IsisCB Explore

Article ID: CBB342675550

L'anamorfosi logaritmica degli intervalli pitagorici (2011)

Bollettino di Storia delle Scienze Matematiche
Volume: 31
Issue: 2
Pages: 177-216
Publication date: 2011
Language: Italian

Outside Links

WorldCat

Google Scholar

JSTOR

Mathematics and art Music Logarithms Pythagoreanism Philosophy Music theory Ancient Pythagoras Ptolemy, Claudius

A music interval is perceived like a distance - and therefore like a difference - between two sounds. But to equal intervals correspond equal ratios, not equal differences. Then, there exists a distortion (an anamorphism) in the way the intervals are perceived. To solve this distortion, logarithms are needed (and indeed they were immediately applied to music theory as soon as they were invented). But Greeks did not have them. So, this distortion caused difficulties not only to the music theory but also to the theory of proportions (which, among Pythagoreans, was born principally in the field of the music theory). The division between Pythagoreans and Aristossenians and the errors made by Ptolemy in assigning numbers to the Aristossenians scales are the most visible effects. On the other hand, the possibility offered by the logarithmic anamorphism of interpreting multiplicative results in additive terms may have helped the discovery of some elementary properties of the proportions.

...More

Citation URI

data.isiscb.org/p/isis/citation/CBB342675550

This citation is part of the Isis database.

Citations Indexes

Similar Citations

Article Fabio Bellissima; (2014)
Arithmetic, Geometric and Harmonic Means in Music Theory (/p/isis/citation/CBB139505675/)

Article Fabio Bellissima; Maria Silvestrini; (2017)
The «Mathematical Possibilities» of the Music Concept of Mode from Ptolemy to Messiaen (/p/isis/citation/CBB413487512/)

Article Fabio Bellissima; (2011)
L'antanairesi e la teoria armonica greca (/p/isis/citation/CBB718056038/)

Article Cecilia Panti; (2017)
Boethius and Ptolemy on Harmony, Harmonics and Human Music (/p/isis/citation/CBB900599050/)

Article Borzacchini, Luigi; (2007)
Incommensurability, Music, and Continuum: A Cognitive Approach (/p/isis/citation/CBB000771561/)

Book Zhmud, Leonid; Windle, Kevin; Ireland, Rosh; (2012)
Pythagoras and the Early Pythagoreans (/p/isis/citation/CBB001451645/)

Article Kennedy, J. B.; (2010)
Plato's Forms, Pythagorean Mathematics, and Stichometry (/p/isis/citation/CBB001021118/)

Book Marco Cilione; (2020)
Pythagorica medica: Scienza e sapienza nella tradizione preippocratica (/p/isis/citation/CBB867692984/)

Book Jacomien Prins; Maude Vanhaelen; (2017)
Sing Aloud Harmonious Spheres: Renaissance Conceptions of Cosmic Harmony (/p/isis/citation/CBB071701613/)

Article BaldisseraPacchetti, Marina; (2014)
Turning Music into Sound: Vincenzo Galilei's Contributions to the History of Acoustics (/p/isis/citation/CBB001201082/)

Thesis Zhuqing Hu; (2019)
From Ut Re Mi to Fourteen-Tone Temperament: The Global Acoustemologies of an Early Modern Chinese Tuning Reform (/p/isis/citation/CBB144734757/)

Chapter Danilo Capecchi; (2016)
Epistemology of Harmonics (/p/isis/citation/CBB603210619/)

Thesis Bianchi, Eric; (2011)
Prodigious Sounds: Music and Learning in the World of Athanasius Kircher (/p/isis/citation/CBB001567278/)

Article Caleon, Imelda; Ramanathan, Subramaniam; (2008)
From Music to Physics: The Undervalued Legacy of Pythagoras (/p/isis/citation/CBB001032881/)

Article Manuel Bertolini; (2016)
La Ruota Armonica: pitagorismo e scienza moderna in Federico Borromeo (/p/isis/citation/CBB299301022/)

Book Joost-Gaugier, Christiane L.; (2009)
Pythagoras and Renaissance Europe: Finding Heaven (/p/isis/citation/CBB001023342/)

Book Joost-Gaugier, Christiane L.; (2006)
Measuring Heaven: Pythagoras and His Influence on Thought and Art in Antiquity and the Middle Ages (/p/isis/citation/CBB000772136/)

Chapter Sophie Gibson; (2016)
The Science of Harmonics and Music Theory in Ancient Greece (/p/isis/citation/CBB920974842/)

Article Aldo Brancacci; (2013)
Musica e filosofia nel I libro del "De musica" di Aristide Quintiliano (/p/isis/citation/CBB628791731/)

Chapter Andrew Barker; (2015)
Musical Pitch and the Enigmatic Octave in Problemata 19 (/p/isis/citation/CBB757602805/)