Ernest Flagg (1857–1947) American architect
Small Houses: Their Economic Design and Construction (1922)
Source: Small Houses: Their Economic Design and Construction (1922), Ch. II
Ernest Flagg (1857–1947) American architect
Small Houses: Their Economic Design and Construction (1922)
Nicomachus (60–120) Ancient Greek mathematician
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)
Vitruvius book De architectura
Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book VI, Chapter II, Sec. 1
George Perle (1915–2009) American composer
Pages 46-47
The Listening Composer
“Music is nothing but ratios and harmonic math, anyways.”
Andrew Sega (1975) musician from America
Static Line interview, 1998
James Gow (scholar) (1854–1923) scholar
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)
Frank Zappa (1940–1993) American musician, songwriter, composer, and record and film producer
As quoted in The Guitar Handbook (2002) by Ralph Denyer, p. 102