"Pitch is the relative frequency of vibration." Keely

A relative frequency within context of other frequencies.

among the Greeks on account of having symmetry in itself. The primitive scale was doubtless that which is the model of all major music; and our minor model is its dual, as Ramsay has shown, which in its genesis indicates the duality of all the rest of the notes, although it is not probable that the Greeks saw the musical elements in this light. It is remarkable and significant that in their modes the Greeks did not lift up the scale of Nature into different pitches, preserving its model form as we do in our twelve major scales, but keeping the model form at one pitch they built up their symmetrical tetrachords, allowing the larger and lesser tones of the primitive scale to arrange themselves in every variety of place, as we have shown in the table of tetrachord modes above. Without seeing the genetic origin of music's duality they were led to arrange the modes by symmetry, which is one of the phases of duality. Symmetry is duality in practice. It may not always be apparent how symmetry originates in Nature; but in music, the art of the ear, duality emerges in the genesis of the minor scale; in the true mathematical build of the major on the root of the major subdominant F, and the true relation of the minor to it in the inverse genesis descending from the top of the minor dominant B. [Scientific Basis and Build of Music, page 46]

The scales march on following each other methodically, whether they be written with sharps or flats, and

"Not a step is out of tune, as the tides obey the moon."

The most natural, because the genetic, way to write the scales is to make the major scales all in sharps, after C, because the major genesis is upward in ratios ascending; and to make the minor scales all in flats, after A, because the minor genesis is downward in ratios descending. Let the young student, however, always keep in mind that the sharps and flats are simply marks to show how Nature, at whatever pitch we are taking the scales, is securely keeping them in the same form as when they are first generated; and in their birthplace no sharps or flats are needed. [Scientific Basis and Build of Music, page 90]

VIOLIN-FINGERING - Whenever the third finger is normally fourth for its own open string, then the passage from the third finger to the next higher open string is always in the ratio of 8:9; and if the key requires that such passage should be a 9:10 interval, it requires to be done by the little finger on the same string, because the next higher open string is a comma too high, as would be the case with the E string in the key of G.
In the key of C on the violin you cannot play on the open A and E strings; you must pitch all the notes in the scale higher if you want to get [Scientific Basis and Build of Music, page 99]

ratio of 5:8; three, 3:5; and one, 16:27. There are seven fifths - one in the ratio of 45:64; one, 27:40; and five, 2:3; and seven corresponding fourths - five in the ratio 3:4; one, 40:54; and one 32:45. These are the ratios of the intervals in their simplest expressions as given in the second outer space above the staff in the plate. In the outer space the intervals are given less exactly, but more appreciable, in commas. The ratios of the vibration-numbers of each interval in particular, counting from C24, are given in the inner space above the staff. These vibration-numbers, however, are not given in concert pitch of the notes, but as they arise in the low audible region into which we first come in the genesis from F1, in the usual way of this work. The ratios would be the same at concert pitch; Nature gives the numbers true at whatever pitch in the audible range, or in the low and high silences which lies out of earshot in our present mortal condition. [Scientific Basis and Build of Music, page 110]

When Plate XIII. is divided up the middle of the column, as in Plate XIV., so as that one side may be slipped up a fifth, representing a new key one-fifth higher, its subdominant made to face the old tonic, the two new notes are then pictorially shown, the second being altered one comma and the seventh four commas. The key at this new and higher pitch is by Nature's unfailing care kept precisely in the same form as the first; and wherever the major scale is pitched, higher or lower, the form remains unaltered, all the intervals arranging themselves in the same order. The ear, and the voice obedient to it, carry Nature's measuring-rule in them, and the writing must use such marks as may truly represent this; hence the use of sharps, flats, and naturals; these, however, be it observed, are only marks in the writing; all is natural at any pitch in the scale itself. All this is equally true of the minor mode at various pitches. These two plates are only another and more pictorial way of showing what the stave and the signature are usually made to express. [Scientific Basis and Build of Music, page 114]

with her irrevocable proportions to measure his scales for him. The stars at the C of the first scale and at the B# of the last show the coincidence of 12 fifths and 7 octaves. The number of B# is 3113 467/512; C24 multiplied 7 times by 2 brings us to the number 3072; these two notes in the tempered system are made one, and the unbroken horizon of the musical world of twelve twofold keys is created. The very small difference between these two pitches is so distributed in the 12 tempered scales that no single key of the 12 has much to bear in the loss of perfect intonation. [Scientific Basis and Build of Music, page 118]

suspected. Let us take as our standard of colours the series given by the disintegration of white light, the so-called spectrum: as our standard of musical notes, let us take the natural or diatonic scale. We may justly compare the two, for the former embraces all possible gradations of simple colours, and the latter a similar gradation of notes of varying pitch. Further, the succession of colours in the spectrum is perfectly harmonious to the eye. Their invariable order is— red, orange, yellow, green, blue, indigo, and violet; any other arrangement of the colours is less enjoyable. Likewise, the succession of notes in the scale is the most agreeable that can be found. The order is—C, D, E, F, G, A, B; any attempt to ascend or descend the entire scale by another order is disagreeable. The order of colours given in the spectrum is exactly the order of luminous wave-lengths, decreasing from red to violet. The order of notes in the scale is also exactly the order of sonorous wave-lengths, decreasing from C to B." [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies2, page 19]

the present, and the future, developing in geometric progression; as the past retires, the future advances. The rests in harmony correspond with silence in the Scriptures, both limiting and illimitable. But there is this essential difference: musical instruments can only be tuned to a certain pitch, whereas the Bible will never need fresh editions or corrections, but as it always has unfolded, it always will unfold, as it is necessary to meet our higher mental powers. I believe that, eventually, scientific minds will arrive at the conclusion that all the energies around us arise from the laws which regulate the life of matter, and cause the continual development of trinities from unities. Continuity everywhere adapts simple laws to wondrous workings. If we evade the belief in the development of trinities, this scheme falls to the ground. We can conceive no grander idea of the power, wisdom, and love of the Parent of the universe than that of His following out His own characteristics, knowing that at any moment, if His life-giving power were withdrawn, all would crumble into dust. Let us link with this thought these glorious promises— [Harmonies of Tones and Colours, Scripture Compared with Scripture, page 47]

W. H. Stone
"The comparison of pitch should not be limited to a few treble instruments, but should begin with drums and double-basses, and so proceed upwards. The process, lastly, should not be carried on by compelling all to tune up to the sharpest, but by bringing the sharper instruments slightly down to a medium pitch; this would obviate the constant need for cutting instruments to pieces which is now felt, and prevent the steady tendency to sharpen, which is ruining our voices, and rendering much classical music impossible to all but singers of rare and exceptional organization.” [W. H. Stone; Excerpt from The Scientific Basis of Music 1878]

See Also

04 - On the Pitch of Musical Sounds
concert pitch
cycles per second
electric pitch
Law of Atomic Pitch
Law of Harmonic Pitch
Law of Pitch of Atomic Oscillation
Law of Variation of Atomic Pitch by Electricity and Magnetism
Law of Variation of Atomic Pitch by Rad-energy
Law of Variation of Atomic Pitch by Temperature
Law of Variation of Pitch of Atomic Oscillation by Pressure
Laws of Being
music note or sound colors
Overtone Series
Part 08 - What Vibration Is. - Part 1
Part 09 - What Vibration Is. - Part 2
Part 11 - SVP Music Model
Progressive Evolution
Square Law
12.40 - Color
12.42 - Tone
8.22 - Law of Harmonic Pitch

Created by Dale Pond. Last Modification: Sunday April 4, 2021 03:32:47 MDT by Dale Pond.