Product Description
During the nineteenth century, a remarkable scientific instrument known as a harmonograph revealed the beautiful patterns found in music. Harmonograph is an introduction to the evolution of simple harmonic theory, from the discoveries of Pythagoras to diatonic tuning and equal temperament. Beautiful drawings show the octave as triangle, the fifth as pentagram; diagrams show the principles of harmonics, overtones, and the monochord. Anthony Ashton examines the phenom… More >>
Harmonograph: A Visual Guide to the Mathematics of Music
Tags: anthony ashton, discoveries, drawings, equal temperament, evolution, Guide, harmonic theory, Harmonograph, Mathematics, monochord, music, nineteenth century, octave, overtones, pythagoras, scientific instrument, triangle, Visual
#1 by Ann Covalt on April 6, 2010 - 10:01 am
One is reminded of the geometry and math of sound; coupled with its artistic presentation.
Rating: 4 / 5
#2 by P. Czerner on April 6, 2010 - 10:05 am
I’m not so sure that a triangle is an octave (2:1) and a fifth (3:2) is a pentagram. A fifth, combined with a fourth (4:3), forms an octave. It would make more sense if the Octave were a biangle (2/1), a fifth were a triangle (3/2/1), a fourth a quadrangle (4/3/2/1), and a major third a pentangle (5/4/3/2/1).(May I write my own book? Continuing, a minor third would be a hexangle (6/5/4/3/2/1), a second or whole tone would be a nonangle (9/8/7/6/5/4/3/2/1), and in between these two are notes that don’t exist in the standard western tuning — those forming a heptangle (7/6/5/4/3/2/1) and an octangle (8/7/6/5/4/3/2/1). ) To summarize, each ratio is just a pair of harmonics to a fundamental pitch, and the series of the harmonics from the fundamental to the ratio pair can be considered to be the corners of a geometric figure.
Rating: 4 / 5
#3 by Coleman M. Greenberg on April 6, 2010 - 12:02 pm
This tiny book is interesting, but not particularly enlightening with regard to the “structure” of music. Regardless, it was worth doing/having.
Rating: 3 / 5
#4 by Paris Treantafeles on April 6, 2010 - 1:59 pm
Short and easy to read with beautiful illustrations, this is a nice addition to your collection if you are interested in the connections between sounds and visuals.
Rating: 4 / 5
#5 by Raul Jimenez Gomez on April 6, 2010 - 3:43 pm
I was really surprised by looking for the first time the visual appearance of music. It looks to me as the our days fractals, shown in a different way.
Rating: 4 / 5