Fractional 3-limit notation - Revision history

MisterShafXen at 20:40, 25 July 2025

2025-07-25T20:40:32Z

← Older revision		Revision as of 20:40, 25 July 2025
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	To obtain the Evo notations, delete the multishaft symbols. There are no equivalent combinations with conventional sharps or flats, as limmas are conventionally notated as the intervals B-C and E-F. The multishaft symbols are not required, even in Revo notation; they merely allow for alternative spellings there. In theory, sharps and flats ''could'' be used with the notations for 33, 40, and 47 because the sharp is one step for them, while it is zero or negative for the other rose EDOs and Sagittal never uses symbols for commas that have been tempered out or tempered negative. But Sagittal recommends not using sharps or flats, conventional or sagittal, with ''any'' limma-fraction notation.		To obtain the Evo notations, delete the multishaft symbols. There are no equivalent combinations with conventional sharps or flats, as limmas are conventionally notated as the intervals B-C and E-F. The multishaft symbols are not required, even in Revo notation; they merely allow for alternative spellings there. In theory, sharps and flats ''could'' be used with the notations for 33, 40, and 47 because the sharp is one step for them, while it is zero or negative for the other rose EDOs and Sagittal never uses symbols for commas that have been tempered out or tempered negative. But Sagittal recommends not using sharps or flats, conventional or sagittal, with ''any'' limma-fraction notation.

			== References ==
	[[Category:Notation]]		[[Category:Notation]]
	[[Category:Sagittal notation]]		[[Category:Sagittal notation]]

Dave Keenan: /* Bad-fifths apotome-fraction notation */ Removed unnecessary parentheses

2024-10-23T23:19:35Z

Bad-fifths apotome-fraction notation: Removed unnecessary parentheses

← Older revision		Revision as of 23:19, 23 October 2024
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	EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is best justified<ref>In just intonation, {{sagittal\| )\| }} doesn't notate any common ratio that would make it valid as 1\59. It does however notate the uncommon ratio 55/49 = (5·11/7²) by representing, as a secondary comma, 441/440 which tempers to 1\59 if only prime 3 is tempered or using the 59d map (second-best approximation of prime 7). Thanks to Roee Sinai for this JI-based justification. 55/49 ranks 87th in popularity among 2,3-free equivalence classes of ratios, according to [[N2D3P9#Table_of_top_100_.282.2C3-equivalent.29_pitch_ratio_classes_by_N2D3P9\|N2D3P9]].</ref> by the apotome-fraction notation, so its notation is a hybrid.		EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is best justified<ref>In just intonation, {{sagittal\| )\| }} doesn't notate any common ratio that would make it valid as 1\59. It does however notate the uncommon ratio 55/49 = 5·11/7² by representing, as a secondary comma, 441/440 which tempers to 1\59 if only prime 3 is tempered or using the 59d map (second-best approximation of prime 7). Thanks to Roee Sinai for this JI-based justification. 55/49 ranks 87th in popularity among 2,3-free equivalence classes of ratios, according to [[N2D3P9#Table_of_top_100_.282.2C3-equivalent.29_pitch_ratio_classes_by_N2D3P9\|N2D3P9]].</ref> by the apotome-fraction notation, so its notation is a hybrid.

	To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.		To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.

Dave Keenan: /* Bad-fifths apotome-fraction notation */ Changed "simple" to "common" and added N2D3P9 rank.

2024-10-23T23:07:57Z

Bad-fifths apotome-fraction notation: Changed "simple" to "common" and added N2D3P9 rank.

← Older revision		Revision as of 23:07, 23 October 2024
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	\|}		\|}

	EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is best justified<ref>In just intonation, {{sagittal\| )\| }} doesn't notate any ~~simple~~ ratio that would make it valid as 1\59. It does however notate the ~~complex~~ ratio 55/49 = (5·11/7²) by representing ~~the~~ comma 441/440 which tempers to 1\59 if only prime 3 is tempered or using the 59d map (second-best approximation of prime 7). Thanks to Roee Sinai for this JI-based justification.</ref> by the apotome-fraction notation, so its notation is a hybrid.		EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is best justified<ref>In just intonation, {{sagittal\| )\| }} doesn't notate any common ratio that would make it valid as 1\59. It does however notate the uncommon ratio 55/49 = (5·11/7²) by representing, as a secondary comma, 441/440 which tempers to 1\59 if only prime 3 is tempered or using the 59d map (second-best approximation of prime 7). Thanks to Roee Sinai for this JI-based justification. 55/49 ranks 87th in popularity among 2,3-free equivalence classes of ratios, according to [[N2D3P9#Table_of_top_100_.282.2C3-equivalent.29_pitch_ratio_classes_by_N2D3P9\|N2D3P9]].</ref> by the apotome-fraction notation, so its notation is a hybrid.

