Top all-time · #5306
Dmitri Tymoczko
Personal blog · dmitri.mycpanel.princeton.edumathscience
Dmitri Tymoczko's personal blog at dmitri.mycpanel.princeton.edu covers math and science. Since 2016, 15 different Hacker News readers have linked it 21 times, most often “What Makes Music Sound Good? (2010) [pdf]”. No feed was found, so read it on the site itself.
Too few sampled comments (16) to say how often HN recommends it.?
Why HN links it
HN readers link Dmitri Tymoczko's Princeton page for his music theory work, mainly A Geometry of Music and What Makes Music Sound Good?, which teach harmony from simple rules based on how people hear.
Summarised by Claude from a sample of 16 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
Most-linked posts?
- /geometry-of-music.html3 people · 3 mentions · first linked 2023-03-11
- /geometry-of-music.html2 people · 3 mentions · first linked 2017-06-16
- What Makes Music Sound Good? (2010) [pdf]2 people · 2 mentions · first linked 2023-08-11
- What Makes Music Sound "Good?"2 people · 2 mentions · first linked 2023-08-13
What Hacker News says?
For this, I would highly recommend the music theorist/composer Dimitri Tymoczko. His career project is to rebuild the basics of harmony from the ground up from (mostly simple) rules, closely based on how people hear. A catchphrase he uses a lot is "why does music sound good?" He teaches a set of 2 comprehensive introductory music theory classes at Princeton, and he makes the lecture notes public: https://dmitri.mycp…
Comment linking /teaching.html
on “Ask HN: How Can I Learn Music Theory?”Submitted What makes music sound “good?” as a story · 186 points
HN discussion> Example: memorize the major scale as a series of whole and half steps but we won’t provide you with any context or motivation for why this is so. I recommend "What Makes Music Sound Good?" by Prof. Dmitri Tymoczko: https://dmitri.mycpanel.princeton.edu/files/pdfs/MUS105hando... There is a part near the beginning where he derives the diatonic scale from first principles. (There is a sequel as well, and a book if yo…
Comment linking /files/pdfs/MUS105handouts.pdf
on “Music Theory for the 21st-Century Classroom”Submitted What Makes Music Sound "Good?" as a story · 5 points
HN discussionThe best work happening in this area is by a Princeton professor named Dmitri Tymoczko [1]. He's discovered some pretty fundamental results that tie together a lot of the previous theories of harmony based on geometry. He was the first music theorist ever published in Science [2] and he wrote an amazing book called A Geometry of Music [3] (technical but readable, a must for anyone trying to really understand why mus…
Comment linking /bio.html
on “Harmony Explained: Progress Towards a Scientific Theory of Music”Submitted The Geometry of Musical Chords [pdf] as a story · 5 points
HN discussionwithout the google referral link (pdf) http://dmitri.mycpanel.princeton.edu/geometry.pdf
Comment linking /geometry.pdf
on “Harmony Explained: Progress Towards a Scientific Theory of Music”Submitted What Makes Music Sound Good? (2010) [pdf] as a story · 1 points
HN discussionThanks 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 The critic, Tymoczko, is the author of A Geometry of Music. Oh, his review…
Comment linking /files/publications/mazzola.pdf
on “The Mathematics of Music [pdf]”Recommended: A Geometry of Music by Dmitri Tymoczko - 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-r... (PDF) - Book - Review https://mtosmt.org/issues/mto.13.19.2/mto.13.19.2.gotham.php
Comment linking /geometry-of-music.html
on “The Mathematics of Music [pdf]”Great list of books on music and mathematics. It's an endlessly fascinating subject that appeals to the intellect and the heart. I remember years ago, reading Godfried Toussaint's paper, "The Euclidean Algorithm Generates Traditional Musical Rhythms". http://cgm.cs.mcgill.ca/~godfried/publications/banff-extende... (PDF) Following the trail, I was glad to find he wrote a whole book, The Geometry of Musical Rhythm, wh…
Comment linking /index.html
on “Music and Geometry: Intervals and Scales”Geometry of Music by Dmitri Tymoczko is a fun book of visualizing chromatic music theory with geometry models, some of it also covered in author's papers https://dmitri.mycpanel.princeton.edu/publications.html
Comment linking /publications.html
on “Music and Geometry: Intervals and Scales”For a more professional and thoughtful look at music and combinatorial math I suggest: http://dmitri.mycpanel.princeton.edu/geometry-of-music.html There's also https://www.amazon.co.uk/Topos-Music-Geometric-Concepts-Perf... Although IMO it's mostly blather - unlike Tymoczko, who's worth reading. There are no complete scientific theories of music and there never will be, because music is a huge and semi-random collec…
Comment linking /geometry-of-music.html
on “Harmony Explained: Progress Towards a Scientific Theory of Music (2014)”Related is Tymoczko's geometry of musical chords [1] see also [2]. [1] http://dmitri.tymoczko.com/geometry-of-music.html [2] http://dmitri.mycpanel.princeton.edu/voiceleading.pdf [3] http://dmitri.mycpanel.princeton.edu/ChordGeometries.html
Comment linking /ChordGeometries.html
on “Bach and the musical Möbius strip”Here's a dense and fun book in that direction.. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice http://dmitri.mycpanel.princeton.edu/geometry-of-music.html
Comment linking /geometry-of-music.html
on “What Is a Major Chord?”A bizarre coincidence: this morning I was reading about a role for the Möbius strip in music, but it had nothing to do with this! It turns out orbifolds have an application in music theory. Orbifolds are a kind of generalization of a continuous manifold [0]. The mathematician Tymoczko (and others) used orbifolds to describe the abstract geometry of musical chords, in which the Möbius strip is the geometry of the dya…
Comment linking /files/publications/science.pdf
on “Music on a Clear Möbius Strip [video]”If you want to go way deep, check out Tymoczko's first book: https://dmitri.mycpanel.princeton.edu/geometry-of-music.html It's a challenging read, but extremely thorough and enlightening. Tymoczko wrote a follow up that extends and reformulates his theories, but I haven't gotten through it yet.
Comment linking /geometry-of-music.html
on “Harmony Explained: Progress Towards a Scientific Theory of Music (2012)”> the major and minor 'scales' are the same 'scale' Indeed, they are two modes of the same pattern. If you look at that pattern in a circle, sometimes called a "necklace", the major and minor scales are rotations of each other. For this way of looking at music, I recommend the book A Geometry of Music by Dmitri Tymoczko, who teaches composition and theory at Princeton. > A Geometry of Music provides an accessible in…
Comment linking /geometry-of-music.html
on “Coltrane: A music theory library with a command-line interface”The short version: https://dmitri.mycpanel.princeton.edu/whatmakesmusicsoundgoo...
Comment linking /whatmakesmusicsoundgood.html
on “What Makes Music Sound Good? (2010) [pdf]”He is a theorist: https://dmitri.mycpanel.princeton.edu/geometry-of-music.html See his work on orbifolds: https://en.wikipedia.org/wiki/Orbifold#Music_theory
Comment linking /geometry-of-music.html
on “What Makes Music Sound Good? (2010) [pdf]”
