Chain-of-fifths notation: Difference between revisions

Line 8:

== Accidentals ==

The [https://w3c.github.io/smufl/latest/ Standard Music Font Layout (SMuFL)] specification provides Unicode codepoints for the standard accidentals of chain-of-fifths notation and for the Stein–Zimmermann accidentals of neutral ~~circle~~-of-fifths notation. Some fonts may not include all symbols, so fonts designed for musical notation, such as Bravura or Leland<ref>[https://www.smufl.org/fonts/ SMuFL | Introducing SMuFL]</ref>, are recommended.

The [https://w3c.github.io/smufl/latest/ Standard Music Font Layout (SMuFL)] specification provides Unicode codepoints for the standard accidentals of chain-of-fifths notation and for the Stein–Zimmermann accidentals of neutral chain-of-fifths notation. Some fonts may not include all symbols, so fonts designed for musical notation, such as Bravura or Leland<ref>[https://www.smufl.org/fonts/ SMuFL | Introducing SMuFL]</ref>, are recommended.

In circumstances where the fonts or codepoints are not quickly accessible, ASCII substitute symbols are used instead of the regular symbols. In addition, the Xenharmonic Wiki provides [[:Category:character templates|character templates]] to enter these symbols easily in wiki pages. The following table includes these equivalences.

{| class="wikitable center-all left-1"

|+ style="font-size: 105%;" | Accidentals in (neutral) ~~circle~~-of-fifths notation

|+ style="font-size: 105%;" | Accidentals in (neutral) chain-of-fifths notation

|-

! Style \ Offset

Line 30:

| Sesquiflat

| Flat

| Half-flat Demiflat Semiflat

| Half-flat Demiflat Semiflat

| Natural

| Half-sharp Demisharp Semisharp

| Half-sharp Demisharp Semisharp

| Sharp

| Sesquisharp

Line 38:

|- style="vertical-align: top;"

| style="vertical-align: middle;" | Standard accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/standard-accidentals-12-edo.html Standard Music Font Layout | Standard accidentals (12-EDO)]</ref>

| 𝄫 (U+1D12B)

| 𝄫 (U+1D12B)

|

| ♭ (U+266D)

| ♭ (U+266D)

|

| ♮ (U+266E)

| ♮ (U+266E)

|

| ♯ (U+266F)

| ♯ (U+266F)

|

| 𝄪 (U+1D12A)

| 𝄪 (U+1D12A)

|- style="vertical-align: top;"

| style="vertical-align: middle;" | Standard accidentals + Stein–Zimmermann accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/stein-zimmermann-accidentals-24-edo.html Standard Music Font Layout | Stein-Zimmermann accidentals (24-EDO)]</ref>

| style="vertical-align: middle;" | Standard accidentals + Stein–Zimmermann accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/stein-zimmermann-accidentals-24-edo.html Standard Music Font Layout | Stein-Zimmermann accidentals (24-EDO)]</ref>

| {{flat2}} (U+E264)

| {{flat2}} (U+E264)

| {{sesquiflat}} (U+E281)

| {{sesquiflat}} (U+E281)

| {{flat}} (U+E260)

| {{flat}} (U+E260)

| {{demiflat}} (U+E280)

| {{demiflat}} (U+E280)

| {{natural}} (U+E261)

| {{natural}} (U+E261)

| {{demisharp}} (U+E282)

| {{demisharp}} (U+E282)

| {{sharp}} (U+E262)

| {{sharp}} (U+E262)

| {{sesquisharp|200%}} (U+E283)

| {{sesquisharp|200%}} (U+E283)

| {{sharp2}} (U+E263)

| {{sharp2}} (U+E263)

|-

| Substitute symbols

Line 72:

| Xen Wiki [[:Category:character templates|character templates]]

| {{tlx|flat2|plaincode}}

| {{tlx|sesquiflat|plaincode}} {{tlx|sesquiflat2|plaincode}}

| {{tlx|sesquiflat|plaincode}} {{tlx|sesquiflat2|plaincode}}

| {{tlx|flat|plaincode}}

| {{tlx|demiflat|plaincode}} {{tlx|demiflat2|plaincode}}

| {{tlx|demiflat|plaincode}} {{tlx|demiflat2|plaincode}}

| {{tlx|natural|plaincode}}

| {{tlx|demisharp|plaincode}} {{tlx|demisharp2|plaincode}}

| {{tlx|demisharp|plaincode}} {{tlx|demisharp2|plaincode}}

| {{tlx|sharp|plaincode}}

| {{tlx|sesquisharp|plaincode}} {{tlx|sesquisharp2|plaincode}}

| {{tlx|sesquisharp|plaincode}} {{tlx|sesquisharp2|plaincode}}

| {{tlx|sharp2|plaincode}}

|}

=== Alternative accidentals ===

While the Stein–Zimmermann accidentals appear to be the most widespread for neutral ~~circle~~-of-fifths notation nowadays, and are most likely to be understood by professional musicians, other accidental sets have been developed and used by various musicians.

While the Stein–Zimmermann accidentals appear to be the most widespread for neutral chain-of-fifths notation nowadays, and are most likely to be understood by professional musicians, other accidental sets have been developed and used by various musicians.

Note that certain symbols may be very similar or identical to standard or Stein–Zimmermann accidentals despite having different Unicode codepoints.