	To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.		To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.

Dave Keenan: /* Bad-fifths apotome-fraction notation */ Changed "only justified" to "best justified" and added footnote

2024-10-23T22:54:43Z

Bad-fifths apotome-fraction notation: Changed "only justified" to "best justified" and added footnote

← Older revision		Revision as of 22:54, 23 October 2024
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	\|}		\|}

	EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is only ~~justified~~ by the apotome-fraction notation, so its notation is a hybrid.		EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is best justified<ref>In just intonation, {{sagittal\| )\| }} doesn't notate any simple ratio that would make it valid as 1\59. It does however notate the complex ratio 55/49 = (5·11/7²) by representing the comma 441/440 which tempers to 1\59 if only prime 3 is tempered or using the 59d map (second-best approximation of prime 7). Thanks to Roee Sinai for this JI-based justification.</ref> by the apotome-fraction notation, so its notation is a hybrid.

	To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.		To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.

Dave Keenan: Undo revision 161715 by Dave Keenan (talk) Oops! I thought I was deleting the version in my sandbox

2024-10-21T05:33:24Z

Undo revision 161715 by Dave Keenan (talk) Oops! I thought I was deleting the version in my sandbox

Show changes

Dave Keenan: Blanked the page

2024-10-21T05:31:51Z

Blanked the page

Show changes

Dave Keenan: Made first occurrence of "JI" into a link to the wiki page.

2024-10-20T22:03:14Z

Made first occurrence of "JI" into a link to the wiki page.

← Older revision		Revision as of 22:03, 20 October 2024
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	A '''fractional-3-limit notation''' is a kind of [[musical notation]] built on a [[chain-of-fifths notation]], which is used for notating [[EDOs]] or [[EDOs to ETs\|ETs]] in a way that avoids favoring any mapping from JI, while preserving the notation of subset EDOs. Fractional-3-limit notations may be contrasted with two other kinds of chain-of-fifths notation for EDOs: ''JI-based notations'', like the good-fifths [[Sagittal\|Sagittal notations]], which assume specific JI mappings, and ''step-count notations'', like [[Ups and downs\|Ups and Downs notations]], which do not preserve the notation of subset EDOs. Fractional-3-limit notations assign symbols to fractions of some tempered 3-limit comma. In practice, this 3-limit comma is either the [[2187/2048\|apotome]] (chromatic semitone) as represented by a sharp or flat, or the [[256/243\|limma]] (diatonic semitone) as represented by the intervals B-C and E-F.		A '''fractional-3-limit notation''' is a kind of [[musical notation]] built on a [[chain-of-fifths notation]], which is used for notating [[EDOs]] or [[EDOs to ETs\|ETs]] in a way that avoids favoring any mapping from [[JI]], while preserving the notation of subset EDOs. Fractional-3-limit notations may be contrasted with two other kinds of chain-of-fifths notation for EDOs: ''JI-based notations'', like the good-fifths [[Sagittal\|Sagittal notations]], which assume specific JI mappings, and ''step-count notations'', like [[Ups and downs\|Ups and Downs notations]], which do not preserve the notation of subset EDOs. Fractional-3-limit notations assign symbols to fractions of some tempered 3-limit comma. In practice, this 3-limit comma is either the [[2187/2048\|apotome]] (chromatic semitone) as represented by a sharp or flat, or the [[256/243\|limma]] (diatonic semitone) as represented by the intervals B-C and E-F.

	== History ==		== History ==

Dave Keenan: Created page with "A '''fractional-3-limit notation''' is a kind of musical notation built on a chain-of-fifths notation, which is used for notating EDOs or ETs in a..."

2024-10-20T21:33:58Z

Created page with "A '''fractional-3-limit notation''' is a kind of musical notation built on a chain-of-fifths notation, which is used for notating EDOs or ETs in a..."

