Talk:Height - Revision history

Cmloegcmluin: /* Counterexample */

2025-04-30T02:38:55Z

Counterexample

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	:: Actually, I'm not really sure if we should be talking about height functions at all, since those properties aren't really used anywhere! The only place heights actuall show up is in the proof for Dirichlet (logflat) badness, where it's actually a height on temperaments, not intervals! And then the actual height functions we do end up using are actually just norms on some vector space. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 11:19, 26 April 2025 (UTC)		:: Actually, I'm not really sure if we should be talking about height functions at all, since those properties aren't really used anywhere! The only place heights actuall show up is in the proof for Dirichlet (logflat) badness, where it's actually a height on temperaments, not intervals! And then the actual height functions we do end up using are actually just norms on some vector space. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 11:19, 26 April 2025 (UTC)

			::: I'd love to do away with heights and stick to complexities. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 02:38, 30 April 2025 (UTC)

Sintel: /* Counterexample */

2025-04-26T11:19:52Z

Counterexample

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	: Agreed. The [[Complexity]] page will also require an update, as it literally states that the complexity of an interval is called "height", whereas this counterexample shows that heights are a subset of interval complexity measures. --[[User:Fredg999\|Fredg999]] ([[User talk:Fredg999\|talk]]) 20:45, 25 April 2025 (UTC)		: Agreed. The [[Complexity]] page will also require an update, as it literally states that the complexity of an interval is called "height", whereas this counterexample shows that heights are a subset of interval complexity measures. --[[User:Fredg999\|Fredg999]] ([[User talk:Fredg999\|talk]]) 20:45, 25 April 2025 (UTC)

			:: Actually, I'm not really sure if we should be talking about height functions at all, since those properties aren't really used anywhere! The only place heights actuall show up is in the proof for Dirichlet (logflat) badness, where it's actually a height on temperaments, not intervals! And then the actual height functions we do end up using are actually just norms on some vector space. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 11:19, 26 April 2025 (UTC)

Fredg999: /* Counterexample */ Re

2025-04-25T20:45:13Z

Counterexample: Re

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	– [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 13:41, 25 April 2025 (UTC)		– [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 13:41, 25 April 2025 (UTC)

			: Agreed. The [[Complexity]] page will also require an update, as it literally states that the complexity of an interval is called "height", whereas this counterexample shows that heights are a subset of interval complexity measures. --[[User:Fredg999\|Fredg999]] ([[User talk:Fredg999\|talk]]) 20:45, 25 April 2025 (UTC)

Sintel: /* gradus suavitatis */

2025-04-25T13:43:36Z

gradus suavitatis

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

			: The gradus suavitatis is indeed a proper height function. It might be worth adding because of its historical significance. Not sure about the other ones, though a lot of those (tenney, te_norm, weil, wilson) are already described as height functions on the wiki. – [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 13:43, 25 April 2025 (UTC)

	== Counterexample ==		== Counterexample ==

Sintel: Counterexample

2025-04-25T13:41:14Z

Counterexample

← Older revision		Revision as of 13:41, 25 April 2025
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	: Could you provide some materials on what it is? [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 07:49, 31 December 2022 (UTC)		: Could you provide some materials on what it is? [[User:FloraC\|FloraC]] ([[User talk: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.

			– [[User:Sintel\|Sintel🎏]] ([[User_talk:Sintel\|talk]]) 13:41, 25 April 2025 (UTC)

FloraC: /* Height is not dissonance */ indent level

2022-12-31T07:50:52Z

Height is not dissonance: indent level

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	:::: 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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 14:56, 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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk: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".'		::: '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]] [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:22, 30 December 2022 (UTC)		::: It's borrowed from mathematics: [[Wikipedia: Height function]] [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk: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. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 07:49, 31 December 2022 (UTC)		:::: Right. Complexity is a subjective concept. Height is a rigorously defined mathematical object. So complexity isn't necessarily measured by height. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 07:49, 31 December 2022 (UTC)

	== gradus suavitatis ==		== gradus suavitatis ==

FloraC: re

2022-12-31T07:49:40Z

← Older revision		Revision as of 07:49, 31 December 2022
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	: '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".'		: '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]] [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:22, 30 December 2022 (UTC)		:: It's borrowed from mathematics: [[Wikipedia: Height function]] [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk: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. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 07:49, 31 December 2022 (UTC)

	== gradus suavitatis ==		== 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) [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:30, 30 December 2022 (UTC)		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) [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:30, 30 December 2022 (UTC)

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

ResonantFrequencies: /* gradus suavitatis */ new section

2022-12-30T19:30:52Z

gradus suavitatis: new section

← Older revision		Revision as of 19:30, 30 December 2022
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	: '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".'		: '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]] [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:22, 30 December 2022 (UTC)		:: It's borrowed from mathematics: [[Wikipedia: Height function]] [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:22, 30 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) [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:30, 30 December 2022 (UTC)

ResonantFrequencies: Reply to User:Cmloegcmluin

2022-12-30T19:22:48Z

Reply to User:Cmloegcmluin

← Older revision		Revision as of 19:22, 30 December 2022
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	:::: 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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 14:56, 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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk: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]] [[User:ResonantFrequencies\|ResonantFrequencies]] ([[User talk:ResonantFrequencies\|talk]]) 19:22, 30 December 2022 (UTC)

Cmloegcmluin at 14:56, 12 April 2022

2022-04-12T14:56:33Z

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	::: 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. --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 06:29, 12 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. --[[User:Xenwolf\|Xenwolf]] ([[User talk: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. --[[User:Cmloegcmluin\|Cmloegcmluin]] ([[User talk:Cmloegcmluin\|talk]]) 14:56, 12 April 2022 (UTC)