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Music by the Numbers: From Pythagoras to Schoenberg
How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth centuryMusic is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system.Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.
176 pages, Kindle Edition
First published January 1, 2018
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Displaying 1 - 30 of 48 reviews
November 5, 2019
Unclear what the book wished to be based on its contents but I found it to be a pretty superficial overview of the relationship between math and music. There is, somewhere out there, a hypothetically beautiful book relaying a history of how the two subjects elucidated one anther's harmonies. This though - was not that book.
While there was a vague construct of a history - it was at most superficial. I sadly must extend my view that this issue of superficiality exists within the texts philosophical elaborations, math, and exposition on music.
Beyond that, it came off as a quite tangential text. I expect though that the author is a pretty smart guy, and as such I will move on to his other writings. But, I am sad to say that I did not enjoy this book.
He ended a book with a quip on string theory. At least -in his eyes - ol Pythagoras had real (verifiable*) strings to play with was silly. (Oy)
Perhaps this will make a good intro book on the relationship between the subjects of math and music. Or rather to simply there exists one at all. All and all I was unimpressed.
Recommended for :
-Those curious about the relationship between number and music
*Shout out to popper
While there was a vague construct of a history - it was at most superficial. I sadly must extend my view that this issue of superficiality exists within the texts philosophical elaborations, math, and exposition on music.
Beyond that, it came off as a quite tangential text. I expect though that the author is a pretty smart guy, and as such I will move on to his other writings. But, I am sad to say that I did not enjoy this book.
He ended a book with a quip on string theory. At least -in his eyes - ol Pythagoras had real (verifiable*) strings to play with was silly. (Oy)
Perhaps this will make a good intro book on the relationship between the subjects of math and music. Or rather to simply there exists one at all. All and all I was unimpressed.
Recommended for :
-Those curious about the relationship between number and music
*Shout out to popper
December 22, 2024
Una buena y sucinta historia de la relación entre las matemáticas, la física y la música.
Antes de leerlo temía encontrarme con muchos tecnicismos de teoría musical que no entendería. Solo al terminar me di cuenta que mis temores eran infundados. En realidad, "La música y los números" tiene más tecnicismos científicos que musicales (sin que estos últimos falten) y creo algunas personas podrían incluso abandonar el libro en los primeros capítulos que están más dedicados a las matemáticas y la historia de la acústica. ¡No lo hagan! A la larga, Maor consigue un buen equilibrio entre los aspectos científicos y musicales de esta Historia.
El libro está lleno de daticos curiosos, tanto de historia como de ciencia y música. Una verdadera pieza ligera de divulgación científica que vale la pena "consumir".
Me ha gustado mucho el estilo de escritura de este autor del que me he prometido buscar más libros.
Antes de leerlo temía encontrarme con muchos tecnicismos de teoría musical que no entendería. Solo al terminar me di cuenta que mis temores eran infundados. En realidad, "La música y los números" tiene más tecnicismos científicos que musicales (sin que estos últimos falten) y creo algunas personas podrían incluso abandonar el libro en los primeros capítulos que están más dedicados a las matemáticas y la historia de la acústica. ¡No lo hagan! A la larga, Maor consigue un buen equilibrio entre los aspectos científicos y musicales de esta Historia.
El libro está lleno de daticos curiosos, tanto de historia como de ciencia y música. Una verdadera pieza ligera de divulgación científica que vale la pena "consumir".
Me ha gustado mucho el estilo de escritura de este autor del que me he prometido buscar más libros.
March 27, 2019
Este es un librito escrito por un apasionado tanto de la física como de la música, intentando explicar la relación de una con la otra. No es un libro fácil de leer, pues el nivel no es bajo. Explica cómo salieron las notas, los estilos de los diferentes autores en la historia, los principios físicos y matemáticos (Fourier, por supuesto), etc. También habla del oído absoluto, cosa que sorprende, pues comenta que obras en diferentes tonos no suenan igual para los que lo tienen.
Muy interesante, pero sólo lo recomendaré si sabes algo de solfeo y tienes claro qué son las series de Fourier. Si no, te pierdes.
