55edo: Difference between revisions

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{{interwiki

| de =

| de = 55-EDO

| en = 55edo

| es = 55 EDO

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}}

== 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. 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.

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 ===

Line 209:

| 26

| 567.3

| 18/13

| [[7/5]], [[18/13]]

| vA4

| downaug 4th

Line 216:

| 27

| 589.1

| ~~7/5,~~ 24/17

| 24/17

| A4, vd5

| aug 4th, downdim 5th

Line 223:

| 28

| 610.9

| ~~10/7,~~ 17/12

| 17/12

| ^A4, d5

| upaug 4th, dim 5th

Line 230:

| 29

| 632.7

| 13/9

| [[10/7]], [[13/9]]

| ^d5

| updim 5th

Line 418:

|}

<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.

[[Alternative symbols for ups and downs notation]] uses sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

=== Sagittal notation ===

==== Evo flavor ====

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 ====

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 ====

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 ==

=== Selected just intervals by error ===

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== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

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| {{mapping| 55 87 }}

| +1.31

| 1.~~1915~~

| 1.19

| 7.21

|-

| 2.3.5

| 81/80, ~~6442450944/6103515625~~

| 81/80, {{monzo| 31 1 -14 }}

| {{mapping| 55 87 128 }}

| −0.13

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| 9.63

|}

=== Uniform maps ===

=== Commas ===

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

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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! ~~Temperaments~~

! Temperament

|-

| 1

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| 14/13

| [[Twothirdtonic]] (55f)

|-

|1

|8\55

|174.5

|[[10/9]]~[[11/10]]

|[[Tetracot]] (55c)

|-

| 1

Line 501:

Line 559:

|-

| 5

| 17\55 (5\55)

| 17\55 (5\55)

| 370.9 (109.1)

| 370.9 (109.1)

| 99/80 (16/15)

| 99/80 (16/15)

| [[Quintosec]]

|-

| 11

| 23\55 (3\55)

| 23\55 (3\55)

| 501.8 (65.5)

| 501.8 (65.5)

| 4/3 (36/35)

| 4/3 (36/35)

| [[Hendecatonic]] (55)

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

<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 ==

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=== Modern renderings ===

; {{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=Y5sIjh_Te40 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (~~1742–1749~~) ~~–~~ rendered by Claudi Meneghin (2024)

* [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=QOPxqNgkVWM "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (~~1742–1749~~) ~~–~~ 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=QOPxqNgkVWM "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)

; {{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"''] ~~&ndash~~; rendered by Claudi Meneghin (~~2024~~)

* [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)

* [https://www.youtube.com/watch?v=GbhpuoIJgxk ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by [[Claudi Meneghin]] (2024)

; {{W|Wolfgang Amadeus Mozart}}

* [https://www.youtube.com/watch?v=C_AML6XW-2g ''Rondo alla Turca'' from the Piano Sonata No. 11, KV 331] (1778) ~~–~~ rendered by Francium (2023)

* [https://www.youtube.com/watch?v=C_AML6XW-2g ''Rondo alla Turca'' from the Piano Sonata No. 11, KV 331] (1778) – rendered by Francium (2023)

* [https://www.youtube.com/watch?v=XgRksdk6zyQ ''Fugue in G minor'', KV 401] (1782) ~~–~~ rendered by Francium (2023)

* [https://www.youtube.com/watch?v=XgRksdk6zyQ ''Fugue in G minor'', KV 401] (1782) – rendered by Francium (2023)

* [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)

* [https://www.youtube.com/watch?v=L24G4Y7tZgI ''Yuutsu no Yuutsu''] (2006) – rendered by MortisTheneRd (2024)

=== 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]]

* [https://www.youtube.com/watch?v=AgsJCTyxqiM ''Double Fugue on "We Wish You a Merry Christmas" for String Quartet''] (2020)

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* [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=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 ==

* [http://tonalsoft.com/monzo/55edo/55edo.aspx Mozart's tuning: 55-edo

* ''[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]]

and its close relative, 1/6-comma meantone] (containing another listening example) on [[Tonalsoft Encyclopedia]]

== References ==

[[Category:Meantone]]

