> 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 introduction to a new, geometrical approach to music theory. The book shows how to construct simple diagrams representing voice-leading relationships among familiar chords and scales. This gives readers the tools to translate between the musical and visual realms, revealing surprising structure in otherwise hard-to-understand pieces.
It's written by Godfried Toussaint, a computer scientist who discovered "Euclidean rhythms", a large set of rhythm patterns generated by a simple algorithm, many of which are common in world music traditions.
> In 2004 he discovered that the Euclidean algorithm for computing the greatest common divisor of two numbers implicitly generates almost all the most important traditional rhythms of the world.
well, at least they are aware they merely discovered this. Because so could I, in fact I am well (ok, not so well) on my way to also discover those same ideas, except I'm not at Princeton nor anywhere near it.
thanks for the tip on the geometry of musical rhythm book. I was aware of the other one but not this one.
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 introduction to a new, geometrical approach to music theory. The book shows how to construct simple diagrams representing voice-leading relationships among familiar chords and scales. This gives readers the tools to translate between the musical and visual realms, revealing surprising structure in otherwise hard-to-understand pieces.
https://dmitri.mycpanel.princeton.edu/geometry-of-music.html
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As an intellectual companion, there's a book called The Geometry of Musical Rhythm.
https://en.wikipedia.org/wiki/The_Geometry_of_Musical_Rhythm
It's written by Godfried Toussaint, a computer scientist who discovered "Euclidean rhythms", a large set of rhythm patterns generated by a simple algorithm, many of which are common in world music traditions.
> In 2004 he discovered that the Euclidean algorithm for computing the greatest common divisor of two numbers implicitly generates almost all the most important traditional rhythms of the world.
The Euclidean algorithm generates traditional musical rhythm - http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf (PDF)