Hemipyth: Difference between revisions
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Simple hemipyth chords can be plucked out of the square root of the Pythagorean segment <math>1:</math> <math>\sqrt{2}:</math> <math>\sqrt{3}:2:</math> <math>\sqrt{6}:</math> <math>\sqrt{8}:3:</math> <math>\sqrt{12}:4:</math> <math>\sqrt{18}:</math> <math>\sqrt{24}:</math> <math>\sqrt{27}:</math> <math>\sqrt{32}:6:</math> <math>\sqrt{48}:</math> <math>\sqrt{54}:8:</math> <math>\sqrt{72}:9:</math> <math>\sqrt{96}:</math> <math>\sqrt{108}:</math> <math>\sqrt{128}:</math> <math>\ldots</math> e.g. <math>2:\sqrt{6}:3</math> is a neutral chord where spicy tension can be added by including the semioctave for <math>2:\sqrt{6}:\sqrt{8}:3</math> with no increase in complexity as far as the generator of the subgroup is concerned. | Simple hemipyth chords can be plucked out of the square root of the Pythagorean segment <math>1:</math> <math>\sqrt{2}:</math> <math>\sqrt{3}:2:</math> <math>\sqrt{6}:</math> <math>\sqrt{8}:3:</math> <math>\sqrt{12}:4:</math> <math>\sqrt{18}:</math> <math>\sqrt{24}:</math> <math>\sqrt{27}:</math> <math>\sqrt{32}:6:</math> <math>\sqrt{48}:</math> <math>\sqrt{54}:8:</math> <math>\sqrt{72}:9:</math> <math>\sqrt{96}:</math> <math>\sqrt{108}:</math> <math>\sqrt{128}:</math> <math>\ldots</math> e.g. <math>2:\sqrt{6}:3</math> is a neutral chord where spicy tension can be added by including the semioctave for <math>2:\sqrt{6}:\sqrt{8}:3</math> with no increase in complexity as far as the generator of the subgroup is concerned. | ||
Here is a [https:// | Here is a [https://luphoria.com/xenpaper/#%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 == | == Musical significance == | ||