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pentatonic scales

Dear list,

I think I can clear this one up at least (in Ed's absence)...

The pentatonic scale is found all over the world (i.e. has been
discovered/invented by many cultures), because it is simple and permits
any note combination in polyphonic music without causing disonance
(i.e. roughness). It does not normally have variations in the scale
steps. That only happens when you approximate it on a diatonically
tuned instrument (for instance, by using the black notes on a piano).
It would normally be equal-tempered with a ratio of 2^1/5 between
successive notes. The reason it never gives dissonance is that 2^1/5,
2^2/5, 2^3/5 and 2^4/5 all approximate simple number ratios, resulting
in maximal conincidence of harmonic frequencies in simultaneous notes.
The same happens for only a subset of powers of 2^1/12 (diatonic scale).

Further reading can be found in Ed Burns' chapter in "The Psychology
of Music", Plomp and Levelt's (1965) JASA paper on dissonance and