[sdiy] 1v/oct and other scales

[Paddock, Toby]

Richard Wentk wrote:
> At 12:08 24/11/2004 -0800, Toby Paddock wrote:
> 
> >Maybe it's as simple as converting a ratio to octaves, and multiplying
> that
> >by 1V?
> >oct= log(ratio)/log(2)        (either log or ln)
> >
> >1/1 -> 0V
> >2/1 -> 1V
> >3/2 -> log(3/2)/log(2) -> ~0.585V
> >
> >Or am I missing something?
> 
> You've got the maths right here, but you need a starting note as a
> reference. If you add your voltage to the starting voltage for the
> reference note you will indeed get a 3/2 interval between the two.
> 
> That's all there is to it.
> 
> But what do you want to do with this? Traditionally there are two and a
> half applications. One is configuring tracking oscillator banks for
> additive synthesis. The second is creating custom scales. The first is
> easy. You just dial in the voltage offset(s). In fact people tend to tune
> parallel oscillators to exact ratios anyway, as they sound more in tune
> than equal tempered ratios.
> 
> Building custom scales is rather harder, because you can potentially
> customise everything, including individual ratios for each note, number of
> notes per repeating subdivsion, and size of the repeating subdivision. (A
> repeating subdivision being usually, but not necessarily, an octave ratio
> of 2:1)

Well... I don't have a clear idea of what I want to do with this. I want to
try something other than equal temperament. And less than 12 notes per
octave would make it simpler. And maybe have a scale where you don't hit
"wrong" notes. And intervals based on whole number ratios look good on an
o-scope.

One thing I'm kind of thinking of would be where I have some control lines
that are individually changing state. Each line is assigned a ratio value,
like 3/2, 4/3, 2/1..., and the voltage required for that ratio gets summed
or not, depending on the state of the control line. So like if the 2/1 line
goes active, its 1 volt gets added and the pitch jumps up an octave. Same
for all the lines. 

I'm still thinking that adding these voltages would result in multiplying
the ratios. Like adding the voltages for 5/4 and 3/2 would give an interval
of (5/4)*(3/2) = 15/8. Mmmm... might not sound too good. Oh well, turn the
sound off and watch it on a scope.

For a source for the control lines, maybe a magnetic pendulum and latching
hall effect switches would be an easy place to start. 

> 
> If you want to keep octaves (usually a good idea) and 12 notes/octave
> (also
> convient) but get away from equal temperament, you'll need some kind of
> resistor bank or perhaps one of those inevitable PIC microprocessors to
> work out the voltages for you.
> 
> (And the half application is creating polyrhythms with VCLFOs...)
> 
> Richard
>