[TCML] on rotary gaps and tone wheels

[Jim Lux <jimlux@xxxxxxxxxxxxx>]

Just in case someone wants to think about it..

Here are the ratios for just intonation (for some of the "black keys" 
various authors have different ratios.. usually larger numerator and 
denominator).  And yes, I do know that Bb and A# are not actually the 
same note, but I'm writing it down that way for convenience. I played 
clarinet as a child, so I naturally think of it as Bb rather than A#, 
because the instrument is in the key of F.


C	2:1
B	15:8
 Bb		9:5
A	5:3
 G#		8:5
G	3:2
 F#		7:5
F	4:3
E	5:4
 Eb		6:5
D	9:8
 C#		16:15
C	1:1

You could use this to figure out how many electrodes on the rotor and 
how many fixed electrodes.. For instance,  say you have 2 fixed 
electrodes and 4 on the rotor you'd get 4 pulses/revolution.  If you 
added a pair of electrodes to the rotor you'd get 6 pulses/rev, or a 
ratio of 3/2 to the first case.. so you can make C and G (a fifth)

You could also do it by gearing different speeds.. It looks like 1/5th 
is a pretty useful ratio for a lot of the "black keys".


An interesting question would be what the minimum number of rotors (with 
a fixed number of electrodes) you could use, with changing the number of 
fixed electrodes (which are easier to switch).  Or, whether you can do 
it with a bunch of rotors on a common shaft.

This would tend to create a just intonation as opposed to a equal 
tempered scale.  That is you'd have a TC that has a distinct key, like a 
woodwind or brass instrument (other than a trombone.. that's the 
variable speed drive on the rotary gap).



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