Muy interesante, pero sólo lo recomendaré si sabes algo de solfeo y tienes claro qué son las series de Fourier. Si no, te pierdes.
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January 14, 2025He makes his point, if you pay attention. Music and math have both influenced each other throughout history, but it's weird to say they are similar fields. Music is emotional. Certain tones convey certain feelings because we are conditioned to associate them by centuries of development and trends. Meanwhile, math is a made-up system of patterns used to rationalize the universe. It is not definitive and undeniable because there is not an undeniable way of measuring quantity or distance or time. Those are constructs that we made up! It's all relative!!
August 5, 2018
Interesting academic (yet readable) book on the crossovers of music, mathematics, physics, acoustics, history, the Enlightenment, etc. You don’t have to be well-versed in, say, advanced calculus to follow along, but if geometry and algebra are daunting, give this a pass. Me, I enjoyed it.
November 16, 2020
Da parte di un professore israeliano di storia della matematica, un libretto agile e comprensibile, oltre che assai bene informato - e soprattutto molto “umile”, nel senso che non si prefigge di dimostrare nessuna tesi - sui legami tra musica, fisica e matematica e la loro storia nel corso del tempo. Si parla ovviamente di tutti gli scienziati e i musicisti che si sono dati da fare ad indagare la questione - per primo Pitagora, poi molti altri - dei principi fisici del suono, del sistema temperato, dei presupposti acustici della scala diatonica, eccetera. Molto interessante il capitolo dedicato a Schoenberg e ad Einstein, alla corrispondenza delle intenzioni del primo di scardinare il sistema tonale togliendo tutti i punti di riferimento delle tonalità, mentre il secondo faceva lo stesso con la fisica newtoniana - ovviamente non è che ci fosse un’intenzione o una complicità, ma la coincidenza degli eventi dice molto sul momento storico e sulla percezione di sé dell’essere umano nell’universo. E anche il fatto che da un lato si continui ad ascoltare musica tonale - lo stesso Schoenberg avrebbe detto, in tarda età, che la tonalità di do maggiore ha ancora molto da dire, e le sue composizioni ancora oggi più ascoltate sono o quelle giovanili, ancora intrise di orchestralità wagneriana, o quelle tardive, non più dodecafoniche - e dall’altro a ragionare in termini newtoniani, significa che se queste sono le leggi della “nostra parte di universo”, come diceva Battiato, in qualche modo ci tocca seguirle. Inoltre l’autore esprime parecchi dubbi in merito al fatto se sia vero che le tonalità - do maggiore, re maggiore, ecc. siano necessarie e se sia vero che tonalità diverse possano esprimere emozioni diverse, come piaceva pensare ai romantici, soprattutto considerato che i portatori di “orecchio assoluto” sono molto rari. (Personalmente ritengo che il dubbio di Maor sia più che legittimo, ma per quello che capisco di musica - lui ammette di capirne poco - ritengo che la diversa espressività delle diverse tonalità, se esiste, dipende dall’uso che se ne è fatto nel corso del tempo, e del diverso comportamento degli strumenti in funzione dell’altezza assoluta del loro suono, come peraltro lui stesso ipotizza. Questo ha evidentemente creato dei “luoghi comuni espressivi” che probabilmente associamo a determinate composizioni e non ad altre; e in qualche modo ciò viene percepito anche senza conoscere nettamente la tonalità della composizione. Inoltre ogni tonalità tende ad essere modulata più agevolmente in altre tonalità più o meno vicine o lontane e non in altre, ed essendo la modulazione qualcosa di più complesso e riconoscibile (anche inconsciamente, per chi non è un addetto ai lavori) del semplice suono privo di riferimenti “relativi”, in qualche modo “colora” e “connota” l’impianto tonale di partenza. Ovviamente da questo ad affermare che una tonalità sia “olimpica e serena” e l’altra “tragica” ce ne corre.
