Talk:Tenney Height/WikispacesArchive

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ARCHIVED WIKISPACES DISCUSSION BELOW

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Contradiction

http://www.plainsound.org/pdfs/JC&ToH.pdf gives Tenney's "harmonic distance" as

  • HD(fa, fb) ∝ log(a) + log(b) = log(ab)

where a/b is the frequency ratio fa/fb in simplified form:

  • a = fa /gcd(fa, fb), b = fb /gcd(fa, fb), and a ≥ b

http://lumma.org/tuning/faq/#heights defines it as sqrt(n*d), which is not the same.

sqrt(100*7) = 26.45

log2(100*7) = 9.45

- Omegatron September 11, 2014, 07:33:46 AM UTC-0700


Tenney *harmonic distance* is not Tenney *height*, which is the topic of this page. My FAQ defines Tenney height as a*b. It says Tenney height is *generalized* to geomean(a*b*c...).

On this wiki, a*b is called Benedetti height. The name was changed after my FAQ was written, since Benedetti had priority.

- clumma February 06, 2015, 08:19:12 PM UTC-0800