Owner`s manual

48
CHAPTER 6 -
Appendices
CHAPTER 6 -
6.1.7
31 Tone Equal Temperament
Many people consider 31root2 to offer the best compromise towards just intonation in an
equal temperament, but it can get very tricky to keep track of the intervals.
6.1.8
Pythagorean C
One of the earliest tuning systems known from history, the Pythagorean scale is
constructed from an upward series of pure  fths (3/2) transposed down into a single
octave. The tuning works well for monophonic melodies against  fth drones, but has a
very narrow palate of good chords to choose from. .
C = 1/1 (261.625 Hz)
1/1 256/243 9/8 32/27 81/64 4/3 729/512 3/2 128/81 27/16
16/9 243/128
6.1.9
Just Intonation in A with 7-limit Tritone at D#
A rather vanilla 5-limit small interval JI, except for a single 7/5 tritone at D#, which offers
some nice possibilities for rotating around bluesy sevenths.
A = 1/1 (440 Hz)
1/1 16/15 9/8 6/5 5/4 7/5 3/2 8/5 5/3 9/5 15/8
6.1.10
3-5 Lattice in A
A pure 3 and 5-limit tuning which resolves to very symmetrical derived relationships
between notes. A = 1/1 (440 Hz)
1/1 16/15 10/9 6/5 5/4 4/3 64/45 3/2 8/5 5/3 16/9 15/8
6.1.11
3-7 Lattice in A
A pure 3 and 7-limit tuning which resolves to very symmetrical derived relationships
between notes. Some of the intervals are very close together, offering several choices for
the same nominal chords.
A= 1/1 (440 Hz)
1/1 9/8 8/7 7/6 9/7 21/16 4/3 3/2 32/21 12/7 7/4 63/32
6.1.12
Other Music 7-Limit Black Keys in C
Created by the group Other Music for their homemade gamelan, this offers a wide range
of interesting chords and modes.
C= 1/1 (261.625 Hz)
1/1 15/14 9/8 7/6 5/4 4/3 7/5 3/2 14/9 5/3 7/4 15/8