Talk:4:5:6 - Revision history

VectorGraphics at 04:20, 22 November 2025

2025-11-22T04:20:15Z

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	: I say keep it. I've also got ways of notating it myself (as you might have seen in some previous versions), but his is more fleshed out. In fact, I've been working with him to flesh it out more and more capable to describe any voicings of ''almost'' any chord. Eventually. --[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 01:33, 22 November 2025 (UTC)		: I say keep it. I've also got ways of notating it myself (as you might have seen in some previous versions), but his is more fleshed out. In fact, I've been working with him to flesh it out more and more capable to describe any voicings of ''almost'' any chord. Eventually. --[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 01:33, 22 November 2025 (UTC)

			:: Ehhh it's really obscure though, and we've been a bit conservative about introducing color notation to interval pages, so this is similar. -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 04:20, 22 November 2025 (UTC)

Eufalesio at 01:33, 22 November 2025

2025-11-22T01:33:05Z

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	Do we keep the obscure kite!notation that seems to have just been added to this page and a couple others recently? -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 01:23, 22 November 2025 (UTC)		Do we keep the obscure kite!notation that seems to have just been added to this page and a couple others recently? -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 01:23, 22 November 2025 (UTC)

			: I say keep it. I've also got ways of notating it myself (as you might have seen in some previous versions), but his is more fleshed out. In fact, I've been working with him to flesh it out more and more capable to describe any voicings of ''almost'' any chord. Eventually. --[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 01:33, 22 November 2025 (UTC)

VectorGraphics: /* Hi-lo notation */ new section

2025-11-22T01:23:19Z

Hi-lo notation: new section

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	::::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 09:40, 13 November 2025 (UTC)		::::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 09:40, 13 November 2025 (UTC)

			== Hi-lo notation ==

			Do we keep the obscure kite!notation that seems to have just been added to this page and a couple others recently? -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 01:23, 22 November 2025 (UTC)

FloraC: /* On the consonance or concordance of 3:4:5 over 4:5:6 */ re

2025-11-13T09:40:59Z

On the consonance or concordance of 3:4:5 over 4:5:6: re

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	:::: --[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:08, 12 November 2025 (UTC)		:::: --[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:08, 12 November 2025 (UTC)

			::::: It's not purely arbitrary. It has stylistic aspects but there's a good psychoacoustic basis too. Octave equivalence is real. Rootedness and virtual fundamentals are real. They have effects on the sound besides the numbers. Say they don't exist and you're into your fantasyland.

			::::: In practice everyone would agree 4:5:6 and 1:3:5 are voicings of the same chord. Otherwise we would need to make distinct articles for each of them.

			::::: I knew what ''<nowiki>'3</nowiki>'', ''<nowiki>'5</nowiki>'', etc. meant. You don't need to explain it to me. You need to explain it to users, by adding a note to the table or something like that.

			::::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 09:40, 13 November 2025 (UTC)

Eufalesio: /* On the consonance or concordance of 3:4:5 over 4:5:6 */

2025-11-12T15:08:46Z

On the consonance or concordance of 3:4:5 over 4:5:6

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	::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:37, 12 November 2025 (UTC)		::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:37, 12 November 2025 (UTC)

			:::: I dissagree that "rootedness" can be a source of stability, because that stability is abstract and does not truly exist, barring my perceived notion that it "feels wrong" to call these chords the same. 4:5:6 being the octave reduced voicing of 1:3:5 is just a mathematical fact, as the two chords are sonically distinct.

			:::: What I agree on is calling a certain octave-reduced rotation of the chord the "root", which represents the "figurehead" of the unique octave-agnostic (or equave-agnostic) combination of integers that make up a chord. Purely arbitrary, just a denomination; due to tradition, due to whatever reason. That way, we have a way of identifying the constituyents of a chord and their voicings across equaves: here, its odd parts. This sense of octave-agnosticism is useful for organizing chords that sound similar, but are not the same.

			:::: The '3 '5 nomenclature is similar to that to what xenpaper does, which is adding octaves. So '3 here means "the voicing where the odd 3 is one octave higher than usual". So for example, 1:3:5 would be a voicing of 4:5:6 ('3''5).

			:::: --[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:08, 12 November 2025 (UTC)

FloraC: Re

2025-11-12T12:37:32Z

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	:: [[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:54, 11 November 2025 (UTC)		:: [[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:54, 11 November 2025 (UTC)

			::: For one thing, rootedness is a source of stability, but to see this you need to take octave equivalence into consideration. Once you have octave equivalence, you should see 5/4 isn't more complex than 4/3, for example, because 5/4 can be simplified to 5/1, whereas 4/3 is in its simplest form and only gets more complex in open voicings. In fact 4:5:6 is the octave-reduced voicing of 1:3:5 (1–3–5), which as you can see is not only rooted but simpler than 3:4:5 (1–4/3–5/3).

			::: P4–M3, P4–P5 and M6–P8 all but point to the fact that 3:4:5 is unstable and wants to move somewhere. P4–M3 is especially relevant cuz the perfect fourth is offset from the major third by a semitone, which has greater tension than the whole tone or minor third.

			::: I like your tables overall, but ''<nowiki>'3</nowiki>'', ''<nowiki>'5</nowiki>'', etc. need explanation. Also ''root'' should be ''closed''; ''root position'' refers to a rotation, equivalent to your ''on 1'', not a voicing.

