55edo - Revision history

Lucius Chiaraviglio: /* Modern renderings */ Add Toru Kitajima's ''Unravel'' (2014) — microtonal cover in 55edo by Bryan Deister (2025)

2026-09-28T07:09:54Z

Modern renderings: Add Toru Kitajima's ''Unravel'' (2014) — microtonal cover in 55edo by Bryan Deister (2025)

← Older revision		Revision as of 07:09, 28 September 2026
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	; {{W\|Scott Joplin}}		; {{W\|Scott Joplin}}
	* ''Maple Leaf Rag'' (1899) – arranged for harpsichord and rendered by [[Claudi Meneghin]] ([https://www.youtube.com/watch?v=GbhpuoIJgxk 2024 version]; [https://www.youtube.com/shorts/3Y9y9I6q1as 2026 version])		* ''Maple Leaf Rag'' (1899) – arranged for harpsichord and rendered by [[Claudi Meneghin]] ([https://www.youtube.com/watch?v=GbhpuoIJgxk 2024 version]; [https://www.youtube.com/shorts/3Y9y9I6q1as 2026 version])

			; {{W\|Toru Kitajima}}
			* [https://www.youtube.com/shorts/b9WZ6YIlJOk ''Unravel''] (2014) — microtonal cover in 55edo by [[Bryan Deister]] (2025)

	; {{W\|Mladen Milićević}}		; {{W\|Mladen Milićević}}

Lucius Chiaraviglio: /* Theory */ Add syntonic comma approximation

2026-09-24T20:38:34Z

Theory: Add syntonic comma approximation

← Older revision		Revision as of 20:38, 24 September 2026
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	== Theory ==		== Theory ==
	55edo supports [[meantone]], and is close to [[1/6-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 [[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 is a [[zeta valley edo]], suggesting it does not approximate the harmonic series very well for its size.		55edo supports [[meantone]], and is close to [[1/6-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; part of the reasoning is that 1\55 is extremely close to the size of the syntonic comma [[81/80]].<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> Indeed, by direct approximation, only [[56edo]] approximates the syntonic comma more closely until reaching much higher edo sizes; the [[patent val]] of 55edo tempers it out, but the 55c val (which supports [[tetracot]]) maps it to 1\55. It can also be used for [[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 is a [[zeta valley edo]], suggesting it does not approximate the harmonic series very well for its size.

Lucius Chiaraviglio: /* Rank-2 temperaments */ Add meantone 7-limit extension and tetracot analog compatible with 55edo patent val

2026-09-24T20:24:00Z

Rank-2 temperaments: Add meantone 7-limit extension and tetracot analog compatible with 55edo patent val

← Older revision		Revision as of 20:24, 24 September 2026
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	\| 8\55		\| 8\55
	\| 174.5		\| 174.5
	\| [[10/9]]~[[11/10]]		\| [[10/9]]~[[11/10]]<br>[[31/28]]
	\| [[Tetracot]] (55c)		\| [[Tetracot]] (55c)<br>Tricesoprimal tetracot analog (55)
	\|-		\|-
	\| 1		\| 1
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	\| 501.8		\| 501.8
	\| 4/3		\| 4/3
	\| [[Meantone]] (55d)		\| [[Meantone]] (55d) / [[Meantone_family#Mildtone\|Mildtone]] (55)
	\|-		\|-
	\| 1		\| 1

Lucius Chiaraviglio: /* Modern renderings */ Add Gabriel Fauré's ''Pavane, Op. 50'' (1887) – arranged for harpsichord and rendered by Claudi Meneghin (2026)

2026-08-31T07:10:14Z

Modern renderings: Add Gabriel Fauré's ''Pavane, Op. 50'' (1887) – arranged for harpsichord and rendered by Claudi Meneghin (2026)

← Older revision		Revision as of 07:10, 31 August 2026
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	; {{W\|Louis Couperin}}		; {{W\|Louis Couperin}}
	* [https://www.youtube.com/shorts/bcgY3k-6rao ''La Piémontoise''] (1658?) – rendered by Claudi Meneghin (2026)		* [https://www.youtube.com/shorts/bcgY3k-6rao ''La Piémontoise''] (1658?) – rendered by Claudi Meneghin (2026)

			; {{W\|Gabriel Fauré}}
			* [https://www.youtube.com/watch?v=XMgSJRXX6PY ''Pavane'', op. 50] (1887) — arranged for harpsichord and rendered by Claudi Meneghin (2026)

	; {{W\|Georg Frideric Handel}}		; {{W\|Georg Frideric Handel}}

Lucius Chiaraviglio: /* Selected just intervals by error */ Add 55cf val — this one surprisingly improves consistency more than the other warts or combinations thereof

2026-06-05T18:43:25Z

Selected just intervals by error: Add 55cf val — this one surprisingly improves consistency more than the other warts or combinations thereof

