A geometry of music
by Dmitri Tymoczko · first published 2011
82% recommend18% neutral
Why HN recommends it
Uses geometric models of chords, scales and voice leading to explain harmony and counterpoint; technical but readable, suited to musicians and mathematically inclined readers curious about why music sounds good.
Summarised by Claude from recommending comments
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The joke about Mazzola is that people who know enough about music to see through his theories are bamboozled by his maths, and vice versa. If you want to explore that space, Tymoczko's A Geometry of Music is more rewarding. But this misses the point. Music isn't just mathematical consonance and dissonance. Music is the practice of using consonance, dissonance, timbre, rhythm, form, and historic and cultural…
on “Phase transitions: the math behind the music” ↗…people working on unified theories of harmonic/Western/tonal music. The author fails to reference the most interesting work done in this area. The ones I've found most convincing are: - Dmitri Tymoczko's Geometry of Music: http://dmitri.tymoczko.com/geometry-of-music.html - Bill Sethares's Tuning Timbre Spectrum Scale approach: http://sethares.engr.wisc.edu/ttss.html - Andrew Duncan's Combinatorial Music Theory: http://andrewduncan.net/cmt/…
on “Harmony Explained: Progress Towards a Scientific Theory of Music (2014)” ↗…desire to be able to freely transpose and to modulate between distant keys. It's a deep topic, but if anyone's interested, I recommend two books: - Timbre, Tuning, Spectrum, Scale by William Sethares - A Geometry of Music by Dmitri Tymoczko
on “Combinatorial Music Theory (1991)” ↗Check out Dmitri Tymoczko's "Geometry of Music". https://www.amazon.com/Geometry-Music-Counterpoint-Extended-... https://www.youtube.com/watch?v=NnvynOyZI-Q
on “Show HN: Encouraging STEM Using Advanced Math in Music” ↗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...…
on “The Mathematics of Music [pdf]” ↗Or http://dmitri.tymoczko.com/geometry-of-music.html
on “Music theory for nerds” ↗…this full story. The two books I found most enlightening in piecing together the "real story" are: - Tuning, Timbre, Spectrum, Scale: https://www.amazon.com/Tuning-Timbre-Spectrum-William-Sethar... - A Geometry of Music: https://www.amazon.com/Geometry-Music-Counterpoint-Extended-...
on “Music theory for nerds” ↗"A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice" by Dmitri Tymoczko.
on “Can a complete novice become a golf pro with 10,000 hours of practice?” ↗…arbitrary timbres. In practice, most of our timbres are highly harmonic. Speaking of which, another theorist, Dmitry Tymoczko, has some fascinating theories on harmony that you might like in his book A Geometry of Music. A few years ago, when I was reading his and Sethares's work, I really felt like their ideas put together would make a fascinating grand theory of tonal music.
on “The Saddest Thing I Know about the Integers” ↗I first heard of Dmitri Tymoczko from his book A Geometry of Music [1], which I found to be very enlightening. This is a cool demo, although I suppose it shows a bit more where the basic texture of western music comes from than songwriting. But what I find most interesting…
on “What makes music sound “good?”” ↗…important, it's just background for the bass and melody lines. So pure chord progressions tend to harken back to harmonic motion that's familiar from the more formal genres. A book I often recommend called A Geometry of Music [1] goes way down the rabbit hole, if you want to obsess over this to the extent that I did. So, modal chord progressions (especially Locrian) really only tend make sense to the extent that they analogize…
on “Musical Chord Progression Arpeggiator” ↗…much of it is beyond my understanding at the beginning (or even at the end). Here are some of my favorites: The Jazz Theory Book (Mark Levine) Huge series of play-along books by Jamey Aebersold The Geometry of Musical Rhythm (Godfried Toussaint) Harmony (Walter Piston) A Geometry of Music - Harmony and Counterpoint in the Extended Common Practice (Dmitri Tymoczko) Lydian Chromatic Concept of Tonal Organization…
on “Ask HN: What are you learning in 2019?” ↗…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 introduction to a new, geometrical approach to music theory. The book shows how to construct…
on “Coltrane: A music theory library with a command-line interface” ↗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
on “Music and Geometry: Intervals and Scales” ↗There are many with various mathematical depth: - Fauvel et al., Music and Mathematics - From Pythagoras to Fractals, 2003, Oxford UP - Loy, Musimatics Volume 1, 2006 MIT Press - Tymoczko, A Geometry of Music, 2011, Oxford UP - Walker, Mathematics and Music, 2013, CRC Press - Toussaint, The Geometry of Musical Rhythm, 2013, CRC Press - Chew, Mathematical and Computational Modeling of Tonality, 2014, Springer…
on “Music and Geometry: Intervals and Scales” ↗