Thu Nov 15 22:53:40 EST 2012

Just intonation

6:5 = Ts (minor third)
5:4 = Tt (major third)
4:3 = Tts (perfect fourth)
3:2 = TTts (perfect fifth)
2:1 = TTTttss (octave)

Melodic distance between these are

16:15 = s (Semitone)
10:9 = t (Minor tone)
9:8 = T (Major tone)

The ratios of these 3 intervals are not essential as they are not
themselves used in harmony. They are the "cruft" that's left over as 3
different "adaptor ratios" once a grid is made with the major third
and fifth and their inversions.  These intervals are only used in
melody, where only their relative proximity is important (next to
their integration in the harmonic background).

Looking at the major triad: 1, 5:4, 3:2 gives the harmonics 4 5 6 of
the 2 octave down subjarmonic.  This is why a major chord is so
"heavy": it suggests a subharmonic of the tonal.  
A full harmonic
series misses only the octave (2) and a fifth above that (3).

The minor triad: 1, 6:5, 3:2 suggests a common subharmonic at :10
which s 3 octaves and a major third down.  Not counting the octaves,
this is a major third down, which will essentially give back a major
triad with a 7th stuck at the end.  This is why a minor triad resolves
to a major triad a major third down, making that "suggested" tone more

[1] http://en.wikipedia.org/wiki/Just_intonation