Talk:Set theory (music)

message: *From user talk:
Would you care to elaborate more on the (dis)connection between set theory and musical set theory? For instance, why tuple, rather than sequence? Feel free to respond in the article itself, as hopefully I/others can write a better introduction to "musical set theory" and the current introduction can become a section which clearly explains the differences. Hyacinth 23:35, 14 Oct 2004 (UTC)
replies: text: Also, you're edit looks great, and I don't want my above question (or the request above it) to appear as criticism in any way. Hyacinth 23:40, 14 Oct 2004 (UTC)
thread_title: Set theory

message: I think this page basically needs to be reconstructed.  Although it is accurate, much more needs to be said in order to achieve even the fundamental concepts of musical set theory. You cannot ignore interval vectors, similarity relations (Rp, Ro, R1, R2), inclusion relations, complementation, derivation, union, intersection, invarience theorems, subset theorems, VTICS, multiplicative operations, rotation etc.... At least present a few different methods for reaching prime form (i.e. Rahn and Forte methods).  Perhaps the author(s) of this page need to read or re-read the basic atonal theory texts, like "Basic Atonal Theory" by Rahn, "The Structure of Atonal Theory" by Forte, and "Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern."  If you wish to even scratch the surface of atonal theory you need to re-write most of the sections that already exist and include many additions, like those mentioned above.  Since set theory has so many dimensions I suggest you summarize some sections and expand upon them in separate articles.  For example, if you were to explore the set-complex it would take up too much space, so there should only be an introduction and a separate article. 04:26, 28 December 2005 (UTC)
replies: text: Dear anonymous friend, I have another idea: why don't you help us get to grips with the basics first? (See unanswered questions above.) Thanks. PizzaMargherita 07:24, 28 December 2005 (UTC)
replies: text: What you are trying to get to grips with is not the basics.  You are getting into a very senseless debate between mathematicians and music theorists over the use of labels in atonal theory.  It should be apparent that the music theory does not properly use terms, as they would be defined in a math book.  Rather, they use the term as it appears in the dictionary, as a very broad word that can be re-interpreted by multiple fields.  This is not an issue only in atonal theory.  It is apparent in most music theory that uses a mathematical perspective, like "The Schillinger System of Music Composition" by Joseph Schillinger.  Schillinger states that he is using a different notation than appropriate in a math text.  This is also an assumption in atonal theory.  You cannot assume that 4/2 means 4 divided by 2, you have to read the context of the theory.  What you are debating is the terms as used in the reference books, and that are common to the theory.  This article is accurate in its use of terms.  So...I have another idea: why don't you come to grips with silly terminologies and actually try to learn the theory Pizza Man. 65.9.15.143 23:25, 28 December 2005 (UTC)
thread_title:  suggestions 

message: I have made substantial revisions to the page.  I can assure any skeptics that the concepts discussed here are central to much thinking about music, both tonal and atonal.  Western music simply would not exist without the notions of transposition and inversion.
There were a fair amount of errors and mistakes in the article, which I have done my best to correct.  The article now provides a basic introduction to the central ideas of musical set theory.  However, as a previous commentator has indicated, there are plenty of concepts that are not discussed.  The article could certainly be expanded, though my own view is that it should remain accessible to non-specialists, and that there is a danger of overloading people with too much information. Tymoczko 15:22, 22 February 2006 (UTC)
replies: text: Even if your speculation Western music simply would not exist... were justified (which it isn't), the notions of transposition and inversion vastly predate the notion of musical set theory.. so I (as a semi-skeptic) am not assured by that! Do you really think that every time Bach transposed some chorale or inverted or augmented a theme in counterpoint, he was thinking of musical set theory? I certainly don't. But I think you did good work on the article. Can you put in something about the history of the development of the field? Zargulon 17:53, 8 March 2006 (UTC)
replies: text: Probably this isn't what Tymoczko was thinking of, but my take on it is that when Bach was, say, transposing a theme up a fifth, he was doing something that can be neatly explained using a set-theoretic approach to pitch classes. It's fatuous to object that Bach wouldn't have given the same explanation were he to be asked what he was doing. A professional cricketer can't necessarily write down and solve the equation of motion for an object accelerating under gravity but he can still catch a ball much better than any physics professor. Doing something and analysing it require different skills and are done with different goals in mind. The fact is, a school of musical analysis exists that uses set theory to provide such analyses. These analyses may or may not be of interest to you; you might, for example, want to know what thought-processes Bach himself might have gone through while composing, in which case a set-theoretic analysis is probably not much help. I still don't get why the existance of a particular analytic method (among numerous others) would worry anyone. ornette 10:37, 27 March 2006 (UTC)
replies: text: Neither do I.. I think you completely misunderstood me. The objection that you describe as fatuous is not one that anyone is making.. you are setting up a fatuous straw man. Equally I don't accept your analogy with the cricketer.. cricket would still exist without the notion of gravity, just as Western music, in my opinion (but not Tymoczkos) would still exist, perhaps exactly as it is now, without the notions of transposition or inversion. That is the point I was making. I hope it is clearer now. Zargulon 10:56, 27 March 2006 (UTC)

