2
| downminor 2nd
| downminor 2nd
Line 62: Line 62:
| 5
| 5
| 109.1
| 109.1
| 16/15
| 16/15, 17/16
| m2
| m2
| minor 2nd
| minor 2nd
Line 69: Line 69:
| 6
| 6
| 130.9
| 130.9
| 14/13, ''13/12''
| 13/12, 14/13
| ^m2
| ^m2
| upminor 2nd
| upminor 2nd
Line 76: Line 76:
| 7
| 7
| 152.7
| 152.7
| 13/12, 12/11, ''11/10''
| 12/11, ''11/10''
| ~2
| ~2
| mid 2nd
| mid 2nd
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| 8
| 8
| 174.5
| 174.5
| ''10/9''
|  
| vM2
| vM2
| downmajor 2nd
| downmajor 2nd
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| 9
| 9
| 196.4
| 196.4
| 9/8, 10/9
| 9/8, ''10/9''
| M2
| M2
| major 2nd
| major 2nd
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| 11
| 11
| 240.0
| 240.0
| 8/7, 15/13
| 8/7
| ^^M2
| ^^M2
| dupmajor 2nd
| dupmajor 2nd
Line 125: Line 125:
| 14
| 14
| 305.5
| 305.5
| 6/5-
| 6/5
| m3
| m3
| minor 3rd
| minor 3rd
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| 15
| 15
| 327.3
| 327.3
| 6/5+
|  
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
Line 146: Line 146:
| 17
| 17
| 370.9
| 370.9
| 16/13
| 26/21, ''16/13''
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
Line 174: Line 174:
| 21
| 21
| 458.2
| 458.2
| 13/10
| ''21/16''
| vv4
| vv4
| dud 4th
| dud 4th
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| 22
| 22
| 480.0
| 480.0
| 21/16
|  
| v4
| v4
| down 4th
| down 4th
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| 23
| 23
| 501.8
| 501.8
| 4/3, 27/20
| 4/3, ''27/20''
| P4
| P4
| perfect 4th
| perfect 4th
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| 24
| 24
| 523.6
| 523.6
| ''27/20''
|  
| ^4
| ^4
| up 4th
| up 4th
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| 25
| 25
| 545.5
| 545.5
| 11/8
| 11/8, 15/11
| ~4
| ~4
| mid 4th
| mid 4th
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| 26
| 26
| 567.3
| 567.3
| 18/13, 25/18
| [[7/5]], [[18/13]]
| vA4
| vA4
| downaug 4th
| downaug 4th
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| 27
| 27
| 589.1
| 589.1
| 7/5
| 24/17
| A4, vd5
| A4, vd5
| aug 4th, downdim 5th
| aug 4th, downdim 5th
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| 28
| 28
| 610.9
| 610.9
| 10/7
| 17/12
| ^A4, d5
| ^A4, d5
| upaug 4th, dim 5th
| upaug 4th, dim 5th
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| 29
| 29
| 632.7
| 632.7
| 13/9, 36/25
| [[10/7]], [[13/9]]
| ^d5
| ^d5
| updim 5th
| updim 5th
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| 30
| 30
| 654.5
| 654.5
| 16/11
| 16/11, 22/15
| ~5
| ~5
| mid 5th
| mid 5th
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| 31
| 31
| 676.4
| 676.4
| ''40/27''
|  
| v5
| v5
| down 5th
| down 5th
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| 32
| 32
| 698.2
| 698.2
| 3/2, 40/27
| 3/2, ''40/27''
| P5
| P5
| perfect 5th
| perfect 5th
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| 33
| 33
| 720.0
| 720.0
| 32/21
|  
| ^5
| ^5
| up 5th
| up 5th
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| 34
| 34
| 741.8
| 741.8
| 20/13
| ''32/21''
| ^^5
| ^^5
| dup 5th
| dup 5th
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| 38
| 38
| 829.1
| 829.1
| 13/8
| 21/13, ''13/8''
| ^m6
| ^m6
| upminor 6th
| upminor 6th
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| 40
| 40
| 872.7
| 872.7
| 5/3-
|  
| vM6
| vM6
| downmajor 6th
| downmajor 6th
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| 41
| 41
| 894.5
| 894.5
| 5/3+
| 5/3
| M6
| M6
| major 6th
| major 6th
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| 44
| 44
| 960.0
| 960.0
| 7/4, 26/15
| 7/4
| vvm7
| vvm7
| dudminor 7th
| dudminor 7th
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| 46
| 46
| 1003.6
| 1003.6
| 16/9, 9/5
| 16/9, ''9/5''
| m7
| m7
| minor 7th
| minor 7th
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| 47
| 47
| 1025.5
| 1025.5
| ''9/5''
|  
| ^m7
| ^m7
| upminor 7th
| upminor 7th
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| 48
| 48
| 1047.3
| 1047.3
| ''20/11'', 11/6, 24/13
| 11/6, ''20/11''
| ~7
| ~7
| mid 7th
| mid 7th
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| 49
| 49
| 1069.1
| 1069.1
| ''24/13'', 13/7
| 13/7, 24/13
| vM7
| vM7
| downmajor 7th
| downmajor 7th
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| 50
| 50
| 1090.9
| 1090.9
| 15/8
| 15/8, ''32/17''
| M7
| M7
| major 7th
| major 7th
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| 51
| 51
| 1112.7
| 1112.7
| 40/21, 48/25
| 40/21, ''17/9'', ''48/25''
| ^M7
| ^M7
| upmajor 7th
| upmajor 7th
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| 52
| 52
| 1134.5
| 1134.5
| 56/27, ''48/25''
| 56/27
| ^^M7
| ^^M7
| dupmajor 7th
| dupmajor 7th
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| 53
| 53
| 1156.4
| 1156.4
| 35/18
| 35/18, ''63/32''
| vv8
| vv8
| dud 8ve
| dud 8ve
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| 54
| 54
| 1178.2
| 1178.2
| 125/64, 63/32, 128/65, 77/39,<br>180/91, 196/99, ''160/81''
| 128/65, 77/39, 196/99, ''125/64''
| v8
| v8
| down 8ve
| down 8ve
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| D
| D
|}
|}
<nowiki />* 55f val (tending flat), inconsistent intervals labeled in ''italic''
== Notation ==
=== Ups and downs notation ===
55edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Sharpness-sharp4a}}
[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}
=== Sagittal notation ===
==== Evo flavor ====
<imagemap>
File:55-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 615 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 160 106 [[896/891]]
rect 160 80 280 106 [[33/32]]
default [[File:55-EDO_Evo_Sagittal.svg]]
</imagemap>
==== Revo flavor ====
<imagemap>
File:55-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 599 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 160 106 [[896/891]]
rect 160 80 280 106 [[33/32]]
default [[File:55-EDO_Revo_Sagittal.svg]]
</imagemap>
==== Evo-SZ flavor ====
<imagemap>
File:55-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 607 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 160 106 [[896/891]]
rect 160 80 280 106 [[33/32]]
default [[File:55-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
=== 31-tone subset ===
The 31-out-of-55edo subset can be notated entirely with the standard notation of 7 each of naturals/sharps/flats, and 5 each of doublesharps/doubleflats, as a 31-tone chain-of-5ths from Gbb to Ax.
[[File:Monzo55Notation.jpeg|400px|frameless|alt=Diagram of 31-tone subset of 55edo using plain Western notation, by Joe Monzo.|Diagram of 31-tone subset of 55edo using plain Western notation, by [[Joe Monzo]].]]
== Approximation to JI ==
[[File:55ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 19-limit intervals approximated in 55edo]]


