Hemipyth: Difference between revisions

Line 131:

These particular definitions were chosen so that C, D, φ, χ, F, G, A, ψ, ω, (C) becomes the 6|2 (Stellerian) mode, all notated without accidentals.

== Musical significance ==

The semioctave sound is very familiar to westerners from repeated exposure of music tempered to 12-tone equal. It can provide a familiar dissonance in an otherwise xenharmonic piece.

The neutral third is featured in [[Arabic, Turkish, Persian music]] etc.

Close approximations to the semifourth can be found in many near-equal pentatonic scales around the world.

Their wide availability in edos makes it worthwhile to become familiar with their sound without having to make further interpretations of their meaning using fractions involving higher prime numbers.

=== Theoretical significance ===

The semioctave is always tuned pure when the octave is tuned pure.

The neutral third receives only half of the tuning damage of the fifth so it has a strong character even if the fifth isn't tuned very pure. The irrational nature of √(3/2) also makes it more tolerant of imprecise tuning.

The same goes for the semifourth. A poorly tuned ~4/3 still results in a decent ~√(4/3) (assuming it's featured in the tuning in the first place).

== Temperament interpretations ==

Under [[ploidacot]] classification diploid temperaments feature ~√2, dicot temperaments have ~√(3/2) and alpha-dicot temperaments feature ~√(4/3) (by virtue of having a ~√3).

Full hemipyth support is indicated by "diploid dicot". Examples include:

{| class="wikitable"

|+ Higher-prime interpretations of hemipyth intervals

|-

! Temperament !! ~√2 !! ~√(3/2) !! ~√(4/3)

|-

| [[decimal]] || ~7/5 || ~5/4 || ~7/6

|-

| [[sruti]] || ~45/32 || ~175/144 || ~81/70

|}

@@ Line 131: / Line 131: @@
 These particular definitions were chosen so that C, D, φ, χ, F, G, A, ψ, ω, (C) becomes the 6|2 (Stellerian) mode, all notated without accidentals.
+== Musical significance ==
+The semioctave sound is very familiar to westerners from repeated exposure of music tempered to 12-tone equal. It can provide a familiar dissonance in an otherwise xenharmonic piece.
+The neutral third is featured in [[Arabic, Turkish, Persian music]] etc.
+Close approximations to the semifourth can be found in many near-equal pentatonic scales around the world.
+Their wide availability in edos makes it worthwhile to become familiar with their sound without having to make further interpretations of their meaning using fractions involving higher prime numbers.
+=== Theoretical significance ===
+The semioctave is always tuned pure when the octave is tuned pure.
+The neutral third receives only half of the tuning damage of the fifth so it has a strong character even if the fifth isn't tuned very pure. The irrational nature of √(3/2) also makes it more tolerant of imprecise tuning.
+The same goes for the semifourth. A poorly tuned ~4/3 still results in a decent ~√(4/3) (assuming it's featured in the tuning in the first place).
+== Temperament interpretations ==
+Under [[ploidacot]] classification diploid temperaments feature ~√2, dicot temperaments have ~√(3/2) and alpha-dicot temperaments feature ~√(4/3) (by virtue of having a ~√3).
+Full hemipyth support is indicated by "diploid dicot". Examples include:
+{| class="wikitable"
+|+ Higher-prime interpretations of hemipyth intervals
+|-
+! Temperament !! ~√2 !! ~√(3/2) !! ~√(4/3)
+|-
+| [[decimal]] || ~7/5 || ~5/4 || ~7/6
+|-
+| [[sruti]] || ~45/32 || ~175/144 || ~81/70
+|}