text: I really don't think there's much of an issue here.  Composers like Bach, Mozart, Beethoven, etc., were unquestionably aware of the concepts "transposition" and "inversion."  These theoretical terms (or their equivalents) are centuries old.  In this sense, the sports analogy is misleading: while one can play baseball without knowing the laws of physics, one simply can't compose convincing classical-style music without a fair degree of training, training that will in one way or another involve the concepts of "transposition" and "inversion."  Modern day musical set theory goes beyond this of course, and introduces concepts that would have been totally foreign to Bach and Mozart.  But its basic notions would have been reasonably familiar. Tymoczko 16:37, 30 March 2006 (UTC)
thread_title:  Substantial Revisions 

message: hello, I'm posting the message below at various pages. I believe that now Wikipedia needs the help of real music experts. Recently some articles are being edited according to an agenda, a sort of plan that is willing to delete almost 30 years of history of popular music and mislead the connections and differences between genres.
This is the message (I apologize in advance if my language may appear as German-Spanish inluenced):
:I have a question for music fans: are you aware that electronic music is not electronic dance music? Did you ever realize that no university in the USA regards electronic music and the music for dancing as the same genre? Are you aware that this is not a music magazine? Are you aware of the meaning of the term encyclopedic? Are you aware of the difference between idiomatic expressions, slang and encyclopedic (formal) language? Are you aware that most of articles claiming to deal with "electronic music subgenres" are unsourced or grounded only on independent websites? Brian W 00:21, 15 June 2006 (UTC)
thread_title: Your help is needed

message: For historical information see the Grove Dictionary of Music and Musicians including the articles Set and Analysis. For instance: 
"Aspects of set theory entered the theory of musical composition with J.M. Hauer’s theory of tropes (1925), and are evident in the writings of René Leibowitz, Josef Rufer, George Perle, George Rochberg (1955, 1959) and Pierre Boulez (1964, chap.2; 1966, part ii). The proper formulation of a set theory of music was the work of Milton Babbitt (1955, 1960, 1961, 1972), Donald Martino, David Lewin and John Rothgeb (JMT, iii–v, x, xi). But while Babbitt’s work, using particularly the mathematical concept of the group, dealt with harmony and with the functions of melodic and rhythmic configurations in 12-note music, and also with the interaction of components over longer spans of time, it belonged to the realm of compositional theory rather than analysis."
From the History section of IAN D. BENT/ANTHONY POPLE: 'Analysis', Grove Music Online ed. L. Macy (Accessed [30 June 2006]), <http://www.grovemusic.com>
--Amazzing5 20:23, 30 June 2006 (UTC)
thread_title:  History 

message: Routine WP:NOR notification.  Note: Citing sources and avoiding original research are inextricably linked: to demonstrate that you are not presenting original research, you must cite reliable sources that provide information directly related to the topic of the article, and that directly support the information as it is presented. Please do not assume readers have prior knowledge of subject matter. Semitransgenic (talk) 13:07, 26 August 2008 (UTC)
replies: text: Is there and how [is] original research in this article? Hyacinth (talk) 13:02, 30 December 2009 (UTC)

text: Removed. Hyacinth (talk) 07:03, 19 September 2010 (UTC)
thread_title:  OR 

message: Why, where, how? Hyacinth (talk) 13:01, 30 December 2009 (UTC)
replies: text: Removed. Hyacinth (talk) 07:03, 19 September 2010 (UTC)
thread_title: Refimprove

