Audio Examples for Kyle Gann's
The Arithmetic of Listening:
Tuning Theory and History for the Impractical Musician

Chapter 5: The Five Limit

The Syntonic Comma

Here is a demonstration of the syntonic comma between 9/8 and 10/9 in the key of F:

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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