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Note

A single-frequency sound (pitch) usually within context of a musical scale. A music note is usually designated by the letters A through G with appropriate accents, sharps or flats.

Russell
"The reason that each succeeding tonal note, which constitutes the elements of matter, are one octave higher is one entirely of increased pressure. You can better understand that by compressing some air in an enclosed box or tube in which you have inserted a whistle. The more air you pump in, the higher the whistle will sound when you open its valve. If you tighten a wire the same thing will happen. The same harp string can give you many tones if you turn the tuning pins higher, or lower. By the time the first octave string has multiplied in cube ratio nine times, the speed of vibration frequencies and intensity of pressure have reached the incredible proportions of 1,073,741,824 times greater in the 9th string than the first string." [Atomic Suicide, page 30-31]

Ramsay
"Of these three chords, which constitute a scale or key, Nature next proceeds to generate, in a similar way, a family of scales or keys, and these in two lines, the Major and the Minor. The twice twelve-fold family of keys is brought forth in much the same way as were the chords which constitute them, and as were the notes which constitute the chords. There is a beautiful growth-like continuity in the production of all." [Scientific Basis and Build of Music, page 20]

"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]

this is the middle of our chord, E, G, B; and remember that this also is G as we found it coming upward, C3 multiplied by 3 being G9. This is another note of the minor, the same in its quantity as that of the major. Now for another chord downward we must divide the root of the one we have found, namely E15, by 3, which will give us A5, the root of a center chord for the minor, and the very key-note of the relative minor to C. And remember that this A5 is just as we found it in coming upward, for F multiplied by 5 gave us A5. Now divide E15 by 5 and we have C3, the middle to our minor chord, A, C, E. Still we must remember that this C3 is just as we found it coming upward, for F multiplied by 3 is C3. Behold how thus far major and minor, though inversely developed, are identically the same in their notes, though not in the order in which they stand in the fifths thus generated. [Scientific Basis and Build of Music, page 32]

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]

It is a degradation of the mathematical primes to apply them to the getting of the semitones of the chromatic scale, as even Euler himself mistakenly does. The mathematical ratios lead the way in getting the notes of the diatonic scale, and that is all that is required of them. The true praise to the ratios is that they have constituted an organic structure with form and life-powers adapted for self-development. It would be little credit to the mother if the child required to be all its life-long pinned to her apron-strings. As the bird when developed so far leaves the shell, and is afterwards fully developed in new conditions; so the System of music when developed so far leaves the law of ratios, its mathematical shell, and is afterwards fully developed by other laws. Music has an inspirational as well as a mathematical basis, and when mathematicians do not recognize this they reckon without their host. [Scientific Basis and Build of Music, page 35]

Mathematicians have not recognized the life-power of the notes, and so they have misapplied their calculations, though these were perfect in themselves. Assuming the place of dictators, they say with an air of authority that, "strictly speaking, nothing could be more scientifically and musically untrue than the chromatic scale of twelve equal semitones as played on a tempered instrument; for in it, as in the diatonic scale, the same natural law prevails that no two tones of equal mathematical relations can melodically succeed each other." Saying that the same natural law prevails implies that they are reasoning from analogy; but in this assumption they are dictating to Nature. In a similar way they might assume that the interval of the octave, like the other intervals, should have a grave harmonic.2 But the fact that the octave interval has not a [Scientific Basis and Build of Music, page 36]

When the major scale has been generated, with its three chords, the subdominant, tonic, and dominant, by the primary mathematical ratios, it consists of forms and orders which in themselves are adapted to give outgrowth to other forms and orders by the law of duality and other laws. All the elements, orders, combinations, and progressions in music are the products of natural laws. The law of Ratio gives quantities, form, and organic structure. The law of Duality gives symmetry, producing the minor mode in response to the major in all that belongs to it. The laws of Permutations and Combinations give orders and rhythms to the elements. The law of Affinity gives continuity; continuity gives unity; and unity gives the sweetness of harmony. The law of Position gives the notes and chords their specific levities and gravities; and these two tendencies, the one upward and the other downward, constitute the vital principle of music. This is the spiritual constitution of music which the Peter Bell mathematicians have failed to discern: [Scientific Basis and Build of Music, page 37]

If the effects of notes and chords had depended entirely on their mathematical ratios, then the effect of the subdominant, tonic, and dominant would have been alike; for these three chords have exactly the same ratios. It is the law of position which gives the tonic chord its importance, and not any special ratios embodied in its structure. The ratio of 2 to 1 has a pure, unmixed, invariable character, always realized in the interval of the octave. The notes produced from 1 by the first, second, and third powers of 3 have different degrees of centrifugal force. The character of the notes produced by the first power of 5 depends on the character of the notes from which they are derived, namely, 1, 3, and 9. The final character of the notes and chords derived by the same ratios is determined by the amount of force which they have acquired from the way in which they have been derived, and from their position in the system; and no matter where these notes may afterwards be [Scientific Basis and Build of Music, page 37]

The extremes of the levities and gravities of a key-system are always at the extent of three fifths; and whatever notes are adopted for these three fifths, the center fifth is the tonic. As there never can be more than three fifths above each other on the same terms, so there can never be more than one such scale at the same time. A fourth fifth is a comma less than the harmonic fifth1; and this is Nature's danger-signal, to show that it is not admissible here. Nature does not sew with a knotless thread in music. The elements are so place that nothing can be added nor anything taken away without producing confusion or defect. What has been created is thus at the same time protected by Nature. [Scientific Basis and Build of Music, page 38]

