Talk:Music and mathematics

Music Part a Joke
"the xylophone progression at the beginning of the 3rd movement occurs at the intervals 1:2:3:5:8:5:3:2:1." is totally unclear exactly what it means - in addition, Bartok doubles the ones, just like Fibonacci.

"an example of Fibonacci chords" - Ha ha ha! That is mapped on to a major scale - what does the major scale have to do with Fibonacci? Use the overtone series or something.

"Many of the important musical events in Krzysztof Penderecki's "Threnody for the Victims of Hiroshima" occur at φ positions." poorly written

Nobody usually listens to me about this stuff, so whatever, but the part on music SUCKS - believe me. (I bet you guys will leave it in there though, as you always do ;). There is a composer you guys are majorly missing here too, btw. — Preceding unsigned comment added by 98.182.18.84 (talk) 15:34, 16 December 2011 (UTC)


 * I agree mostly. Mentioning Fibonacci in terms of music gets people into circular reasoning in no time. The sad truth is that most of WP's music articles are written a) by people who are amateurs at best and b) music and/or musicology students who compensate for getting less recognition than their peers.

David Cope
I'm not sure the link to the David Cope article is relevant? Or is it? Madder 13:47, 18 August 2006 (UTC)

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)


 * 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)


 * 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)
 * 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)

Link to MIT Press website
While I understand that we should keep Wikipedia free from commercial links, I would argue that the website in the Musicmath reference is very useful, for it contains a table of content. It helps readers of this article to get a quick overview on the topic of Music and Mathematics. Please do not remove the link without having discussed it on this talk page. Thank you Matthias Röder 23:12, 31 May 2007 (UTC)
 * I disagree. First, the link is to information that's fairly far from the topic of this article (see WP:EL). Second, the link is to a highly promotional webpage (see WP:SPAM).
 * If this information gives a quick overview, it should be added to the article itself rather than only being accessible in a link that's placed in such an inconspicuous spot. -- Ronz 00:44, 2 June 2007 (UTC)
 * Thanks for your input, Ronz! I agree that the site contains a lot of promotional blurp. What about this: we could link to this site instead: http://www.musimathics.com/ It contains a detailed table of contents and information about the topic and author. We could add this site to a "external links" section instead of linking it from the book title itself. After the book citationwe could add something like "see external links for further information about this book) Does that sound like a good compromise? Cheers! Matthias Röder 10:14, 2 June 2007 (UTC)
 * Yes, I think that is a better link. Where should it go, though?  Generally, if we want it to be used as you suggest, it should go in the External links section.  I'd like to hear others' opinions. -- Ronz  02:28, 4 June 2007 (UTC)
 * Let's put into the External links section, ok? Matthias Röder 17:02, 10 June 2007 (UTC)

I just changed the URL and I hope this is ok. :-) Matthias Röder 09:15, 14 June 2007 (UTC)

This looks bad...
Over the next few days I'm going to make some serious revisions to the article. Here are some problems I see in the current article:

(1) The introduction is short and not very informative. (2) It doesn't outline all the important applications of mathematics to music. (3) The discussion of time signatures has little to do with number theory. (4) The section on the Golden ratio and Fibonacci numbers mentions several examples in which the mathematical concepts do not play any fundamental role in the music. (5) There are several disconnected sections on intonation.

Willow1729 23:06, 26 August 2007 (UTC)


 * On talk pages, please put new sections at the bottom using the '+' button. —Tamfang 07:44, 27 August 2007 (UTC)

Harmonic series
It seems odd that there is no discussion of the harmonic series on this page. Aren't the ratios of the harmonic series and the properties of waves the most fundamental aspect of the interaction between math and music? Things like set theory, while interesting, seem much more peripheral. Cazort (talk) 17:06, 31 December 2007 (UTC)

Unequal Temperaments book and website
Dear friends,

The Unequal Temperaments book of 1978 was described-in writing-as the definitive reference on the matter by authorities such as John Barnes, Hubert Bédard, Kenneth Gilbert, Igor Kipnis, Rudolf Rasch and others. In the 1990's I also developed the first professional-grade temperament spreadsheets.

Eventually I setup the "Unequal Temperaments" website, where I uploaded the spreadsheets which, kept permanently updated, are available for FREE. I also uploaded years ago a provisional "Update" to the book of 1978.

The website lately gives information on the recently released new version of Unequal Temperaments 2008, which includes a discussion of Music and Mathematics in relation to studies of temperament and scales. (The website does NOT sell the book). Two favourable reviews of this book (one in the US the other in the UK) have now been published.

I would find it useful to Wikipedia readers if my website was included among External Links:


 * Unequal Temperaments website, with Preview of the new 2008 book by Claudio Di Veroli

Kind regards

Claudio

Dr. Claudio Di Veroli 86.42.128.58 (talk) 17:21, 26 February 2009 (UTC)

Perfect 7th?
This page mentions a Perfect 7th, but I've never heard of this before? —Preceding unsigned comment added by 194.200.65.239 (talk) 12:12, 27 July 2009 (UTC)

Flagged OR - request
The section below has been flagged OR for some time. I myself cannot refer it to any RS (or, I admit, see the point). Can anyone help, please? Redheylin (talk) 16:06, 17 December 2009 (UTC)


 * Helmoltz's On the Sensations of Tone could probably help. (My copy is in a box somewhere.) —Tamfang (talk) 19:15, 18 December 2009 (UTC)


 * I have both of my copies handy (original and Dover reprint), and there's one online. But I can't make any sense out of this section. Dicklyon (talk) 20:44, 18 December 2009 (UTC)

What other equal tempered scales have harmonic identities 1-8 represented?
The diagram below compares/contrasts several good equal-tempered scales. The frequencies are plotted on a logarithmic scale so that each step is equally spaced. On a linear frequency scale, the steps would exponentially grow in size. It is clear how nearly each scale approximates the exact M3, P5, and P7. (The P7 is seldom used in Western music.) Note: the scale steps are the black bars separating the colored spaces.



trivial consistency

 * The following graph reveals how accurately various equal tempered scales approximate three important harmonic identities ...