Sebbene ci siano parecchie formule ed equazioni, il libro è accessibile anche a chi non ha conoscenze matematiche particolarmente approfondite. Ho solo trovato un clamoroso errore a pagina 152, dove si dice che le trombe sono intonate in si diesis. Se fosse così, esse suonerebbero in… do maggiore, proprio per via del sistema temperato nella spiegazione del quale l’autore si è dilungato, giustamente, per molte pagine, e pertanto non sarebbero strumenti traspositori. Sicuramente intendeva si bemolle, anche perché afferma che hanno due alterazioni in chiave, e la tonalità, del tutto teorica, di si diesis di alterazioni ne avrebbe ben di più. Ma penso che sia un errore di stampa o di traduzione.
Sebbene ci siano parecchie formule ed equazioni, il libro è accessibile anche a chi non ha conoscenze matematiche particolarmente approfondite. Ho solo trovato un clamoroso errore a pagina 152, dove si dice che le trombe sono intonate in si diesis. Se fosse così, esse suonerebbero in… do maggiore, proprio per via del sistema temperato nella spiegazione del quale l’autore si è dilungato, giustamente, per molte pagine, e pertanto non sarebbero strumenti traspositori. Sicuramente intendeva si bemolle, anche perché afferma che hanno due alterazioni in chiave, e la tonalità, del tutto teorica, di si diesis di alterazioni ne avrebbe ben di più. Ma penso che sia un errore di stampa o di traduzione.
January 7, 2023
“Though I have worked all my life in sound, from an academic point of view I do not even know what sound is.”
Such an interesting read. Maor’s passion for both topics was evident and explained brilliantly. His frequent breaks for information he found interesting were entirely welcome, and I learned just as much about music as I did the math and science behind it. Even if the math explanations occasionally went over my head, I am all the better for knowing reasons behind why music sounds the way it does.
Four stars for a unique intersection of topics by an author who’s passion is infectious.
Such an interesting read. Maor’s passion for both topics was evident and explained brilliantly. His frequent breaks for information he found interesting were entirely welcome, and I learned just as much about music as I did the math and science behind it. Even if the math explanations occasionally went over my head, I am all the better for knowing reasons behind why music sounds the way it does.
Four stars for a unique intersection of topics by an author who’s passion is infectious.
July 7, 2018
Relevant to my interests in many ways.
Much was review for me, having studied basic music theory formally & informally + having a renewed interest in applied maths more recently. But much was also new & illuminating. The musical maths of the eponymous bookends (Pythagoras & Schoenberg) were already particularly well-worn territory, but much of the middle stuff was not:
* 18th Century physical / musical / mathematical string debates of math / stats luminaries: Bernoulli, Euler, D'Alembert & Lagrange
* The ear's ability to perform Fourier transformations, decomposing complex tonalities into their constituent fundamentals (to the shame of the eye, which can only see blended color frequencies but never dissect them -- e.g. we see "green", not "blue & yellow simultaneously")
* Schoenberg as the 'Einstein of music', unmooring the discipline from its stable referents & into the relative sea (recalling an earlier reading of mine)
It's a brief survey, necessarily shallower, narrower & less complete than a proper study, but a pithy & substantive foray nonetheless. Also good looking.
Much was review for me, having studied basic music theory formally & informally + having a renewed interest in applied maths more recently. But much was also new & illuminating. The musical maths of the eponymous bookends (Pythagoras & Schoenberg) were already particularly well-worn territory, but much of the middle stuff was not:
* 18th Century physical / musical / mathematical string debates of math / stats luminaries: Bernoulli, Euler, D'Alembert & Lagrange
* The ear's ability to perform Fourier transformations, decomposing complex tonalities into their constituent fundamentals (to the shame of the eye, which can only see blended color frequencies but never dissect them -- e.g. we see "green", not "blue & yellow simultaneously")
* Schoenberg as the 'Einstein of music', unmooring the discipline from its stable referents & into the relative sea (recalling an earlier reading of mine)
It's a brief survey, necessarily shallower, narrower & less complete than a proper study, but a pithy & substantive foray nonetheless. Also good looking.
