math, sequence, frequencies, tuning and formula
hey everybody, Excuse me in advance if I'm not clear, my english is not very good.
I want to find a formula from a tuning system for a synth.
here is the concept, it's a sort of "just intonation" tuning system.
Musical tuning systems based on 33 hertz
1 tone equal temperament (this one is super simple x = 33. * pow(2, x) )
33
66
132
264
528
1056
2112
4224
8448
16896
But when we try with two (or more) notes per octave, I don't understand how to find the formula. Here are the frequencies.
2 tone equal temperament
33 49.5
66 99
132 198
264 396
528 792
1056 1584
2112 3168
4224 6336
8448 12672
16896
Can you help me please?
Thank you very much for your help.
Guillaume
If you're talking about equal divisions of the octave, the smallest step is the Nth root of 2, where N is the interval to be divided.
Not sure about the formula, but here is how you can generate exactly this sequence of numbers:
I find the wikipedia articles about equal temperament https://en.wikipedia.org/wiki/Equal_temperament and Bohlen-Pierce-scale https://en.wikipedia.org/wiki/Bohlen–Pierce_scale most insightful.
you could do it on the linear layer and then put an mtof at the end:
when for a 12-tone scale
note number 60 -> [mtof] -> is ~261 Hz
and the next note will be 61 (+ 1, or count , or uzi)
then for a 13 tone scale you would add +(1/13*12)
which is around 0.923 per step
so the next note will be note number 60.923
then again apply [mtof] to convert these note numbers to hertz.
here's a patch with explicit formula:
note that your original calculations in your post are incorrect (click on preset 4), and that valery's maths in his post is not correct either.