Stein–Zimmermann–Gould notation - Revision history

Tristanbay: /* Higher sharpness values */typo fix

2026-07-06T22:29:27Z

Higher sharpness values: typo fix

← Older revision		Revision as of 22:29, 6 July 2026
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	Provided with more stacks of arrows, or the ability to attach arrows to demi- and sesqui-sharps and flats, edos of higher sharpness value can be notated in the same method as above.		Provided with more stacks of arrows, or the ability to attach arrows to demi- and sesqui-sharps and flats, edos of higher sharpness value can be notated in the same method as above.

	{{W\|SMuFL}} ~~curently~~ supplies [https://w3c.github.io/smufl/latest/tables/extended-stein-zimmermann-accidentals.html extended Stein-Zimmermann accidentals (U+E290–U+E29F)], which contains demi- and sesqui-sharps and flats with a single arrow.		{{W\|SMuFL}} currently supplies [https://w3c.github.io/smufl/latest/tables/extended-stein-zimmermann-accidentals.html extended Stein-Zimmermann accidentals (U+E290–U+E29F)], which contains demi- and sesqui-sharps and flats with a single arrow.

	Here is an example of a notation scheme for sharp-10 edos.		Here is an example of a notation scheme for sharp-10 edos.

Dave Keenan: /* Higher sharpness values */ Added sharp-12 example.

2026-05-16T01:36:54Z

Higher sharpness values: Added sharp-12 example.

← Older revision		Revision as of 01:36, 16 May 2026
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	Here is an example of a notation scheme for sharp-10 edos.		Here is an example of a notation scheme for sharp-10 edos.
	{{Sharpness-sharp10-qt1-szg}}		{{Sharpness-sharp10-qt1-szg}}

			Here is an example for sharp-12.
			{{Sharpness-sharp12-qt1-szg}}

	And here is an example for sharp-14.		And here is an example for sharp-14.

FloraC: Adopt new template

2026-05-12T11:47:22Z

Adopt new template

← Older revision		Revision as of 11:47, 12 May 2026
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	=== Sharp-1 ===		=== Sharp-1 ===
	Sharp-1 edos have a sharp that raises 1 step. Edos of this category include {{EDOs\| 5, 12, 19, 26, and 33 }}. Standard chain-of-fifths notation can be used since an up-arrow is exactly equivalent to a sharp.		Sharp-1 edos have a sharp that raises 1 step. Edos of this category include {{EDOs\| 5, 12, 19, 26, and 33 }}. Standard chain-of-fifths notation can be used since an up-arrow is exactly equivalent to a sharp.
	{{Sharpness-sharp1}}		{{Sharpness-sharp1-szg}}

	=== Sharp-2 ===		=== Sharp-2 ===
	Sharp-2 edos have a sharp that raises 2 steps. Edos of this category include {{EDOs\| 10, 17, 24, 31, 38, and 45 }}. Stein–Zimmermann accidentals, Gould arrows, or a combination of both may be used.		Sharp-2 edos have a sharp that raises 2 steps. Edos of this category include {{EDOs\| 10, 17, 24, 31, 38, and 45 }}. Stein–Zimmermann accidentals, Gould arrows, or a combination of both may be used.
	{{Sharpness-sharp2}}		{{Sharpness-sharp2-szg}}

	=== Sharp-3 ===		=== Sharp-3 ===
	Sharp-3 edos have a sharp that raises 3 steps. Edos of this category include {{EDOs\| 8, 15, 22, 29, 36, 43, and 50 }}. This is first sharpness value where Gould arrows must be used.		Sharp-3 edos have a sharp that raises 3 steps. Edos of this category include {{EDOs\| 8, 15, 22, 29, 36, 43, and 50 }}. This is first sharpness value where Gould arrows must be used.
	{{Sharpness-sharp3}}		{{Sharpness-sharp3-szg}}

	In some cases, some notes or intervals may be best spelled with double arrows:		In some cases, some notes or intervals may be best spelled with double arrows:
	{{Sharpness-sharp3-extended}}		{{Sharpness-sharp3-extended-szg}}