August 24, 2021
This might be interesting to people with strong math background and significant interest but little knowledge about classical music, however, reading it from a musician's perspective, I found the musical substance of this to be mostly pretty unrewarding. (And the mathematical parallels largely went above my head.) The musical examples were mostly pretty pedestrian, or oversimplified, or just not that accurate. (For instance - repeatedly citing Mahler as an important progressive figure in the transition away from traditional tonal harmony, on the same footing at Wagner or Schoenberg, but completely ignoring Débussy's (incomparably more important than Mahler's) role in that change.)
It's probably a great source of conversation topics for academic mathematicians at parties, but not so great for people who don't fit in that niche.
It's probably a great source of conversation topics for academic mathematicians at parties, but not so great for people who don't fit in that niche.
November 5, 2020
Eccellente e scorrevolissimo libro particolarmente indicato a chi fosse interessato alla storia degli intervalli musicali (ossia dei rapporti matematici che li mettono in relazione fra di loro), alla storia e alla teoria del temperamento equabile e alla relazione del pitagorismo con la teoria musicale. Interessante anche il capitolo biografico su Schönberg e Einstein. L'edizione italiana presenta alcuni errori, trascurabili.
December 27, 2022
To start with the good parts: I've actually learned new things and the book explains some physical foundations of music quite well. Combined with the briefness this is mostly the reason why the book is worth to read.
The bad parts: Even though the author collects many physical, mathematical, psychological, historical, and practical reasons on how music/accustics (e.g. notes, scales, key, beats, bars) works the way it does, many concepts are taken for granted in the first chapters or pulled out of thin air. This gives the whole music and accustic theory bit a somewhat autotelic character. That's really a pity because all the material is there and could have been rearranged to provide a really nice intro.
The ugly part: the comparison of physics and music is in large – pardon my French – utter bullshit. Sure if you believe in unicorns you'll see them everywhere. Naming chapters after after physical theories (e.g. "string theory") but then providing a far fetched, hand waving comparison doesn't exactly spark confidence in the author's expertise. The rejection of most scientific contributions to music with a smart-alecky undertone doesn't help either. In the end the book leaves an impression of musicians relationship to physics that is similar to what a hemopathy believer has to medicine and the scientific method.
The bad parts: Even though the author collects many physical, mathematical, psychological, historical, and practical reasons on how music/accustics (e.g. notes, scales, key, beats, bars) works the way it does, many concepts are taken for granted in the first chapters or pulled out of thin air. This gives the whole music and accustic theory bit a somewhat autotelic character. That's really a pity because all the material is there and could have been rearranged to provide a really nice intro.
The ugly part: the comparison of physics and music is in large – pardon my French – utter bullshit. Sure if you believe in unicorns you'll see them everywhere. Naming chapters after after physical theories (e.g. "string theory") but then providing a far fetched, hand waving comparison doesn't exactly spark confidence in the author's expertise. The rejection of most scientific contributions to music with a smart-alecky undertone doesn't help either. In the end the book leaves an impression of musicians relationship to physics that is similar to what a hemopathy believer has to medicine and the scientific method.
April 26, 2024
This book is often just a history of classical music disguised as a math book; or, alternatively, a history of math disguised as a music book. Often, after a brief explanation of a concept in one of these fields, it quickly departs into the other. For example, in the “Rhythm, Meter, and Metric” chapter, the book spends about 1 page on the technical details of rhythm and then 5 pages on how shocking Stravinsky was to his audiences. Or, when describing musical keys and Schoenberg’s atonal challenge to their authority, the book makes sure to sprinkle in some paragraphs about Einstein’s theory of relatively.
But maybe that’s the point: music and math evolved alongside each other, but rarely did one directly influence the other. While math occasionally impacted music (e.g. the 12 tone scale); or music math (e.g. vibrating strings informing calculus), they remained mostly independent.
For those hungry for the technical, this is NOT your book. But it’s shallowness makes it quite readable for anyone even loosely interested in the histories of either music and math.
But maybe that’s the point: music and math evolved alongside each other, but rarely did one directly influence the other. While math occasionally impacted music (e.g. the 12 tone scale); or music math (e.g. vibrating strings informing calculus), they remained mostly independent.
For those hungry for the technical, this is NOT your book. But it’s shallowness makes it quite readable for anyone even loosely interested in the histories of either music and math.