[[Category:Historical]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{interwiki
-| de =
+| de = 55-EDO
 | en = 55edo
 | es = 55 EDO
@@ Line 6: / Line 6: @@
 }}
 {{Infobox ET}}
-{{EDO intro|55}}
+{{ED intro}}
 == Theory ==
-edo 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. 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.
+edo 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 ===
@@ Line 209: / Line 209: @@
 | 26
 | 567.3
-| 18/13
+| [[7/5]], [[18/13]]
 | vA4
 | downaug 4th
@@ Line 216: / Line 216: @@
 | 27
 | 589.1
-| 7/5, 24/17
+| 24/17
 | A4, vd5
 | aug 4th, downdim 5th
@@ Line 223: / Line 223: @@
 | 28
 | 610.9
-| 10/7, 17/12
+| 17/12
 | ^A4, d5
 | upaug 4th, dim 5th
@@ Line 230: / Line 230: @@
 | 29
 | 632.7
-| 13/9
+| [[10/7]], [[13/9]]
 | ^d5
 | updim 5th
@@ Line 418: / Line 418: @@
 |}
 <nowiki />* 55f val (tending flat), inconsistent intervals labeled in ''italic''
+== Notation ==
+=== Ups and downs notation ===
+edo 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 ===
 {{Q-odd-limit intervals|55}}
@@ Line 427: / Line 473: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br />8ve Stretch (¢)
+! rowspan="2" | Optimal<br>8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
@@ Line 440: / Line 487: @@
 | {{mapping| 55 87 }}
 | +1.31
-| 1.1915
+| 1.19
 | 7.21
 |-
 | 2.3.5
-| 81/80, 6442450944/6103515625
+| 81/80, {{monzo| 31 1 -14 }}
 | {{mapping| 55 87 128 }}
 | −0.13
@@ Line 450: / Line 497: @@
 | 9.63
 |}
+=== Uniform maps ===
+{{Uniform map|edo=55}}
 === Commas ===
+{{Todo|cleanup|inline=true}}
 '''5-limit commas''': [[81/80]], [[Quintosec_family|{{monzo| 47 -15 -10 }}]], {{monzo| 31 1 -14 }}, {{monzo| 27 5 -15 }}
@@ Line 464: / Line 516: @@
 |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
 |-
-! Periods<br />per 8ve
+! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br />Ratio*
+! Associated<br>ratio*
-! Temperaments
+! Temperament
 |-
 | 1
@@ Line 475: / Line 527: @@
 | 14/13
 | [[Twothirdtonic]] (55f)
+|-
+|1
+|8\55
+|174.5
+|[[10/9]]~[[11/10]]
+|[[Tetracot]] (55c)
 |-
 | 1
@@ Line 501: / Line 559: @@
 |-
 | 5
-| 17\55<br />(5\55)
+| 17\55<br>(5\55)
-| 370.9<br />(109.1)
+| 370.9<br>(109.1)
-| 99/80<br />(16/15)
+| 99/80<br>(16/15)
 | [[Quintosec]]
 |-
 | 11
-| 23\55<br />(3\55)
+| 23\55<br>(3\55)
-| 501.8<br />(65.5)
+| 501.8<br>(65.5)
-| 4/3<br />(36/35)
+| 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 it is distinct
+<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 ==
@@ Line 520: / Line 591: @@
 === Modern renderings ===
 ; {{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) &ndash; 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=Y5sIjh_Te40 "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742&ndash;1749) &ndash; rendered by Claudi Meneghin (2024)
+* [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=QOPxqNgkVWM "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742&ndash;1749) &ndash; 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=QOPxqNgkVWM "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
 ; {{W|Nicolaus Bruhns}}
-* [https://www.youtube.com/watch?v=OfOt3nOp-f8 ''Prelude in E Minor "The Great"''] &ndash; 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"''] &ndash; rendered by Claudi Meneghin (2024)
+* [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) &ndash; arranged for harpsichord and rendered by Claudi Meneghin (2024)
+* [https://www.youtube.com/watch?v=GbhpuoIJgxk ''Maple Leaf Rag''] (1899) – arranged for harpsichord and rendered by [[Claudi Meneghin]] (2024)
 ; {{W|Wolfgang Amadeus Mozart}}
-* [https://www.youtube.com/watch?v=C_AML6XW-2g ''Rondo alla Turca'' from the Piano Sonata No. 11, KV 331] (1778) &ndash; rendered by Francium (2023)
+* [https://www.youtube.com/watch?v=C_AML6XW-2g ''Rondo alla Turca'' from the Piano Sonata No. 11, KV 331] (1778) – rendered by Francium (2023)
-* [https://www.youtube.com/watch?v=XgRksdk6zyQ ''Fugue in G minor'', KV 401] (1782) &ndash; rendered by Francium (2023)
+* [https://www.youtube.com/watch?v=XgRksdk6zyQ ''Fugue in G minor'', KV 401] (1782) – rendered by Francium (2023)
-* [http://www.seraph.it/dep/int/AdagioKV540.mp3 ''Adagio in B minor'', KV 540] (1788) &ndash; 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) &ndash; 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) &ndash; rendered by MortisTheneRd (2024)
+* [https://www.youtube.com/watch?v=L24G4Y7tZgI ''Yuutsu no Yuutsu''] (2006) – rendered by MortisTheneRd (2024)
 === 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]]
 * [https://www.youtube.com/watch?v=AgsJCTyxqiM ''Double Fugue on "We Wish You a Merry Christmas" for String Quartet''] (2020)
@@ Line 546: / 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=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 ==
-* [http://tonalsoft.com/monzo/55edo/55edo.aspx Mozart's tuning: 55-edo
+* ''[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]]
-and its close relative, 1/6-comma meantone] (containing another listening example) on [[Tonalsoft Encyclopedia]]
+== References ==
+<references />
 [[Category:Meantone]]
 [[Category:Historical]]
 [[Category:Listen]]