Talk:PFDO

The formula

When I use the formula (a/b + 2^p * (b-a)/b)^1/p, it does give me reasonable answers, but it gives the answers going in degrees down the scale, not up the scale.

For example, it tells me that the 7th interval of 12AFDO is 1.417, which is true if you count down from the root, not up. And it tells me the 7th interval of 12IFDO is 1.263, which again is true if you count down from the root instead of up.

If this is intentional, it might be worth mentioning in the article that it gives the scale degrees counting down from the root, not up.

If this is not intentional, and you are intending for the formula to give scale degrees in ascending order instead, then I think this formula would work: ((b-a)/b + 2^p * a/b)^1/p It gives me the answers ascending up the scale rather than descending down.

It might also be worth saying in the article that this formula gives the answer as a frequency, not a pitch. I think most people will figure that out on their own, but just in case, I think it's still worth clarifying.

One other thing is that, because of the "1/P", the formula requires you to divide by zero if you want to calculate an EDO degree, which results in the answer being "undefined". Is that supposed to happen? If so, that's worth warning people about in the article. I feel like that's not supposed to happen and I might be doing something wrong? If I am doing something wrong, it might be worth telling people in the article how to avoid doing whatever dumb thing I did, hehe. --BudjarnLambeth (talk) 09:11, 25 April 2023 (UTC)

Update: I did notice that when I took the mean of the formula results for p=1 and p=-1, it gave an answer that was close to the expected value for p=0. (Any error may have been rounding error from not using enough decimal places?) Is that what I'm supposed to do for p=0, use p=1 and p=-1 and then take the average of the two answers? If so, it would be worth explicitly saying that in the page. --BudjarnLambeth (talk) 09:13, 25 April 2023 (UTC)

Divisions of non-octave intervals

Is it also possible to generalise this to non-octave intervals? E.g., could you have an AFD3 or IFD3 analogous to an ED3? Could you have an AFD3/2 or IFD3/2 analogous to an ED3/2?

If so, this is definitely worth mentioning as well. Or, if you've already described this in another page, then it's worth linking to that page at the end of this one. --BudjarnLambeth (talk) 09:11, 25 April 2023 (UTC)