Talk:POTE tuning
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"Find POTE = T/T[1]"
It doesn't seem to handle the case where the period is a fraction of an octave. For example, try this diaschismic mapping: [⟨2, 2, 7, 15], ⟨0, 1, -2, -8]]. We know the period is half an octave. Indeed,
T = [599.44659699 703.03185125]
Now POTE = T/T[1] gives
POTE = [1200. 1407.36176623]
Is this correct?
Besides, since I don't see a definition of TE generator, I don't know if it should be octave reduced, period reduced or left as is. Changing the basis definitely changes the result. Does TE generators specify a basis or whatever maps are accepted?
From my perspective, this seems more intuitive:
- Find the TE octave: (TV)1, that is, the first entry of TV.
- POTE = T/(TV)1
resulting in
POTE = [600. 703.68088312]
Video tutorial
Is someone able and willing to make a video? Or is there an article with illustrations that enables even non-mathematicians like me to follow the process? Thanks in advance for your help. --Xenwolf (talk) 13:49, 6 December 2020 (UTC)
Justification
This article fails to justify why POTE is a good idea. The Kees Height is a complexity measure on JI intervals, not an error metric on tempered intervals, so I can't see how the resulting tuning is optimal in this sense.
As I understand it, the POTE tuning simply finds the least-squares tuning under the TE norm, and then does a completely ad-hoc adjustment to get the octaves just. In constrast, the constrained TE tuning is actually optimal under the TE norm, in the subspace where the octave is just. It seems like a much better candidate for a 'standard' tuning.