message: Mathematics does speak of 'ordered sets', and musical 'ordered sets', as they are, are covered.  —Preceding unsigned comment added by 41.185.115.52 (talk) 11:34, 17 January 2011 (UTC)
replies: text: Nice rant. Did you have any suggestions for improving this article?—Jerome Kohl (talk) 22:14, 9 February 2011 (UTC)
replies: text: "I adore Babbit, Cage, Gloria Coates and a lot of other cats you have never heard of. " original hipster, this one is. 164.76.148.252 (talk) 17:35, 21 September 2011 (UTC)
thread_title: Ordered sets

message: As a professional musician with no credentials other than playing, writing, arranging, being leader and member of ensembles too numerous and eclectic to remember entirely and having an utter devotion to the notion of music being art of the highest order and having the most profound ability to affect its audience of any art form- especially in its immediacy- I would love to see academia be less selfish and grandiose in its scope.  Granted, science has long since left the layman in the intellectual dust and we are better off for it inasmuch to a large degree.  However, the beauty of music is not in its analysis, nor are we more enlightened in our experience because of it.  If I have to analyze every piece of music to "get it" then I will probably never enjoy it like some other inexplicably simple musics that make the pain and joy of life more appreciable.  And, before anyone says it- I adore Babbit, Cage, Gloria Coates and a lot of other cats you have never heard of.  But when I've finished this rant, I will pick up my horn and play whatever comes to mind, for no other reason than that I'm urged to.   That's all I'll write now, I've got other things to do. Sammyflow (talk) 21:43, 9 February 2011 (UTC)
replies: text: Nice rant. Did you have any suggestions for improving this article?—Jerome Kohl (talk) 22:14, 9 February 2011 (UTC)
replies: text: "I adore Babbit, Cage, Gloria Coates and a lot of other cats you have never heard of. " original hipster, this one is. 164.76.148.252 (talk) 17:35, 21 September 2011 (UTC)
thread_title: Purpose

message: I have initiated a formal RM action to move Musical scale to Scale (music). Contributions and comments would be very welcome; decisions of this kind could affect the choice of title for many music theory articles.
NoeticaTea? 00:12, 21 June 2012 (UTC)
thread_title:  Requested move: "Musical scale" → "Scale (music)" 

message: 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) 06:43, 16 December 2012 (UTC)
replies: text: On the face of it you are correct, though of course 8 is the inversion of 4, and therefore the smaller number is the interval class representing both intervals. The first question to ask here, however, is whether the diagram correctly reproduces the example in Schuijer's book, from which it is taken. If it is an accurate transcription, then the question must be directed to Schuijer; if not, then it should be corrected.—Jerome Kohl (talk) 07:53, 16 December 2012 (UTC)
replies: text: Oops. You're right. Thanks. Since the numbers represent intervals between pitch classes then octaves don't count and the interval between pitch-class C and pitch-class G-sharp is 4. Probably then the example is correctly reproduced, but I'll let the creator of the image, Hyacinth, answer that. I also asked this question on the file talk page  because I didn't know who was watching what. I've redirected people who'll read the question there to the answer on this talk page. Incidentally, I've learned since then that this was not an appropriate use of an image file talk page. Signed: Basemetal (write to me here) 08:46, 16 December 2012 (UTC)

text: See Interval class and Interval vector. Hyacinth (talk) 10:18, 16 December 2012 (UTC)
thread_title:  First image in the article 

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thread_title:  External links modified 

message: Currently, the article begins: "Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson (1960) in connection with tonal music," I looked at the Hanson book. It says nothing about set theory that I could find. I did a search on an online version of the book for "set " and got exactly one hit that was not about set theory. If the idea is that the categories and their relationships that Hanson defines are similar to concepts in set theory then I agree but whether I agree or not doesn't matter, IMO the reference clearly doesn't support that opening sentence, and inferring something from another reference rather than using that reference to directly support your point is wp:OR. If no one responds with an explanation then I'm either going to either edit the intro or put an wp:OR tag on this article. --MadScientistX11 (talk) 23:33, 25 January 2018 (UTC)
replies: text: Maybe this is splitting hairs, but it does not seem to me the the opening sentence makes any claim that Hanson uses the term "set theory"—only that he first elaborated "many of the notions" used in it. What I notice more about the opening sentence is that it contains references at all. The article lead is supposed merely to summarize the article content. If Hanson's contribution is adequately documented in the body of the article, then it does not need to be supported (again) in the lead; if it is not adequately referenced in the article, then it should be removed, not so much on grounds of original research, as because it is not summarizing the article.—Jerome Kohl (talk) 04:10, 26 January 2018 (UTC)
replies: text: While I agree that references aren't normally found in intro sections the more important point is if the claim is supported. The sentence says "Many of the notions [of musical set theory] were first elaborated by Howard Hanson (1960) in connection with tonal music," If Hanson didn't talk about what he was doing as Musical set theory or draw any parallels with set theory then I don't think the claim is supported. I only glanced through the Hanson book but I didn't see anything that sounded directly like set theory.  I'm going to look at Hanson's book in more detail though, perhaps he uses ideas from set theory without mentioning sets per se. That seems unlikely to me but it's possible. --MadScientistX11 (talk) 04:45, 26 January 2018 (UTC)