Is a graph missing? This sentence is followed by a table showing the frequencies and log-frequencies of the tempered intervals, but no mention of harmonies. —Tamfang (talk) 14:49, 31 October 2010 (UTC)

Music or not Music, this is the Question
Without the boundaries of rhythmic structure – a fundamental equal and regular arrangement of pulse repetitivity, accent, phrase and duration – music would be impossible.

I realize this statement is sourced, but I don't think it's accurate at all. By this definition many examples of Gregorian Chants, Free Jazz, Avantgarde, Ambient and Experimental music would not be considered music anymore. This section should be changed accordingly. 91.44.20.166 (talk) 11:41, 29 January 2012 (UTC)

Tuning systems
I have edited/added some things to make the comment about Arabic music re: equal temperament more accurate. Now, however, it seems a bit out of place where it is. If anyone has any suggestions, it would be appreciated. Eflatmajor7th (talk) 08:55, 3 September 2012 (UTC)

A referenced graph is missing. The paragraph above second table in this Section begins "The following graph reveals..." – but there is no graph. Lost in edits? Would correct if I could. SirHolo (talk) 03:16, 10 November 2014 (UTC)

Rhythm and Powers of Two
The rhythm section seemed painfully lacking to me so I threw in some stuff. All music's rhythm seems to be based on powers of two for some reason so I explained a little bit about that. Admittedly, I have no clue why this is. Perhaps our auditory cortex computes things in binary? I wikified it a bit but I feel like maybe I should add some citation needed here things.

By the way, I have written songs with a ton of triplets and found looking back over it that most classically trained people would have probably just written the song in 12 - that's how I realized that pretty much all songs are actually in 4-4, as long as it uses some multiple of 3 or 4 beats per measure and doesn't change. I.e. this doesn't work for Rush songs, which obey their own mathematical laws. KagakuKyouju (talk) 03:25, 27 January 2013 (UTC)
 * There is a lot of engaging music being played with five or seven beats to a measure. __ Just plain Bill (talk) 15:14, 27 January 2013 (UTC)
 * Bulgarian_dances
 * Tala_(music)
 * Rhythm_in_Sub-Saharan_African_music
 * Eflatmajor7th (talk) 20:47, 27 January 2013 (UTC)
 * In the math and music context, I think it would be appropriate to mention that the tempo (in bpm) is the ratio of musical and physical time units, this is, the derivative of the musical time. Giving the tempo as information in the score means giving the derivative of the musical time for each musical time point. Clearly speaking, the link between musical and physical time is given as an ordinary differential equation. For example, if the tempo increases linearly w.r.t. musical time (like an increase of 5 bpm every beat, starting from 60bpm), we are given an ODE $$m' = 60 + 5m$$. By variation of parameters and initial condition $$m(0)=0$$, we get the solution $$m(t) = 12e^{5t}-12$$ which means that the tempo actually doubles every $$\tfrac{\log2}5$$ minutes $$\approx 8.3$$ seconds. Long story short, the tempo actually in increases exponentially w.r.t. physical time because the linear part is just the right-hand side of an ODE.
 * If the tempo of each voice is constant, this is simple. If all voices have the same tempo, it does not matter. But if there are voices with different and varying tempo, this gets very weird and mathematically interesting. DrPhimor (talk) 14:50, 26 October 2022 (UTC)

No rhyme or reason to this
In the first section, it says:

"In Old English the word "rhyme", derived from "rhythm", became associated and confused with rim..."

But the second section reads:

"The word "rhyme" was not derived from "rhythm" (see Oxford and Collins dictionaries) but from old English "rime"."

Now, I don't mean to split hairs or anything, but that's completely inconsistent. 184.148.152.132 (talk) 03:26, 16 February 2013 (UTC)

Group Theory section needs to be explained better
The section on Group Theory is comprehensible only by people who already understand group theory. In other words, it is not educational. — Preceding unsigned comment added by 69.180.235.142 (talk) 15:41, 18 June 2014 (UTC)

External links modified (February 2018)
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Xenharmonic
Due to the closure of Wikispaces, the following link was removed from the article:
 * https://xenharmonic.wikispaces.com/The+Riemann+Zeta+Function+and+Tuning

Evidently the wiki was about Xenharmonic music. Perhaps the content is subsumed by the wiki in this Project. With the advance of music beyond equal temperament, the article could benefit from appropriate references and links. — Rgdboer (talk) 21:22, 6 October 2019 (UTC)

"Music theory has no axiomatic foundation in modern mathematics"
Does this work by Guerino Mazzola (The Topos of Music: Geometric Logic of Concepts, Theory, and Performance) count as an axiomatic foundation of music theory in modern mathematics using topos theory? (Volume can be found here). 73.168.5.183 (talk) 16:33, 3 February 2020 (UTC)