As the author writes, “The book describes those physical and mathematical aspects of sound waves that underlie our experience of music.” It is interesting to learn just how much math has to do with the creation and appeal of music, because math underlies so much of what works in our universe.

Indeed, Mario Livio poses the question “Is God a mathematician?” in his book of the same name, because of the “unreasonable effectiveness of mathematics” in explaining the nature of the universe.

Math certainly seems to explain (in part, at least) the appeal of music to the human brain. There are other factors reviewed by the author such as the nature of our anatomy, including our voice apparatus, ears, and even our brains. He talks about people who have had defects, diseases, or injuries that have caused inability to recognize music, and others who could no longer speak but could still sing. Clearly there are areas of the brain responsible to music. He also reviews such developments as improvements in instruments that increased the variety of orchestral and vocal sound. But in the end, it is the mathematical characteristics of sound that are the most determinative.

Chapters include:

Sound and Music
Periodicity, Pitch, and Waves
Sine Waves and Resonance
Scales and Beats
Helmholtz and Consonance
Rameau and Harmony
Ears to Hear With
Power and Loudness
Masking
Other Phenomena of Hearing
Architectural Acoustics
Sound Reproduction
Analysis, Synthesis, and Timbre
Perception, Illusion, and Effect

Appendices include sections on terminology, physical quantities and units, information on waves and more.

Evaluation: Much in the book is rather technical, but even perusing it without delving into any equations will give readers a sense of what makes sounds into music, and what determines our perceptions of it. ( )

Los temas tratados en este libro son los siguientes: Sonido y Música; Periodicidad, altura y ondas; Ondas sinusoidales y resonancia; Escalas y compases; Helmholtz y consonancia; Rameau y armonía; Oídos para oír; Potencia y sonoridad; Enmascaramiento; Otros fenómenos auditivos; Acústica arquitectónica; Reproducción del sonido; Análisis, síntesis y timbre; Percepción, ilusión y efecto…
El libro describe aquellos aspectos físicos y matemáticos de las ondas sonoras que son la base de nuestra experiencia musical y auditiva. Además, describe, en particular, la psicoacústica del sonido musical. La psicoacústica es la rama de la psicología experimental que relaciona los sonidos físicos con sus características percibidas. Quienes se dedican a ella estudian la intensidad de los sonidos apenas audibles, las mínimas diferencias en intensidad sonora, la sonoridad de los sonidos y otros muchos aspectos complejos de la percepción sonora… El lector no debe tener el más mínimo temor a perderse entre complejidades. La audición es la audición. Por mucho que profundicemos en su estudio, la audición sigue siendo parte de nuestra experiencia diaria. La prueba definitiva es cómo suenan las cosas… Escribo sobre el sonido tal y como lo percibimos y, en particular, sobre el sonido musical. Sobre electrónica, fisiología y neurofisiología, sobre ondas sonoras y su generación, sólo digo lo que me parece imprescindible para comprender y apreciar lo que percibimos.
En definitiva, se trata de un libro extraordinario acerca del sonido, cuyo estudio aportará grandes alegrías a titiriteros, músicos, directores de escena y al espectador interesado en saber porqué escucha lo que escucha.

Read this many years ago, but came across a reference to it earlier today in the forward, written by Max Matthews, to the very impressive looking Musimathics. I'm digging into my vague memory of what he wrote to paraphrase what he says: essentially, all you need to read to understand computer music is the two volumes of Musimathics (on the list!) and this book. I'm adding this back to my to re-read stack. ;~) ( )

The Science of Musical Sound
Scientific American Library
John R. Pierce
June 30, 2012

The publication date for this book is 1983, and since some of it concerns computer-generated music, it is dated. The book even comes with vinyl records of some of the sounds! The basic physics of waves, and harmonics, does not go out of date, however. I learned again about listening for beats occurring when two notes that are close to each other are sounded together, and how to tune using this phenomenon. A vibrating string produces a note; if the string is shortened to 2/3 of its length the note is a fifth higher (if the string is at its original length sounds a C, at 2/3 length it will sound a G). If shortened to 1/2 of its length it is one octave higher; if a C-string is shortened to 5/6 of its length it is at E flat (minor third interval), and if shortened to 4/5 of its length it is an E (major third). The frequencies of vibration are the inverse of the fractions times the base frequency. Instruments of all kinds, except bells and percussion instruments, have harmonic partial frequencies at interger multiples of the base frequency. Rameau founded his ideas about harmony on the bass frequency of major triad, a note that is two octaves below the root of the chord. The effects of masking noise, and precedence, are part of the psychophysics of hearing. Concert halls are designed taking into mind the reverberation time, and total sound absorbtion, as well as details like the need for the orchestra to hear itself with reflected sound. The case of New York philharmonic hall, and the terrible result before re-design into Avery Fisher hall, is discussed in detail. ( )