== Selected just intervals by error ==
=== Selected just intervals by error ===
The following table shows how [[15-odd-limit]] just intervals are represented in 55edo (ordered by absolute error).
{{Q-odd-limit intervals|55}}
{{15-odd-limit|55}}
{{Q-odd-limit intervals|55.05|apx=val|header=none|tag=none|title=15-odd-limit intervals by 55d val mapping}}


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|-87 55}}
! rowspan="2" | [[Comma list]]
|{{mapping|55 87}}
! rowspan="2" | [[Mapping]]
| +1.1903
! rowspan="2" | Optimal<br>8ve stretch (¢)
| 1.1915
! colspan="2" | Tuning error
| 5.46
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -87 55 }}
| {{mapping| 55 87 }}
| +1.31
| 1.19
| 7.21
|-
|-
|2.3.5
| 2.3.5
|81/80, 6442450944/6103515625
| 81/80, {{monzo| 31 1 -14 }}
|{{mapping|55 87 128}}
| {{mapping| 55 87 128 }}
| -0.1309
| −0.13
| 2.1012
| 2.10
| 9.63
| 9.63
|}
|}
=== Uniform maps ===
{{Uniform map|edo=55}}


=== Commas ===
=== Commas ===
'''5-limit commas''': [[81/80]], {{monzo|31 1 -14}}, {{monzo|27 5 -15}}
{{Todo|cleanup|inline=true}}
 
'''5-limit commas''': [[81/80]], [[Quintosec_family|{{monzo| 47 -15 -10 }}]], {{monzo| 31 1 -14 }}, {{monzo| 27 5 -15 }}


