User Manual

131
Pro 3 User’s Guide
Appendix E: Alternative Tunings
5. 1/4 Tone Equal Temperament
24 notes per octave, equally spaced 24root2 intervals. Mexican composer
Julian Carillo used this for custom-built pianos in the early 20th century.
6. 19 Tone Equal Temperament
19 notes per octave (19root2) offering better thirds than 12 ET, a better
overall compromise if you can gure out the keyboard patterns.
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.
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 melo-
dies 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
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
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
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