13 ms·
The Mathematics of Music [pdf]
- brudgers 6y agothe software can be found here, https://imaginary.org/programs https://imaginary.org/programs
- TheOtherHobbes 6y agoI'm not sure whom this is aimed at. The name "La La Lab" and the interactivity suggests kids, but there's a Fourier integral on Page 7 which immediately suggests undergraduates.
- nathell 6y agoWhy would the interactivity be limited to kids? I think the name is a pun on "La La Land", a musical film.
- elondaits 6y agoNeither... I suggested the name in a brainstorming session. We wanted to transmit the exhibition was like a Lab and I joined with the “La La La” you would use to warm up your voice, or the onomatopoeia of singing. We were concerned of the movie association, but this exhibition was initially targeted at Germany so it wouldn’t be as strong as in the US. Edit: the exhibition IS kid-friendly though... we have lots of families and schools visiting. Surprised and happy to find a mention to LA LA LAB here ️ We just launched a digital exhibition on AI at www.i-am.ai
- empath75 6y agothe expression predates the film by many years, fwiw.
- bluetwo 6y agoI have the same confusion about the target audience but there are some interesting tidbits. Seems more like a brain dump.
- 082349872349872 6y agoC, E-flat, and G go into a bar. The bartender says, "Sorry, but we don't serve minors." So E-flat leaves, and C and G have an open fifth between them. After a few drinks, the fifth is diminished, and G is out flat. F comes in and tries to augment the situation, but is not sharp enough. D comes in and heads for the bathroom, saying, "Excuse me; I'll just be a second." Then A comes in, but the bartender is not convinced that this relative of C is not a minor. Then the bartender notices B-flat hiding at the end of the bar and says, "Get out! You're the seventh minor I've found in this bar tonight." E-flat comes back the next night in a three-piece suit with nicely shined shoes. The bartender says, "You're looking sharp tonight. Come on in, this could be a major development." Sure enough, E-flat soon takes off his suit and everything else, and is au natural. Eventually C sobers up and realizes in horror that he's under a rest. C is brought to trial, found guilty of contributing to the diminution of a minor, and is sentenced to 10 years of D.S. without Coda at an upscale correctional facility.
- arc_of_descent 6y agoMade my day!
- deleted 6y ago[deleted]
- georgiatestprep 6y agoAmazing and incredible La la MATH...
- kevindeasis 6y agoI started learning music recently, and another type that I would like to see, is mathematics for music genres, mathematics for music effects and mathematics for music theory
- peterkos 6y ago> mathematics for music theory Oh boy now that's a fun one There's a great book called "The Oxford Handbook of Algorithmic Music"[0] that has many insights into that! Some philosophical, some really mathy. [0] https://global.oup.com/academic/product/the-oxford-handbook-of-algorithmic-music-9780190226992 https://global.oup.com/academic/product/the-oxford-handbook-...
- mhh__ 6y agoMathematics for music effects is called digital signal processing. Proakis's book is good if you can handle analysis. Also, a word of warning/advice: Music theory is not mathematics - it's just a way of storing patterns that sound nice on western instruments. There are some musical genres that you can basically generate algorithmically, but if you want to actually learn musicianship stay well clear. Mark Levine's books are a good "textbook style" music theory book with lots of examples of actual jazz music.
- parenthesis 6y agoActually, there is lots of nice maths in music theory. Yes, music theory is descriptive rather than prescriptive. But messing around (mathematically) with its ideas can help one find nice musical possibilities one might not otherwise have considered. For example, the major scale, the (ascending) melodic minor scale, and the harmonic minor scale are all seven-note scales such that all scale-wise thirds are major or minor. This is important, because people like using harmony built on stacking major and minor thirds. But are there any other seven-note scales whose thirds are all major or minor, beside the aforementioned (and their modes)? Yes, the harmonic major scale (and its modes). Not so well known, it presents lots of different, but still ultimately convential, possibilities.
- 6y ago
- siraben 6y agoIn a similar vein, there's the Topos of Music book[0], which, according to Wikipedia, has been somewhat controversial among mathematicians and musicians alike. [0] https://www.amazon.com/Topos-Music-Geometric-Concepts-Performance/dp/3764357312 https://www.amazon.com/Topos-Music-Geometric-Concepts-Perfor...
- lioeters 6y agoThanks for the book recommendation. I was curious about the controversy, so dug into it a bit. From the Wikipedia page of the author: > Dmitri Tymoczko..said of Mazzola: "If you can't learn algebraic geometry, he sometimes seems to be saying, then you have no business trying to understand Mozart." https://en.wikipedia.org/wiki/Guerino_Mazzola https://en.wikipedia.org/wiki/Guerino_Mazzola The critic, Tymoczko, is the author of A Geometry of Music. Oh, his review of Topos of Music is online. http://dmitri.mycpanel.princeton.edu/files/publications/mazzola.pdf http://dmitri.mycpanel.princeton.edu/files/publications/mazz... (PDF) Abstract: This paper critiques Guerino Mazzola’s derivation of traditional counterpoint rules, arguing that those rules are not well-modeled by pitch-class intervals; that Mazzola’s differential treatment of fifths and octaves is not supported musically or by traditional counterpoint texts; that Mazzola’s specific calculations are not reproducible; that there are a number of intuitive considerations weighing against Mazzola’s explanation; that the fit between theory and evidence is not good; and that Mazzola’s statistical arguments are flawed. This leads to some general methodological reflections on different approaches to mathematical music theory, as well as to an alternative model of first-species counterpoint featuring the orbifold T2/S2.