	=== Sharp-4 ===		=== Sharp-4 ===
	Sharp-4 edos have a sharp that raises 4 steps. Edos of this category include {{EDOs\| 20, 27, 34, 41, 48, 55, and 62 }}. This is first sharpness where the Stein–Zimmermann–Gould notation works in its full form.		Sharp-4 edos have a sharp that raises 4 steps. Edos of this category include {{EDOs\| 20, 27, 34, 41, 48, 55, and 62 }}. This is first sharpness where the Stein–Zimmermann–Gould notation works in its full form.
	{{Sharpness-sharp4}}		{{Sharpness-sharp4-szg}}

	=== Sharp-5 ===		=== Sharp-5 ===
	Sharp-5 edos have a sharp that raises 5 steps. Edos of this category include {{EDOs\| 32, 39, 46, 53, 60, 67, and 74 }}.		Sharp-5 edos have a sharp that raises 5 steps. Edos of this category include {{EDOs\| 32, 39, 46, 53, 60, 67, and 74 }}.
	{{Sharpness-sharp5}}		{{Sharpness-sharp5-szg}}

	In some cases, some notes or intervals may be best spelled with triple arrows:		In some cases, some notes or intervals may be best spelled with triple arrows:
	{{Sharpness-sharp5-extended}}		{{Sharpness-sharp5-extended-szg}}

	=== Sharp-6 ===		=== Sharp-6 ===
	Sharp-6 edos have a sharp that raises 6 steps. Edos of this category include {{EDOs\| 44, 51, 58, 65, 72, 79, and 86 }}.		Sharp-6 edos have a sharp that raises 6 steps. Edos of this category include {{EDOs\| 44, 51, 58, 65, 72, 79, and 86 }}.
	{{Sharpness-sharp6}}		{{Sharpness-sharp6-szg}}

	Attaching arrows to semi- and sesquisharps and flats is also another option instead of using double arrows:		Attaching arrows to semi- and sesquisharps and flats is also another option instead of using double arrows:
	{{Sharpness-sharp6-qt}}		{{Sharpness-sharp6-qt-szg}}

	=== Sharp-7 ===		=== Sharp-7 ===
	Sharp-7 edos have a sharp that raises 7 steps. Edos of this category include {{EDOs\| 56, 63, 70, 77, 84, 91, and 98 }}.		Sharp-7 edos have a sharp that raises 7 steps. Edos of this category include {{EDOs\| 56, 63, 70, 77, 84, 91, and 98 }}.
	{{Sharpness-sharp7}}		{{Sharpness-sharp7-szg}}

	=== Sharp-8 ===		=== Sharp-8 ===
	Sharp-8 edos have a sharp that raises 8 steps. Edos of this category include {{EDOs\| 61, 68, 75, 82, 89, 96, and 103 }}.		Sharp-8 edos have a sharp that raises 8 steps. Edos of this category include {{EDOs\| 61, 68, 75, 82, 89, 96, and 103 }}.
	{{Sharpness-sharp8}}		{{Sharpness-sharp8-szg}}

	=== Higher sharpness values ===		=== Higher sharpness values ===
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	Here is an example of a notation scheme for sharp-10 edos.		Here is an example of a notation scheme for sharp-10 edos.
	{{Sharpness-sharp10-qt1}}		{{Sharpness-sharp10-qt1-szg}}

	And here is an example for sharp-14.		And here is an example for sharp-14.
	{{Sharpness-sharp14-qt1}}		{{Sharpness-sharp14-qt1-szg}}

	=== Flat-1 ===		=== Flat-1 ===
	For edos such as {{EDOs\| 9, 16, 23, and 30 }}, if you notate them as if their native antidiatonic scales were diatonic, you would find that the sharp actually ''lowers'' by one step. If one wishes to "translate" diatonic songs into these edos, this is useful.		For edos such as {{EDOs\| 9, 16, 23, and 30 }}, if you notate them as if their native antidiatonic scales were diatonic, you would find that the sharp actually ''lowers'' by one step. If one wishes to "translate" diatonic songs into these edos, this is useful.
	{{Sharpness-flat1}}		{{Sharpness-flat1-szg}}