Line 90:

{| class="wikitable center-all left-1"

|+ style="font-size: 105%;" | Alternative accidentals in (neutral) ~~circle~~-of-fifths notation

|+ style="font-size: 105%;" | Alternative accidentals in (neutral) chain-of-fifths notation

|-

! Style \ Offset

Line 104:

|- style="vertical-align: top;"

| style="vertical-align: middle;" | Gould arrow quartertone accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/gould-arrow-quartertone-accidentals-24-edo.html Standard Music Font Layout | Gould arrow quartertone accidentals (24-EDO)]</ref><ref group="note">Symbols for five-quarter-tones accidentals are also available.</ref>

| {{~~flat2~~}}

| {{Flat2}}

| {{Bravura|}} (U+E271) (U+1D12D) {{Bravura|}} (U+E278)

| {{Bravura|}} (U+E271) (U+1D12D) {{Bravura|}} (U+E278)

| {{~~flat~~}}

| {{Flat}}

| {{Bravura|}} (U+E270) (U+1D12C) {{Bravura|}} (U+E273) (U+1D12F)

| {{Bravura|}} (U+E270) (U+1D12C) {{Bravura|}} (U+E273) (U+1D12F)

| {{~~natural~~}}

| {{Natural}}

| {{Bravura|}} (U+E275) (U+1D131) {{Bravura|}} (U+E272) (U+1D12E)

| {{Bravura|}} (U+E275) (U+1D131) {{Bravura|}} (U+E272) (U+1D12E)

| {{~~sharp~~}}

| {{Sharp}}

| {{Bravura|}} (U+E274) (U+1D130) {{Bravura|}} (U+E277)

| {{Bravura|}} (U+E274) (U+1D130) {{Bravura|}} (U+E277)

| {{~~sharp2~~}}

| {{Sharp2}}

|- style="vertical-align: top;"

| style="vertical-align: middle;" | Persian accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/persian-accidentals.html Standard Music Font Layout | Persian accidentals]</ref>

|

| {{~~flat~~}}

| {{Flat}}

| {{Bravura|}} Koron (U+E460)

| {{Bravura|}} Koron (U+E460)

| {{~~natural~~}}

| {{Natural}}

| {{Bravura|}} Sori (U+E461)

| {{Bravura|}} Sori (U+E461)

| {{~~sharp~~}}

| {{Sharp}}

|

|- style="vertical-align: top;"

| style="vertical-align: middle;" | [[Sagittal]] accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/spartan-sagittal-single-shaft-accidentals.html Standard Music Font Layout | Spartan Sagittal single-shaft accidentals]</ref><ref>[https://www.w3.org/2021/03/smufl14/tables/spartan-sagittal-multi-shaft-accidentals.html Standard Music Font Layout | Spartan Sagittal multi-shaft accidentals]</ref><ref group="note">In mixed Sagittal notation, standard sharps and flats may be used instead of sagittal sharps and flats, and sagittal accidentals may be used to the left of those to alter them. Also, Sagittal notation includes many more accidentals besides those included in the table.</ref>

| {{Bravura|}} (U+E335)

| {{Bravura|}} (U+E335)

| {{Bravura|}} (U+E327)

| {{Bravura|}} (U+E327)

| {{Bravura|}} (U+E319)

| {{Bravura|}} (U+E319)

| {{Bravura|}} (U+E30B)

| {{Bravura|}} (U+E30B)

| {{natural}}

| {{Bravura|}} (U+E30A)

| {{Bravura|}} (U+E30A)

| {{Bravura|}} (U+E318)

| {{Bravura|}} (U+E318)

| {{Bravura|}} (U+E326)

| {{Bravura|}} (U+E326)

| {{Bravura|}} (U+E334)

| {{Bravura|}} (U+E334)

|- style="vertical-align: top;"

| style="vertical-align: middle;" | [[Wyschnegradsky]] accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/wyschnegradsky-accidentals-72-edo.html Standard Music Font Layout | Wyschnegradsky accidentals (72-EDO)]</ref><ref group="note">Wyschnegradsky accidentals also include twelfth-tone ([[72edo]]) accidentals.</ref>

| {{flat2}}

| {{Bravura|}} (U+E433)

| {{Bravura|}} (U+E433)

| {{Bravura|}} (U+E430)

| {{Bravura|}} (U+E430)

| {{Bravura|}} (U+E42D)

| {{Bravura|}} (U+E42D)

| {{natural}}

| {{Bravura|}} (U+E422)

| {{Bravura|}} (U+E422)

| {{Bravura|}} (U+E425)

| {{Bravura|}} (U+E425)

| {{Bravura|}} (U+E428)

| {{Bravura|}} (U+E428)

| {{sharp2}}

|}

Line 157:

! Edo

! Fifth

! Fifth-detuning abs (~~¢~~), rel (%)

! Fifth-detuning abs (¢), rel (%)

! Major 2nd

! Major 2nd

! Minor 2nd

! Minor 2nd

! Augmented 1sn

! Augmented 1sn

|-

! [[12edo| 12]]

! [[12edo|12]]

| 7 || −2.0 ( −2.0%) || 2 || 1 || 1

|-

! [[17edo| 17]]

! [[17edo|17]]

| 10 || +3.9 ( +5.6%) || 3 || 1 || 2

|-

! [[19edo| 19]]

! [[19edo|19]]

| 11 || −7.2 (−11.4%) || 3 || 2 || 1

|-

! [[22edo| 22]]

! [[22edo|22]]

| 13 || +7.1 (+13.1%) || 4 || 1 || 3

|-

! [[26edo| 26]]

! [[26edo|26]]

| 15 || −9.6 (−20.9%) || 4 || 3 || 1

|-

! [[27edo| 27]]

! [[27edo|27]]

| 16 || +9.2 (+20.6%) || 5 || 1 || 4

|-

! [[29edo| 29]]

! [[29edo|29]]

| 17 || +1.5 ( +3.6%) || 5 || 2 || 3

|-

! [[31edo| 31]]

! [[31edo|31]]

| 18 || −5.2 (−13.4%) || 5 || 3 || 2

|-

! [[32edo| 32]]

! [[32edo|32]]

| 19 || +10.5 (+28.1%) || 6 || 1 || 5

|-

! [[33edo| 33]]

! [[33edo|33]]

| 19 || −11.0 (−30.4%) || 5 || 4 || 1

|-

! [[37edo| 37]]

! [[37edo|37]]

| 22 || +11.6 (+35.6%) || 7 || 1 || 6

|-

! [[39edo| 39]]

! [[39edo|39]]

| 23 || +5.7 (+18.6%) || 7 || 2 || 5

|-

! [[40edo| 40]]

! [[40edo|40]]

| 23 || −12.0 (−39.9%) || 6 || 5 || 1

|-

! [[41edo| 41]]

