Talk:Music and mathematics
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I'm not sure the link to the David Cope article is relevant? Or is it? Madder 13:47, 18 August 2006 (UTC)
[edit] Further development of this article
notes for the reader: (1) English is not my native language. Hope you'll be able to 'read thru' my obvious writing and languages errors (2) contributing to the Wikipedia is a new for me.
Reading the title music and mathematics I was very much interested about the content. By contributing to the discussion and, in second stage, the article itself I hope to gain more insights in the theoretical developments in the area. So actually the start of my discussion is to get in contact with the original writer(s) and see if we can take the article further from there. So please see this discussion as an open invitation.
As interested as I was when reading the articles title I must admit I was rather critical when reading it. Once again: this is an open invitation and please see my first (from the top of my head) remarks as openings to further developments and discussions.
a. group theory
I agree that grouping tones is something that can relate to mathematics.
(1) What I don't understand is that you choose to group music elements into one group of 13 elements. Probably because you add the octave in the group of individual tones/elements. I would suggest to group the tones into one group of 12. Since western/classical music uses 12 different tones. This group could be called the 'root-material' since it contains all elements with which western/classical music is constructed. Interesting, but not very mathematical, is the fact that the root-material' content is culturally influenced. There are cultures that use more (or less) than our 12 tones. And in our contemporary music there have been many experiments with more than 12 tones. Strange enough this is not only a result of modernism but actually has it's roots in the tuning of instruments. It's only since we're playing music in the equal temperament tuning that we use only 12 pitches.
Further I think it's important to pay attention to the fact that musically grouped pitches (like scales and modes) not only represent a group but (more important) that the elements in the group have very specific relations to each other. These relations are what we call tonality or modality. Also pitch class sets (a analyses method for contemporary music) have internal relations (and are described based on these relations) but relate (as a group) to other pitch class sets.
b. number theory
(1) the formula you have chosen is not accurate. Although it is common to write the three quarter measure in a text passage as 3/4 measure you should realize this is this is purely done for typographical reasons. In the music itself you won't find the '/' sign at all. Mathematically 3/4 would be equal to 0,75. In music this makes no sense at all. In fact 3/4 means 'in this measure 3 notes of 1/4 fit' This is hardly a mathematical description. I agree with you that measure, rhythm meter etc have a lot to do with numbers. But I think maybe rather more with the grouping of time into 2 and 3. Also a topic worth for further study I suggest. Without explaining right how I think the notation of measures and rhythm and the practice of playing the actual music has to do with the mathematical elements of grouping (in layers) of groups of 2 and 3 AND with the human influence we could maybe describe as chaos (theory). This because our music notation on time (measure and rhythm) is no more than a imperfect model. good enough to let the musician know what is the intention but not more than this.
(2) It's musical theoretically incorrect to say that a 12/8 measure can be described a s 4 times a 3/8. A 12/8 measure is grouped in two times two groups of 3 1/8 notes. The difference is that you should consider the relation between the elements within the 12/8 measure In a 12/8 measure you'll experience a meter like" heavy-light-heavy-light . In 4 3/8 measures you will experience a meter of four equal elements. These are very important differences for the actual 'face' of the meter (let's say the groove).
(3) the remark on the prime numbers is interesting. I agree with you that these measures are more complex. Not because the denometer is a prime but simply because the meter/measure is a combination of groups of 2 and 3. Now to say these are more difficult is far from a mathematical conclusion. The fact is; they're not. If you happen to visit countries like Hungary, former Yugoslavia Romania and Bulgaria you'll notice that little children there clap 11/8, 6/8 etc etc measure without blinking their eyes once. So it's all a matter of behaviourism (and not mathematics)
(4) numbers can be found in music but than in a more 'encryption' manner instead of purely mathematical. BACH used the numbers 2 1 3 8 (together 14) many times in his compositions. Interesting is that he only uses the tones BACH (in German the B-flat is called b and the b is called h) also called the 'BACH-theme' only once in his compositions (the incomplete fugue he composed at the end of his life).
c. Golden ration and Fibonacci
Interesting and surely something where mathematics and music (and all arts) meet Maybe also good to add examples from earlier music. Sure (for Fibonacci) you should mention Xenakis. The greek composer and architect. Using Finonacci is something composers and architects have in common. Further is worth trying to divide the golden ratio and the Fibonacci numbers into: a. where they are used as a tool for composingg music (more the contemporary copmposers) b. as a principle of structure that can be found in many master pieces from all ages.
And last but not least maybe there's something to be said about the Fibonacci numbers and measures/rhythm 1,2,3,5,8 are very common denometers. Just a thought and worth further investigation as the topic of music theory and mathematic itself I would say....
Yom Langhorst 09:30, 19 January 2007 (UTC)
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- Hi Yom Langhorst, please remember that the article is made up of contributions by many different people, and that anyone can contribute. So if you spot a mistake or want to add content to the article, you can do so as long as it is a fact and not your personal opinion. Feel free to edit the article as long as it is encyclopaedic :-) Madder 16:42, 19 January 2007 (UTC)
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- Hi Madder,thanks for your reaction. The concept of the wiki is clear to me. However music and math in the way it's presented in this article (thus not in the purely physical sence where math is important to describe the physics behind sound (waveforms etc) the topic isn't studied and described all that well yet. I mean there's not a lot of commonly accepted knowledge to start from. Therefor I think it would be very interesting to find recourses, discuss and weight them (before putting them in an article) in a forum such as this. And in the mean time I'm wondering why so many personal opinions and non scientific ('proven') information is put in the article. Ofcourse you could say that it is my opinion but nevertheless I do have strong argument to support my opinion. So my primer goal is to 'start up' the discussion on the topic and not (in the first place) to write the article. Hopefully this will be the start of an intersting quest...
Yom Langhorst 09:11, 30 January 2007 (UTC)
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- Unless your proposed changes are very radical, the best way to get things moving is to make edits to the article. This encourages others to make edits too. It's the only way forward. Any statements that you make should be referenced, this is how arguments are avoided. Hope you can help improve article. Best, Madder 15:02, 31 January 2007 (UTC)
