Neither Fish Nor Fowl

Charles Shere has placed a very good article by Douglas Leedy on the midtone (or three-quarter or neutral second) interval online (go here for Charles's comment and link to the article.) My enthusiasm for Leedy's work should be well-known to readers of this page. He is a fascinating scholar and a composer of some of the best music I know.

I have a small difference here with Leedy over whether Javanese pélog actually uses a three-quarter tone interval (it does, but only as a compromise or temperament, in the instruments of fixed pitch, between two tones which voices and the rebab distinguish depending upon the mode or pathet being played). Leedy asks why the midtone, ubiquitous in musics of the southern half of the Mediterranean, is all but missing from music in the European tradition: Would mid intervals be a commonplace of Western music today had Charles Martel failed to defeat the Muslim forces at Tours in 732-33, when European music was still an essentially monophonic art? and I believe that he is right on focusing upon the issue of a melodic versus a contrapuntal, harmonic music. I suspect that eliminating such intervals, a loss in melodic complexity, representing a level of intervallic distinction and corresponding to harmonic structures found in a region of the harmonic series beyond the tenth partial or so, was — for better or worse — a price paid for the vertical complexity found in European music.

[For what it's worth, AFAIC the greatest mystery in the history of musical materials is the apparent disappearance of the Greek enharmonic genus with the semitone-sized pyknon devided into two smaller intervals. The evidence we have of the actual use of the enharmonic is limited; we cannot say for certain, for example, if the successive microtones were used melodically in succession or were used only as alternative values for a single position in an anhemitonic trichord.]

[For what it's also worth: If someone had in mind the project of a system of counterpoint and harmony for voices and conventional instrumental timbres using intervals including midtones AND having consonance/dissonance distinctions like those found in the European traditions, that is to say, a tonal music with a very different interval vocabulary, I strongly suspect that many questions of consonance and dissonance will be register dependent. An 11:9 netral third, for example, may be an acceptable consonance so long as it is voiced high enough in register to support a plausible position in an implied, potentially audible, harmonic series. This is rather Rameau-vian, but why not?]