- OscarCunningham 6y agoAnother good book in the same vein is Dave Benson's 'Music: a Mathematical Offering'. https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...
- enriquto 6y agoThat's an incredible book! The observation that harmony depends on the timbre of instruments was mind blowing (e.g., if we used different musical instruments, the consonant and dissonant intervals would be different).
- OscarCunningham 6y agoWilliam Sethares has a good webpage about this (https://sethares.engr.wisc.edu/consemi.html https://sethares.engr.wisc.edu/consemi.html). He talks about how you can create a synthesised instrument to fit a given scale. He even has example pieces you can listen to that are written in scales that would sound terrible with our usual instruments.
- enriquto 6y agoNotice that the "scalelab" tool of TFA allows you to also synthesize dissonant octaves and whatnot: https://github.com/IMAGINARY/ScaleLab https://github.com/IMAGINARY/ScaleLab
- lioeters 6y agoRecommended: A Geometry of Music by Dmitri Tymoczko - http://dmitri.mycpanel.princeton.edu/geometry-of-music.html http://dmitri.mycpanel.princeton.edu/geometry-of-music.html The Geometry of Musical Rhythm by Godfried Toussaint - Original paper - http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-rhythm.pdf http://cgm.cs.mcgill.ca/~godfried/publications/geometry-of-r... (PDF) - Book - Review https://mtosmt.org/issues/mto.13.19.2/mto.13.19.2.gotham.php https://mtosmt.org/issues/mto.13.19.2/mto.13.19.2.gotham.php
- RogueBurger 6y agoI picked that book up on a whim a couple years ago and was surprised how engaged I was. It introduces you to some very interesting concepts.
- lioeters 6y agoI admit much of it's over my head, but that's exactly the kind of books I like. I keep coming back to chew on different parts.
- addictedcs 6y agoMusimathics is great [1]. If you want a more interactive source you can play with python notebooks from the music information retrieval site [2]. I've found it helpful, as you try some of the described music theory concepts in a programming environment. Shameless plug, I've also written about how audio fingerprinting works [3], which touches on some of the topics regarding music theory. [1] http://www.musimathics.com http://www.musimathics.com [2] https://musicinformationretrieval.com https://musicinformationretrieval.com [3] https://emysound.com/blog/open-source/2020/06/12/how-audio-fingerprinting-works.html https://emysound.com/blog/open-source/2020/06/12/how-audio-f...
- motohagiography 6y agoHave posted this link before, but so relevant to the discussion: https://softwareengineering.stackexchange.com/questions/136085/is-musical-notation-turing-complete https://softwareengineering.stackexchange.com/questions/1360... If music were Turing complete, it could imply we've been developing the ability to derive theorems in it as a species forever, which has some speculatively interesting philosophical implications as well. :)
- totemandtoken 6y agoWhat would some of those philosophic implications be? Also, this link asks if music notation is Turing complete, not music itself. Is out method of writing musc turing complete or is the music itself turing complete? What about something like maqam or other microtonal systems? Or temperament beyond the twelve-tone temperament we know and love? Good find though, that's a very interesting question...
- motohagiography 6y agoIANA-Philosopher, but if music, geometry, and logic could each encode all the same things, and we have a musical "sense," for its rules and symmetry, it's reasonable to speculate that music is an artifact of patterns and theorems that appear in these other areas, and where we don't have an matching rule in one area, it implies one should exist in the other. It's stuff like the machine learning kit that produced a new AC/DC song (https://www.youtube.com/watch?v=vpEVsDN84Hc https://www.youtube.com/watch?v=vpEVsDN84Hc), meaning that machine learning has discovered an algorithm for producing outputs from rules effectively hidden in the band members heads. The function the ML model discovered that produces theorems in the domain of plausible AC/DC songs isn't as useful to us as the one that produces plausible fluid dynamics models, but the possibility that the properties (or category) of that function might contain other analogies and isomorphisms to geometric figures, graphs, and other objects may imply that when we listen to music or compose, it our minds could just be in effect, "doing math," - and whether we in fact do anything that is "not math," either. High level, I suspect this may have been what Hofstadter, Dennett, and Searle were on about.
- aaron-santos 6y agoAbsolutely fascinating section on Lissajous figures. I had only been exposed to the concept through orbits.[1] [1] - https://en.wikipedia.org/wiki/Lissajous_orbit https://en.wikipedia.org/wiki/Lissajous_orbit
- kian 6y agoI highly recommend Drew Nobile's book or papers on functional circuits as an adjunct to this on how to recursively generate songs from an initial seed progression.