## math, sequence, frequencies, tuning and formula

Mar 05 2019 | 8:33 am
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
Thank you very much for your help.
Guillaume

• Mar 05 2019 | 3:00 pm
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.
• Mar 05 2019 | 4:37 pm
Not sure about the formula, but here is how you can generate exactly this sequence of numbers:
• Mar 05 2019 | 5:17 pm
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.
• Mar 06 2019 | 5:50 pm
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.
• Mar 07 2019 | 12:38 am
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.