! [[41edo|41]]

| 24 || +0.5 ( +1.7%) || 7 || 3 || 4

|-

! [[42edo| 42]]

! [[42edo|42]]

| 25 || +12.3 (+43.2%) || 8 || 1 || 7

|-

! [[43edo| 43]]

! [[43edo|43]]

| 25 || −4.3 (−15.3%) || 7 || 4 || 3

|-

! [[45edo| 45]]

! [[45edo|45]]

| 26 || −8.6 (−32.3%) || 7 || 5 || 2

|-

! [[46edo| 46]]

! [[46edo|46]]

| 27 || +2.4 ( +9.2%) || 8 || 3 || 5

|-

! [[47edo| 47]]

! [[47edo|47]]

| 27 || −12.6 (−49.3%) || 7 || 6 || 1

|-

! [[49edo| 49]]

! [[49edo|49]]

| 29 || +8.2 (+33.7%) || 9 || 2 || 7

|-

! [[50edo| 50]]

! [[50edo|50]]

| 29 || −6.0 (−24.8%) || 8 || 5 || 3

|-

! [[53edo| 53]]

! [[53edo|53]]

| 31 || −0.1 ( -0.3%) || 9 || 4 || 5

|-

! [[55edo| 55]]

! [[55edo|55]]

| 32 || −3.8 (−17.3%) || 9 || 5 || 4

|-

! [[56edo| 56]]

! [[56edo|56]]

| 33 || +5.2 (+24.2%) || 10 || 3 || 7

|-

! [[59edo| 59]]

! [[59edo|59]]

| 35 || +9.9 (+48.7%) || 11 || 2 || 9

|-

! [[61edo| 61]]

! [[61edo|61]]

| 36 || +6.2 (+31.7%) || 11 || 3 || 8

|-

! [[63edo| 63]]

! [[63edo|63]]

| 37 || +2.8 (+14.7%) || 11 || 4 || 7

|-

! [[64edo| 64]]

! [[64edo|64]]

| 37 || −8.2 (−43.8%) || 10 || 7 || 3

|-

! [[65edo| 65]]

! [[65edo|65]]

| 38 || −0.4 ( -2.3%) || 11 || 5 || 6

|-

! [[67edo| 67]]

! [[67edo|67]]

| 39 || −3.4 (−19.2%) || 11 || 6 || 5

|-

! [[69edo| 69]]

! [[69edo|69]]

| 40 || −6.3 (−36.2%) || 11 || 7 || 4

|-

! [[70edo| 70]]

! [[70edo|70]]

| 41 || +0.9 ( +5.3%) || 12 || 5 || 7

|-

! [[71edo| 71]]

! [[71edo|71]]

| 42 || +7.9 (+46.8%) || 13 || 3 || 10

|-

! [[73edo| 73]]

! [[73edo|73]]

| 43 || +4.9 (+29.8%) || 13 || 4 || 9

|-

! [[74edo| 74]]

! [[74edo|74]]

| 43 || −4.7 (−28.7%) || 12 || 7 || 5

|-

! [[75edo| 75]]

! [[75edo|75]]

| 44 || +2.0 (+12.8%) || 13 || 5 || 8

|-

! [[77edo| 77]]

! [[77edo|77]]

| 45 || −0.7 ( −4.2%) || 13 || 6 || 7

|-

! [[79edo| 79]]

! [[79edo|79]]

| 46 || −3.2 (−21.2%) || 13 || 7 || 6

|-

! [[80edo| 80]]

! [[80edo|80]]

| 47 || +3.0 (+20.3%) || 14 || 5 || 9

|-

! [[81edo| 81]]

! [[81edo|81]]

| 47 || −5.7 (−38.2%) || 13 || 8 || 5

|-

! [[83edo| 83]]

! [[83edo|83]]

| 49 || +6.5 (+44.8%) || 15 || 4 || 11

|-

! [[88edo| 88]]

! [[88edo|88]]

| 51 || −6.5 (−47.7%) || 14 || 9 || 5

|-

! [[89edo| 89]]

! [[89edo|89]]

| 52 || −0.8 ( -6.2%) || 15 || 7 || 8

|-

! [[90edo| 90]]

! [[90edo|90]]

| 53 || +4.7 (+35.3%) || 16 || 5 || 11

|-

! [[91edo| 91]]

! [[91edo|91]]

| 53 || −3.1 (−23.2%) || 15 || 8 || 7

|-

! [[94edo| 94]]

! [[94edo|94]]

| 55 || +0.2 ( +1.4%) || 16 || 7 || 9

|-

! [[95edo| 95]]

! [[95edo|95]]

| 56 || +5.4 (+42.9%) || 17 || 5 || 12

|-

! [[97edo| 97]]

! [[97edo|97]]

| 57 || +3.2 (+25.9%) || 17 || 6 || 11

|-

! [[98edo| 98]]

! [[98edo|98]]

| 57 || −4.0 (−32.6%) || 16 || 9 || 7

|-

! [[99edo| 99]]

! [[99edo|99]]

| 58 || +1.1 ( +8.9%) || 17 || 7 || 10

|}</div>

Line 317:

|+ style="font-size: 105%;" | Diatonic edos fit for neutral chain-of-fifths notation

|-

! Edo !! Fifth !! Fifth-detuning abs (~~¢~~), rel (%) !! Major 2nd !! Minor 2nd !! Augmented 1sn

! Edo !! Fifth !! Fifth-detuning abs (¢), rel (%) !! Major 2nd !! Minor 2nd !! Augmented 1sn

|-

! [[17edo| 17]]

! [[17edo|17]]

| 10 || +3.9 ( +5.6%) || 3 || 1 || 2

|-

! [[24edo| 24]]

! [[24edo|24]]

| 14 || −4.0 (−4.0%) || 4 || 2 || 2

|-

! [[27edo| 27]]

! [[27edo|27]]

| 16 || +9.2 (+20.6%) || 5 || 1 || 4

|-

! [[31edo| 31]]

! [[31edo|31]]

| 18 || −5.2 (−13.4%) || 5 || 3 || 2

|-

! [[37edo| 37]]

