Reply to skyler S.

>Hello all ye tuning wizards.
>I'd like to ask what your definition of the Diatonic set (scale) is,
>assuming you would consider it to be
>independant of a specific tuning scheme.

>Thanks!

One approach to answering this question is found in Easley Blackwood's
book, "The Structure of Recognizable Diatonic Tunings." Essentially he
focuses on tunings where there are two distinct step sizes, Large and
Small, in the pattern LLSLLLS (which can be rotated at will). There have
been some attempts to generalize the properties of the diatonic scale so
as to include the pentatonic and point the way towards new microtonal
scales. My paper in Xenharmonikon 17 (a version is at
http://www-math.cudenver.edu/~jstarret/22ALL.pdf) contains my own
attempt (leading to 10-note scales in 22-tone equal temperament) and a
critique of other attempts at generalizing diatonicity. My approach
looks at both melodic and harmonic criteria as well as tonality -- the
latter exemplified by the predominance of the major and minor modes over
the other five modes in music since the Baroque.

-Paul