The tuning in music is an excellent example of that the
human perceptive mechanism uses various multivalued systems
of information coding. The ambiguous intervals in  the Just
Intonation Set are the  second and the minor seventh and the
tritone (the relative  frequencies 10/9, 9/8, 8/7 and  7/4,
16/9, 18/10 and 45/32, 64/45, respectively). Pythagorean
Tuning is also 17-valued. In the present paper we find a
17-valued diatonic tone system which is a consequence of
the unique solution of a Diophantine equation describing the
basic acoustic relations among octave, perfect fifth and
major (minor) third. This system has properties of the Just
Intonation Set (it involves octave, perfect fifth, perfect
fourth, major third, minor third, major whole tone, minor
whole tone, diatonic semitone and chromatic semitone) and
also of Pythagorean Tuning. We bring applications of our
theory to superparticular ratios and partial   monounary
algebras.