July 14, 2021
MUSIC GRAPHS ARE SO PRETTY
THE BOOK IS SO PRETTY
MATHS BEAUTIFUL
THE BOOK IS SO PRETTY
MATHS BEAUTIFUL
August 13, 2024
one of the best educational books i have ever read. I hate math and numbers on a deep spiritual level, but this book made me love it and UNDERSTAND it. the connection between music and numbers is divine, and i have cried multiple times throughout this read just out of pure amazement and joy of how beautiful and calculated the world around us is. I am ending the last page of this book much more knowledgable and forever changed as a women with new views on the universe. I Love Music by the Numbers.
October 15, 2018
Really good book. Maor explores the relationships between Mathematics and sounds/music with a lot of backgrounds. It's pretty satisfying especially if you can handle some musical instruments (I actually play guitar, bass, piano and I'm moderately expert in music theory) but, to be perfectly honest, there are plenty of free YouTube videos that do the same thing this book does in a more interesting way. Nevertheless I still think this little book deserve five stars. Once your pc is shut off, you still can open the book. And grab a guitar and understand how math rules!
June 26, 2020
This book was both easy and difficult to read. I have somewhat of a mathematical/physics background, and this book has shed a lot of light on topics I thought I understood before. It also brushes up on both mathematics and music history.
I would highly recommend this book to anyone interested in mathematics, but I'd suggest having at least basic knowledge of musical notation and terminology.
I would highly recommend this book to anyone interested in mathematics, but I'd suggest having at least basic knowledge of musical notation and terminology.
November 6, 2025
Very enjoyable as a quick overview of the history of music, as it relates to math - From names of Pythagoras to Fourier. The book is packed with interesting facts and goes quite in depth on topics like tone ratios, the harmonic series, etc.
My math knowledge has been collecting dust in the recesses of my mind and Eli Maor drops a lot of mathematical language on the reader. On one hand it made me dive deep into trigonometry, as I've felt I needed a better understanding of sine-waves, as someone who is passionate about music and how it springs from the workings of the world. This was rewarding to get a better grasp on, but much of the math language I just assumed to be true and couldn't follow.
I enjoyed learning more about the developments in physics and math, but I couldn't help wonder if it was just a fascination of the author, and this book gave him the excuse to write about it - rather than there being such a strong parallel between numbers and music.
The overarching framework felt a bit forced, drawing comparisons between developments in music and physics where the connection really isn't that strong. Especially the comparison between Einstein and his theory of relativity and the 12-tone system by Schoenberg was too much. The author spends an entire chapter on this, and he himself shoots down the idea in the end, as the "revolution" of enforcing a communist equality on the semitones within the octave is truly light-years away from all the things that Einstein has achieved.
Most of the topics are described well and all accurately, but I missed some cohesion in the end. Who is this book really for? It can go too deep into some subjects and barely touch others and vice versa. It was worth the read, but if you want to learn more about this topic I would prefer to go straight to the source and pick up some Helmholtz instead.
My math knowledge has been collecting dust in the recesses of my mind and Eli Maor drops a lot of mathematical language on the reader. On one hand it made me dive deep into trigonometry, as I've felt I needed a better understanding of sine-waves, as someone who is passionate about music and how it springs from the workings of the world. This was rewarding to get a better grasp on, but much of the math language I just assumed to be true and couldn't follow.
I enjoyed learning more about the developments in physics and math, but I couldn't help wonder if it was just a fascination of the author, and this book gave him the excuse to write about it - rather than there being such a strong parallel between numbers and music.
The overarching framework felt a bit forced, drawing comparisons between developments in music and physics where the connection really isn't that strong. Especially the comparison between Einstein and his theory of relativity and the 12-tone system by Schoenberg was too much. The author spends an entire chapter on this, and he himself shoots down the idea in the end, as the "revolution" of enforcing a communist equality on the semitones within the octave is truly light-years away from all the things that Einstein has achieved.
Most of the topics are described well and all accurately, but I missed some cohesion in the end. Who is this book really for? It can go too deep into some subjects and barely touch others and vice versa. It was worth the read, but if you want to learn more about this topic I would prefer to go straight to the source and pick up some Helmholtz instead.