← Older revision		Revision as of 18:43, 5 June 2026
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	{{Q-odd-limit intervals\|55.05\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55d val mapping}}		{{Q-odd-limit intervals\|55.05\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55d val mapping}}
	{{Q-odd-limit intervals\|54.95\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55f val mapping}}		{{Q-odd-limit intervals\|54.95\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55f val mapping}}
			{{Q-odd-limit intervals\|54.91\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55cf val mapping}}

	== Regular temperament properties ==		== Regular temperament properties ==

Lucius Chiaraviglio: /* Modern renderings */ Add Moart's ''Gigue KV 574 («Leipziger Gigue»)'' (1789) – organ rendition by Claudi Meneghin (2026)

2026-05-24T03:43:08Z

Modern renderings: Add Moart's ''Gigue KV 574 («Leipziger Gigue»)'' (1789) – organ rendition by Claudi Meneghin (2026)

← Older revision		Revision as of 03:43, 24 May 2026
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	** [https://www.youtube.com/watch?v=p88MWgdio14&list=PLC6ZSKWKnVz0mOTLQkCUi9ydWGLpBP8gZ&index=2 Fortepiano rendition] (2025)		** [https://www.youtube.com/watch?v=p88MWgdio14&list=PLC6ZSKWKnVz0mOTLQkCUi9ydWGLpBP8gZ&index=2 Fortepiano rendition] (2025)
	** [https://www.youtube.com/shorts/7jt-jzziDBg Harpsichord rendition] (2026)		** [https://www.youtube.com/shorts/7jt-jzziDBg Harpsichord rendition] (2026)
			** [https://www.youtube.com/shorts/9J1DkS5UGzE Organ rendition] (2026)

	; {{W\|Keiichi Okabe}}		; {{W\|Keiichi Okabe}}

Lucius Chiaraviglio: /* Modern renderings */ Add John Bull's ''Fantasia «Ut Re Mi Fa Sol La»'' (late 1500s/early 1600s, from ''Fitzwilliam Virginal Book Vol.1 No.51'') – rendered by Claudi Meneghin (2026)

2026-05-18T16:22:50Z

Modern renderings: Add John Bull's ''Fantasia «Ut Re Mi Fa Sol La»'' (late 1500s/early 1600s, from ''Fitzwilliam Virginal Book Vol.1 No.51'') – rendered by Claudi Meneghin (2026)

← Older revision		Revision as of 16:22, 18 May 2026
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	* [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)		* [https://www.youtube.com/watch?v=tuIPIhSxUPs ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024)

			; {{W\|John Bull (composer)\|John Bull}}
			* [https://www.youtube.com/watch?v=I2d-540RuoM ''Fantasia «Ut Re Mi Fa Sol La»''] (late 1500s/early 1600s, from ''Fitzwilliam Virginal Book Vol.1 No.51'') – rendered by Claudi Meneghin (2026)

	; {{W\|Louis Couperin}}		; {{W\|Louis Couperin}}

Fitzgerald Lee: /* Selected just intervals by error */added 55f interval mappings

2026-05-17T03:43:02Z

Selected just intervals by error: added 55f interval mappings

← Older revision		Revision as of 03:43, 17 May 2026
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	{{Q-odd-limit intervals\|55}}		{{Q-odd-limit intervals\|55}}
	{{Q-odd-limit intervals\|55.05\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55d val mapping}}		{{Q-odd-limit intervals\|55.05\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55d val mapping}}
			{{Q-odd-limit intervals\|54.95\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 55f val mapping}}

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: /* Notation */ improve description

2026-05-12T14:17:00Z

Notation: improve description

← Older revision		Revision as of 14:17, 12 May 2026
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	== Notation ==		== Notation ==
	=== Stein–Zimmermann–Gould notation ===		=== Stein–Zimmermann–Gould notation ===
	[[Stein–Zimmermann–Gould notation]] uses sharps, flats~~, half-~~ and ~~sesquisharps, and half- and sesquiflats with~~ arrows:		[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
	{{Sharpness-sharp4-szg}}		{{Sharpness-sharp4-szg}}

FloraC: /* Notation */ SZG notation

2026-05-12T13:47:16Z

Notation: SZG notation

← Older revision		Revision as of 13:47, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould 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.		[[Stein–Zimmermann–Gould notation]] uses sharps, flats, half- and sesquisharps, and half- and sesquiflats with arrows:
			{{Sharpness-sharp4-szg}}

			=== Kite's ups and downs notation ===
			55edo can also be notated with [[Kite's ups and downs notation\|Kite's 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.
	{{Ups and downs sharpness}}		{{Ups and downs sharpness}}

	[[Alternative symbols for ups and downs notation]] uses sharps, flats, half- and sesquisharps, and half- and sesquiflats with arrows, borrowed from extended [[Helmholtz–Ellis notation]] and [[24edo #Stein–Zimmermann accidentals\|Stein-Zimmerman accidental set]]:
	~~{{Sharpness-sharp4}}~~

	=== Sagittal notation ===		=== Sagittal notation ===