Diachrome: Difference between revisions

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''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.

== Structure ==

5sC has two chains of "fifths" 3L + m + 3s both having 6 notes and offset by 3L + m + 2s. 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.

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.

== Temperament interpretations ==

Diachrome is most accurate to JI in tunings that have quasi-just or Parapyth fifths. In both interpretations below, L + s = 9/8, and m = 256/243.

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 ''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.
 == Structure ==
-sC has two chains of "fifths" 3L + m + 3s both having 6 notes and offset by 3L + m + 2s. 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.
+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.
 == Temperament interpretations ==
 Diachrome is most accurate to JI in tunings that have quasi-just or Parapyth fifths. In both interpretations below, L + s = 9/8, and m =  256/243.