
Small Houses: Their Economic Design and Construction (1922)
Source: Small Houses: Their Economic Design and Construction (1922), Ch. II
Small Houses: Their Economic Design and Construction (1922)
this harmonic proportion may be expressed as <math>\frac{12}{6}=\frac{12-8}{8-6}</math> or inversely.
Nicomachus of Gerasa: Introduction to Arithmetic (1926)
Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book VI, Chapter II, Sec. 1
“Music is nothing but ratios and harmonic math, anyways.”
Static Line interview, 1998
Nicomachus gives another reason for the name, viz. that a cube being of 3 equal dimensions, was the pattern άρμονία: and having 12 edges, 8 corners, 6 faces, it gave its name to harmonic proportion, since:<center>12:6 :: 12-8:8-6</center>
Footnote, citing Vide Cantor, Vorles [Vorlesüngen über Geschichte der Mathematik ?] p 152. Nesselmann p. 214 n. Hankel. p. 105 sqq.
A Short History of Greek Mathematics (1884)
As quoted in The Guitar Handbook (2002) by Ralph Denyer, p. 102