There is nothing extraordinary in this. It is another fact which gives this one its importance, and that is that the musical system is composed of three fifths rising one out of another; so this note by 3/4 becomes the root not only of a chord, but the root of all the three chords, of which the middle one is the tonic; the chord of the balance of the system, the chord of the key; the one out of which it grows, and the one which grows out of it, being like the scales which sway on this central balance-beam. Thus F takes its place, C in the center, and G above. These are the 3 fifths of the system on its masculine or major side. The fractions for A, E, and B, the middle notes of the three chords, are 4/5, 3/5, and 8/15; this too tells a tale; 5 is a new ingredient; and as 3 gives fifths, 5 gives thirds. From these two primes, 3 and 5, along with the integer or unit, all the notes of the system are evolved, the octaves of all being always found by 2. When the whole system has been evolved, the numbers which are the lengths of the strings in the masculine or major mode are the numbers of the vibrations of the notes of the feminine or minor mode; and the string-length-numbers of the minor or feminine are the vibration-numbers of the notes of the major or masculine mode. These two numbers, the one for lengths and one for vibrations, when multiplied into each other, make in every case 720; the octave of 360, the number of the degrees of the circle. [Scientific Basis and Build of Music, page 76]

D27 of the major scale; and the number 27 as string-length will give the vibrations of D26 2/3 in the minor scale, and so all through; they stand thus:-

Lengths    30 26 2/3 24   22 1/2   20 18 16 15 Vibrations
Vibrations 24    27    30    32        36 40 45 48 Lengths
[Scientific Basis and Build of Music, page 88]

See Also

harp string
Laws of String Vibration
nine string chord
quantities of strings
Ramsay - Duality in Quantities of Strings and Vibrations
Ramsay - PLATE XXIV - Vibrations of the Major are the String-lengths for the Minor
strand of wire or gut-string
String Theory
sympathetic string

Created by Dale Pond. Last Modification: Saturday December 5, 2020 03:16:43 MST by Dale Pond.