'''7-limit commas''': 31104/30625, [[6144/6125]], 81648/78125, 16128/15625, 28672/28125, 33075/32768, 83349/80000, 1029/1000, [[686/675]], [[10976/10935]], [[Cloudy comma|16807/16384]], 84035/82944
'''7-limit commas''': 31104/30625, [[6144/6125]], 81648/78125, 16128/15625, 28672/28125, 33075/32768, 83349/80000, 1029/1000, [[686/675]], [[10976/10935]], [[Cloudy comma|16807/16384]], 84035/82944
Line 459: Line 514:
=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator
! Generator*
! Temperaments
! Cents*
! Associated<br>ratio*
! Temperament
|-
|-
| 1
| 1
| 6\55
| 6\55
| [[Twothirdtonic]]
| 130.9
| 14/13
| [[Twothirdtonic]] (55f)
|-
|1
|8\55
|174.5
|[[10/9]]~[[11/10]]
|[[Tetracot]] (55c)
|-
|-
| 1
| 1
| 16\55
| 16\55
| [[Vicentino]] / [[mohajira]]
| 349.1
| 11/9
| [[Mohaha]]
|-
|-
| 1
| 1
| 23\55
| 23\55
| [[Meantone]]
| 501.8
| 4/3
| [[Meantone]] (55d)
|-
|-
| 1
| 1
| 26\55
| 26\55
| [[Liese]]
| 567.3
| 7/5
| [[Liese]] (55)
|-
|-
| 1
| 1
| 27\55
| 27\55
| [[Untriton]] / [[aufo]]
| 589.1
| 45/32
| [[Untriton]] (55d) / [[aufo]] (55)
|-
|-
| 5
| 5
| 6\55
| 17\55<br>(5\55)
| [[Qintosec]]
| 370.9<br>(109.1)
| 99/80<br>(16/15)
| [[Quintosec]]
|-
|-
| 11
| 11
| 3\55
| 23\55<br>(3\55)
| [[Hendecatonic]]
| 501.8<br>(65.5)
| 4/3<br>(36/35)
| [[Hendecatonic]] (55)
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Scales ==
; Subsets of twothirdtonic[37]
* Undecimal otonal-like pentatonic: 17 8 7 12 11
; Subsets of hendecatonic[33]
* Septimal pentatonic-like: 10 13 9 13 10
* Septimal minor blues-like: 13 10 4 5 13 10
* Septimal heptatonic blues-like: 13 10 4 5 8 5 10
; Others
* Sakura-like scale containing [[phi]]: 9 6 18 5 17
* Quasi-[[equiheptatonic]] scale: 8 8 7 9 7 9 7


== Instruments ==
== Instruments ==
Line 500: Line 592:
; {{W|Johann Sebastian Bach}}
; {{W|Johann Sebastian Bach}}
* [https://www.youtube.com/watch?v=oymJKnYzzOw "Jesus bleibet meine Freude" from ''Herz und Mund und Tat und Leben'', BWV 147] (1723) – arranged for two organs, rendered by Claudi Meneghin (2021)
* [https://www.youtube.com/watch?v=oymJKnYzzOw "Jesus bleibet meine Freude" from ''Herz und Mund und Tat und Leben'', BWV 147] (1723) – arranged for two organs, rendered by Claudi Meneghin (2021)
* [https://www.youtube.com/watch?v=xoCNOIsjfeU "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by [[Claudi Meneghin]] (2024)
* [https://www.youtube.com/watch?v=OkRVNo19guo "Ricercar a 6" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2025)
* [https://www.youtube.com/watch?v=Y5sIjh_Te40 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=Y5sIjh_Te40 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=QOPxqNgkVWM "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)


; {{W|Nicolaus Bruhns}}
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=OfOt3nOp-f8 ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
* [https://www.youtube.com/watch?v=OfOt3nOp-f8 ''Prelude in E Minor "The Great"''] – rendered by [[Claudi Meneghin]] (2023)
* [https://www.youtube.com/watch?v=tuIPIhSxUPs ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)
 
; {{W|Georg Frideric Handel}}
* [https://www.youtube.com/watch?v=rDvKPuzsno8 ''Fugue'' from "Suite in E minor", HWV 429] (1720) – arranged for Baroque ensemble and drums, rendered by Claudi Meneghin (2025)
 
; {{W|Scott Joplin}}
* [https://www.youtube.com/watch?v=GbhpuoIJgxk ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by [[Claudi Meneghin]] (2024)


