Diasem: Difference between revisions

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=== Negative-s blackdye ===

Consider right-hand diasem, fixing a choice of positive step sizes. There exists a way of superimposing a left-hand diasem mode on the right hand diasem so that the right-hand diasem and the left-hand diasem overlap in 8 notes, yielding a scale of 10 notes, possibly after changing the mode of right-hand diasem. For example, superimposing LMLSLMLSL (RH Aeolian) and LMLSLMLLS (LH Dark Aeolian) gives LMLSLMLS(L-S)S (in fifth-based notation on C: C D Ebv Fv F G Abv Bbv Bb Cv C, where v denotes lowering by s). Note that the union is achiral~~; we have removed the chirality of diasem by taking the "best" possible union of LH and RH diasem~~. This new scale has two chains of perfect fifths each spanning 5 notes:

Consider right-hand diasem, fixing a choice of positive step sizes. There exists a way of superimposing a left-hand diasem mode on the right hand diasem so that the right-hand diasem and the left-hand diasem overlap in 8 notes, yielding a scale of 10 notes, possibly after changing the mode of right-hand diasem. For example, superimposing LMLSLMLSL (RH Aeolian) and LMLSLMLLS (LH Dark Aeolian) gives LMLSLMLS(L-S)S (in fifth-based notation on C: C D Ebv Fv F G Abv Bbv Bb Cv C, where v denotes lowering by s). Note that the union is achiral. This new scale has two chains of perfect fifths each spanning 5 notes:

Chain 1: '''Bb''' (L-S)SLMLS '''F''' LMLS(L-S)S '''C''' LMLSL '''G''' MLS(L-S)SL '''D'''

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 === Negative-s blackdye ===
-Consider right-hand diasem, fixing a choice of positive step sizes. There exists a way of superimposing a left-hand diasem mode on the right hand diasem so that the right-hand diasem and the left-hand diasem overlap in 8 notes, yielding a scale of 10 notes, possibly after changing the mode of right-hand diasem. For example, superimposing LMLSLMLSL (RH Aeolian) and LMLSLMLLS (LH Dark Aeolian) gives LMLSLMLS(L-S)S (in fifth-based notation on C: C D Ebv Fv F G Abv Bbv Bb Cv C, where v denotes lowering by s). Note that the union is achiral; we have removed the chirality of diasem by taking the "best" possible union of LH and RH diasem. This new scale has two chains of perfect fifths each spanning 5 notes:
+Consider right-hand diasem, fixing a choice of positive step sizes. There exists a way of superimposing a left-hand diasem mode on the right hand diasem so that the right-hand diasem and the left-hand diasem overlap in 8 notes, yielding a scale of 10 notes, possibly after changing the mode of right-hand diasem. For example, superimposing LMLSLMLSL (RH Aeolian) and LMLSLMLLS (LH Dark Aeolian) gives LMLSLMLS(L-S)S (in fifth-based notation on C: C D Ebv Fv F G Abv Bbv Bb Cv C, where v denotes lowering by s). Note that the union is achiral. This new scale has two chains of perfect fifths each spanning 5 notes:
 Chain 1: '''Bb''' (L-S)SLMLS '''F''' LMLS(L-S)S '''C''' LMLSL '''G''' MLS(L-S)SL '''D'''