Sagittal notation - Revision history

Matea: correct 49/11C from 99/88 (9/8) to 99/98 (9.11/2.49)

2026-09-05T20:58:07Z

correct 49/11C from 99/88 (9/8) to 99/98 (9.11/2.49)

← Older revision		Revision as of 20:58, 5 September 2026
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	{{sge\| ~¦ \| ~! \| s \| 2187/2176 \| 17k }}		{{sge\| ~¦ \| ~! \| s \| 2187/2176 \| 17k }}
	{{sge\| )~¦ \| )~! \| sr \| 144/143 \| 143C }}		{{sge\| )~¦ \| )~! \| sr \| 144/143 \| 143C }}
	{{sge\| ~~¦ \| ~~! \| sh \| 99/88 \| 49/11C }}		{{sge\| ~~¦ \| ~~! \| sh \| 99/98 \| 49/11C }}
	{{sge\| )¦~ \| )!~ \| raz \| 19683/19456 \| 19C }}		{{sge\| )¦~ \| )!~ \| raz \| 19683/19456 \| 19C }}
	{{sge\| )¦) \| )!) \| rat \| 57/56 \| 19/7C }}		{{sge\| )¦) \| )!) \| rat \| 57/56 \| 19/7C }}
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	{{sge\| ~¦¦¦ \| ~!!! \| s \| 2187/2176 \| 17k }}		{{sge\| ~¦¦¦ \| ~!!! \| s \| 2187/2176 \| 17k }}
	{{sge\| )~¦¦¦ \| )~!!! \| sr \| 144/143 \| 143C }}		{{sge\| )~¦¦¦ \| )~!!! \| sr \| 144/143 \| 143C }}
	{{sge\| ~~¦¦¦ \| ~~!!! \| sh \| 99/88 \| 49/11C }}		{{sge\| ~~¦¦¦ \| ~~!!! \| sh \| 99/98 \| 49/11C }}
	{{sge\| )¦¦¦~ \| )!!!~ \| raz \| 19683/19456 \| 19C }}		{{sge\| )¦¦¦~ \| )!!!~ \| raz \| 19683/19456 \| 19C }}
	{{sge\| )¦¦¦) \| )!!!) \| rat \| 57/56 \| 19/7C }}		{{sge\| )¦¦¦) \| )!!!) \| rat \| 57/56 \| 19/7C }}

Lucius Chiaraviglio: /* External links */ Add Youtube link to the introductory video from the official site (currently they are the same video, but that could change if they come out with an updated version and/or a part 2, etc.)

2026-07-21T04:25:29Z

External links: Add Youtube link to the introductory video from the official site (currently they are the same video, but that could change if they come out with an updated version and/or a part 2, etc.)

← Older revision		Revision as of 04:25, 21 July 2026
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	== External links ==		== External links ==
	* [http://sagittal.org/ Official site] (with an introductory video)		* [http://sagittal.org/ Official site] (with an introductory video)
			* [https://www.youtube.com/watch?v=LRLUZzIYUwk ''Sagittal: the universal microtonal notation system''] — Introductory video from the above site, on YouTube (version dated 2024-07-21)
	* [http://forum.sagittal.org Sagittal Forum]		* [http://forum.sagittal.org Sagittal Forum]
	* [http://sagittal.org/sagittal.pdf The original Xenharmonikon article (updated)]		* [http://sagittal.org/sagittal.pdf The original Xenharmonikon article (updated)]

Dave Keenan at 03:48, 2 June 2026

2026-06-02T03:48:08Z

← Older revision		Revision as of 03:48, 2 June 2026
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	[[file:sagittal_sample.gif]]		[[file:sagittal_sample.gif]]

	'''Sagittal notation''' is a [[musical notation]] system capable of notating almost any conceivable tuning while preserving, as much as possible, the notation of harmonies across different tunings. It uses arrow-like symbols made up of four simple components whose visual size is proportional to their alteration. It was developed by [[Dave Keenan]] and [[George Secor]] with significant contributions from numerous others.		'''Sagittal notation''' is a [[musical notation]] system capable of notating almost any conceivable tuning while preserving, as much as possible, the notation of harmonies across different tunings. It uses arrow-like symbols made up of four simple components whose visual size is proportional to their alteration and whose alterations sum. It was developed by [[Dave Keenan]] and [[George Secor]] with significant contributions from numerous others.

