The Mudcat Café TM
Thread #137393   Message #3142548
Posted By: Jack Campin
26-Apr-11 - 06:46 AM
Thread Name: Easy way to draw a circle of 5ths
Subject: RE: Easy way to draw a circle of 5ths
The Reid Musical Instrument Museum in Edinburgh has a 19th century boxwood slide rule on display specially made for calculating pitches in just intonation, meantone and equal temperament. I haven't made one yet, but I have an idea in my head for how to make something much more sophisticated.

What I would like to do is compare just intonation, equal temperament, and a whole bunch of other tuning schemes, like 19-tone equal temperament (approximates one of the Baroque meantone schemes), 31-tone ET (another Renaissance/Baroque scheme), 53-tone equal temperament (the system used in Turkish art music theory), the 22-shruti unequal temperament systems of Indian music, the 5-tone equally tempered Indonesian slendro scale, Harry Partch's 41-tone unequal temperament and so on.

Raw material: the transparent uncoated disks you get as the cover for packs of CDRs.

Mark using a protractor, by geometric constructions like josepp's, or (for the tricky ones like 53-tone ET) take two disks, guess, rotate, interpolate, copy, guess again... bisection interpolation converges very fast, so this should only take about three go-rounds to produce 53 equal divisions of the circle to within the limit of human visual perception.

Stack the disks up and you have a calculator that answers questions like: roughly how flat or sharp you have to play when trying to play in a 7-tone equally tempered African scale using an equally tempered Western flute and microtonally tweaked fingerings?