Adam Neely | Benedetti's Puzzle (mathematically impossible music) @AdamNeely | Uploaded 4 years ago | Updated 1 hour ago
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
youtu.be/XnGqVIW51JA
Schoenberg on Comma Pumps
music.stackexchange.com/questions/11898/natural-vs-tempered-semi-tones
Benedetti: example for comma pump in a letter to Cipriano de Rore
youtube.com/watch?v=Tn0VZInlhoo
Cipriano de Rore, Giovanni Battista Benedetti, and the Just Tuning Conundrum
Ross w. Duffin
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! ⦿
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http://www.facebook.com/adamneely
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⦿ Check out some of my music ⦿
http://sungazermusic.bandcamp.com
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http://adamneelymusic.bandcamp.com
Peace,
Adam
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
youtu.be/XnGqVIW51JA
Schoenberg on Comma Pumps
music.stackexchange.com/questions/11898/natural-vs-tempered-semi-tones
Benedetti: example for comma pump in a letter to Cipriano de Rore
youtube.com/watch?v=Tn0VZInlhoo
Cipriano de Rore, Giovanni Battista Benedetti, and the Just Tuning Conundrum
Ross w. Duffin
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! ⦿
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
