Mathematics, science, and Music

[Harvey]

An interesting article discussing mathematical patterns in the music of Mozart and Beethoven: Mozart's Formula, Beethoven and Group Theory.

Also a book that discussed music from the perspective of a scientist who is also a musician: The Physical Basis of Music and its Implications for Musical Performance. Open the chapter pdf files to see the various topics. It is a fascinating book. Here is a list of the chapters:

1. DEFINING OUR GOALS
2. ORIGINS OF MUSICAL INSTRUMENTS
3. DEVELOPMENT OF THE PIANO
4. BACKGROUND OF OUR STUDY
5. MECHANICAL FACTS OF PIANO PLAYING
6. PHYSIOLOGY OF PIANO PLAYING
7. MOZART AND BEETHOVEN COMPARED (see note below)
8. ELECTRONIC MUSICAL INSTRUMENTS AND DEVICES

NOTE: Please be aware that the author seems to have a bone to pick with Mozart and treats him pretty harshly. I am in no position to judge the author's assessment of Mozart, but what he says [about the structure in Mozart's music] does generally fit with what the first link above, Mozart's Formula, Beethoven and Group Theory , says about Mozart's music.

[dahc]

Thank you for these articles.
I often thought a musical composition is a mathematical structure as is in architecture. Even if you just sketch out a drawing of a house the mathematical structure within the drawing is implied by the visual geometry.
I feel Mozart and Beethoven created their musical structure intuitively. They might not have been able to explain their process mathematically because it was already implied. Or maybe they could explain it.
But we can spend hours trying to analyse.

[AeolianHarp]

An interesting article discussing mathematical patterns in the music of Mozart and Beethoven: Mozart's Formula, Beethoven and Group Theory.

Also a book that discussed music from the perspective of a scientist who is also a musician: The Physical Basis of Music and its Implications for Musical Performance. Open the chapter pdf files to see the various topics. It is a fascinating book. Here is a list of the chapters:

1. DEFINING OUR GOALS
2. ORIGINS OF MUSICAL INSTRUMENTS
3. DEVELOPMENT OF THE PIANO
4. BACKGROUND OF OUR STUDY
5. MECHANICAL FACTS OF PIANO PLAYING
6. PHYSIOLOGY OF PIANO PLAYING
7. MOZART AND BEETHOVEN COMPARED (see note below)
8. ELECTRONIC MUSICAL INSTRUMENTS AND DEVICES

NOTE: Please be aware that the author seems to have a bone to pick with Mozart and treats him pretty harshly. I am in no position to judge the author's assessment of Mozart, but what he says [about the structure in Mozart's music] does generally fit with what the first link above, Mozart's Formula, Beethoven and Group Theory , says about Mozart's music.

Looks interesting Harvey! Will read it later, though I doubt I will understand much of it- I am a maths dunce lol.

[Peter]

Thank you for these articles.
I often thought a musical composition is a mathematical structure as is in architecture. Even if you just sketch out a drawing of a house the mathematical structure within the drawing is implied by the visual geometry.
I feel Mozart and Beethoven created their musical structure intuitively. They might not have been able to explain their process mathematically because it was already implied. Or maybe they could explain it.
But we can spend hours trying to analyse.

Absolutely and perhaps Bach is the most mathematical of all! The Sonata form of the classical era is indeed akin to architecture and Beethoven the supreme architect (on earth ) Moving on to the Romantics, Bruckner's symphonies are often described as cathedrals in sound.

[dahc]

Yes the form has to support its own weight and then some. Beethoven is a good stone mason/architect.