New page

A '''fractional-3-limit notation''' is a kind of [[musical notation]] built on a [[chain-of-fifths notation]], which is used for notating [[EDOs]] or [[EDOs to ETs|ETs]] in a way that avoids favoring any mapping from JI, while preserving the notation of subset EDOs. Fractional-3-limit notations may be contrasted with two other kinds of chain-of-fifths notation for EDOs: ''JI-based notations'', like the good-fifths [[Sagittal|Sagittal notations]], which assume specific JI mappings, and ''step-count notations'', like [[Ups and downs|Ups and Downs notations]], which do not preserve the notation of subset EDOs. Fractional-3-limit notations assign symbols to fractions of some tempered 3-limit comma. In practice, this 3-limit comma is either the [[2187/2048|apotome]] (chromatic semitone) as represented by a sharp or flat, or the [[256/243|limma]] (diatonic semitone) as represented by the intervals B-C and E-F.

== History ==
[[Chain-of-fifths_notation#Accidentals|Stein-Zimmermann notation]] can be viewed as a very simple apotome-fraction notation, notating only half-apotomes.

In 2016,<ref>https://www.facebook.com/groups/497105067092502/permalink/840445019425170</ref> [[Cryptic Ruse]] introduced the idea of using a combination of apotome-fraction and limma-fraction notations to cover all EDOs up to 72. This may have been the first proposal of a limma fraction notation. Although Cryptic Ruse later abandoned these ideas, they were adopted by George Secor and Dave Keenan to simplify the notation of EDOs with bad fifths in the Sagittal notation system.

== Sagittal fractional 3-limit notations ==
The Sagittal system uses fractional 3-limit notations only for EDOs with bad fifths, defined as having errors of more than 10.5 cents from just. EDOs with good fifths have JI-based notations.

When the EDO has fifths so narrow that the apotome becomes very small or negative (e.g. 33-EDO), a limma-fraction notation must be used. When the EDO has fifths so wide that the limma becomes very small or negative (e.g. 32-EDO), an apotome-fraction notation must be used.

The symbols were chosen from the Sagittal repertoire so they progressively increase in width and have consistent flag arithmetic. Beyond those requirements, the choice might have been arbitrary, but it turned out to be possible to choose symbols whose tempered-JI meaning is valid in most of the EDOs they notate. And when a single-shaft symbol only has flags on one side of its shaft, they are always on the left for apotome-fractions and on the right for limma-fractions.

=== Bad-fifths apotome-fraction notation ===
This notation is used for EDOs with fifths of 712.5 cents or more. These are the gold colored EDOs on the [https://sagittal.org/#periodic-table Periodic Table].

{| class="wikitable center-all"
|+ Sagittal bad-fifths apotome-fraction accidentals
|-
! colspan="2" | Up symbol !! rowspan="2" | Pronunciation (Sagispeak) !! rowspan="2" | Apotome fractions represented
|-
! [[Sagittal#Evo|Evo]] !! [[Sagittal#Revo|Revo]]
|-
| colspan="2" | {{sagittal| )| }} || rai || 1/10, 1/9, 1/8, 1/7, 1/6
|-
| colspan="2" | {{sagittal|)~| }} || slai || 1/5, 2/9, 1/4
|-
| colspan="2" | {{sagittal| )|( }} || ranai || 3/10
|-
| colspan="2" | {{sagittal| /| }} || pai || 2/7, ↑ , 1/3, 3/8, 2/5
|-
| colspan="2" | {{sagittal| /|) }} || patai || 3/7, 4/9
|-
| colspan="2" | {{sagittal| (|\ }} || jakai || 1/2, 5/9, 4/7
|-
| {{sagittal| \! }}{{sagittal| # }} || {{sagittal| ||\ }} || sharp pao || 3/5, 5/8, 2/3, ↓ , 5/7
|-
| {{sagittal| )!( }}{{sagittal| # }} || {{sagittal|//|| }} || sharp ranao || 7/10
|-
| {{sagittal|)~! }}{{sagittal| # }} || {{sagittal| ~||\ }} || sharp slao || 3/4, 7/9, 4/5
|-
| {{sagittal| )! }}{{sagittal| # }} || {{sagittal| (||~ }} || sharp rao || 5/6, 6/7, 7/8, 8/9, 9/10
|-
| {{sagittal| # }} || {{sagittal| /||\ }} || sharp || 1
|}

The corresponding down notations replace sharps with flats and mirror the sagittals vertically, while their pronunciations replace "sharp" with "flat" and swap "ai" (high) and "ao" (down) endings.

