|WikiProject Music theory||(Rated Stub-class)|
Not clear enough for non-mathematicians
I have attempted to clarify the sentence about modular complements, but confess I know little about this subject.
OTOH, I am completely unable to clarify this:
In set theory the traditional concept of complementation may be distinguished as literal pitch class complement while, due to the definition of equivalent sets, the concept may be broadened to include "not only the literal pc complement of that set but also any transposed or inverted-and-tranposed form of the literal complement." This is due to the fact that since P is equivalent to M, and M is the complement of M, P is also the complement of M, "from a logical and musical point of view," even though not its literal pc complement.
What exactly do P, M and M stand for? In what way are P and M "equivalent"? What exactly is a literal pitch class? I suspect most readers (like me) are baffled enough by the serial methodology to have no clue about what all this actually means. (Eg, a transposed interval is still the same interval so why make the point in the first place; and why not inverted-only?)
- I don't know if "literal pitch class" is anything but traditional "literal pitch class complementation" is contrasted with nontraditional 'set class' "complementation".
- P, M, and M are variables. Hyacinth (talk) 10:19, 25 December 2009 (UTC)
- Yes, OTOH: I have tried to clarify one part but, on the other hand, I am unable to clarify the other part.
- I still can't. Those figures are indeed variables which means they are not constant... We have no frame of reference: what specifically are these variables supposed to represent?
- I know absolutely nothing about either of those theories but the article assumes I do... and I am still none the wiser after reading this article. Specifically, why does set theory have a different way of looking at complementation; have I correctly summarised the modular theory; and what exactly do P, M and M stand for? Basically, we must clarify what on earth this is trying to say in this article! It is not good enough to expect a reader to wade through the protracted explanation of those theories in Set theory (music) and Modular arithmetic (which also assume too much mathematical expertise). This has to explained here. After all, we are talking to musicians not "modular mathematicians" or "set theorists". --Jubilee♫clipman 23:14, 25 December 2009 (UTC)
- Also, the added image of Schoenberg's "nonliteral" complementation is more confusing again: M contains more notes than M so how is this an inversion or complement? Worse still, M does not invert to P: there is a minor second at the top of M but a major second at the bottom of P and none of the other intervals correspond in any way that is obvious to me... Is that why it is "non-literal"? Or am I still not getting this? I thought it was like this: when the same set of chords (in which the second and fourth chords are complements) are played at a different pitch later on we can also say the second chord of the original and the fourth chord of the transposition are also complements even though they don't "literally" complement each other. Now I am even more confused... --Jubilee♫clipman 23:28, 25 December 2009 (UTC)
- Oh wait.. I think I am beginning to get this: M contains B, C♯, D, E, B♭ while M contains all the other notes of the chromatic scale. In other words, this is a totally different meaning of complement! However, I still don't see how P is the "inversion" of M. Nor does it "complement" M in the sense I just explained since it contains identical notes plus two others... I am getting there though I think! I also feel that the first part of this section needs a lot more clarity: I can now see that P-0 and I-3 are the inverse of each other and that the last hexachord of each one contains the same notes as the first hexachord of the other one, but this took ages to spot! That assumes that I have correctly identified the reason for the arrows... --Jubilee♫clipman 00:39, 26 December 2009 (UTC)
First, just because one is a musician doesn't mean one is an idiot.
Secondly, as I've said before, if you've never heard of a concept you are not the best person to explain it. I would be disappointed if I went to the doctor and, due to a sense of urgency, some untrained person walked in off the street and started guessing instead of a qualified MD. As such, you are a great person to read an article such as this, point out what needs clarification and ask questions, but you may not be the best person to write in this article. Hyacinth (talk) 08:51, 26 December 2009 (UTC)
- I never said that musicians are idiots, I simply pointed out that they are not necessarily either mathematicians or music theorists. Perhaps I am not the best person to explain this subject with authority but I am perhaps best placed to attempt to understand it for the first time and, in the process, bring fresh insight and clarity into articles such as this. After all, someone struggling to understand a subject will try to explain it in the simplest possible terms. No contribution is wrong on WP: this is not like a single non-doctor trying to diagnose an ailment because every singe edit here is subject to the entire www's scrutiny. Hopefully, the actual doctor will appear at some point to correct the mistakes; hopefully the doctor will retain any clarity in the attempted edits by the new student or add clarity if it is lacking! (BTW, I think were starting to make sense of article between us: this is great collaboration!) --Jubilee♫clipman 01:43, 27 December 2009 (UTC)