Hemipyth: Difference between revisions

Line 78:

The Pythagorean 2.3 part of hemipyth can be notated using traditional notation where octaves represent multiples of 2/1, chain of fifths denotes multiples of 3/2, the sharp sign is equal to 2187/2048 etc.

A prototypical 5L 2s 5|1 (Ionian) scale would be spelled C, D, E, F, G, A, B, (C).

=== Neutral thirds ===

The 2.√(3/2) part can be notated using [[neutral chain-of-fifths notation]]. This introduces a neutral interval quality between major and minor, semisharps (a.k.a. demisharps) etc.

A representative 3L 4s 4|2 (kleeth) scale would be spelled C, D, E{{demiflat2}}, F, G, A{{demiflat2}}, B{{demiflat2}}, (C).

=== Semioctaves ===

In traditional notation the octave spans 7 diasteps which means that it splits into two interordinal 3½ diasteps or two perfect 4.5ths if we wish to remain backwards compatible with the 1-indexed traditional notation.

Line 112:

Line 114:

Where to put the greek notes on a staff is still being decided. Probably on the same lines as traditional notes but with distinct noteheads. E.g. a middle η would look like a middle C, but with an upwards pointing triangular notehead.

A representative 10L 2s 10|0(2) scale would be spelled C, η, D, α, E, β, γ, G, δ, A, ε, B, (C).

=== Semifourths ===

Luckily we don't need to introduce any more generalizations to the notation to indicate √(4/3). It's a neutral 2½ or a α{{demiflat2}} (alp semiflat) w.r.t middle C.

@@ Line 78: / Line 78: @@
 The Pythagorean 2.3 part of hemipyth can be notated using traditional notation where octaves represent multiples of 2/1, chain of fifths denotes multiples of 3/2, the sharp sign is equal to 2187/2048 etc.
+A prototypical 5L 2s 5|1 (Ionian) scale would be spelled C, D, E, F, G, A, B, (C).
 === Neutral thirds ===
 The 2.√(3/2) part can be notated using [[neutral chain-of-fifths notation]]. This introduces a neutral interval quality between major and minor, semisharps (a.k.a. demisharps) etc.
+A representative 3L 4s 4|2 (kleeth) scale would be spelled C, D, E{{demiflat2}}, F, G, A{{demiflat2}}, B{{demiflat2}}, (C).
 === Semioctaves ===
 In traditional notation the octave spans 7 diasteps which means that it splits into two interordinal 3½ diasteps or two perfect 4.5ths if we wish to remain backwards compatible with the 1-indexed traditional notation.
@@ Line 112: / Line 114: @@
 Where to put the greek notes on a staff is still being decided. Probably on the same lines as traditional notes but with distinct noteheads. E.g. a middle η would look like a middle C, but with an upwards pointing triangular notehead.
+A representative 10L 2s 10|0(2) scale would be spelled C, η, D, α, E, β, γ, G, δ, A, ε, B, (C).
 === Semifourths ===
 Luckily we don't need to introduce any more generalizations to the notation to indicate √(4/3). It's a neutral 2½ or a α{{demiflat2}} (alp semiflat) w.r.t middle C.