The following table shows all the gold EDOs/ETs. Notice how the notation of subsets is preserved; there are never two different symbols in the same column.

{| class="wikitable center-all"
|+ Revo sagittal bad-fifths apotome-fraction notations
|-
! rowspan="2" | EDOs b-ETs !! rowspan="2" | [[sharpness|Sharpness]] ({{nbhsp}}{{sagittal| # }} = ) !! colspan="33" | Apotome fraction
|-
! 0 !! 1/10 !! 1/9 !! 1/8 !! 1/7 !! 1/6 !! 1/5 !! 2/9 !! 1/4 !! 2/7 !! 3/10 !! 1/3 !! 3/8 !! 2/5 !! 3/7 !! 4/9 !! 1/2 !! 5/9 !! 4/7 !! 3/5 !! 5/8 !! 2/3 !! 7/10 !! 5/7 !! 3/4 !! 7/9 !! 4/5 !! 5/6 !! 6/7 !! 7/8 !! 8/9 !! 9/10 !! 1
|-
| bgcolor="#f6ebd5" | 5 || 1 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | 10 || 2 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || bgcolor="#f1f2f6" | {{sagittal| (|\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | (8), 15 || 3 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| /| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || {{sagittal| ||\ }} || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | (6), (13), 20 || 4 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || {{sagittal| )~| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || bgcolor="#f1f2f6" | {{sagittal| (|\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || || || bgcolor="#f1f2f6" | {{sagittal| ~||\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | (18), 25, 32 || 5 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| )~| }} || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| /| }} || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| ||\ }} || || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| ~||\ }} || || || || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | 23b, 30, 37 || 6 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| )| }} || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| /| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || bgcolor="#f1f2f6" | {{sagittal| (|\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || {{sagittal| ||\ }} || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| (||~ }} || || || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | 35b, 42 || 7 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| )| }} || bgcolor="#f1f2f6" | || || || || bgcolor="#f1f2f6" | {{sagittal| /| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| /|) }} || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| (|\ }} || || || || || {{sagittal| ||\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || {{sagittal| (||~ }} || || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | 47b || 8 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| )| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || {{sagittal| )~| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| /| }} || bgcolor="#f1f2f6" | || || || bgcolor="#f1f2f6" | {{sagittal| (|\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || {{sagittal| ||\ }} || || || || bgcolor="#f1f2f6" | {{sagittal| ~||\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || {{sagittal| (||~ }} || || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#d0f6d0" | [59] || 9 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| )| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || {{sagittal| )~| }} || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| /| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || {{sagittal| /|) }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| (|\ }} || bgcolor="#f1f2f6" | || || || {{sagittal| ||\ }} || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| ~||\ }} || bgcolor="#f1f2f6" | || || || || {{sagittal| (||~ }} || || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|-
| bgcolor="#f6ebd5" | 64b || 10 || || bgcolor="#f1f2f6" | {{sagittal| )| }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| )~| }} || || || bgcolor="#f1f2f6" | || {{sagittal| )|( }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| /| }} || || || bgcolor="#f1f2f6" | {{sagittal| (|\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| ||\ }} || || || bgcolor="#f1f2f6" | {{sagittal| //|| }} || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| ~||\ }} || || || || || {{sagittal| (||~ }} || bgcolor="#f1f2f6" | {{sagittal| /||\ }}
|}

EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is only justified by the apotome-fraction notation, so its notation is a hybrid.

To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.

With the gold EDOs that are multiples of 5, and with 23b, Sagittal recommends using a pentatonic notation that avoids the nominals B and F (the extremes on the chain of nominal fifths FCGDAEB), as the limmas B-C and E-F are of zero size or negative for them.

=== Bad-fifths limma-fraction notation ===
This notation is used for EDOs with fifths of 691.5 cents or less. These are the rose colored EDOs on the [https://sagittal.org/#periodic-table Periodic Table].