	However, a much more intuitive solution is to swap the meaning of sharps and flats in regards to fifthspan (so that sharp still raises and flat still lowers), allowing the accidentals to more naturally notate these edos' native antidiatonic (in this case, the normal set of sharp-1 accidentals would be used).		However, a much more intuitive solution is to swap the meaning of sharps and flats in regards to fifthspan (so that sharp still raises and flat still lowers), allowing the accidentals to more naturally notate these edos' native antidiatonic (in this case, the normal set of sharp-1 accidentals would be used).
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	=== Flat-2 ===		=== Flat-2 ===
	Flat-2 edos (virtually [[11edo]] only), if you pretend their native antidiatonic scales are diatonic, have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between. It makes the most sense to notate them as subsets.		Flat-2 edos (virtually [[11edo]] only), if you pretend their native antidiatonic scales are diatonic, have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between. It makes the most sense to notate them as subsets.
	{{Sharpness-flat2}}		{{Sharpness-flat2-szg}}

	=== Zero ===		=== Zero ===
	The lower three multiples of 7 ({{EDOs\| 7, 14, and 21 }}) are known as "perfect" or sharp-0 edos, since, by tempering out the Pythagorean apotome of [[2187/2048]], the traditional sharps and flats are redundant and cannot raise or lower the pitch. Here, the notes can only be modified by arrows. [[28edo]] and [[35edo]] also fall into this category using their native fifths, but they are better notated as subsets.		The lower three multiples of 7 ({{EDOs\| 7, 14, and 21 }}) are known as "perfect" or sharp-0 edos, since, by tempering out the Pythagorean apotome of [[2187/2048]], the traditional sharps and flats are redundant and cannot raise or lower the pitch. Here, the notes can only be modified by arrows. [[28edo]] and [[35edo]] also fall into this category using their native fifths, but they are better notated as subsets.
	{{Sharpness-0}}		{{Sharpness-0-szg}}

	== Limitations ==		== Limitations ==

FloraC: FloraC moved page Alternative symbols for ups and downs notation to Stein–Zimmermann–Gould notation

2026-05-12T10:42:41Z

FloraC moved page Alternative symbols for ups and downs notation to Stein–Zimmermann–Gould notation

← Older revision	Revision as of 10:42, 12 May 2026
(No difference)

FloraC: Full rework by community request

2026-05-12T10:42:00Z

Full rework by community request

Show changes

Fredg999: Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

2025-08-20T01:07:17Z

Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

← Older revision		Revision as of 01:07, 20 August 2025
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	{{main\|Ups and downs notation}}		{{main\|Ups and downs notation}}

	This article discusses about an alternative set of symbols based on current practice of microtonal music with some experimental extrapolation. The notation is, in essence, [[Ups and ~~Downs Notation~~\|ups and downs notation]] with a different look.		This article discusses about an alternative set of symbols based on current practice of microtonal music with some experimental extrapolation. The notation is, in essence, [[Ups and downs notation\|ups and downs notation]] with a different look.

	Alternative symbols may be useful for the following reasons:		Alternative symbols may be useful for the following reasons:

VectorGraphics at 08:57, 17 March 2025

2025-03-17T08:57:30Z

← Older revision		Revision as of 08:57, 17 March 2025
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	=== Flat-1 ===		=== Flat-1 ===
	~~Flat-1~~ edos ~~have a sharp that ''lowers'' 1 step. Edos of this category are~~ {{EDOs\| 9, 16, 23, and 30 }}~~. To have a~~ sharp ~~that~~ actually lowers ~~the pitch is logical for these edos, yet counter-intuitive~~. ~~Since none of~~ these edos~~' fifths will generate a normal [[diatonic scale]]~~, ~~it makes the most sense to notate each of them as a [[subset notation\|subset of a larger edo]]~~.		For edos such as {{EDOs\| 9, 16, 23, and 30 }}, if you notate them as if their native antidiatonic scales were diatonic, you would find that the sharp actually ''lowers'' by one step. If one wishes to "translate" diatonic songs into these edos, this is useful.
	{{Sharpness-flat1}}		{{Sharpness-flat1}}
			However, a much more intuitive solution is to swap the meaning of sharps and flats in regards to fifthspan (so that sharp still raises and flat still lowers), allowing the accidentals to more naturally notate these edos' native antidiatonic (in this case, the normal set of sharp-1 accidentals would be used).

