Hemipyth: Difference between revisions

Line 147:

Or equivalently with semiquartal nicknames:

C, η, D, φ, E{{demiflat2}}, χ, F{{demisharp2}}, γ, G, δ, A{{demiflat2}}, ψ, B{{demiflat2}}, ω, (C)

The 4L 6s 4|4(2) scale (called Pacific), can be spelled like so:

C, η, α{{demiflat2}}, E{{demiflat2}}, F, γ, G, A{{demiflat2}}, ε{{demiflat2}}, ζ, C

[[User:2^67-1|Cole]] prefers to spell it on D, giving:

D, α, β{{demiflat2}}, F{{demisharp2}}, G, δ, A, B{{demiflat2}}, ζ{{demisharp2}}, η, D

Simple hemipyth chords can be plucked out of the square root of the Pythagorean segment 1:√2:√3:2:√6:√8:3:√12:4:√18:√24:√27:√32:6:√48:√54:8:√72:9:√96:√108:√128:... e.g. 2:√6:3 is a neutral chord where spicy tension can be added by including the semioctave for 2:√6:√8:3 with no increase in complexity as far as the generator of the subgroup is concerned.

Here is a [https://xenpaper.com/#%7B58edo%7D%0A%23_5L_2s_5%7C1_(Ionian)%0A0_10_20_24_34_44_54_58_54_44_34_24_20_10_0%0A....%0A%23_3L_4s_4%7C2_(kleeth)%0A0_10_17_24_34_41_51_58_51_41_34_24_17_10_0%0A....%0A%23_10L_2s_10%7C0(2)%0A0_5_10_15_20_25_29_34_39_44_49_54_58_54_49_44_39_34_29_25_20_15_10_5_0%0A....%0A%23_5L_4s_6%7C2_(Stellerian)%0A0_10_12_22_24_34_44_46_56_58_56_46_44_34_24_22_12_10_0%0A....%0A%23_10L_4s_10%7C2(2)_(Squashed_Ionian)%0A0_5_10_12_17_22_27_29_34_39_41_46_51_56_58_56_51_46_41_39_34_29_27_22_17_12_10_5_0%0A....%0A%23_4L_6s_4%7C4(2)_(Pacific)%0A0_5_12_17_24_29_34_41_46_53_58_53_46_41_34_29_24_17_12_5_0 Xenpaper demo] of all five representative scales listed above.

== Musical significance ==

@@ Line 147: / Line 147: @@
 Or equivalently with semiquartal nicknames:
 C, η, D, φ, E{{demiflat2}}, χ, F{{demisharp2}}, γ, G, δ, A{{demiflat2}}, ψ, B{{demiflat2}}, ω, (C)
+The 4L 6s 4|4(2) scale (called Pacific), can be spelled like so:
+C, η, α{{demiflat2}}, E{{demiflat2}}, F, γ, G, A{{demiflat2}}, ε{{demiflat2}}, ζ, C
+[[User:2^67-1|Cole]] prefers to spell it on D, giving:
+D, α, β{{demiflat2}}, F{{demisharp2}}, G, δ, A, B{{demiflat2}}, ζ{{demisharp2}}, η, D
 Simple hemipyth chords can be plucked out of the square root of the Pythagorean segment 1:√2:√3:2:√6:√8:3:√12:4:√18:√24:√27:√32:6:√48:√54:8:√72:9:√96:√108:√128:... e.g. 2:√6:3 is a neutral chord where spicy tension can be added by including the semioctave for 2:√6:√8:3 with no increase in complexity as far as the generator of the subgroup is concerned.
+Here is a [https://xenpaper.com/#%7B58edo%7D%0A%23_5L_2s_5%7C1_(Ionian)%0A0_10_20_24_34_44_54_58_54_44_34_24_20_10_0%0A....%0A%23_3L_4s_4%7C2_(kleeth)%0A0_10_17_24_34_41_51_58_51_41_34_24_17_10_0%0A....%0A%23_10L_2s_10%7C0(2)%0A0_5_10_15_20_25_29_34_39_44_49_54_58_54_49_44_39_34_29_25_20_15_10_5_0%0A....%0A%23_5L_4s_6%7C2_(Stellerian)%0A0_10_12_22_24_34_44_46_56_58_56_46_44_34_24_22_12_10_0%0A....%0A%23_10L_4s_10%7C2(2)_(Squashed_Ionian)%0A0_5_10_12_17_22_27_29_34_39_41_46_51_56_58_56_51_46_41_39_34_29_27_22_17_12_10_5_0%0A....%0A%23_4L_6s_4%7C4(2)_(Pacific)%0A0_5_12_17_24_29_34_41_46_53_58_53_46_41_34_29_24_17_12_5_0 Xenpaper demo] of all five representative scales listed above.
 == Musical significance ==