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Put to good use?
I took out something which wasn't explained enough to really make sense. It would be a good idea to put it back, telling how, exactly, the Lucas numbers can be put to good use. It seems logical, since ratios between them appear. Is that what you meant?
- genewardsmith December 31, 2011, 10:03:09 AM UTC-0800
The exponents of phi are Lucas numbers? I don't know what to make of that yet. I know what I was trying to say though, and I was simply off the mark. It isn't the simple Fibonacci number harmonics that phi^n approximates...
phi^1 ~ 13/8
phi^2 ~ 21/8
phi^3 ~ 34/8
phi^4 ~ 55/8
All because phi~13/8 which is actually the definition of sephiroth temperament! But there are other Fibonacci sequences that still approximate phi, and while I don't know if they do it more or less quickly than the traditional 1+1, they are probably too!
And because, I assume - maybe it's not that easy, any number can be defined as the limit of the ratio between successive terms of some sequence, perhaps this can be developed as an atomic definition of any rank-2 (or maybe any) temperament?
- Kosmorsky December 31, 2011, 01:03:11 PM UTC-0800
- probably relevant too, to the characteristics of the temperament.
Furthermore, the nucleation point of any of the temperaments, where that the ratio is something like 13/8 that they all build off, can be any of those equivalences; the closer the more accurate.
13/8 is good because octaves make short work of the 8 in the denominator, but like I said, next come tritaves, and so on.
- Kosmorsky December 31, 2011, 01:08:26 PM UTC-0800
- NOT equivalences, I meant ratios which approximate the number. I have a way with words.
- Kosmorsky December 31, 2011, 01:09:38 PM UTC-0800