The diamond arrangement Tonality diamond

-



1 diamond arrangement

1.1 5-limit
1.2 7-limit
1.3 11-limit
1.4 15-limit





the diamond arrangement

partch arranged elements of tonality diamond in shape of rhombus, , subdivided (n+1)/4 smaller rhombuses. along upper left side of rhombus placed odd numbers 1 n, each reduced octave (divided minimum power of 2 such



1
≤
r
<
2


{\displaystyle 1\leq r<2}

). these intervals arranged in ascending order. along lower left side placed corresponding reciprocals, 1 1/n, reduced octave (here, multiplied minimum power of 2 such



1
≤
r
<
2


{\displaystyle 1\leq r<2}

). these placed in descending order. @ other locations placed product of diagonally upper- , lower-left intervals, reduced octave. gives elements of tonality diamond, repetition. diagonals sloping in 1 direction form otonalities , diagonals in other direction form utonalities. 1 of partch s instruments, diamond marimba, arranged according tonality diamond.


5-limit

this diamond contains 3 identities (1, 3, 5).


7-limit

this diamond contains 4 identities (1, 3, 5, 7).


11-limit

tonal basis of harry partch s tuning system: 11-limit tonality diamond



this diamond contains 6 identities (1, 3, 5, 7, 9, 11). harry partch used 11-limit tonality diamond, flipped 90 degrees.


15-limit

this diamond contains 8 identities (1, 3, 5, 7, 9, 11, 13, 15).



a lattice showing mapping of 15 limit diamond.







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