Talk:Height

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Height is not dissonance

Not a big fan of this opening:

The height is a tool to measure the dissonance of JI intervals.

It measures the complexity. This might be related to dissonance, but not in an obvious way.

-Sintel (talk) 14:20, 11 April 2022 (UTC)

Agreed. Feel free to improve it. FloraC (talk) 15:44, 11 April 2022 (UTC)

Agreed. As far as I can tell, "height" and "complexity" are synonymous. If they're not, then it may be a good idea to explain the difference on the page. I don't understand what the motivation is for using the term "height" when we already have the descriptive and in-common-use term "complexity". --Cmloegcmluin (talk) 15:56, 11 April 2022 (UTC)

Maybe that's naive, but I'd say, it's not obvious that complexity (in a more common sense) needs to be measured in one dimension. Height seems to be a one-dimensional measure. --Xenwolf (talk) 06:29, 12 April 2022 (UTC)

Sorry, but I'm a little confused by your previous post; I don't understand whether you're saying that what I had just said was naive or that what you say next is naive. Because I'm confused by that, I'm not sure whether you agree with me or not. In either case, what you say next reads to me as a defense of "complexity" over "height", because many of the "heights" we use in xen are indeed measurements of multidimensional objects: prime-count vectors representing JI intervals. So that's another good point, and one that I hadn't considered before. --Cmloegcmluin (talk) 14:56, 12 April 2022 (UTC)

'I don't understand what the motivation is for using the term "height" when we already have the descriptive and in-common-use term "complexity".'

It's borrowed from mathematics: Wikipedia: Height function ResonantFrequencies (talk) 19:22, 30 December 2022 (UTC)

Right. Complexity is a subjective concept. Height is a rigorously defined mathematical object. So complexity isn't necessarily measured by height. FloraC (talk) 07:49, 31 December 2022 (UTC)

gradus suavitatis

Does Euler's gradus suavitatis count? What about the other metrics listed in Scala? (DEPTH, ENTROPY, GRADUS, HARMON, HEIGHT, MANN, MAX, PROOIJEN, RHSM, RECTANGULAR, TENNEY, TE_NORM, TRIANGLE, TR_LOG, VOGEL, WEIL, WILSON) ResonantFrequencies (talk) 19:30, 30 December 2022 (UTC)

Could you provide some materials on what it is? FloraC (talk) 07:49, 31 December 2022 (UTC)

Counterexample

Not sure how relevant this is, but I was wondering why we have "height" and "complexity" as different things. A counterexample might clear up the difference. Consider the total number of prime factors of a number. This is some kind of complexity measure. It's really just the unweighted l_1 norm when expressed in vector form, so it seems quite sensible. For example 5/4 = 2^-2 * 5^1, so h(5/4) = 3. Similarly we have h(81/80) = 9. This satisfies all of the criteria except finiteness, all prime numbers p have h(p/1) = 1. So there are infinitely many rationals for which h(x) <= C.

So this defines a complexity which is not a height.

– Sintel🎏 (talk) 13:41, 25 April 2025 (UTC)