			::: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 12:37, 12 November 2025 (UTC)

Eufalesio at 15:56, 11 November 2025

2025-11-11T15:56:57Z

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	:: Saying that [3:4:5 -> 4:5:6] "the fourth above the root contrasts and therefore wants to move to the missing major third" is a stylistic choice. Just as saying that [3:4:5 -> 2:3:4] "the fourth wants to move to the missing fifth and the sixth rises up to the octave for pure consonance".		:: Saying that [3:4:5 -> 4:5:6] "the fourth above the root contrasts and therefore wants to move to the missing major third" is a stylistic choice. Just as saying that [3:4:5 -> 2:3:4] "the fourth wants to move to the missing fifth and the sixth rises up to the octave for pure consonance".

	:: Apart from that, I wonder what your thoughts are for the voicings. I included voicings in the chord articles for completeness and to not obviate compound intervals. After all, 4:5:6 is not the same as 2:3:5 or 1:5:12, ~~not numerically, not sonically~~.		:: Apart from that, I wonder what your thoughts are for the voicings. I included voicings in the chord articles for completeness and to not obviate compound intervals. After all, 4:5:6 is not the same as 2:3:5 or 2:5:12, even if they are all On 1.

	--[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:54, 11 November 2025 (UTC)		:: [[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:54, 11 November 2025 (UTC)

Eufalesio at 15:54, 11 November 2025

2025-11-11T15:54:43Z

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	:: Apart from that, I wonder what your thoughts are for the voicings. I included voicings in the chord articles for completeness and to not obviate compound intervals. After all, 4:5:6 is not the same as 2:3:5 or 1:5:12, not numerically, not sonically.		:: Apart from that, I wonder what your thoughts are for the voicings. I included voicings in the chord articles for completeness and to not obviate compound intervals. After all, 4:5:6 is not the same as 2:3:5 or 1:5:12, not numerically, not sonically.

			--[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 15:54, 11 November 2025 (UTC)

Eufalesio at 15:54, 11 November 2025

2025-11-11T15:54:31Z

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	: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:30, 11 November 2025 (UTC)		: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:30, 11 November 2025 (UTC)

			:: I don't see why 4:5:6 would be "perfectly" stable, even more so than 3:4:5. 4:5:6 has the 5/4 before the 3/2, which is a more complex interval, unlike 3:4:5 which has 4/3 before 5/3, which is less numerically complex. It would be reasonable to say that 4:5:6 is more stable than 3:4:5, but that claim would surely come from the Western tradition of harmony/counterpoint.

			:: Saying that [3:4:5 -> 4:5:6] "the fourth above the root contrasts and therefore wants to move to the missing major third" is a stylistic choice. Just as saying that [3:4:5 -> 2:3:4] "the fourth wants to move to the missing fifth and the sixth rises up to the octave for pure consonance".

			:: Apart from that, I wonder what your thoughts are for the voicings. I included voicings in the chord articles for completeness and to not obviate compound intervals. After all, 4:5:6 is not the same as 2:3:5 or 1:5:12, not numerically, not sonically.

FloraC: Re

2025-11-11T14:30:25Z

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	== Scale information off-topic? Why? ==		== Scale information off-topic? Why? ==

	I recently tried to expand the article by mentioning scale information because I think it's good to know how certain microtonal chords can be used in composition. I fail to see how such information is off-topic. If there's guidelines for what sorts of information to add to these chord pages that I don't know about, then would someone mind explaining that to me? --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 02:48, 30 October 2025 (UTC)		I recently tried to expand the article by mentioning scale information because I think it's good to know how certain microtonal chords can be used in composition. I fail to see how such information is off-topic. If there's guidelines for what sorts of information to add to these chord pages that I don't know about, then would someone mind explaining that to me? --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 02:48, 30 October 2025 (UTC)

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	== On the consonance or concordance of 3:4:5 over 4:5:6 ==		== On the consonance or concordance of 3:4:5 over 4:5:6 ==
			What reasons are there to conclude that 3:4:5 isn't more consonant than 4:5:6, even if it has less harmonic entropy? And what distinction is there between consonance and concordance? --[[User:Eufalesio\|Eufalesio]] ([[User talk:Eufalesio\|talk]]) 13:47, 11 November 2025 (UTC)

	~~What reasons are there~~ to ~~conclude that~~ 3:4:5 isn't ~~more consonant than~~ 4:5:6, ~~even if~~ it ~~has less harmonic entropy? And what distinction~~ is ~~there between consonance~~ and ~~concordance? --~~[[User:~~Eufalesio~~\|~~Eufalesio~~]] ([[User talk:~~Eufalesio~~\|talk]]) 13:47, 11 November 2025 (UTC)		: 4:5:6 is rooted up to octave equivalence; 3:4:5 isn't. 4:5:6 is perfectly stable; 3:4:5 has a perfect fourth on the bass, which contrasts the missing major third and suggests moving towards it. I've mentioned these things in the article.

			: Sonance is more contextual than cordance, for a minimalistic answer. You can read more about it in ''Consonance and dissonance'' (and the corresponding Wikipedia article).

			: —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:30, 11 November 2025 (UTC)