Below is a
5-limit
lattice-diagram
showing the mapping of
ratios
to
pitches.
The {3,5}
vector appears
under the letter-name, showing the exponents in the
-factorization
of the ratios, which in turn makes obvious their location
along the 2 axes of the lattice.
A E B F# C#
[-3 1]...[-2 1]...[-1 1]...[0 1]...[1 1]
40/27 10/9 5/3 5/4 15/8
| | | | |
| | | | |
F C G D A E
[-3 0]...[-2 0]...[-1 0]...[0 0]...[1 0]...[2 0]
32/27 16/9 4/3 1/1 3/2 9/8
JustMusic harmonic analysis:
Track 1 (melody)
Track 2 5 3 | 15 3 | 5 3 | 15 15 | 45 27 15
Track 3 1 5 | 3 5 | 1 5 | 3 3 | 5 45 3
Track 4 3 1 | 5 1 | 3 1 | 5 5 | 15 9
Track 5 1 1 | 1 1 | 1 1 | 1 1 | 1 5
--- --- ----- ----- ---- ---- ----- ---- ---- ------------
n0 31 | 3-1 31 | n0 31 | 3-1 3-3 | 3-2 (3-1)
-
updated:
2002.10.26 -- score graphic and lattice diagram added
2002.3.23 -- page created with only JustMusic harmonic analysis
