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Music and Geometry: Intervals and Scales

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Re: Music and Geometry: Intervals and Scales

#51

Post by TheOtherHobbes »

Rochus wrote: post #38
brcmthrowaway wrote: post #27

Earlier quoted context omitted.

How does this differ to Max/MSP or PureData

It has nothing in common with Max nor Pd. The latter specifiy signal flow and operators on the signal. Nodal instead represents events and time distances between them; this way you can design musical patterns; time is two dimensional, so you can draw loops; then you can associate musical information with the events and add logical operations so that your loops vary in time. It's a very nice experimenting and composit…

With some persuasion, Max can do everything Nodal does. It's not convenient and you have to use numbers instead of line lengths. But it's untrue they have "nothing in common."

Re: Music and Geometry: Intervals and Scales

#52

Post by Rochus »

TheOtherHobbes wrote: post #51
Rochus wrote: post #38

Earlier quoted context omitted.

It has nothing in common with Max nor Pd. The latter specifiy signal flow and operators on the signal. Nodal instead represents events and time distances between them; this way you can design musical patterns; time is two dimensional, so you can draw loops; then you can associate musical information with the events and add logical operations so that your loops vary in time. It's a very nice experimenting and composit…

With some persuasion, Max can do everything Nodal does. It's not convenient and you have to use numbers instead of line lengths. But it's untrue they have "nothing in common."

Well, that requires a demonstration ;-)

> you have to use numbers instead of line lengths

That's the whole point of Nodal; you represent musical patterns (and control flow) with graphical means. Entering numbers is close to Midi event lists and has little to do with Nodal's approach. Max/Pd are great tools, but focus on the processing and signal flow aspect (i.e. the machine which generates the music/noise), not the representation of the music.

Re: Music and Geometry: Intervals and Scales

#53

Post by lachlan_gray »

BaculumMeumEst wrote: post #41

Somewhat unrelated: I’m looking for a comprehensive overview of why the CAGED system works on guitar. I see lots of mechanical explanations of how to use it to play various chords down the neck, but nothing explaining the theory behind it.

I was super obsessed with this for a while! When you have a string instrument tuned in 4ths, there are 2D patterns that emerge which you can use to "derive" or "extrapolate" what a scale shape/pattern will look like across the whole neck

Using a 6-string bass as an example: https://bradleyfish.com/the-notes-on-the-6-string-bass-guita...

You can find a 2D pattern in the white notes (green notes in the pic) that you can use to understand how the pattern will extend from a given point. For example notice EF+BC always appear in the same 2x2 box shape. Also how those boxes repeat in a diagonal line, and how boxes are connected vertically by a "strip" of 3 notes ADG

The only difference for guitar is that you have to correct for the G/B strings which are separated by a 3rd instead of a 4th, by scooting the pattern on the B+E strings up by one fret

Re: Music and Geometry: Intervals and Scales

#54

Post by derekerdmann »

BaculumMeumEst wrote: post #41

Somewhat unrelated: I’m looking for a comprehensive overview of why the CAGED system works on guitar. I see lots of mechanical explanations of how to use it to play various chords down the neck, but nothing explaining the theory behind it.

Take a look at Fretboard Theory by Desi Serna - it spends a lot of time on how different scales are constructed and relating different patterns and chord forms back to the underlying concepts.

Re: Music and Geometry: Intervals and Scales

#55

Post by giancaIta »

Oh that's my cup of tea, love this stuff!

I've created a 3d guitar fretboard here, where the height of the blocks corresponds to the height of the pitches: https://www.fachords.com/guitar-fretboard-3d/

And here are the shapes of the different chord qualities in the Circle Of Fifths: https://www.fachords.com/circle-of-fifths-chord-shape/

Re: Music and Geometry: Intervals and Scales

#57

Post by aanet »

Fantastic resource! Thanks for sharing this. I love both the math, the music, and math&music combo. Tickles my inner geek. I'd love to see if anyone has done this geometric / visualization for Indian classical (specifically, Hindustani) music??

Perhaps there's specific shapes / visualizations in certain Ragas that naturally emanate?

Note that in the Indian classical (Hindustani) music system, the Ragas are a "framework" for melody, not really a mode (as in Western music theory).

Re: Music and Geometry: Intervals and Scales

#58

Post by aanet »

giancaIta wrote: post #55

Oh that's my cup of tea, love this stuff! I've created a 3d guitar fretboard here, where the height of the blocks corresponds to the height of the pitches: https://www.fachords.com/guitar-fretboard-3d/ And here are the shapes of the different chord qualities in the Circle Of Fifths: https://www.fachords.com/circle-of-fifths-chord-shape/

Thanks - this looks great! I might download / get one of the books!

<3

Re: Music and Geometry: Intervals and Scales

#59

Post by BaculumMeumEst »

derekerdmann wrote: post #54
BaculumMeumEst wrote: post #41

Somewhat unrelated: I’m looking for a comprehensive overview of why the CAGED system works on guitar. I see lots of mechanical explanations of how to use it to play various chords down the neck, but nothing explaining the theory behind it.

Take a look at Fretboard Theory by Desi Serna - it spends a lot of time on how different scales are constructed and relating different patterns and chord forms back to the underlying concepts.

Thanks, this is exactly what I needed. It's amazing how much of this information other people decided to omit.

Re: Music and Geometry: Intervals and Scales

#60

Post by lioeters »

Rochus wrote: post #50
jvvw wrote: post #45

Earlier quoted context omitted.

This sounds interesting. As a mathematician (in the sense that I have a PhD in group theory), is there a good guide to music theory for mathematicians? There seems to be lots of stuff along the lines of 'if you understand music, here is some mathematics to help you think about it' but not much 'if you understand mathematics, but not so much about music, here is how to think about music'.

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 - Hook,…

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, where the article forms the basis of a chapter. It's one of my favorite books I keep returning to re-read different parts.

I hadn't seen "Exploring Musical Spaces", looking forward to reading it.

Dmitri Tymoczko's book is wonderful too, A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Rich with ideas and insights, I like how he tells the history and development of Western music theory.

Oh I just learned from the author's website that he has a new book released.

> I have just finished a second book, Tonality: An Owner's Manual, that proposes a new, hierarchical, and geometrical model of musical stucture.

> One interesting outgrowth is the musical programming language arca. This line of thinking has also led me to contemplate a third book about category theory and music.

https://dmitri.mycpanel.princeton.edu/index.html

---

This video of your live performance setup as a one-man band. Amazing.

https://www.youtube.com/shorts/S82hsEDY8Pc

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