; {{W|Wolfgang Amadeus Mozart}}
; {{W|Wolfgang Amadeus Mozart}}
Line 510: Line 612:
* [http://www.seraph.it/dep/int/AdagioKV540.mp3 ''Adagio in B minor'', KV 540] (1788) – rendered by Carlo Serafini (2011) ([http://www.seraph.it/blog_files/706c4662272db7703def4d57edfcb955-119.html blog entry])
* [http://www.seraph.it/dep/int/AdagioKV540.mp3 ''Adagio in B minor'', KV 540] (1788) – rendered by Carlo Serafini (2011) ([http://www.seraph.it/blog_files/706c4662272db7703def4d57edfcb955-119.html blog entry])
* [https://www.youtube.com/watch?v=pFjJCj2MBTM ''Allegro'' from the Piano Sonata No. 16, KV 545] (1788) – rendered by Francium (2023)
* [https://www.youtube.com/watch?v=pFjJCj2MBTM ''Allegro'' from the Piano Sonata No. 16, KV 545] (1788) – rendered by Francium (2023)
* [https://www.youtube.com/watch?v=p88MWgdio14&list=PLC6ZSKWKnVz0mOTLQkCUi9ydWGLpBP8gZ&index=2 ''Mozart's Gigue KV 574, Arranged for Fortepiano (55-edo)''] – rendered by [[Claudi Meneghin]] (2025)
; {{W|Keiichi Okabe}}
* [https://www.youtube.com/watch?v=L24G4Y7tZgI ''Yuutsu no Yuutsu''] (2006) – rendered by MortisTheneRd (2024)


=== 21st century ===
=== 21st century ===
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/l62rb8ULCXs ''55edo improv''] (2025)
* [https://www.youtube.com/watch?v=kVmToKkZU88 ''Waltz in 55edo''] (2025)
; [[James Kukula]]
* ''[https://app.box.com/s/8hq89cb3rqqkrhvkxgvqtppa255kcqrq?fbclid=IwY2xjawISjSlleHRuA2FlbQIxMAABHcl5t8n_C7QUJqdEnwSaWBc5u3BpldmcAjhQQljsQIPl1qJ-zdCr9T8NMw_aem_Ez0m-Ls_ZqI0-c0Ld-28Yg 55edo Melted Syntonic]'' (2025)
; [[Budjarn Lambeth]]
* ''[https://www.youtube.com/watch?v=9c5MtrZFNhA Improvisation One in 55edo]'' (2025)
* ''[https://www.youtube.com/watch?v=ggFGUn1Ya2A Improvisation Two in 55edo]'' (2025)
; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=AgsJCTyxqiM ''Double Fugue on "We Wish You a Merry Christmas" for String Quartet''] (2020)
* [https://www.youtube.com/watch?v=AgsJCTyxqiM ''Double Fugue on "We Wish You a Merry Christmas" for String Quartet''] (2020)
Line 517: Line 634:
* [https://www.youtube.com/watch?v=hCUIx1RzvEk ''Chacony "Lament & Deception"'' for Two Violins and Cello] (2021), [https://www.youtube.com/watch?v=abJP4euMlsg for Baroque Wind Ensemble] (2023)
* [https://www.youtube.com/watch?v=hCUIx1RzvEk ''Chacony "Lament & Deception"'' for Two Violins and Cello] (2021), [https://www.youtube.com/watch?v=abJP4euMlsg for Baroque Wind Ensemble] (2023)
* [https://www.youtube.com/watch?v=9zfWeO0eJdA Fantasy "Almost a Fugue" on a Theme by Giuliani, for String Quartet] (2021)
* [https://www.youtube.com/watch?v=9zfWeO0eJdA Fantasy "Almost a Fugue" on a Theme by Giuliani, for String Quartet] (2021)
* [https://www.youtube.com/watch?v=jOiub14Cskw ''Double Fugue on "Old McDonald" + "Shave & a Haircut"''] (2024)
; [[Herman Miller]]
* ''[https://soundcloud.com/morphosyntax-1/road-trip-to-nowhere Road Trip to Nowhere]'' (2021)
* ''[https://soundcloud.com/morphosyntax-1/migration Migration]'' (2025)


== External links ==
== External links ==
* [http://tonalsoft.com/monzo/55edo/55edo.aspx "Mozart's tuning: 55edo"] (containing another listening example) in the [[Tonalsoft Encyclopedia]]
* ''[http://tonalsoft.com/monzo/55edo/55edo.aspx Mozart's tuning: 55-edo and its close relative, 1/6-comma meantone]'' (containing another listening example) on [[Tonalsoft Encyclopedia]]
 
== References ==
<references />


[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Historical]]
[[Category:Historical]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/55edo"