	=== Flat-2 ===		=== Flat-2 ===
	Flat-2 edos (virtually [[11edo]] only) have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between. It makes the most sense to notate them as subsets.		Flat-2 edos (virtually [[11edo]] only), if you pretend their native antidiatonic scales are diatonic, have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between. It makes the most sense to notate them as subsets.
	{{Sharpness-flat2}}		{{Sharpness-flat2}}

ArrowHead294 at 19:48, 5 February 2025

2025-02-05T19:48:35Z

← Older revision		Revision as of 19:48, 5 February 2025
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	== Symbol set ==		== Symbol set ==
	The symbol set comprises traditional accidentals (sharps, flats, and naturals), ~~Stein–Zimmermann~~ quartertone accidentals (semisharps and semiflats) with and up and down arrows via Gould arrow quarter tone symbols or [[Helmholtz–Ellis notation\|~~Helmholtz–Ellis~~ just intonation accidentals]].		The symbol set comprises traditional accidentals (sharps, flats, and naturals), Stein–Zimmermann quartertone accidentals (semisharps and semiflats) with and up and down arrows via Gould arrow quarter tone symbols or [[Helmholtz–Ellis notation\|Helmholtz–Ellis just intonation accidentals]].

	The traditional accidentals, as specified in ups and downs notation, modify the note by the sharpness value, which equals the steps of a chromatic semitone (apotome, [[2187/2048]]).		The traditional accidentals, as specified in ups and downs notation, modify the note by the sharpness value, which equals the steps of a chromatic semitone (apotome, [[2187/2048]]).

	The ~~Stein–Zimmermann~~ quartertone accidentals modify the note by half the sharpness value. They apply to [[edo]]s of even sharpness value only.		The Stein–Zimmermann quartertone accidentals modify the note by half the sharpness value. They apply to [[edo]]s of even sharpness value only.

	The Gould arrow accidentals are up and down arrows attached to sharps, flats, or naturals, and modify the note by one step. They appear very similar to ~~Helmholtz–Ellis~~ accidentals, and are fully interchangeable with them.		The Gould arrow accidentals are up and down arrows attached to sharps, flats, or naturals, and modify the note by one step. They appear very similar to Helmholtz–Ellis accidentals, and are fully interchangeable with them.

	== Usage guide for each sharpness value ==		== Usage guide for each sharpness value ==

BudjarnLambeth: Category

2025-01-25T01:02:01Z

ArrowHead294 at 18:40, 1 January 2025

2025-01-01T18:40:22Z

← Older revision		Revision as of 18:40, 1 January 2025
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	Some edos have odd-numbered sharpness values 9 and above, and are difficult to notate due to the lack of support for the stacks of arrows required. Edos below 72 known to be impractical for this reason are {{EDOs\| 59 and 66 }}. Therefore, such edos are capped from their full strength.		Some edos have odd-numbered sharpness values 9 and above, and are difficult to notate due to the lack of support for the stacks of arrows required. Edos below 72 known to be impractical for this reason are {{EDOs\| 59 and 66 }}. Therefore, such edos are capped from their full strength.

	Conclusively, this set of symbols still covers most edos up to 72.		Conclusively, this set of symbols still covers most edos up to 72.

			{{Navbox notation}}

	[[Category:Notation]]		[[Category:Notation]]
	[[Category:Ups and Downs Notation]]		[[Category:Ups and Downs Notation]]

← Older revision		Revision as of 01:02, 25 January 2025
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	[[Category:Notation]]		[[Category:Notation]]
	[[Category:Ups and ~~Downs Notation~~]]		[[Category:Ups and downs notation]]