	== Flavors of Sagittal notation ==		== Flavors of Sagittal notation ==

Dave Keenan at 03:46, 2 June 2026

2026-06-02T03:46:03Z

← Older revision		Revision as of 03:46, 2 June 2026
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	[[file:sagittal_sample.gif]]		[[file:sagittal_sample.gif]]

	'''Sagittal notation''' is a [[musical notation]] system capable of notating almost any conceivable tuning while preserving, as much as possible, the notation of harmonies across different tunings~~, using~~ arrow-like symbols made up of four simple components whose visual size is proportional to their alteration. It was developed by [[Dave Keenan]] and [[George Secor]] with significant contributions from numerous others.		'''Sagittal notation''' is a [[musical notation]] system capable of notating almost any conceivable tuning while preserving, as much as possible, the notation of harmonies across different tunings. It uses arrow-like symbols made up of four simple components whose visual size is proportional to their alteration. It was developed by [[Dave Keenan]] and [[George Secor]] with significant contributions from numerous others.

	== Flavors of Sagittal notation ==		== Flavors of Sagittal notation ==

Dave Keenan: Added some distinguishing features of Sagittal to the first paragraph.

2026-06-02T03:45:01Z

Added some distinguishing features of Sagittal to the first paragraph.

← Older revision		Revision as of 03:45, 2 June 2026
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	[[file:sagittal_sample.gif]]		[[file:sagittal_sample.gif]]

	'''Sagittal notation''' is a [[musical notation]] system capable of notating almost any conceivable tuning. It was developed by [[Dave Keenan]] and [[George Secor]] with significant contributions from numerous others.		'''Sagittal notation''' is a [[musical notation]] system capable of notating almost any conceivable tuning while preserving, as much as possible, the notation of harmonies across different tunings, using arrow-like symbols made up of four simple components whose visual size is proportional to their alteration. It was developed by [[Dave Keenan]] and [[George Secor]] with significant contributions from numerous others.

	== Flavors of Sagittal notation ==		== Flavors of Sagittal notation ==

Dave Keenan: /* Evo */ Deleted supposed exception with its details that are too specific and complex for an introductory example, while making it clear that this case was already covered in the preceding paragraph.

2026-06-02T03:33:18Z

Evo: Deleted supposed exception with its details that are too specific and complex for an introductory example, while making it clear that this case was already covered in the preceding paragraph.

← Older revision		Revision as of 03:33, 2 June 2026
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	The '''Evo''' flavor (short for "evolutionary", previously called "mixed") uses only single-shaft Sagittal symbols, e.g. {{sagittal\| /\| }} {{sagittal\| \! }} {{sagittal\| \|) }} {{sagittal\| !) }}, alone or in combination with conventional sharps and flats and their doubles. Only the large variant of the double sharp {{sagittal\| x }} (U+E47D) is considered to be stylistically-compatible with Sagittal symbols. Evo is much easier to learn, but it results in a greater number of symbols on the sheet, which can give it a more cluttered appearance, particularly with chords, and it may be confusing when two symbols alter the same note in opposite directions.		The '''Evo''' flavor (short for "evolutionary", previously called "mixed") uses only single-shaft Sagittal symbols, e.g. {{sagittal\| /\| }} {{sagittal\| \! }} {{sagittal\| \|) }} {{sagittal\| !) }}, alone or in combination with conventional sharps and flats and their doubles. Only the large variant of the double sharp {{sagittal\| x }} (U+E47D) is considered to be stylistically-compatible with Sagittal symbols. Evo is much easier to learn, but it results in a greater number of symbols on the sheet, which can give it a more cluttered appearance, particularly with chords, and it may be confusing when two symbols alter the same note in opposite directions.

	A sub-flavor of Evo is '''Evo-SZ''' (Evo with Stein–Zimmermann). This is where any sagittals that are notating exactly half the alteration of a sharp or flat (most often {{sagittal\| /\|\ }} {{sagittal\| \!/ }}) are replaced by the Stein–Zimmermann semisharp {{sagittal\| > }} and narrow reversed flat {{sagittal\| < }}, and the corresponding combinations (most often {{sagittal\| /\|\ }}{{sagittal\| # }} and {{sagittal\| \!/ }}{{sagittal\| b }}) are replaced by {{sagittal\| ># }} and {{sagittal\| <b }}. The narrow variants of the fractional flats {{sagittal\| < }} (U+E284) and {{sagittal\| <b }} (U+E285) are preferred because they preserve the Sagittal principle that the visual size of a symbol should indicate the relative size of its alteration and they reduce left-right confusion.		A sub-flavor of Evo is '''Evo-SZ''' (Evo with Stein–Zimmermann). This is where, in tempered systems, any sagittals that are notating exactly half the alteration of a sharp or flat (most often {{sagittal\| /\|\ }} {{sagittal\| \!/ }}) are replaced by the Stein–Zimmermann semisharp {{sagittal\| > }} and narrow reversed flat {{sagittal\| < }}, and the corresponding combinations (most often {{sagittal\| /\|\ }}{{sagittal\| # }} and {{sagittal\| \!/ }}{{sagittal\| b }}) are replaced by {{sagittal\| ># }} and {{sagittal\| <b }}. The narrow variants of the fractional flats {{sagittal\| < }} (U+E284) and {{sagittal\| <b }} (U+E285) are preferred because they preserve the Sagittal principle that the visual size of a symbol should indicate the relative size of its alteration and they reduce left-right confusion.

