Talk:Interval vector

First image in article

Unless I misunderstood something, the top figure in both examples in the first image file should be 8 and not 4.Signed: Basemetal (write to me here) 06:51, 16 December 2012 (UTC)

Same question answered on Talk:Set theory (music).—Jerome Kohl (talk) 07:57, 16 December 2012 (UTC)

Second image in article

Interval vector: C major chord {0,4,7}: 001110.

Just when I thought I'd got something down. Why are you now notating (2nd image, C major chord example) the interval between pitch class C and pitch class G with 7 and not 5? Signed: Basemetal (write to me here) 08:12, 21 December 2012 (UTC)

See: inversion (music). The formula for the inverse of X is easy, it's 12-X. 12-7 = 5 = 7 = 12-5. Hyacinth (talk) 00:45, 19 February 2017 (UTC)

Calculus context

As soon as I can figure out how to work the WP math markup, I'll write out the formulas. They're mostly basic pre-college math (simple 2 + 2 as far as vectors are concerned). The irony lies only in that music theorists don't usually realize these things were first and foremost math before they ever were music theory. — Preceding unsigned comment added by 24.242.14.23 (talk) 20:12, 18 January 2014 (UTC)

I think you will find that the music theorists who actually formulated these ideas (Babbitt, Forte, Martino, Lewin) were acutely aware of their source in mathematics. Perhaps it is true that some later theorists who have adopted the concepts are not so aware. However, as David Lewin has gone to some pains to point out, the long-established conventions of music theory are sometimes at odds with those of mathematics, and therefore demand formatting that may lead the mathematician to conclude that the music theorist is ill-informed. In other cases, it may be that the theorist is in fact ill-informed, or chooses to modify or limit the mathematical concept to suit his own purposes, without explicitly stating that this is the case. In any event, it is always best to explain the differences for the benefit of both the mathematician (who may stumble on an article like this and wonder why the maths aren't kosher) and the mathematically innocent musician (who may not know the difference). I wish I could help you with the math markup, but that is an area I have not gotten much into. I look forward to your eventual explanations.—Jerome Kohl (talk) 22:29, 18 January 2014 (UTC)

Too technical?

How and/or why might this article be too technical for most readers to understand? Hyacinth (talk) 01:28, 19 February 2017 (UTC)

@Hyacinth: As someone with no music theory background who arrived here via Template:Grading scheme which uses this as an example of a Start-class article, here's what I get out of the first sentence and paragraph...

"In musical set theory, an interval vector is an array that expresses the intervallic content of a pitch-class set."

• The word "intervalic", which is a wikilink to Interval (music). I've heard the term before, and I understand what an interval is, but the adjective term is quite unfamiliar. Does it have some specific technical meaning?
• "pitch-class set". A pitch class is itself a set, so at first I thought this was the set 12ℤ. Oh, no, it's a set of pitch classes.
• And later it's revealed that we're counting repetitions, so "set" is misleading. I think not technically wrong, since it's counting repetitions of intervals in a set of pitches, but that's a little awkward to follow.

How about something like:

In musical set theory, an interval vector is an array of natural numbers which summarize the intervals present in a set of pitch classes. (That is, a set of pitches where octaves are disregarded.)

In particular, "summarizes" is an improvement over "expresses" because it makes clear that some details are discarded.

• Also, "Z17" in the first figure caption needs a wikilink to 5-Z17 or Farben chord. Or just delete it; the source of the notes is not particularly relevant to the example. And it's unclear if the Z in the name is related to the Z-relation.
• Later on the terminology "T_n-type and T_n/T_nI-type." is introduced without any attempt at definition or wikilink to definition. Definitely a way to lose people.
• One thing that would help is to pull the paragraph about "they quickly show the sound qualities that are created by different collections of pitch class" up a lot. Burying "what use is it" under a couple pages of definitions is classic (bad) mathematician writing.
• On non-technical grounds, the WP:LEADLENGTH is too long. I'm not sure if I'm up to rewriting it, but it's half the prose in the article.

71.41.210.146 (talk) 12:45, 28 March 2017 (UTC)

One thing for sure is that the "lede" segued straight into the body of the article, which is what made it seem disproportionate. I have fixed this by inserting a header, but that is only a small patch on a boat with many leaks. We are to some extent dealing here with differences between standard mathematical terminology and music-theory borrowings of those same words, which have taken on standards of their own. For example, musicians do not think of a "pitch class" as a "set", though mathematically this is obviously the case. The adjective "interval(l)ic" (OED: "adj. Of or pertaining to an interval or intervals") is commonplace in music theory, without having any specialized technical meaning. Does this need explaining to the layman and, if so, how?—Jerome Kohl (talk) 19:08, 28 March 2017 (UTC)

@Jerome Kohl: 'musicians do not think of a "pitch class" as a "set",' You might want to tell pitch class that, which jumps straight into the set definition. In general, in mathematics, a class is a generalization of a set (all sets are classes, as are some non-set things called "proper classes"), so just the word implies that it is a set.

As for "intervalic", I may have never seen it before, but the meaning is not hard to infer. It's just that in combination with a specialized technical definition, one is left wondering. The simple way to introduce it is to use more familiar forms of the word first, which is one thing I tried to do with my replacement first sentence.

One thing I'd try to point out fairly early is that the interval vector is invariant under inversion, permutation, and transposition. But there's the "Z-transform" too. What I'm not sure of is whether those transformations are enough to generate the complete equivalence class.

If you feel you understand this, I can take a stab at some heavy editing, but I'll need someone to fix the errors I introduce. 71.41.210.146 (talk) 04:26, 29 March 2017 (UTC)

I think I can follow all that, though I certainly do not have the maths chops necessary to properly critique any heavy editing. My area is music theory, not maths, though I am familiar enough with the kinds of misunderstandings that can occur when these two areas collide. I can also appreciate your wariness concerning a seemingly innocuous word that might turn out to have a very specialised meaning in a particular discipline. Your proposed revision of the lede looks accurate enough to me, and certainly avoids this last problem (at least, until someone worries that "interval" might have a specialised technical meaning in music theory, which of course it does). Although musicians are apt to balk at expressions like "natural numbers", linking the term should be at least as adequate as linking "intervallic" to "interval". I'd say go ahead and try it, and see whether it provokes either applause or objections. For more "heavy" editing, it might be a good idea to bring your suggestions here to the Talk page, where we "poor musicians" can whine about technical stuff we might not understand, before it goes into the article.—Jerome Kohl (talk) 15:43, 29 March 2017 (UTC)

One suggestion I would make is to remove the triad example. This type of analysis fails when applied to tonal harmony because it cannot distinguish between major and minor triads; both reduce to <001110> Joeofarrell (talk) 14:46, 26 June 2017 (UTC)

Perhaps the phrasing could be improved, but I read that paragraph as a warning about precisely this shortcoming. The business about "root position" is a red herring, inasmuch as it is almost immediately contradicted by the statement that inversion has no effect on the interval vector.—Jerome Kohl (talk) 23:37, 26 June 2017 (UTC)

T_n vs T_n

I think the distinction between the triangular number T_n and the transpositional set class T_n is far too subtle - it left me quite confused until I realized that they were referring to different things. BridgeTheMasterBuilder (talk) 03:05, 11 July 2017 (UTC)