159edo/Notation: Difference between revisions
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[[File:159edo-accidentals.png|320px|thumb|Accidentals in the [[9/8]] space. Reworked version.]] | [[File:159edo-accidentals.png|320px|thumb|Accidentals in the [[9/8]] space. Reworked version.]] | ||
= Helmholtz-Ellis-based notation = | == Helmholtz-Ellis-based notation == | ||
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, with mainstream quartertone accidentals being used to represent them. This is because undecimal quartertones are actually useful in modulation to keys that are not on the same circle of fifths while being simultaneously within an unnoticeable comma's distance from the quartertone of [[24edo]], which many musicians outside the microtonal community proper have at least a passing familiarity with. It should be noted that most of the symbols listed in this section derive their functions from JI. In addition, it should be noted that accidentals are not just modifiers for single notes, but signs that indicate the change of both the tonal and modal base, and can thus appear in key signatures. | 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, with mainstream quartertone accidentals being used to represent them. This is because undecimal quartertones are actually useful in modulation to keys that are not on the same circle of fifths while being simultaneously within an unnoticeable comma's distance from the quartertone of [[24edo]], which many musicians outside the microtonal community proper have at least a passing familiarity with. It should be noted that most of the symbols listed in this section derive their functions from JI. In addition, it should be noted that accidentals are not just modifiers for single notes, but signs that indicate the change of both the tonal and modal base, and can thus appear in key signatures. | ||
== Available base glyphs == | === Available base glyphs === | ||
=== Quartertones and Syntonic commas === | ==== Quartertones and Syntonic commas ==== | ||
As in [[HEJI]], classic accidentals and arrows for syntonic commas are combined. Beyond HEJI, quartertone accidentals are also used, being combined with syntonic comma arrows in the same way. | As in [[HEJI]], classic accidentals and arrows for syntonic commas are combined. Beyond HEJI, quartertone accidentals are also used, being combined with syntonic comma arrows in the same way. | ||
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=== Septimal commas and darts === | ==== Septimal commas and darts ==== | ||
Glyphs for septimal commas and darts are also used, but are generally not combined with each other except in certain musical contexts such as modulation. That said, if this system were to be extended to the 13-limit, the septimal comma glyphs would likely be combined with the 13-limit glyphs due to both 7-limit and 13-limit intervals having close connections to trientones (one third tones). | Glyphs for septimal commas and darts are also used, but are generally not combined with each other except in certain musical contexts such as modulation. That said, if this system were to be extended to the 13-limit, the septimal comma glyphs would likely be combined with the 13-limit glyphs due to both 7-limit and 13-limit intervals having close connections to trientones (one third tones). | ||
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== Combined accidentals == | === Combined accidentals === | ||
The following table illustrates modification of a given tone by accidentals up to 30 steps of 159edo. 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 primary and secondary glyphs usually reflect different intervals in Just Intonation. For reference, the just whole tone interval, [[9/8]], is mapped to 27 steps of 159 edo (or 9 steps of [[53edo]]) which is (27*1200/159=) 203.77 cents (0.2 cents flat). | The following table illustrates modification of a given tone by accidentals up to 30 steps of 159edo. 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 primary and secondary glyphs usually reflect different intervals in Just Intonation. For reference, the just whole tone interval, [[9/8]], is mapped to 27 steps of 159 edo (or 9 steps of [[53edo]]) which is (27*1200/159=) 203.77 cents (0.2 cents flat). | ||
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= Ups-and-Downs-based notation = | == Ups-and-Downs-based notation == | ||
Another system proposed by [[User:TallKite|TallKite]] involves simpler notation, with as few extra accidental pairs as possible. While one could do with only one extra pair, only ups and downs (that is, darts), but one would need at least septuple ups, and in practice octuple or more, rendering such a system impractical, so as a result, this system has two extra pairs of accidentals. | Another system proposed by [[User:TallKite|TallKite]] involves simpler notation, with as few extra accidental pairs as possible. While one could do with only one extra pair, only ups and downs (that is, darts), but one would need at least septuple ups, and in practice octuple or more, rendering such a system impractical, so as a result, this system has two extra pairs of accidentals. | ||