45/32

I tune my fretless acoustic guitar to: 1/1 5/4 3/2 15/8 9/8 45/32...sounds killer...Hstick
myspace.com/microstick

Hi there,

I'm not really following the details of this discussion, but one little point may be of interest perhaps in clarifying the area of discourse.

> My working definition is that any single interval, for which someone
can reliably hear beating when it is tempered (given some instrumental
timbre consisting of the harmonic series), and which one can tune by
ear through elimination of beats, can be meaningfully called pure.

Just the observation that typically there isn't just one set of beats but lots of simultaneous beats at different frequencies, which may merge together to just give a sensation of "roughness" but if one listens to them in long sustained chords one may be able to distinguish them and indeed count the beats for each frequency, getting a list of several different numbers for the numbers of beats rather than just one number.

So you could tune an interval to be beatless at one frequency while simultaneously it has strong beats at another. In fact, no reason why one has to always tune the most obvious beats to be beatless. If one wanted to for some reason one could tune one of the weaker beating frequencies to be beatless.

I don't know if one could tune a pure 45/32 that way - seems rather high in the harnonic series. But some people can hear separate individual frequencies in a sound more easily than others, e.g. bell tuners have to develop this ability acutely if they tune bells by ear - and by extension it seems at least theoretically, there may be some with truly exceptional abilities to discern the pitches who can hear the beats for the 45th harmonic if present, because it is at a different frequency from any other beating partials.

It's a bit tangential to the main discussion but perhaps it may help clear up something or other?

Robert