Italian mathematician Giovanni Battista Benedetti wrote several letter to the composer Cipriano de Rore, the contents of which contained several puzzles that demonstrate the issues of tuning music to pure intervals.

“Comma Pump,” the the phenomenon that Benedetti describes. What is it? And why should we care??

Just Intonation in Renaissance Theory & Practice, Introduction
https://casfaculty.case.edu/ross-duff...

Pitch Drift in Choral Music
https://ccrma.stanford.edu/~hiroko/pi...

Os justi - The mouth of the righteous - A Bruckner - 2015
   • Os justi | The mouth of the righteous...  

Schoenberg on Comma Pumps
https://music.stackexchange.com/quest...

Benedetti: example for comma pump in a letter to Cipriano de Rore
   • Benedetti: example for comma pump in ...  

Cipriano de Rore, Giovanni Battista Benedetti, and the Just Tuning Conundrum
Ross w. Duffin
https://www.brepolsonline.net/doi/abs...

Diversarum speculationum mathematicarum et physicarum liber (1585)
http://echo.mpiwg-berlin.mpg.de/ECHOd...

Dictionary of the History of Ideas MUSIC AND SCIENCE
http://xtf.lib.virginia.edu/xtf/view?...

JUST INTONATION by Joe Monzo
http://www.tonalsoft.com/enc/j/just.aspx



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