	In tempered systems, Evo-SZ {{sagittal\|>}} {{sagittal\|<}} {{sagittal\|>#}} {{sagittal\|<b}} accidentals ''may instead'' be distinct from Sagittals like {{sagittal\| /\|\ }}{{sagittal\| \!/ }}, when the apotome can be split in two equal parts as in [[Hemipyth\|Hemipythagorean]] as literal half-sharps and half-flats, with a distinction between mapped neutral thirds like [[11/9\|~11/9]] or ~[[16/13]] and [[Sqrt(3/2)\|hemififths]] which might be mapped to another interval like [[49/40]] in particularly fine-grained EDOs like [[270edo\|270]] or [[311edo\|311]]. There is no need for this in coarser EDOs like [[24edo\|24]], [[31edo\|31]] or [[41edo\|41]], where in this case the [[243/242\|rastma]] is tempered out, and thus the mappings of the irrational hemififth and [[11/9]] coincide.

	=== Revo ===		=== Revo ===

Dave Keenan: /* Revo */ Restored some examples of apotome complements and pointed out differences.

2026-04-26T05:17:17Z

Revo: Restored some examples of apotome complements and pointed out differences.

← Older revision		Revision as of 05:17, 26 April 2026
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	=== Revo ===		=== Revo ===
	The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal\| /\|\|\ }} {{sagittal\| \!!/ }} {{sagittal\| /X\ }} {{sagittal\| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal\| /\| }}{{sagittal\| # }} becomes {{sagittal\| /\|\|\| }} and {{sagittal\| !) }}{{sagittal\| b }} becomes {{sagittal\| !!!) }}, as expected. [[2187/2048#Notation\|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, do not have a simple rule in Revo. One must simply memorize the complements one needs, as shown below.		The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal\| /\|\|\ }} {{sagittal\| \!!/ }} {{sagittal\| /X\ }} {{sagittal\| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal\| /\| }}{{sagittal\| # }} becomes {{sagittal\| /\|\|\| }} and {{sagittal\| !) }}{{sagittal\| b }} becomes {{sagittal\| !!!) }}, as expected. [[2187/2048#Notation\|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, do not have a simple rule in Revo. One must simply memorize the complements one needs, as shown below. For example, {{sagittal\| \! }}{{sagittal\| # }} becomes {{sagittal\| \|\|\ }} (flag swaps sides) while {{sagittal\| !) }}{{sagittal\| # }} becomes {{sagittal\| \|\|) }} (flag stays on same side).

	{\| class="wikitable"		{\| class="wikitable"

Dave Keenan: /* Revo */

2026-04-26T05:09:12Z

Revo

← Older revision		Revision as of 05:09, 26 April 2026
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	=== Revo ===		=== Revo ===
	The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal\| /\|\|\ }} {{sagittal\| \!!/ }} {{sagittal\| /X\ }} {{sagittal\| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal\| /\| }}{{sagittal\| # }} becomes {{sagittal\| /\|\|\| }} and {{sagittal\| !) }}{{sagittal\| b }} becomes {{sagittal\| !!!) }}, as expected. [[2187/2048#Notation\|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, do not have a simple rule in Revo. One must simply memorize ~~any~~ complements one needs, as shown below.		The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal\| /\|\|\ }} {{sagittal\| \!!/ }} {{sagittal\| /X\ }} {{sagittal\| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal\| /\| }}{{sagittal\| # }} becomes {{sagittal\| /\|\|\| }} and {{sagittal\| !) }}{{sagittal\| b }} becomes {{sagittal\| !!!) }}, as expected. [[2187/2048#Notation\|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, do not have a simple rule in Revo. One must simply memorize the complements one needs, as shown below.

	{\| class="wikitable"		{\| class="wikitable"

Dave Keenan: /* Revo */ Added a table of the most common apotome complements. Collapsed the complete table.

2026-04-26T05:08:35Z

Revo: Added a table of the most common apotome complements. Collapsed the complete table.

