Benedetti's Puzzle (mathematically impossible music)

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-duffin/just-intonation-in-renaissance-theory-practice/introduction/ Pitch Drift in Choral Music https://ccrma.stanford.edu/~hiroko/pitchdrift/paper221A.pdf Os justi - The mouth of the righteous - A Bruckner - 2015 https://youtu.be/XnGqVIW51JA Schoenberg on Comma Pumps https://music.stackexchange.com/questions/11898/natural-vs-tempered-semi-tones Benedetti: example for comma pump in a letter to Cipriano de Rore https://www.youtube.com/watch?v=Tn0VZInlhoo Cipriano de Rore, Giovanni Battista Benedetti, and the Just Tuning Conundrum Ross w. Duffin https://www.brepolsonline.net/doi/abs/10.1484/J.JAF.5.115544 Diversarum speculationum mathematicarum et physicarum liber (1585) http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/mpiwg/online/permanent/library/163127KK&viewMode=images&pn=5 Dictionary of the History of Ideas MUSIC AND SCIENCE http://xtf.lib.virginia.edu/xtf/view?docId=DicHist/uvaBook/tei/DicHist3.xml;chunk.id=dv3-32 JUST INTONATION by Joe Monzo http://www.tonalsoft.com/enc/j/just.aspx (⌐■_■) ⦿ Adam Neely T-shirts! ⦿ https://teespring.com/stores/adam-neely-merchandise ⦿ SUPPORT ME ON PATREON ⦿ http://www.patreon.com/adamneely ⦿ FOLLOW ME ON THE INTERNETS ⦿ http://www.facebook.com/adamneely http://www.instagram.com/its_adamneely ⦿ Check out some of my music ⦿ http://sungazermusic.bandcamp.com http://insideoutsidemusic.bandcamp.com http://adamneelymusic.bandcamp.com Peace, Adam