! [[37edo|37]]

| 22 || +11.6 (+35.6%) || 7 || 1 || 6

|-

! [[38edo| 38]]

! [[38edo|38]]

| 22 || −7.2 (−22.9%) || 6 || 4 || 2

|-

! [[41edo| 41]]

! [[41edo|41]]

| 24 || +0.5 ( +1.7%) || 7 || 3 || 4

|-

! [[44edo| 44]]

! [[44edo|44]]

| 26 || +7.1 (+26.2%) || 8 || 2 || 6

|-

! [[45edo| 45]]

! [[45edo|45]]

| 26 || −8.6 (−32.3%) || 7 || 5 || 2

|-

! [[52edo| 52]]

! [[52edo|52]]

| 30 || −9.6 (−41.8%) || 8 || 6 || 2

|-

! [[55edo| 55]]

! [[55edo|55]]

| 32 || −3.8 (−17.3%) || 9 || 5 || 4

|-

! [[58edo| 58]]

! [[58edo|58]]

| 34 || +1.5 ( +3.6%) || 10 || 4 || 6

|-

! [[61edo| 61]]

! [[61edo|61]]

| 36 || +6.2 (+31.7%) || 11 || 3 || 8

|-

! [[65edo| 65]]

! [[65edo|65]]

| 38 || −0.4 (−2.3%) || 11 || 5 || 6

|-

! [[69edo| 69]]

! [[69edo|69]]

| 40 || −6.3 (−36.2%) || 11 || 7 || 4

|-

! [[71edo| 71]]

! [[71edo|71]]

| 42 || +7.9 (+46.8%) || 13 || 3 || 10

|-

! [[75edo| 75]]

! [[75edo|75]]

| 44 || +2.0 (+12.8%) || 13 || 5 || 8

|-

! [[78edo| 78]]

! [[78edo|78]]

| 46 || +5.7 (+37.3%) || 14 || 4 || 10

|-

! [[79edo| 79]]

! [[79edo|79]]

| 46 || −3.2 (−21.2%) || 13 || 7 || 6

|-

! [[86edo| 86]]

! [[86edo|86]]

| 50 || −4.3 (−30.7%) || 14 || 8 || 6

|-

! [[89edo| 89]]

! [[89edo|89]]

| 52 || −0.8 (−6.2%) || 15 || 7 || 8

|-

! [[92edo| 92]]

! [[92edo|92]]

| 54 || +2.4 (+18.3%) || 16 || 6 || 10

|-

! [[95edo| 95]]

! [[95edo|95]]

| 56 || +5.4 (+42.9%) || 17 || 5 || 12

|-

! [[99edo| 99]]

! [[99edo|99]]

| 58 || +1.1 (+8.9%) || 17 || 7 || 10

|}

Line 394:

== Expansions ==

* [[Syntonic-rastmic subchroma notation]] – ~~Built~~ on neutral chain-of-fifths notation

* [[Syntonic-rastmic subchroma notation]] – built on neutral chain-of-fifths notation

* [[Ups and downs notation]] – ~~Built~~ on chain-of-fifths notation

* [[Ups and downs notation]] – built on chain-of-fifths notation

** Neutral ups and downs notation (~~→~~ [[Alternative symbols for ups and downs notation]])

** Neutral ups and downs notation (→ [[Alternative symbols for ups and downs notation]])

* [[Diamond-mos notation]] – ~~Built~~ on neutral chain-of-fifths notation

* [[Diamond-mos notation]] – built on neutral chain-of-fifths notation

* [[Sagittal notation]] (''evo flavor'') – ~~Built~~ on chain-of-fifths notation or neutral chain-of-fifths notation

* [[Sagittal notation]] (''evo flavor'') – built on chain-of-fifths notation or neutral chain-of-fifths notation

* [[Extended meantone notation]] – ~~Built~~ on chain-of-fifths notation or neutral chain-of-fifths notation

* [[Extended meantone notation]] – built on chain-of-fifths notation or neutral chain-of-fifths notation

* [[Fractional sharp notation]] – ~~Built~~ on chain-of-fifths notation

* [[Fractional sharp notation]] – built on chain-of-fifths notation

== See also ==

Line 407:

* [[Fifthspan]]

* [[Pythagorean tuning]]

* [[User:Xenwolf/cofn]] – ~~Sortable~~ table with more intervals (all fifths within the interval [4\7, 3\5], the "[[diatonic range]]")

* [[User:Xenwolf/cofn]] – sortable table with more intervals (all fifths within the interval [4\7, 3\5], the "[[diatonic range]]")

