Talk:POTE tuning: Difference between revisions
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POTE issues |
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: Make sure to ask Paul Erlich. It's a shame he isn't here to help. I added some of his words but that was a tip of the iceberg. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:39, 19 December 2021 (UTC) | : Make sure to ask Paul Erlich. It's a shame he isn't here to help. I added some of his words but that was a tip of the iceberg. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:39, 19 December 2021 (UTC) | ||
OK, after reading up on exterior algebra, POTE just seems wrong. On the page [[Tenney-Euclidean tuning]] a justification is given (which should be moved here anyway): | |||
: "The justification for this is that T does not only define a point, but a line through the origin lying in the subspace defining the temperament, or in other words, a point in the linear subspace of projective space corresponding to the temperament, and hence is a projective object." | |||
This only works for rank-1 (eg edos) though. In general, for a rank-r temperament, you have some subspace/hyperplane of dimension r. By only looking at the line from 0 to T, you are missing all the other degrees of freedom that you can optimize. (Again, something CTE does correctly.) | |||
- [[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 16:11, 11 April 2022 (UTC) | |||