June 23, 2025
A relatively short book (about 150 pages) but one that is not easy to read, or at least not read quickly. I had hoped it would give me some better understanding of musical theory and musical terminology by linking it to the underlying maths. It was very interesting but I don't think it has truly enhanced my understanding as much as I had hoped. For me some better explanation on the musical theory would have probably helped me better understand the book. Perhaps I'll revisit the book if and when I have a better understanding of the musical terminology. Though in some cases it seems to me that the link between mathematical terminology and musical terminology is not there, e.g. mathematically a semitone (half a tone) is very close to a whole tone and the musical terminology using half does not make sense to me.
It was difficult to provide a rating of the book, as I'm not clear whether the things I could not understand are due to a lack in required underlying knowledge or due to the explanations not being as good as they should be; i.e. whether the fault lies with me or the book. In the end I used the labels related to the stars, and I did 'like' the book but did not 'really like it'; hence three stars.
It was difficult to provide a rating of the book, as I'm not clear whether the things I could not understand are due to a lack in required underlying knowledge or due to the explanations not being as good as they should be; i.e. whether the fault lies with me or the book. In the end I used the labels related to the stars, and I did 'like' the book but did not 'really like it'; hence three stars.
September 6, 2023
“The fact is, we are all earthbound creatures, born with a natural frame of reference in which gravity defines our personal ‘down’. It is perhaps no accident that gravity and grave come from the same word. This holds also true in music: without a tonal frame of reference, a central key to gravitate toward, we feel lost, wandering aimlessly in an ocean of sound.”
“Our ability to resolve a musical sound into it’s individual pure-tone components - and more generally, to hear as separate notes any combination if individual notes played simultaneously - is one of the most amazing gifts nature has bestowed on us. The entire theory of musical harmony rests on it, enabling us to hear a triad of notes such as C-E-G as individual notes even when they are played together in a C major chord. The sense of vision does not have this ability: as already mentioned, when two colours are being mixed, we see only a single third colour. There is no such thing as an optical chord.”
“Our ability to resolve a musical sound into it’s individual pure-tone components - and more generally, to hear as separate notes any combination if individual notes played simultaneously - is one of the most amazing gifts nature has bestowed on us. The entire theory of musical harmony rests on it, enabling us to hear a triad of notes such as C-E-G as individual notes even when they are played together in a C major chord. The sense of vision does not have this ability: as already mentioned, when two colours are being mixed, we see only a single third colour. There is no such thing as an optical chord.”
January 22, 2019
Un libro non proprio semplice, specialmente se uno la musica la ha, poco, studiata solo alle elementari e medie. Sarebbe piaciuto maggiormente al mio cugino musicologo e organista.
Di certo solleva qualche riflessione sull'insegnamento della musica in Italia, anche se non si parla mai dell'Italia, e sul valore che la musica ha nella formazione della mente.
Io ho apprezzato soprattutto l'ultimo capitolo, con il parallelismo tra Einstein e Schoemberg. Inoltre è un bene che si viva nell'età di Youtube: molte, se non tutte, le musiche e i pezzi citati come esempio si possono comodamente ascoltare mentre si legge il capitolo in cui se ne parla.
Di certo solleva qualche riflessione sull'insegnamento della musica in Italia, anche se non si parla mai dell'Italia, e sul valore che la musica ha nella formazione della mente.
Io ho apprezzato soprattutto l'ultimo capitolo, con il parallelismo tra Einstein e Schoemberg. Inoltre è un bene che si viva nell'età di Youtube: molte, se non tutte, le musiche e i pezzi citati come esempio si possono comodamente ascoltare mentre si legge il capitolo in cui se ne parla.
April 29, 2021
Not very engagingly written unfortunately, it's basically a 150-page summary of the main math-music-linkages in this interdisciplinary history. I wish Maor would've added more personal elements in his book, like in the last chapter, where he describes his experience when looking for Schoenberg CDs in his library and only finding one compilation in the catalogue. Imagine you are looking for books on Picasso or James Joyce and only find a single book in your library's catalogue! Absolutely unimaginable! Yet here lies the story of how 20th century modern music has been culturally neglected by culture itself.