== Notes ==

@@ Line 8: / Line 8: @@
 == Accidentals ==
-The [https://w3c.github.io/smufl/latest/ Standard Music Font Layout (SMuFL)] specification provides Unicode codepoints for the standard accidentals of chain-of-fifths notation and for the Stein–Zimmermann accidentals of neutral circle-of-fifths notation. Some fonts may not include all symbols, so fonts designed for musical notation, such as Bravura or Leland<ref>[https://www.smufl.org/fonts/ SMuFL | Introducing SMuFL]</ref>, are recommended.
+The [https://w3c.github.io/smufl/latest/ Standard Music Font Layout (SMuFL)] specification provides Unicode codepoints for the standard accidentals of chain-of-fifths notation and for the Stein–Zimmermann accidentals of neutral chain-of-fifths notation. Some fonts may not include all symbols, so fonts designed for musical notation, such as Bravura or Leland<ref>[https://www.smufl.org/fonts/ SMuFL | Introducing SMuFL]</ref>, are recommended.
 In circumstances where the fonts or codepoints are not quickly accessible, ASCII substitute symbols are used instead of the regular symbols. In addition, the Xenharmonic Wiki provides [[:Category:character templates|character templates]] to enter these symbols easily in wiki pages. The following table includes these equivalences.
 {| class="wikitable center-all left-1"
-|+ style="font-size: 105%;" | Accidentals in (neutral) circle-of-fifths notation
+|+ style="font-size: 105%;" | Accidentals in (neutral) chain-of-fifths notation
 |-
 ! Style \ Offset
@@ Line 30: / Line 30: @@
 | Sesquiflat
 | Flat
-| Half-flat<br />Demiflat<br />Semiflat
+| Half-flat<br>Demiflat<br>Semiflat
 | Natural
-| Half-sharp<br />Demisharp<br />Semisharp
+| Half-sharp<br>Demisharp<br>Semisharp
 | Sharp
 | Sesquisharp
@@ Line 38: / Line 38: @@
 |- style="vertical-align: top;"
 | style="vertical-align: middle;" | Standard accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/standard-accidentals-12-edo.html Standard Music Font Layout | Standard accidentals (12-EDO)]</ref>
-| 𝄫<br />(U+1D12B)
+| 𝄫<br>(U+1D12B)
 |
-| ♭<br />(U+266D)
+| ♭<br>(U+266D)
 |
-| ♮<br />(U+266E)
+| ♮<br>(U+266E)
 |
-| ♯<br />(U+266F)
+| ♯<br>(U+266F)
 |
-| 𝄪<br />(U+1D12A)
+| 𝄪<br>(U+1D12A)
 |- style="vertical-align: top;"
-| style="vertical-align: middle;" | Standard accidentals<br />+ Stein–Zimmermann accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/stein-zimmermann-accidentals-24-edo.html Standard Music Font Layout | Stein-Zimmermann accidentals (24-EDO)]</ref>
+| style="vertical-align: middle;" | Standard accidentals<br>+ Stein–Zimmermann accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/stein-zimmermann-accidentals-24-edo.html Standard Music Font Layout | Stein-Zimmermann accidentals (24-EDO)]</ref>
-| {{flat2}}<br />(U+E264)
+| {{flat2}}<br/>(U+E264)
-| {{sesquiflat}}<br />(U+E281)
+| {{sesquiflat}}<br>(U+E281)
-| {{flat}}<br />(U+E260)
+| {{flat}}<br>(U+E260)
-| {{demiflat}}<br />(U+E280)
+| {{demiflat}}<br>(U+E280)
-| {{natural}}<br />(U+E261)
+| {{natural}}<br>(U+E261)
-| {{demisharp}}<br />(U+E282)
+| {{demisharp}}<br>(U+E282)
-| {{sharp}}<br />(U+E262)
+| {{sharp}}<br>(U+E262)
-| {{sesquisharp|200%}}<br />(U+E283)
+| {{sesquisharp|200%}}<br>(U+E283)
-| {{sharp2}}<br />(U+E263)
+| {{sharp2}}<br>(U+E263)
 |-
 | Substitute symbols
@@ Line 72: / Line 72: @@
 | Xen Wiki [[:Category:character templates|character templates]]
 | {{tlx|flat2|plaincode}}
-| {{tlx|sesquiflat|plaincode}}<br />{{tlx|sesquiflat2|plaincode}}
+| {{tlx|sesquiflat|plaincode}}<br>{{tlx|sesquiflat2|plaincode}}
 | {{tlx|flat|plaincode}}
-| {{tlx|demiflat|plaincode}}<br />{{tlx|demiflat2|plaincode}}
+| {{tlx|demiflat|plaincode}}<br>{{tlx|demiflat2|plaincode}}
 | {{tlx|natural|plaincode}}
-| {{tlx|demisharp|plaincode}}<br />{{tlx|demisharp2|plaincode}}
+| {{tlx|demisharp|plaincode}}<br>{{tlx|demisharp2|plaincode}}
 | {{tlx|sharp|plaincode}}
-| {{tlx|sesquisharp|plaincode}}<br />{{tlx|sesquisharp2|plaincode}}
+| {{tlx|sesquisharp|plaincode}}<br>{{tlx|sesquisharp2|plaincode}}
 | {{tlx|sharp2|plaincode}}
 |}
 === Alternative accidentals ===
