Music: a Mathematical Offering by Dave Benson

By Dave Benson

Because the time of the traditional Greeks, a lot has been written concerning the relation among arithmetic and tune: from concord and quantity thought, to musical styles and crew conception. Benson presents a wealth of data the following to allow the instructor, the coed, or the novice to appreciate, at various degrees of technicality, the true interaction among those old disciplines. the tale is lengthy in addition to wide and contains physics, biology, psycho acoustics, the background of technology, and electronic know-how in addition to, after all, arithmetic and tune. beginning with the constitution of the human ear and its dating with Fourier research, the tale proceeds through the math of musical tools to the tips of consonance and dissonance, after which to scales and temperaments. this can be a must-have e-book that allows you to learn about the tune of the spheres or electronic song and lots of issues in among.

Show description

Read Online or Download Music: a Mathematical Offering PDF

Best music books

Guitarist (March 2013)

Guitarist is the longest verified united kingdom guitar journal, delivering apparatus studies, artist interviews and strategies classes, counsel and tricks.

http://www. musicradar. com/guitarist

Springsteen on Springsteen: Interviews, Speeches, and Encounters (Musicians in Their Own Words)

Supplying fanatics an in depth examine the artist's personal phrases through the prior 4 a long time, Springsteen on Springsteen brings jointly Q&A–formatted articles, speeches, and lines that include major interview fabric. nobody is best certified to discuss Springsteen than the guy himself, and he's frequently as articulate and provocative in interviews and speeches as he's emotive onstage and in recordings.

Brian Eno's Another Green World (33 1/3 Series)

PITCHFORK: POPTIMIST #35
[Tom Ewing, January 2011]

“The Nylon model of the anecdote comes from Geeta Dayal’s nice booklet approximately Eno and his 1975 masterpiece, one other eco-friendly global. published as a part of Continuum Books’ 33 0.33 sequence on vintage albums, the publication in most cases sidesteps the completed LP to make the method the hero. Eno’s use of collaboration, likelihood, and cybernetics to strength creativity makes for a desirable tale, enlivened by means of the occasionally bemused yet constantly fond memories of contributors from the ’70s and after. [. .. ] Eno himself it sounds as if enjoyed the ebook, deciding to buy copies for neighbors. This isn’t surprising– an curiosity in approach has been a relentless of his paintings for 4 a long time. [. .. ] Dayal’s ebook leaves you with the sensation that one other eco-friendly international is a list whose dislocated, spectral features are ghost-impressions of the opposite files its techniques may need created. ”

The Essence of Bruckner: An essay towards the understanding of his music

This can be a revised and improved version of Robert Simpson's research, first released in 1967, of Bruckner's track. It contains extra fabric at the third, 4th and eighth symphonies, whose unique types have just recently develop into to be had, and a brand new bankruptcy at the String Quintet. Dr Simpson, himself a composer, is additionally the writer of "Carl Nielsen, Symphonist" and the BBC song consultant, "Beethoven Symphonies".

Additional info for Music: a Mathematical Offering

Example text

Forced harmonic motion is responsible for the production of sound in most musical instruments, as well as the perception of sound in the cochlea. We shall see that forced harmonic motion is what gives rise to the phenomenon of resonance. There are two steps to the solution of the equation. 10, to give the complementary function. 1). This is called a particular integral. 1) is the sum of the particular integral and the complementary function. Examples 1. Consider the equation y¨ + 4y˙ + 5y = 10t2 − 1.

Suppose that f (θ) is periodic with period 2π, and that it is continuous and has a bounded continuous derivative except at a finite number of points in the interval [0, 2π]. 1) converges to f (θ) at all points where f (θ) is continuous. Proof. See K¨ orner [70], Theorem 1 and Chapters 15 and 16. An important special case of the above theorem is the following. A C 1 function is defined to be a function which is differentiable with continuous derivative. If f (θ) is a periodic C 1 function with period 2π, then f ′ (θ) is continuous on the closed interval [0, 2π], and hence bounded there.

6. Complex coefficients The theory of Fourier series is considerably simplified by the introduction of complex exponentials. See Appendix C for a quick summary of complex numbers and complex exponentials. 1) n=−∞ 1 1 where α0 = 21 a0 , and for m > 0, αm = 12 am + 2i bm and α−m = 12 am − 2i bm . 1) using a0 = 2α0 , am = αm + α−m and bm = i(αm − α−m ) for m > 0. 7) are replaced by αm = 1 2π 2π e−imθ f (θ) dθ. 2) 0 Exercises 1. 2, show that αm = 2/imπ 0 m odd m even. 10Note that we are dealing with complex valued functions of a real periodic variable, and not with functions of a complex variable here.

Download PDF sample

Rated 4.77 of 5 – based on 32 votes