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
    Can you help me please?
    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.