{| class="wikitable center-all"
|+ Sagittal bad-fifths limma-fraction accidentals
|-
! colspan="2" | Up symbol !! rowspan="2" | Pronunciation (Sagispeak) !! rowspan="2" | Limma fractions represented
|-
! [[Sagittal#Evo|Evo]] !! [[Sagittal#Revo|Revo]]
|-
| colspan="2" | {{sagittal| |( }} || nai || 1/6, 1/5
|-
| colspan="2" | {{sagittal| |) }} || tai || 1/4, 1/3, 2/5
|-
| colspan="2" | {{sagittal| |\ }} || kai || 1/2
|-
| colspan="2" | {{sagittal| (|\ }} || jakai || 3/5, 2/3, 3/4
|-
| E-F{{nbhsp}}{{sagittal| !( }} || {{sagittal| ||) }}|| limmai nao || 4/5, 5/6
|-
| E-F || {{sagittal| ||\ }}|| limmai || 1
|}

The corresponding down notations replace E-F with F-E (or B-C with C-B) and mirror the sagittals vertically, while their pronunciations replace "ai" (high) and "ao" (down) endings.

The following table shows all the rose EDOs/ETs. Notice how the notation of subsets is preserved; there are never two different symbols in the same column.

{| class="wikitable center-all"
|+ Revo sagittal bad-fifths limma-fraction notations
|-
|-
! rowspan="2" | EDOs b-ETs !! rowspan="2" | [[Sharpness#limmanosity|Limmanosity]] (EF = ) !! colspan="13" | Limma fraction
|-
! 0 !! 1/6 !! 1/5 !! 1/4 !! 1/3 !! 2/5 !! 1/2 !! 3/5 !! 2/3 !! 3/4 !! 4/5 !! 5/6 !! 1
|-
| bgcolor="#f6e9e9" | 7 || 1 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || bgcolor="#f1f2f6" | || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| ||\ }}
|-
| bgcolor="#f6e9e9" | 9, 14 || 2 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || || || bgcolor="#f1f2f6" | {{sagittal| |\ }} || || || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| ||\ }}
|-
| bgcolor="#f6e9e9" | (11), 16, 21 || 3 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || || {{sagittal| |) }} || || bgcolor="#f1f2f6" | || || {{sagittal| (|\ }} || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| ||\ }}
|-
| bgcolor="#f6e9e9" | 23, 28, 33 || 4 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| |) }} || || || bgcolor="#f1f2f6" | {{sagittal| |\ }} || || || {{sagittal| (|\ }} || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | || {{sagittal| ||\ }}
|-
| bgcolor="#f6e9e9" | 30b, 35, 40 || 5 || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| |( }} || || || {{sagittal| |) }} || bgcolor="#f1f2f6" | || {{sagittal| (|\ }} || || || bgcolor="#f1f2f6" | {{sagittal| ||) }} || bgcolor="#f1f2f6" | || {{sagittal| ||\ }}
|-
| bgcolor="#f6e9e9" | 42b, 47 || 6 || || bgcolor="#f1f2f6" | {{sagittal| |( }} || bgcolor="#f1f2f6" | || || {{sagittal| |) }} || || bgcolor="#f1f2f6" | {{sagittal| |\ }} || || {{sagittal| (|\ }} || || bgcolor="#f1f2f6" | || bgcolor="#f1f2f6" | {{sagittal| ||) }} || {{sagittal| ||\ }}
|}

(11)-EDO is in parenthesis because its fifth is so narrow it is usually notated as a subset of 22-EDO which has a good fifth.

To obtain the Evo notations, delete the multishaft symbols. There are no equivalent combinations with conventional sharps or flats, as limmas are conventionally notated as the intervals B-C and E-F. The multishaft symbols are not required, even in Revo notation; they merely allow for alternative spellings there. In theory, sharps and flats ''could'' be used with the notations for 33, 40, and 47 because the sharp is one step for them, while it is zero or negative for the other rose EDOs and Sagittal never uses symbols for commas that have been tempered out or tempered negative. But Sagittal recommends not using sharps or flats, conventional or sagittal, with ''any'' limma-fraction notation.

[[Category:Notation]]
[[Category:Sagittal notation]]