musical system

"Gravity and levity, and centrifugal force; these musical forces do not here refer to the center of the earth, but the center of the musical system, e.g., E in the scale of C." [Scientific Basis and Build of Music, page 27]

"centrifugal force. A third note produced by the prime 5 is derived from the note produced by the first power of 3, and this note by the first power of 5 having being slightly acted on by the force of gravity, and the first power of 5 having only a little centrifugal force, the result is that this note E in the scale of C, derived from the first power of 3 by the prime 5, is balanced between the two forces. It is the only note in the system which in the octave scale has not a large interval on the one side of it nor on the other, and consequently it is the only note which attracts and is attracted by two notes from proximity. Thus it is that the musical system is composed of three notes having specific gravity and three having specific levity or bouyancy, and one note, E, the center of the tonic chord, balanced between these two forces. As the attractions of notes from proximity take place when the notes with downward tendency meet the note with upward tendency, had the notes been animated by only one of these forces there could have been no system of resolutions of the notes either in melody or harmony; they would all have been by gravity weighing it downwards, or by levity soaring upwards." [Scientific Basis and Build of Music, page 28]

The law of gravitation is the law of Music as well as of Astronomy. The cycles of the distances, that is the intervals, in Music correspond to the cycles of the periods in Astronomy. In Astronomy the distances and quantities of matter are primary, and determine the periods; in Music the periods and quantities are primary, and determine the distances or intervals. In Astronomy the distances are commensurable; in Music the periods are commensurable. In Astronomy the periods are incommensurable; in Music the distances or intervals are incommensurable. In Astronomy, because the simplicity is not in the periods, the conjunctions are very few at one time; in Music, because the simplicity is in the periods, the conjunctions are very many at one time. And herein lies in the one case the harmony and permanence of the solar system, and in the other case the harmony and beauty of the musical system. The periods and distances in Astronomy and Music are inversely related. [Scientific Basis and Build of Music, page 30]

Either the one or the other must be at fault. Had the dictates of the mathematicians and the scale of mathematical intonation wholly ruled, the advent of the great masters would have been impossible. It was well said by one writing in The Choir - "Theory should be made from music, and not music from theory . . . the final judge of music is the Ear." The Great Masters are the exponent artists of what is true in the Science of Music, though it may differ from what has been taught by the merely mathematical-intonation advocates of music science. It should not be forgotten that the science of the mathematical theorists is one thing, and that of the composers is another. Schubert, Beethoven, Mozart, Haydin, Mendelssohn, and such inspired musicians, who walked in the liberty wherewith Nature made them free, are sufficient authority against the bondage of the one-law theorists who would tie us down to the mathematical command which comes from without, but who know nothing of the life within music which is the law unto itself.1
With twelve divisions in the Octave, each note is adapted to serve in any capacity, and does serve in every capacity by turns. It is quite clear that this cannot be said of the mathematically perfect notes. And this is where it is seen that what is perfect in mathematical ratios becomes imperfect in the Musical System. Indeed, the mathematical intonation does not give a boundary within which to constitute a System at all, but goes off into never-ending cycles.
In music, Nature begins by producing the Diatonic Octave of seven notes, derived by the mathematical ratios2; [Scientific Basis and Build of Music, page 34]

The number 3 is the creative power in music, producing fifths, but it is under the control of the Octave prime - the number 2. It is the supreme octave which forms a boundary by making twelve fifths and seven octaves unite in one note. Within this horizon lies the musical system in its threefoldness - major, minor, and chromatic. [Scientific Basis and Build of Music, page 35]

There is no one musical interval which is the perfect measuring rule for the others. But the octave has been divided into 53 parts called commas, and these commas are as near a commensurable rule as we need seek for measuring the musical intervals; always remembering that, strictly speaking, these intervals are incommensurable. The large second has 9 commas; the medium second has 8; and the small second 5; and all other intervals, being of course composed of some of these seconds, can be measured accordingly. Thus the comma, though not itself an interval of our musical system, is the handy and sufficiently perfect inch, let us call it, for practical purposes in music. [Scientific Basis and Build of Music, page 75]

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]

At the first, in the laws of quantities and motions adjusting musical vibrations, there is one chord of the three notes, F, A, C, the root, middle, and top of the five notes which compose the true natural scale; this one chord can be reproduced a fifth higher, C, E, G, in the same mathematical form, taking the top of the first for the root of the second chord. In like manner this second can be reproduced another fifth higher, G, B, D, still in the same mathematical form, and so fit to be a member of the chord-scale of a key. But the law does not admit of another reproduction without interfering with the first chord, so that a fourth fifth produces no new effect; but the whole key is simply a fifth higher, i.e., if the fourth fifth has been properly produced by multiplying the top of the third fifth by 3 and by 5, the generating primes in music. That this carries us into a new scale is seen in that the F is no longer the F♮ but F#, and the A is no longer A♮ but A,. But if we suppose the fourth fifth to be simply the old notes with their own vibration numbers, then D, F, A would not be a fifth belonging either to the major or the minor mode, but a fifth a comma less. The letters of it would read like the minor subdominant, D, F, A; but the intervals, as found in the upward development of the major genesis, instead of being, when expressed in commas, 9, 5, 8, 9, which is the minor subdominant, would be 8, 5, 9, 8, which is not a fifth of the musical system; these having always, whether major or minor, two 9's, one [Scientific Basis and Build of Music, page 77]

8, and one 5, making 31 commas, while this supposed fourth-fifth major would only have 30. The fifths of the musical system are thus strictly kept as a symbol of the Trinity of the Creator, Three in One. [Scientific Basis and Build of Music, page 78]

"All the bodies in the Solar System, in a general way, are attracted to the sun according to the Law of Masses; but all the satellites are attracted to their planets according to the Law of Distance. The subdominant and dominant chords in the Musical System, in a general way, are attracted to the tonic center; but each note in the octave scale is attracted to its nearest note by the Law of Proximity. [Scientific Basis and Build of Music, page 96]

See Also

Laws of Music
musical system of vibrations
Ramsay - Nature's Grand Fugue - The System of Musical Vibrations
System of Musical Sounds
System of musical vibration
system of musical vibrations
The Musical System

Created by Dale Pond. Last Modification: Saturday December 12, 2020 03:38:58 MST by Dale Pond.