AW.: consistency

stearns@capecod.net:

<< which would seem to be
entirely consistent in 5e despite the fact that 81/64 and 4/3 are both
approximated by 2/5, and that 243/128 and 2/1 are both approximated by
5/5... >>

You're right on here. In central Javanese Slendro -- which is close to 5tet
and where the pitches within an octave are numbered 12356 with "fifths"
ordered 1-5-2-6-3-1 -- players use pitch three as both the "fifth" above
pitch six and the "fifth" below pitch one, thus compounding the 81/64 and 4/3
implications. The gongsmith has to temper his tuning so that both functions
can be covered within reasonable tolerance, while the players of instruments
without fixed pitches find a variety of ways to nuance the relationship. In
_gender_ playing, the 6-3 interval is less critical in that it does not
function as _seleh_ (the "goal" interval of a gender pattern), so that there
may be a bias in the tuning towards the the 3-1 interval.

A characteristic by-product of this tempered pythagorean cycle of five is the
introduction of melodic steps close to the septimal intervals 8/7 and 7/6.