-While the Stein–Zimmermann accidentals appear to be the most widespread for neutral circle-of-fifths notation nowadays, and are most likely to be understood by professional musicians, other accidental sets have been developed and used by various musicians.
+While the Stein–Zimmermann accidentals appear to be the most widespread for neutral chain-of-fifths notation nowadays, and are most likely to be understood by professional musicians, other accidental sets have been developed and used by various musicians.
 Note that certain symbols may be very similar or identical to standard or Stein–Zimmermann accidentals despite having different Unicode codepoints.
@@ Line 90: / Line 90: @@
 {| class="wikitable center-all left-1"
-|+ style="font-size: 105%;" | Alternative accidentals in (neutral) circle-of-fifths notation
+|+ style="font-size: 105%;" | Alternative accidentals in (neutral) chain-of-fifths notation
 |-
 ! Style \ Offset
@@ Line 104: / Line 104: @@
 |- style="vertical-align: top;"
 | style="vertical-align: middle;" | Gould arrow quartertone accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/gould-arrow-quartertone-accidentals-24-edo.html Standard Music Font Layout | Gould arrow quartertone accidentals (24-EDO)]</ref><ref group="note">Symbols for five-quarter-tones accidentals are also available.</ref>
-| {{flat2}}
+| {{Flat2}}
-| {{Bravura|&#xE271;}}<br />(U+E271)<br />(U+1D12D)<br />{{Bravura|&#xE278;}}<br />(U+E278)
+| {{Bravura|&#xE271;}}<br>(U+E271)<br>(U+1D12D)<br>{{Bravura|&#xE278;}}<br>(U+E278)
-| {{flat}}
+| {{Flat}}
-| {{Bravura|&#xE270;}}<br />(U+E270)<br />(U+1D12C)<br />{{Bravura|&#xE273;}}<br />(U+E273)<br />(U+1D12F)
+| {{Bravura|&#xE270;}}<br>(U+E270)<br>(U+1D12C)<br>{{Bravura|&#xE273;}}<br>(U+E273)<br>(U+1D12F)
-| {{natural}}
+| {{Natural}}
-| {{Bravura|&#xE275;}}<br />(U+E275)<br />(U+1D131)<br />{{Bravura|&#xE272;}}<br />(U+E272)<br />(U+1D12E)
+| {{Bravura|&#xE275;}}<br>(U+E275)<br>(U+1D131)<br>{{Bravura|&#xE272;}}<br>(U+E272)<br>(U+1D12E)
-| {{sharp}}
+| {{Sharp}}
-| {{Bravura|&#xE274;}}<br />(U+E274)<br />(U+1D130)<br />{{Bravura|&#xE277;}}<br />(U+E277)
+| {{Bravura|&#xE274;}}<br>(U+E274)<br>(U+1D130)<br>{{Bravura|&#xE277;}}<br>(U+E277)
-| {{sharp2}}
+| {{Sharp2}}
 |- style="vertical-align: top;"
 | style="vertical-align: middle;" | Persian accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/persian-accidentals.html Standard Music Font Layout | Persian accidentals]</ref>
 |
 |
-| {{flat}}
+| {{Flat}}
-| {{Bravura|&#xE460;}}<br />Koron<br />(U+E460)
+| {{Bravura|&#xE460;}}<br>Koron<br>(U+E460)
-| {{natural}}
+| {{Natural}}
-| {{Bravura|&#xE461;}}<br />Sori<br />(U+E461)
+| {{Bravura|&#xE461;}}<br>Sori<br>(U+E461)
-| {{sharp}}
+| {{Sharp}}
 |
 |
 |- style="vertical-align: top;"
 | style="vertical-align: middle;" | [[Sagittal]] accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/spartan-sagittal-single-shaft-accidentals.html Standard Music Font Layout | Spartan Sagittal single-shaft accidentals]</ref><ref>[https://www.w3.org/2021/03/smufl14/tables/spartan-sagittal-multi-shaft-accidentals.html Standard Music Font Layout | Spartan Sagittal multi-shaft accidentals]</ref><ref group="note">In mixed Sagittal notation, standard sharps and flats may be used instead of sagittal sharps and flats, and sagittal accidentals may be used to the left of those to alter them. Also, Sagittal notation includes many more accidentals besides those included in the table.</ref>
-| {{Bravura|&#xE335;}}<br />(U+E335)
+| {{Bravura|&#xE335;}}<br>(U+E335)
-| {{Bravura|&#xE327;}}<br />(U+E327)
+| {{Bravura|&#xE327;}}<br>(U+E327)
-| {{Bravura|&#xE319;}}<br />(U+E319)
+| {{Bravura|&#xE319;}}<br>(U+E319)
-| {{Bravura|&#xE30B;}}<br />(U+E30B)
+| {{Bravura|&#xE30B;}}<br>(U+E30B)
 | {{natural}}
-| {{Bravura|&#xE30A;}}<br />(U+E30A)
+| {{Bravura|&#xE30A;}}<br>(U+E30A)
-| {{Bravura|&#xE318;}}<br />(U+E318)
+| {{Bravura|&#xE318;}}<br>(U+E318)
-| {{Bravura|&#xE326;}}<br />(U+E326)
+| {{Bravura|&#xE326;}}<br>(U+E326)
-| {{Bravura|&#xE334;}}<br />(U+E334)
+| {{Bravura|&#xE334;}}<br>(U+E334)
 |- style="vertical-align: top;"
 | style="vertical-align: middle;" | [[Wyschnegradsky]] accidentals<ref>[https://www.w3.org/2021/03/smufl14/tables/wyschnegradsky-accidentals-72-edo.html Standard Music Font Layout | Wyschnegradsky accidentals (72-EDO)]</ref><ref group="note">Wyschnegradsky accidentals also include twelfth-tone ([[72edo]]) accidentals.</ref>
