Talk:Tenney norm: Difference between revisions

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~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~

~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

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== ~~Contradiction~~ ==

== Move to Tenney norm ==

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

~~<ul class=~~"~~quotelist~~"~~><li>HD(fa~~, ~~fb) ∝ log~~(a) ~~+ log(b) = log~~(ab)~~</li></ul>~~

This complexity is defined as a norm, which is (mostly) a stronger condition than being a height function.

In fact, the whole reason it is useful is because it is a norm, not a height.

For this reason, the title should be either "Tenney norm", or "Tenney harmonic distance", because that's what it was called originally.

– [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 18:18, 30 April 2025 (UTC)

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

: Agreed. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:46, 30 April 2025 (UTC)

: Agreed. If "norm" is more commonly used than "harmonic distance" (for the Tenney case but also in general), then "norm" should be given priority despite Tenney calling it "harmonic distance". --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 21:53, 30 April 2025 (UTC)

~~<ul class="quotelist"><li>a = fa /gcd~~(~~fa, fb~~), ~~b = fb /gcd~~(~~fa, fb~~)~~, and a ≥ b</li></ul>~~

~~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~~

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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~~

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-= ARCHIVED WIKISPACES DISCUSSION BELOW =
+{{WSArchiveLink}}
-'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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-== Contradiction ==
+== Move to Tenney norm ==
-http://www.plainsound.org/pdfs/JC&amp;ToH.pdf gives Tenney's "harmonic distance" as
-<ul class="quotelist"><li>HD(fa, fb) ∝ log(a) + log(b) = log(ab)</li></ul>
+This complexity is defined as a norm, which is (mostly) a stronger condition than being a height function.
+In fact, the whole reason it is useful is because it is a norm, not a height.
+For this reason, the title should be either "Tenney norm", or "Tenney harmonic distance", because that's what it was called originally.
+– [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 18:18, 30 April 2025 (UTC)
-where a/b is the frequency ratio fa/fb in simplified form:
+: Agreed. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:46, 30 April 2025 (UTC)
+: Agreed. If "norm" is more commonly used than "harmonic distance" (for the Tenney case but also in general), then "norm" should be given priority despite Tenney calling it "harmonic distance". --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 21:53, 30 April 2025 (UTC)
-<ul class="quotelist"><li>a = fa /gcd(fa, fb), b = fb /gcd(fa, fb), and a ≥ b</li></ul>
-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
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-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
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