[sdiy] 1v/oct and other scales

[Richard Wentk]

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)

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