 | {{flat2}}
-| {{Bravura|&#xE433;}}<br />(U+E433)
+| {{Bravura|&#xE433;}}<br>(U+E433)
-| {{Bravura|&#xE430;}}<br />(U+E430)
+| {{Bravura|&#xE430;}}<br>(U+E430)
-| {{Bravura|&#xE42D;}}<br />(U+E42D)
+| {{Bravura|&#xE42D;}}<br>(U+E42D)
 | {{natural}}
-| {{Bravura|&#xE422;}}<br />(U+E422)
+| {{Bravura|&#xE422;}}<br>(U+E422)
-| {{Bravura|&#xE425;}}<br />(U+E425)
+| {{Bravura|&#xE425;}}<br>(U+E425)
-| {{Bravura|&#xE428;}}<br />(U+E428)
+| {{Bravura|&#xE428;}}<br>(U+E428)
 | {{sharp2}}
 |}
@@ Line 157: / Line 157: @@
 ! Edo
 ! Fifth
-! Fifth-detuning<br />abs (&#162;), rel (%)
+! Fifth-detuning<br>abs (¢), rel (%)
-! Major<br />2nd
+! Major<br>2nd
-! Minor<br />2nd
+! Minor<br>2nd
-! Augmented<br />1sn
+! Augmented<br>1sn
 |-
-! [[12edo| 12]]
+! [[12edo|12]]
 | 7 || −2.0 ( −2.0%) || 2 || 1 || 1
 |-
-! [[17edo| 17]]
+! [[17edo|17]]
 | 10 || +3.9 ( +5.6%) || 3 || 1 || 2
 |-
-! [[19edo| 19]]
+! [[19edo|19]]
 | 11 || −7.2 (−11.4%) || 3 || 2 || 1
 |-
-! [[22edo| 22]]
+! [[22edo|22]]
 | 13 || +7.1 (+13.1%) || 4 || 1 || 3
 |-
-! [[26edo| 26]]
+! [[26edo|26]]
 | 15 || −9.6 (−20.9%) || 4 || 3 || 1
 |-
-! [[27edo| 27]]
+! [[27edo|27]]
 | 16 || +9.2 (+20.6%) || 5 || 1 || 4
 |-
-! [[29edo| 29]]
+! [[29edo|29]]
 | 17 || +1.5 ( +3.6%) || 5 || 2 || 3
 |-
-! [[31edo| 31]]
+! [[31edo|31]]
 | 18 || −5.2 (−13.4%) || 5 || 3 || 2
 |-
-! [[32edo| 32]]
+! [[32edo|32]]
 | 19 || +10.5 (+28.1%) || 6 || 1 || 5
 |-
-! [[33edo| 33]]
+! [[33edo|33]]
 | 19 || −11.0 (−30.4%) || 5 || 4 || 1
 |-
-! [[37edo| 37]]
+! [[37edo|37]]
 | 22 || +11.6 (+35.6%) || 7 || 1 || 6
 |-
-! [[39edo| 39]]
+! [[39edo|39]]
 | 23 || +5.7 (+18.6%) || 7 || 2 || 5
 |-
-! [[40edo| 40]]
+! [[40edo|40]]
 | 23 || −12.0 (−39.9%) || 6 || 5 || 1
 |-
-! [[41edo| 41]]
+! [[41edo|41]]
 | 24 || +0.5 ( +1.7%) || 7 || 3 || 4
 |-
-! [[42edo| 42]]
+! [[42edo|42]]
 | 25 || +12.3 (+43.2%) || 8 || 1 || 7
 |-
-! [[43edo| 43]]
+! [[43edo|43]]
 | 25 || −4.3 (−15.3%) || 7 || 4 || 3
 |-
-! [[45edo| 45]]
+! [[45edo|45]]
 | 26 || −8.6 (−32.3%) || 7 || 5 || 2
 |-
-! [[46edo| 46]]
+! [[46edo|46]]
 | 27 || +2.4 ( +9.2%) || 8 || 3 || 5
 |-
-! [[47edo| 47]]
+! [[47edo|47]]
 | 27 || −12.6 (−49.3%) || 7 || 6 || 1
 |-
-! [[49edo| 49]]
+! [[49edo|49]]
 | 29 || +8.2 (+33.7%) || 9 || 2 || 7
 |-
-! [[50edo| 50]]
+! [[50edo|50]]
 | 29 || −6.0 (−24.8%) || 8 || 5 || 3
 |-
-! [[53edo| 53]]
+! [[53edo|53]]
 | 31 || −0.1 ( -0.3%) || 9 || 4 || 5
 |-
-! [[55edo| 55]]
+! [[55edo|55]]
 | 32 || −3.8 (−17.3%) || 9 || 5 || 4
 |-
-! [[56edo| 56]]
+! [[56edo|56]]
 | 33 || +5.2 (+24.2%) || 10 || 3 || 7
 |-
-! [[59edo| 59]]
+! [[59edo|59]]
 | 35 || +9.9 (+48.7%) || 11 || 2 || 9
 |-
-! [[61edo| 61]]
+! [[61edo|61]]
 | 36 || +6.2 (+31.7%) || 11 || 3 || 8
 |-
-! [[63edo| 63]]
+! [[63edo|63]]
 | 37 || +2.8 (+14.7%) || 11 || 4 || 7
 |-
-! [[64edo| 64]]
+! [[64edo|64]]
 | 37 || −8.2 (−43.8%) || 10 || 7 || 3
 |-
-! [[65edo| 65]]
+! [[65edo|65]]
 | 38 || −0.4 ( -2.3%) || 11 || 5 || 6
 |-
-! [[67edo| 67]]
+! [[67edo|67]]
 | 39 || −3.4 (−19.2%) || 11 || 6 || 5
 |-
-! [[69edo| 69]]
+! [[69edo|69]]
 | 40 || −6.3 (−36.2%) || 11 || 7 || 4
 |-
-! [[70edo| 70]]
+! [[70edo|70]]
 | 41 || +0.9 ( +5.3%) || 12 || 5 || 7
 |-
-! [[71edo| 71]]
+! [[71edo|71]]
 | 42 || +7.9 (+46.8%) || 13 || 3 || 10
 |-
-! [[73edo| 73]]
+! [[73edo|73]]
 | 43 || +4.9 (+29.8%) || 13 || 4 || 9
 |-
-! [[74edo| 74]]
+! [[74edo|74]]
 | 43 || −4.7 (−28.7%) || 12 || 7 || 5
 |-
-! [[75edo| 75]]
+! [[75edo|75]]
 | 44 || +2.0 (+12.8%) || 13 || 5 || 8
 |-
-! [[77edo| 77]]
+! [[77edo|77]]
 | 45 || −0.7 ( −4.2%) || 13 || 6 || 7
 |-
-! [[79edo| 79]]
+! [[79edo|79]]
 | 46 || −3.2 (−21.2%) || 13 || 7 || 6
 |-
-! [[80edo| 80]]
+! [[80edo|80]]
 | 47 || +3.0 (+20.3%) || 14 || 5 || 9
 |-
-! [[81edo| 81]]
+! [[81edo|81]]
 | 47 || −5.7 (−38.2%) || 13 || 8 || 5
 |-
-! [[83edo| 83]]
+! [[83edo|83]]
 | 49 || +6.5 (+44.8%) || 15 || 4 || 11
 |-
-! [[88edo| 88]]
+! [[88edo|88]]
 | 51 || −6.5 (−47.7%) || 14 || 9 || 5
 |-
-! [[89edo| 89]]
+! [[89edo|89]]
 | 52 || −0.8 ( -6.2%) || 15 || 7 || 8
 |-
-! [[90edo| 90]]
+! [[90edo|90]]
 | 53 || +4.7 (+35.3%) || 16 || 5 || 11
 |-
-! [[91edo| 91]]
+! [[91edo|91]]