text: It is important to keep an historical perspective here. How could Hanson speak of his ideas as being "musical set theory" or "draw parallels with set theory" if the idea of set theory had not yet been formulated? On the other hand, I do not find these claims verified (or even mentioned) in the body of the article, so they really do not belong in the article lead. The issue is not so much Hanson's role, as the question of when the idea of "set theory" was transferred from mathematics to music, yes?—Jerome Kohl (talk) 07:08, 26 January 2018 (UTC)
replies: text: Jerome, when you say: "How could Hanson speak of his ideas as being "musical set theory" or "draw parallels with set theory" if the idea of set theory had not yet been formulated?" it seems you are implying that set theory had not yet been formulated when Hanson wrote his book. Hanson wrote his book in the 1960's. Set theory goes back to the 19th century. Zermelo–Fraenkel set theory which is the foundation for most conventional modern math was defined in the 1920's. The work that Turing and Church did on the Entscheidungsproblem (proving that FOL is undecidable) was done in the 30's and set theory is a major component of that work. When mathematicians talk about First Order Logic they are talking about set theory as well. If you look at any rigorous book on mathematical topics like calculus, statistics, linear algebra that was written in the 60's (if it is a book whose audience is mathematicians rather than engineers or others who wouldn't be interested in theory) they will all start by grounding their specific math domain in set theory. So I think the ideas were definitely there when Hanson wrote his book. Also, I looked at Hanson's book more closely and there is nothing that I can find that is directly parallel with set theory except his notion of a compliment, although he just seems to be using the natural English meaning of compliment which in this case corresponds to the technical definition in set theory. Again, if someone wants to quote specific passages of Hanson's book and explain to me how they justify the claim please do so, but I'm more convinced now that it doesn't. The issue is at least partly Hanson's role because he is cited at the beginning of the article as supporting the idea of "Musical set theory" and I find nothing in the reference that is used to support that contention. Perhaps just removing that initial phrase or re-wording it to something like "some of the ideas that became musical set theory were first described by Hanson" I don't know enough music theory (although I know a lot of set theory) to feel like I should edit the article but I do feel pretty strongly that the current opening about Hanson is worded in a misleading way, and gives the reader the wrong idea.  --MadScientistX11 (talk) 14:01, 26 January 2018 (UTC)
replies: text: One other reply to Jerome's comment, when he says "The issue is not so much Hanson's role, as the question of when the idea of "set theory" was transferred from mathematics to music, yes?" I agree with that. Perhaps I misunderstood his original comment and he wasn't saying that "set theory" didn't exist when Hanson wrote his book but rather "musical set theory" didn't. Sorry if that is what you meant, if so then we agree. I'm also a little skeptical of some of the other references. For example the concept of an "ordered set" really jumps out at me. No mathematician that I know of would ever talk about an ordered set. It's an oxymoron. A set BY DEFINITION is unordered. Talking about an "ordered set" is the equivalent of talking about a "married bachelor". As I commented above a sequence is a kind of set that represents order but it's not an ordered set. When you look at the actual sequence the order in each set still is irrelevant. But I suppose it's possible the people who defined Musical Set theory use different terms. I'm getting a couple of the main references to take a look, they look interesting to me anyway. --MadScientistX11 (talk) 15:19, 26 January 2018 (UTC)

text: Yes, I meant musical set theory. Sorry about the ambiguity. There are many slippery issues when a term from one field is borrowed by writers working in another one. While a set is by (mathematical) definition unordered, in music theory it may be treated as either unordered or ordered, and careful theorists will use different modes of presentation for these two distinct conditions. Unfortunately, the careful theorists seem to be outnumbered by the sloppy kind but, then, music is an art, not a science.—Jerome Kohl (talk) 17:00, 26 January 2018 (UTC)
thread_title:  The opening sentences in this article seem like OR