Wikipedia:Reference desk/Archives/Mathematics/2020 July 26

= July 26 =

Plotting Musical Notes in 3 Dimensional Space
I'm back again. I haven't received a proper answer to my last doubt, but never mind. Currently I'm bubbling with ideas, but I seem to have ended up in this particular idea that has completely stormed my mind. My idea is this : if we are able to plot musical notes in a 3D space, we will be able to make music from any 3D object around us, by taking arbitrary points in its mesh, or taking its vertices and so on. Currently I tried a bit of regression analysis on a scatter plot of numbers 1 to 12 vs the frequencies of notes C0 to B0 [including the sharp notes] at 440 Hz tuning, and ended up in a function to (at least) round up to the actual frequencies. Thus, I felt that a space with the notes C0 to B0 plotted as integers -12 to +12 on the X -axis, the beat count on the Y- axis and pitch between -∞ and +∞ on the Z - axis may help in plotting musical notes in 3D space, or to get varieties of musical progressions from a single object. Also, I believe such a system may help in studying the scores of many songs and soundtracks deeper than before.--Sam Ruben Abraham (talk) 07:23, 26 July 2020 (UTC)


 * You appear to use the term "pitch" in a different sense than musicians. For the rest, is there a question here (and if so, is it about a mathematical topic)? The Reference Desk is not a chat room. --Lambiam 08:27, 26 July 2020 (UTC)


 * I know this is no chat room. I am bubbling with ideas (I don't know if you people find it silly), but I can't resist my desire to share an idea, to talk about it, dream about it and to bring it out. Well, any answers ? If required, I'll also attach my code for the regression analysis I did in an upcoming reply.Plus, pitch of a sound is our perception of its frequency, right ? --Sam Ruben Abraham (talk) 08:54, 26 July 2020 (UTC)
 * Not all sounds have a defined frequency; in fact, most don't. For a pitch is identifiable, the frequency spectrum needs to be relatively stable in time and have one or more peaks. Even for purely repetitive sound waves, the pitch (as perceived) can be ambiguous and context-dependent. But in almost all classical non-experimental music, there is a direct correspondence between pitch and frequency, and plotting these with different axes will therefore add very little additional information. --Lambiam 10:06, 26 July 2020 (UTC)


 * Ok, so it seems like I haven't added the actual question .... my doubt is : is the method mentioned above feasible, ? --Sam Ruben Abraham (talk) 08:56, 26 July 2020 (UTC)
 * Whether it is feasible or not is definitely not a mathematical topic. It will be a lot of work; I have my opinion about whether this is likely to be a rewarding exercise, but this is not a place to discuss opinions. I take it, though, that you are not a practising musician. Discussions about mathematics and music are welcome at the ##cymatics freenode. --Lambiam 10:06, 26 July 2020 (UTC)
 * Where can I find the rules for Reference desk? Philosophic topics highly resemble opinions. Does it mean philosophic topics are also forbidden in Reference desk? - Justin545 (talk) 05:24, 27 July 2020 (UTC)
 * – Of course not. But if a questioner asks a question like, "Do humans have free will?", the volunteer editors trying to provide answers (if they follow our guidelines for editors) are not going to supply their own points of view but will refer the questioner to our article Free will, which gives an overview of the ways philosophers have addressed this question through the ages. --Lambiam 06:53, 27 July 2020 (UTC)
 * Agree. Thank you for the clarification. There are many guidelines that need to be complied with here. I must admit that these qualified Wikipedians (like you) are quite outstanding :-) - Justin545 (talk) 13:39, 27 July 2020 (UTC)
 * Okay .... thanks for the advice. I asked about its feasibility to learn about its math aspects, which you are well aware of. By the way, thank you.--Sam Ruben Abraham (talk) 10:10, 26 July 2020 (UTC)
 * Really, you ought to stop asking your questions here. It's approaching the point where we switch from just telling you this isn't a mathematics forum to where we actively tell you to stop, because it's not Wikipedia's purpose.--Jasper Deng (talk) 00:49, 27 July 2020 (UTC)
 * Sorry if I created a nuisance for you. You see, I thought asking you any way may get me some mathematical insights into the ideas that I propose. Um... I didn't think kids like me would hurt your community of well - educated people.--Sam Ruben Abraham (talk) 05:30, 27 July 2020 (UTC)
 * Plus, I understand that this is no forum or homework help website, and this site aims to make knowledge accessible to all. I respect you people, but I never knew I was a nerd.--Sam Ruben Abraham (talk) 05:33, 27 July 2020 (UTC)
 * You can also pose your questions at the School of Mathematics Help Desk over at our sister project Wikiversity, which is not a reference desk like here, and is more directed to interacting and helping each other figure out how to learn things. --Lambiam 07:27, 27 July 2020 (UTC)

Plotting music in higher dimensions is discussed in Christopher Longuet-Higgins's book Mental Processes. The idea iirc was to treat powers of small integer ratios (i.e. musical intervals, like 3/2=perfect fifth) as coordinate axes, so you get a lattice of points in multi-dimensional space where you can locate chords and see transitions between neighboring chords in that space. I suspect music theorists have also done stuff with this idea but it's not my area so I don't know what else is out there. 2601:648:8202:96B0:0:0:0:5B74 (talk) 04:13, 29 July 2020 (UTC)
 * Thanks, but I am not considering chords here. I am only planning to plot the notes in the treble clef as per the idea I mentioned. I did a bit of regression analysis on a data set, where the independent variable was made to vary in the interval [1,12] or $$N = $${$$x : x \in Z, 1 \le x \le 12$$}(such that the variable yielded only integer values) and the dependent variable was the frequency of the notes C, C#, D, D#,....etc. to B at pitch 0 and the standard tuning (of 440 Hz). The regression model seemed to do well (it showed a linear correlation between the variables), but yes a few errors did occur, while the rest were somewhere nearer to the expected values. So, basically, if the errors aren't considered, we can plot the notes at pitch 0 as integers 1 to 12 on any of those axes, if I am correct.--Sam Ruben Abraham (talk) 05:10, 29 July 2020 (UTC)
 * Sorry if I'm causing some sort of confusion. I talked of my idea with respect to square waves.--Sam Ruben Abraham (talk) 04:26, 30 July 2020 (UTC)