@@ Line 15: / Line 15: @@
 === Revo ===
-The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal| /||\ }} {{sagittal| \!!/ }} {{sagittal| /X\ }} {{sagittal| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal| /| }}{{sagittal| # }} becomes {{sagittal| /||| }} and {{sagittal| !) }}{{sagittal| b }} becomes {{sagittal| !!!) }}, as expected. [[2187/2048#Notation|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, are not predictable. {{sagittal| \! }}{{sagittal| # }} becomes {{sagittal| ||\ }},  {{sagittal| |) }}{{sagittal| b }} becomes {{sagittal| !!) }}, {{sagittal| \!/ }}{{sagittal| # }} becomes {{sagittal|(|) }}, {{sagittal| \!)}}{{sagittal| # }} becomes {{sagittal|(|\}} ; one must learn these ''apotome complements'' by rote memorization.
+The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal| /||\ }} {{sagittal| \!!/ }} {{sagittal| /X\ }} {{sagittal| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal| /| }}{{sagittal| # }} becomes {{sagittal| /||| }} and {{sagittal| !) }}{{sagittal| b }} becomes {{sagittal| !!!) }}, as expected. [[2187/2048#Notation|''Apotome'']] ''complements'', that arise when the Sagital accidental alters in the opposite direction to the apotome, do not have a simple rule in Revo. One must simply memorize any complements one needs, as shown below.
 {| class="wikitable"
-|+Table of apotome complements<ref>https://sagittal.org/sagittal.pdf p. 24 Figure 13</ref>
+|+Table of Spartan (most common) <br> apotome complements<ref>https://sagittal.org/sagittal.pdf p. 7 Figure 4</ref>
 |Symbol
 |<big>{{sagittal|h}}</big>
@@ Line 75: / Line 97: @@
 |<big>{{sagittal||\)}}</big>
 |}
 == Notation software support ==

Dave Keenan: /* External links */ Added "(with an introductory video)"

2026-04-26T04:12:45Z

External links: Added "(with an introductory video)"

← Older revision		Revision as of 04:12, 26 April 2026
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	== External links ==		== External links ==
	* [http://sagittal.org/ Official site]		* [http://sagittal.org/ Official site] (with an introductory video)
	* [http://forum.sagittal.org Sagittal Forum]		* [http://forum.sagittal.org Sagittal Forum]
	* [http://sagittal.org/sagittal.pdf The original Xenharmonikon article (updated)]		* [http://sagittal.org/sagittal.pdf The original Xenharmonikon article (updated)]

← Older revision		Revision as of 20:58, 5 September 2026
Line 263:		Line 263:
	{{sge\| ~¦ \| ~! \| s \| 2187/2176 \| 17k }}		{{sge\| ~¦ \| ~! \| s \| 2187/2176 \| 17k }}
	{{sge\| )~¦ \| )~! \| sr \| 144/143 \| 143C }}		{{sge\| )~¦ \| )~! \| sr \| 144/143 \| 143C }}
	{{sge\| ~~¦ \| ~~! \| sh \| 99/88 \| 49/11C }}		{{sge\| ~~¦ \| ~~! \| sh \| 99/98 \| 49/11C }}
	{{sge\| )¦~ \| )!~ \| raz \| 19683/19456 \| 19C }}		{{sge\| )¦~ \| )!~ \| raz \| 19683/19456 \| 19C }}
	{{sge\| )¦) \| )!) \| rat \| 57/56 \| 19/7C }}		{{sge\| )¦) \| )!) \| rat \| 57/56 \| 19/7C }}
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	{{sge\| ~¦¦¦ \| ~!!! \| s \| 2187/2176 \| 17k }}		{{sge\| ~¦¦¦ \| ~!!! \| s \| 2187/2176 \| 17k }}
	{{sge\| )~¦¦¦ \| )~!!! \| sr \| 144/143 \| 143C }}		{{sge\| )~¦¦¦ \| )~!!! \| sr \| 144/143 \| 143C }}
	{{sge\| ~~¦¦¦ \| ~~!!! \| sh \| 99/88 \| 49/11C }}		{{sge\| ~~¦¦¦ \| ~~!!! \| sh \| 99/98 \| 49/11C }}
	{{sge\| )¦¦¦~ \| )!!!~ \| raz \| 19683/19456 \| 19C }}		{{sge\| )¦¦¦~ \| )!!!~ \| raz \| 19683/19456 \| 19C }}
	{{sge\| )¦¦¦) \| )!!!) \| rat \| 57/56 \| 19/7C }}		{{sge\| )¦¦¦) \| )!!!) \| rat \| 57/56 \| 19/7C }}