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159edo/Notation: Difference between revisions

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Xenwolf (talk | contribs)
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added some more symbols and symbol combinations to the table, the rest I leave to my collaborator Aura as an exercise 🙂
Aura (talk | contribs)
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Expanded the table to accomodate more of the accidentals.
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The 159edo-notation system proposed by [[User:Aura|Aura]] modifies the [[Helmholtz-Ellis notation]] in such a way that undecimal quartertones play a central role alongside the traditional accidentals.
The 159edo-notation system proposed by [[User:Aura|Aura]] modifies the [[Helmholtz-Ellis notation]] in such a way that undecimal quartertones play a central role alongside the traditional accidentals.


The following table (under construction) shows the symbols and describes their function. The signs in the remarks section reflect absolute displacements, <code>-</code> means down, <code>+</code> means up.
The following table (under construction) shows the symbols and describes their function. The terms in the glyph name sections reflect absolute displacements, <code>-</code> means down, <code>+</code> means up.  Furthermore, symbols with multiple names will have both names sharing the same cell.  The choice between the primary and secondary glyphs for any given step is often determined both by absolute TE error and by harmonic and melodic context for any given score, particularly as the simple and composite glyphs reflect different intervals in Just Intonation.


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 7: Line 7:
|+ Change in 1\159
|+ Change in 1\159
|-
|-
! Glyph
! Delta
! Delta
! Primary Glyph
! Primary Glyph Name
! Secondary Glyph
! Secondary Glyph Name
! Remarks
! Remarks
|-
|-
| 0
| [[File:Heji18.svg|48x48px]]
| [[File:Heji18.svg|48x48px]]
| 0
| Natural
| Neutral
|
|
|  
|-
|-
| -1
| [[File:Dart-d1.svg|48x48px]]
| [[File:Dart-d1.svg|48x48px]]
| -1
| Dart down
| Dart down
|
|
| This is nothing more than a better version of the <code>v</code> marking from Ups and Downs Notation.
|-
|-
| +1
| [[File:Dart-u1.svg|48x48px]]
| [[File:Dart-u1.svg|48x48px]]
| +1
| Dart up
| Dart up
|
|
| This is nothing more than a better version of the <code>^</code> marking from Ups and Downs Notation.
|-
|-
| -2
| [[File:Dart-d2.svg|48x48px]]
| [[File:Dart-d2.svg|48x48px]]
| -2
| Double dart down
| Double dart down
|
|
| This is two darts down fused into a single glyph for a more compact representation of <code>vv</code> from Ups and Downs Notation.
|-
|-
| +2
| [[File:Dart-u2.svg|48x48px]]
| [[File:Dart-u2.svg|48x48px]]
| +2
| Double dart up
| Double dart up
|
|
| This is two darts up fused into a single glyph for a more compact representation of <code>^^</code> from Ups and Downs Notation.
|-
|-
| -3
| [[File:Heji17.svg|48x48px]]
| Natural –Syntonic comma
| [[File:HeQd1.svg|48x48px]][[File:Heji38.svg|48x48px]]
| [[File:HeQd1.svg|48x48px]][[File:Heji38.svg|48x48px]]
| -3
| Quarter flat +Septimal comma, Demiflat +Septimal comma
| Quarter flat –Septimal comma
| The intervals represented by the primary and secondary glyphs for this step differ by [[385/384]] in Just Intonation.
|-
|-
| +3
| [[File:Heji19.svg|48x48px]]
| Natural +Syntonic comma
| [[File:HeQu1.svg|48x48px]][[File:Heji37.svg|48x48px]]
| [[File:HeQu1.svg|48x48px]][[File:Heji37.svg|48x48px]]
| +3
| Quarter sharp –Septimal comma, Demisharp +Septimal comma
| Quarter sharp +Septimal comma
| The intervals represented by the primary and secondary glyphs for this step differ by [[385/384]] in Just Intonation.
|-
|-
| -4
| [[File:HeQd1-su1.svg|48x48px]]
| [[File:HeQd1-su1.svg|48x48px]]
| -4
| Quarter flat +Syntonic comma, Demiflat +Syntonic comma
| Quarter flat –Syntonic comma
| [[File:Heji37.svg|48x48px]]
| Septimal comma down