August 16, 2023
Un libro scritto eccezionalmente, ma dal punto di vista di un musicista (o almeno di un ragazzo che lo vorrà diventare) tutte le informazioni sembrano essere incentrate molto più sulla matematica che sulla teoria della musica, presentando teorie abbastanza complesse ad una mente magari non troppo matematica e accennando alle teorie musicali in maniera più generale; dal punto di vista di un matematico potrà sembrare però esattamente il contrario, ma la lettura resta in linea di massima piacevole dato che la passione dell'autore nelle rispettive materie trattate salta estremamente all'occhio, anche se i vari capitoli sembrano vari argomenti poco legati tra loro e un po' frammentari.
August 18, 2025
Delusa. Non è chiaro l'intento di questo libro. Per quanto riguarda la musica sappiate che ne troverete pochissima. Più che altro l'autore focalizza la sua attenzione sugli studi di fenomeni acustici fatti dai grandi scienziati del passato. Ho trovato al suo interno moltissime formule, finalizzate a dimostrare non si sa bene cosa. Avessi voluto studiare acustica avrei comprato un libro che riportava questo termine nel suo titolo e non di certo questo. Non approfondisce e non aggiunge nulla al pensiero musicale, né illumina particolarmente sui processi mentali astratti che in qualche modo legano la scienza matematica con l'arte musicale.
December 16, 2024
A book that is hard to characterize. It is not a music theory book (which I was looking for initially) but has some interesting preliminary music theory concepts such as mathematical and historical fact about temper, rhythm, meter. It is not a music history book but has interesting facts about how composers' related to music over the ages. It is a small manuscript which ably intertwines basic music theory to some basic mathematics (and physics I guess). Not what I was looking for but glad I read it.
January 20, 2022
El propósito del libro me atrajo sobremanera: conectar la historia de las matemáticas, de la física y de la música, y dilucidar las posibles influencias entre las tres disciplinas.
Desgraciadamente, todos los eventos, descubrimientos y creaciones se tratan de forma muy superficial, por lo que la obra se acerca más a una simple y llana enumeración que a una explicación detallada de los episodios que va mencionando.
Desgraciadamente, todos los eventos, descubrimientos y creaciones se tratan de forma muy superficial, por lo que la obra se acerca más a una simple y llana enumeración que a una explicación detallada de los episodios que va mencionando.
April 5, 2020
Atractiva monografía que discute los paralelismos e interacciones entre música, matemática y física. El centro del libro es relacionar los aportes de A. Einstein a la física y los de A. Schoenberg a la música. Se requiere unos conocimientos mínimos de matemática para disfrutar el texto, pero no tanto de música, pues sería ventajoso conocer los rudimentos de la lectura de partituras.
December 8, 2022
The book had a lot of insights and I enjoyed many parts of it. Yet, it seemed a bit fragmented to me. It was like a group of articles sticked together to fit in a book (which caused it to lack coherence). In some parts the author spent a long time to explain the concepts and in some parts he hasted through them and didn't cover them sufficiently.
December 17, 2025
Un saggio divertente e coinvolgente che, più di raccontare la musica dalla matematica, affianca il percorso storico delle due discipline raccontando aneddoti e protagonisti dei loro intrecci.
Non è per nulla difficile: i principi matematici sono al massimo materia di liceo e la musica è spiegata passo passo anche per un profano.
Piacevolissimo
Non è per nulla difficile: i principi matematici sono al massimo materia di liceo e la musica è spiegata passo passo anche per un profano.
Piacevolissimo
November 15, 2020
I mainly pick this book for the cover, which arise from a current research. While the mathematics are easy to understand, as well as the history of some of the greatest mathemathicians, the musical concepts are not for an easy reading if you are not a musician (such is my case).
January 3, 2022
This book will be exceptionally interesting a specific cross-section of readers who are interested in both music and mathematics/engineering. That said, like the author somewhat self-consciously notes, there’s probably too much math for musicians and too much music for mathematicians.
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