Vals and tuning space: Difference between revisions
m Text replacement - "(\[\[\:(dev|es|purdal|de|en):[^[:space:]\|]*) (.*])" to "$1|$3" |
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<math>\displaystyle | <math>\displaystyle | ||
||v|| = \sqrt{\left( | ||v|| = \sqrt{\left(\frac{v_2}{\log_2(2)}\right)^2 + \left(\frac{v_3}{\log_2(3)}\right)^2 + \left(\frac{v_5}{\log_2(5)}\right)^2 + ... + \left(\frac{v_p}{\log_2(p)}\right)^2} | ||
</math> | |||
It useful to renormalize to the RMS (root mean square) instead, which requires dividing the above by sqrt(n), where n = pi(p) is the number of primes up to p. This is the TE, or Tenney-Euclidean, norm. | It useful to renormalize to the RMS (root mean square) instead, which requires dividing the above by sqrt(n), where n = pi(p) is the number of primes up to p. This is the TE, or Tenney-Euclidean, norm. | ||
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<math>\displaystyle | <math>\displaystyle | ||
\left<31 \; \frac{49}{log_2(3)} \; \frac{72}{log_2(5)} \; \frac{87}{log_2(7)}\right| | \left<31 \; \frac{49}{\log_2(3)} \; \frac{72}{\log_2(5)} \; \frac{87}{\log_2(7)}\right| | ||
%original was <31 49/log2(3) 72/log2(5) 87/log2(7)|</math> | %original was <31 49/log2(3) 72/log2(5) 87/log2(7)|</math> | ||