Kyle Gann: The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician Chapter 5: The Five Limit
Benedetti's Paradox
Here is Giovanni Battista Benedetti's demonstration of the unworkability of just intonation, as published in his Diversarum speculationem mathematicarum & physicorum liber of 1585:
Here is a piano version played faster to make the pitch shift more obvious:
Interlude: Terry Riley examples
Here is the passage of "Premonition Rag" from Terry Riley's The Harp of New Albion transcribed in the interlude:
Here is the passage of "Circles of Wolves" from Terry Riley's The Harp of New Albion transcribed in the interlude:
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