| The primary glyph overall represents a lowering by [[55/54]].
|-
|-
| +4
| [[File:HeQu1-sd1.svg|48x48px]]
| [[File:HeQu1-sd1.svg|48x48px]]
| +4
| Quarter sharp –Syntonic comma, Demisharp –Syntonic comma
| Quarter sharp +Syntonic comma
| [[File:Heji38.svg|48x48px]]
| Septimal comma up
| The primary glyph overall represents a raising by [[55/54]].
|-
|-
| -5
| [[File:HeQd1.svg|48x48px]][[File:Dart-u2.svg|48x48px]]
| [[File:HeQd1.svg|48x48px]][[File:Dart-u2.svg|48x48px]]
| -5
| Quarter flat with double dart up, Demiflat with double dart up
| Quarter flat with dart up
|
|
|
|-
|-
| +5
| [[File:HeQu1.svg|48x48px]][[File:Dart-d2.svg|48x48px]]
| [[File:HeQu1.svg|48x48px]][[File:Dart-d2.svg|48x48px]]
| +5
| Quarter sharp with double dart down, Demisharp with double dart down
| Quarter sharp with double dart down
|
|
|
|-
|-
| -6
| [[File:HeQd1.svg|48x48px]][[File:Dart-u1.svg|48x48px]]
| [[File:HeQd1.svg|48x48px]][[File:Dart-u1.svg|48x48px]]
| -6
| Quarter flat with dart up, Demiflat with dart up
| Quarter flat with dart up
|
|
|
|-
|-
| +6
| [[File:HeQu1.svg|48x48px]][[File:Dart-d1.svg|48x48px]]
| [[File:HeQu1.svg|48x48px]][[File:Dart-d1.svg|48x48px]]
| +6
| Quarter sharp with dart down, Demisharp with dart down
| Quarter sharp with dart down
|
|
|
|-
|-
| -7
| [[File:HeQd1.svg|48x48px]]
| [[File:HeQd1.svg|48x48px]]
| -7
| Quarter flat, Demiflat
| Quarter flat
|
|
| This glyph represents a lowering by [[33/32]], much like its identical Helmholtz-Ellis notation equivalent.
|-
|-
| +7
| [[File:HeQu1.svg|48x48px]]
| [[File:HeQu1.svg|48x48px]]
| +7
| Quarter sharp, Demisharp
| Quarter sharp
|
|
| This glyph represents a raising by [[33/32]], replacing its Helmholtz-Ellis notation equivalent, [[File:Heji41.svg|48x48px]].
|-
|-
| colspan="3" | todo: 8..10
| colspan="3" | todo: 8..10
|-
|-
| -11
| [[File:Heji11.svg|48x48px]][[File:Heji38.svg|48x48px]]
| [[File:Heji11.svg|48x48px]][[File:Heji38.svg|48x48px]]
| -11
| Flat +Septimal comma
| Flat +Septimal comma
|-
|-
| +11
| [[File:Heji25.svg|48x48px]][[File:Heji37.svg|48x48px]]
| [[File:Heji25.svg|48x48px]][[File:Heji37.svg|48x48px]]
| +11
| Sharp –Septimal comma
| Sharp –Septimal comma
|-
|-
| -12
| [[File:Heji12.svg|48x48px]]
| [[File:Heji12.svg|48x48px]]
| -12
| Flat +Syntonic comma
| Flat +Syntonic comma
|-
|-
| +12
| [[File:Heji24.svg|48x48px]]
| [[File:Heji24.svg|48x48px]]
| +12
| Sharp –Syntonic comma
| Sharp –Syntonic comma
|-
|-
| colspan="3" | todo: 13, 14
| colspan="3" | todo: 13, 14
|-
|-
| -15
| [[File:Heji11.svg|48x48px]]
| [[File:Heji11.svg|48x48px]]
| -15
| Flat
| Flat
|-
|-
| +15
| [[File:Heji25.svg|48x48px]]
| [[File:Heji25.svg|48x48px]]
| +15
| Sharp
| Sharp
|-
|-
| colspan="3" | todo: 16, 17
| colspan="3" | todo: 16, 17
|-
|-
| -18
| [[File:Heji10.svg|48x48px]]
| [[File:Heji10.svg|48x48px]]
| -18
| Flat –Syntonic comma
| Flat –Syntonic comma
|-
|-
| +18
| [[File:Heji26.svg|48x48px]]
| [[File:Heji26.svg|48x48px]]
| +18
| Sharp +Syntonic comma
| Sharp +Syntonic comma
|-
|-
| -19
| [[File:Heji11.svg|48x48px]][[File:Heji37.svg|48x48px]]
| [[File:Heji11.svg|48x48px]][[File:Heji37.svg|48x48px]]
| -19
| Flat –Septimal comma
| Flat –Septimal comma
|-
|-
| +19
| [[File:Heji25.svg|48x48px]][[File:Heji38.svg|48x48px]]
| [[File:Heji25.svg|48x48px]][[File:Heji38.svg|48x48px]]
| +19
| Sharp +Septimal comma
| Sharp +Septimal comma
|-
|-
| colspan="3" | todo: 20..26
| colspan="3" | todo: 20..26
|-
|-
| -27
| [[File:Heji5.svg|48x48px]]
| [[File:Heji5.svg|48x48px]]
| -27
| Double flat +Syntonic comma
| Double flat +Syntonic comma
|-
|-
| +27
| [[File:Heji31.svg|48x48px]]
| [[File:Heji31.svg|48x48px]]
| +27
| Double sharp –Syntonic comma
| Double sharp –Syntonic comma
|-
|-
| colspan="3" | todo: 31, 32
| colspan="3" | todo: 31, 32
|-
|-
| -30
| [[File:Heji4.svg|48x48px]]
| [[File:Heji4.svg|48x48px]]
| -30
| Double flat
| Double flat
|-
|-
| +30
| [[File:Heji32.svg|48x48px]]
| [[File:Heji32.svg|48x48px]]
| +30
| Double sharp
| Double sharp
|}
|}
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