 | 53 || −3.1 (−23.2%) || 15 || 8 || 7
 |-
-! [[94edo| 94]]
+! [[94edo|94]]
 | 55 || +0.2 ( +1.4%) || 16 || 7 || 9
 |-
-! [[95edo| 95]]
+! [[95edo|95]]
 | 56 || +5.4 (+42.9%) || 17 || 5 || 12
 |-
-! [[97edo| 97]]
+! [[97edo|97]]
 | 57 || +3.2 (+25.9%) || 17 || 6 || 11
 |-
-! [[98edo| 98]]
+! [[98edo|98]]
 | 57 || −4.0 (−32.6%) || 16 || 9 || 7
 |-
-! [[99edo| 99]]
+! [[99edo|99]]
 | 58 || +1.1 ( +8.9%) || 17 || 7 || 10
 |}</div>
@@ Line 317: / Line 317: @@
 |+ style="font-size: 105%;" | Diatonic edos fit for neutral chain-of-fifths notation
 |-
-! Edo !! Fifth !! Fifth-detuning<br />abs (&#162;), rel (%) !! Major<br />2nd !! Minor<br />2nd !! Augmented<br />1sn
+! Edo !! Fifth !! Fifth-detuning<br>abs (¢), rel (%) !! Major<br>2nd !! Minor<br>2nd !! Augmented<br>1sn
 |-
-! [[17edo| 17]]
+! [[17edo|17]]
 | 10 || +3.9 ( +5.6%) || 3 || 1 || 2
 |-
-! [[24edo| 24]]
+! [[24edo|24]]
 | 14 || −4.0 (−4.0%) || 4 || 2 || 2
 |-
-! [[27edo| 27]]
+! [[27edo|27]]
 | 16 || +9.2 (+20.6%) || 5 || 1 || 4
 |-
-! [[31edo| 31]]
+! [[31edo|31]]
 | 18 || −5.2 (−13.4%) || 5 || 3 || 2
 |-
-! [[37edo| 37]]
+! [[37edo|37]]
 | 22 || +11.6 (+35.6%) || 7 || 1 || 6
 |-
-! [[38edo| 38]]
+! [[38edo|38]]
 | 22 || −7.2 (−22.9%) || 6 || 4 || 2
 |-
-! [[41edo| 41]]
+! [[41edo|41]]
 | 24 || +0.5 ( +1.7%) || 7 || 3 || 4
 |-
-! [[44edo| 44]]
+! [[44edo|44]]
 | 26 || +7.1 (+26.2%) || 8 || 2 || 6
 |-
-! [[45edo| 45]]
+! [[45edo|45]]
 | 26 || −8.6 (−32.3%) || 7 || 5 || 2
 |-
-! [[52edo| 52]]
+! [[52edo|52]]
 | 30 || −9.6 (−41.8%) || 8 || 6 || 2
 |-
-! [[55edo| 55]]
+! [[55edo|55]]
 | 32 || −3.8 (−17.3%) || 9 || 5 || 4
 |-
-! [[58edo| 58]]
+! [[58edo|58]]
 | 34 || +1.5 ( +3.6%) || 10 || 4 || 6
 |-
-! [[61edo| 61]]
+! [[61edo|61]]
 | 36 || +6.2 (+31.7%) || 11 || 3 || 8
 |-
-! [[65edo| 65]]
+! [[65edo|65]]
 | 38 || −0.4 (−2.3%) || 11 || 5 || 6
 |-
-! [[69edo| 69]]
+! [[69edo|69]]
 | 40 || −6.3 (−36.2%) || 11 || 7 || 4
 |-
-! [[71edo| 71]]
+! [[71edo|71]]
 | 42 || +7.9 (+46.8%) || 13 || 3 || 10
 |-
-! [[75edo| 75]]
+! [[75edo|75]]
 | 44 || +2.0 (+12.8%) || 13 || 5 || 8
 |-
-! [[78edo| 78]]
+! [[78edo|78]]
 | 46 || +5.7 (+37.3%) || 14 || 4 || 10
 |-
-! [[79edo| 79]]
+! [[79edo|79]]
 | 46 || −3.2 (−21.2%) || 13 || 7 || 6
 |-
-! [[86edo| 86]]
+! [[86edo|86]]
 | 50 || −4.3 (−30.7%) || 14 || 8 || 6
 |-
-! [[89edo| 89]]
+! [[89edo|89]]
 | 52 || −0.8 (−6.2%) || 15 || 7 || 8
 |-
-! [[92edo| 92]]
+! [[92edo|92]]
 | 54 || +2.4 (+18.3%) || 16 || 6 || 10
 |-
-! [[95edo| 95]]
+! [[95edo|95]]
 | 56 || +5.4 (+42.9%) || 17 || 5 || 12
 |-
-! [[99edo| 99]]
+! [[99edo|99]]
 | 58 || +1.1 (+8.9%) || 17 || 7 || 10
 |}
@@ Line 394: / Line 394: @@
 == Expansions ==
-* [[Syntonic-rastmic subchroma notation]] – Built on neutral chain-of-fifths notation
+* [[Syntonic-rastmic subchroma notation]] – built on neutral chain-of-fifths notation
-* [[Ups and downs notation]] – Built on chain-of-fifths notation
+* [[Ups and downs notation]] – built on chain-of-fifths notation
-** Neutral ups and downs notation (&rarr; [[Alternative symbols for ups and downs notation]])
+** Neutral ups and downs notation (→ [[Alternative symbols for ups and downs notation]])
-* [[Diamond-mos notation]] – Built on neutral chain-of-fifths notation
+* [[Diamond-mos notation]] – built on neutral chain-of-fifths notation
-* [[Sagittal notation]] (''evo flavor'') – Built on chain-of-fifths notation or neutral chain-of-fifths notation
+* [[Sagittal notation]] (''evo flavor'') – built on chain-of-fifths notation or neutral chain-of-fifths notation
-* [[Extended meantone notation]] – Built on chain-of-fifths notation or neutral chain-of-fifths notation
+* [[Extended meantone notation]] – built on chain-of-fifths notation or neutral chain-of-fifths notation
-* [[Fractional sharp notation]] – Built on chain-of-fifths notation
+* [[Fractional sharp notation]] – built on chain-of-fifths notation
 == See also ==
@@ Line 407: / Line 407: @@
 * [[Fifthspan]]
 * [[Pythagorean tuning]]
-* [[User:Xenwolf/cofn]] – Sortable table with more intervals (all fifths within the interval [4\7, 3\5], the "[[diatonic range]]")
+* [[User:Xenwolf/cofn]] – sortable table with more intervals (all fifths within the interval [4\7, 3\5], the "[[diatonic range]]")
 == Notes ==