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Music and Geometry: Intervals and Scales

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Re: Music and Geometry: Intervals and Scales

#61

Post by Rochus »

lioeters wrote: post #60
Rochus wrote: post #50

Earlier quoted context omitted.

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, whe…

Thanks for the comment. The new book by Tymoczko is interesting, but written in a more philosophical, narrative than scientific/mathematical style, why I didn't mention it. There is no mention of a programming language in the book, but he has published some examples at https://www.madmusicalscience.com. I look forward to more of his books, but I find it a little regrettable that many free spirits hinder themselves by feeling they have to justify themselves and appease with the "old curia" for their findings; as a result, a lot of material gets into these books that distracts from the actual ideas and tries to follow the traditional, authority-based style instead of one shaped by independent science.

Thanks for the feedback. The video shows my setup ten years ago; my most recent musical results are here: http://rochus-keller.ch/?p=1317.

Re: Music and Geometry: Intervals and Scales

#63

Post by dizhn »

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.

Open chord shapes are just the barre shapes but the nut becomes fret zero that's barred. Looking at it this way it's easy to see why they can be moved around the neck. The shape remains the same because the relationship of the strings and the notes on them remain the same. Like root-3rd-5th would remain the same relationship only with a different tone combination.

By the way I think the most difficult thing about CAGED is that it's way too overhyped. It promises too much (scales?) but delivers too little. (Doesn't even have minors)

Re: Music and Geometry: Intervals and Scales

#64

Post by BaculumMeumEst »

dizhn wrote: post #63
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.

Open chord shapes are just the barre shapes but the nut becomes fret zero that's barred. Looking at it this way it's easy to see why they can be moved around the neck. The shape remains the same because the relationship of the strings and the notes on them remain the same. Like root-3rd-5th would remain the same relationship only with a different tone combination. By the way I think the most difficult thing about CAG…

I've seen a few complaints about the limitations of CAGED so I've been trying to focus on theory rather than just mindlessly learn tricks and regurgitate songs. Having a lot of fun so far.

The book I'm reading (recommended in another comment) does talk about minor forms of CAGED forms, though - pentatonic scale patterns, arpeggio patterns, and chord forms.

Re: Music and Geometry: Intervals and Scales

#65

Post by dizhn »

BaculumMeumEst wrote: post #64
dizhn wrote: post #63

Earlier quoted context omitted.

Open chord shapes are just the barre shapes but the nut becomes fret zero that's barred. Looking at it this way it's easy to see why they can be moved around the neck. The shape remains the same because the relationship of the strings and the notes on them remain the same. Like root-3rd-5th would remain the same relationship only with a different tone combination. By the way I think the most difficult thing about CAG…

I've seen a few complaints about the limitations of CAGED so I've been trying to focus on theory rather than just mindlessly learn tricks and regurgitate songs. Having a lot of fun so far. The book I'm reading (recommended in another comment) does talk about minor forms of CAGED forms, though - pentatonic scale patterns, arpeggio patterns, and chord forms.

Almost everything I've seen about CAGED is retrofits. CAGED is chord based. By definition it's only 3 notes (some repeated). Scales start from 5 and go up to 7 notes. It's a whole "draw the rest of the fucking owl" situation. Might as well learn what a scale is and consruct the arpeggios, triads, chords with guitar at hand. That's a much better learning experience.
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