Diachrome: Difference between revisions

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* 5sR: LmsLsLsLmsLs

* 5sC: LsLsLmsLsLsm

5sL and 5sR are [[chiral]] pairs, and 5sC is achiral. The three chiralities are also determined by the number of ms and sm substrings they have.

''Diachrome'' is named from ''diatonic'' and ''chromatic'' for the [[5L 7s|5L7s]] and [[7L 5s|7L5s]] children of [[5L2s]] that the L=m and m=s tunings reflect.

''Diachrome'' is named from ''diatonic'' and ''chromatic'' for the [[5L 7s|5L7s]] and [[7L 5s|7L5s]] children of [[5L2s]] that the L = m and m = s tunings reflect.

== ~~Lattice structure~~ ==

== Structure ==

5sC has two chains of "fifths" (the 7-step 3L + m + 3s) both having 6 notes and offset by 3L + m + 2s. The interval L + s is thus reached by stacking two fifths and reducing, and m is reached by stacking -5 fifths and reducing.

5sC has two chains of "fifths" (the 7-step 3L + m + 3s) both having 6 notes and offset by 3L + m + 2s. The interval L + s is thus reached by stacking two fifths and reducing, and m is reached by stacking -5 fifths and reducing. The three leftmost notes of the lower chain (the one not offset by 3L + m + 2s) are joined to the three rightmost notes of the upper chain by 2L + m. 5sL (resp. 5sR) similarly has two chains of fifths, but the lower chain has 7 (resp. 5) notes and the upper chain 5 (resp. 7) notes.

The three leftmost notes of the lower chain (the one not offset by 3L + m + 2s) are joined to the three rightmost notes of the upper chain by 2L + m. 5sL (resp. 5sR) similarly has two chains of fifths, but the lower chain has 7 (resp. 5) notes and the upper chain 5 (resp. 7) notes.

In terms of [[MOS substitution]], 5sL = subst('''XXXXXXmXXXXm''', '''X''', '''Ls'''), 5sL = subst('''XXXXXXmXXXXm''', '''X''', '''sL'''), and 5sC = subst('''XXXXXmXXXXXm''', '''X''', '''Ls''').

== Diachrome in edos ==

Diachrome is available in good RTT edos that have quasi-just or Parapyth fifths.

@@ Line 3: / Line 3: @@
 * 5sR: LmsLsLsLmsLs
 * 5sC: LsLsLmsLsLsm
 sL and 5sR are [[chiral]] pairs, and 5sC is achiral. The three chiralities are also determined by the number of ms and sm substrings they have.
-''Diachrome'' is named from ''diatonic'' and ''chromatic'' for the [[5L 7s|5L7s]] and [[7L 5s|7L5s]] children of [[5L2s]] that the L=m and m=s tunings reflect.
+''Diachrome'' is named from ''diatonic'' and ''chromatic'' for the [[5L 7s|5L7s]] and [[7L 5s|7L5s]] children of [[5L2s]] that the L = m and m = s tunings reflect.
-== Lattice structure ==
+== Structure ==
-sC has two chains of "fifths" (the 7-step 3L + m + 3s) both having 6 notes and offset by 3L + m + 2s. The interval L + s is thus reached by stacking two fifths and reducing, and m is reached by stacking -5 fifths and reducing.
+sC has two chains of "fifths" (the 7-step 3L + m + 3s) both having 6 notes and offset by 3L + m + 2s. The interval L + s is thus reached by stacking two fifths and reducing, and m is reached by stacking -5 fifths and reducing. The three leftmost notes of the lower chain (the one not offset by 3L + m + 2s) are joined to the three rightmost notes of the upper chain by 2L + m. 5sL (resp. 5sR) similarly has two chains of fifths, but the lower chain has 7 (resp. 5) notes and the upper chain 5 (resp. 7) notes.
-The three leftmost notes of the lower chain (the one not offset by 3L + m + 2s) are joined to the three rightmost notes of the upper chain by 2L + m. 5sL (resp. 5sR) similarly has two chains of fifths, but the lower chain has 7 (resp. 5) notes and the upper chain 5 (resp. 7) notes.
+In terms of [[MOS substitution]], 5sL = subst('''XXXXXXmXXXXm''', '''X''', '''Ls'''), 5sL = subst('''XXXXXXmXXXXm''', '''X''', '''sL'''), and 5sC = subst('''XXXXXmXXXXXm''', '''X''', '''Ls''').
 == Diachrome in edos ==
 Diachrome is available in good RTT edos that have quasi-just or Parapyth fifths.