B, namely G#, they come in touch of each other like the two D's. When this three fifths below F major and three fifths above B minor have been developed, the extremes A♭ and G#, though standing like the two D's in duality, are so near that here again one note can be made to serve both. The major series of scales and the minor series at these limits are thus by two notes which have duality in themselves hermetically sealed; but not till Nature has measured off for any one of these scales a sphere of twelve keys in which to move in perfect freedom of kinship by softly going modulations. [Scientific Basis and Build of Music, page 39]

RESOLUTION - The tendency and going of a note of one chord to some note of the next chord. [Scientific Basis and Build of Music, page 40]

It is according to the Law of Duality that the keys on the piano have the same order above and below D, and above and below G# and A♭, which is one note. In these two places the dual notes are given by the same key; but in every other case in which the notes are dual, the order above the one and below the other is the same. The black keys conform to the scale, and the fingering conforms to the black keys. On that account in the major scale with flats, for the right hand the thumb is always on F and C; and as the duals of F and C are B and E in the minor scale with sharps, for the left hand thumb is always on B and E. [Scientific Basis and Build of Music, page 44]

It is in their inverse relations that the major and the minor are equal. Every note, chord, and progression in the one has its reciprocal or corresponding note, chord, and progression in the other. This is the Law of Duality. And this general law of Nature is so deeply rooted in music, that is the numbers which represent the vibrations in the major system be made to represent quantities of string, these quantities will produce the minor system (beginning, of course, with the proper notes and numbers); so that when the quantities are minor the tones are major, and when the quantities are major the tones are minor.1[Scientific Basis and Build of Music, page 44]

There was, then, something of truth and beauty in the Greek modes as seen in the light now thrown upon them by the Law of Duality, at last discerned, and as now set forth in the genesis and wedlock of the major and minor scales. The probably symmetrical arrangement of the modes, all unwitting to them, is an interesting exhibition of the true duality of the notes, which may be thus set in view by duality lines of indication. We now know that B is the dual of F, G the dual of A, C the dual of E, and D minor the dual of D major. Now look at the Greek modes symmetrically arranged:

D EF G A BC D
C D EF G A BC EF G A BC D E
A BC D EF G A G A BC D EF G
F G A BC D EF BC D EF G A B


Thus seen they are perfectly illustrative of the duality of music as it springs up in the genetic scales. The lines reach from note to note of the duals. [Scientific Basis and Build of Music, page 46]

It should not be supposed that this division of the notes into semitones, as we call them, is something invented by man; it is only something observed by him. The cutting of the notes into twelve semitones is Nature's own doing. She guides us to it in passing from one scale to another as she builds them up. When we pass, for example, from the key of C to the key of G, Nature divides one of the intervals into two nearly equal parts. This operation we mark by putting a # to F. We do not put the # to F to make it sharp, but to show [Scientific Basis and Build of Music, page 47]

that Nature has done so.1 And in every new key into which we modulate Nature performs the same operation, till in the course of the twelve scales she has cut every greater note into two, and made the notes of the scale into twelve instead of seven. These we, as a matter of convenience, call semitones; though they are really as much tones as are the small intervals which Nature gave us in the genesis of the first scale between B-C and E-F. She only repeats the operation for every new key which she had performed at the very first. It is a new key, indeed, but exactly like the first. The 5 and 9 commas interval between E and G becomes a 9 and 5 comma interval; and this Nature does by the rule which rests in the ear, and is uttered in the obedient voice, and not by any mathematical authority from without. She cuts the 9-comma step F to G into two, and leaving 5 commas as the last interval of the new key of G, precisely as she had made 5 commas between B and C as the last interval of the key of C, she adds the other 4 commas to the 5-comma step E to F, which makes this second-last step a 9-comma step, precisely as she had made it in the key of C.2 [Scientific Basis and Build of Music, page 48]

This subtracting and adding process of Nature by which she so freely handles the notes is the way she gives us the materials of the Chromatic Scale, in which an entirely new series of chords with strikingly different effects, and with exceedingly interesting, subtle, and at the same time easy progressions, is put in possession of the practical musician. This new series of chords forms, in fact, materials for the Chromatic System, which D. C. Ramsay has discovered, and which he has elaborated, as his custom was, exhaustively - his last labor in the interests of music science and art. [Scientific Basis and Build of Music, page 48]

The common chord is a group of notes which come together by generic affinity, much like the chemical combinations of our system of atoms. The common chord is a triplet, and in the progression from one chord to another these triplets have always something in common; by the law of continuity one of the notes of the chord first is also found in chord second; and chord second also finds one of its notes in chord third. This is the way Nature gives them to us [Scientific Basis and Build of Music, page 48]

in their birthplace - F A C, C E G, G B D. Indeed in their birth not only is it so, but still further, the top note of the first chord is the root and generator of the third. They are linked in generative continuity. [Scientific Basis and Build of Music, page 49]

In the progression - that is, the going on from one to another - of these triplets in harmonizing the octave scale ascending, Nature goes on normally till we come to the passage from the sixth to the seventh note of the scale, whose two chords have no note in common, and a new step has to be taken to link them together. And here the true way is to follow the method of Nature in the birthplace of chords.1 The root of the subdominant chord, to which the sixth of the octave scale belongs, which then becomes a 4-note chord, and is called the dominant seventh; F, the root of the subdominant F, A, C, is added to G, B, D, the notes of the dominant, which then becomes G, B, D, F; the two chords have now a note in common, and can pass on to the end of the octave scale normally. In going down the octave scale with harmony, the passage from the seventh to the sixth, where this break exists, meets us at the very second step; but following Nature's method again, the top of the dominant goes over to the root of the subdominant, and F, A, C, which has no note in common with G, B, D, becomes D, F, A, C, and is called the subdominant sixth; and continuity being thus established, the harmony then passes on normally to the bottom of the scale, every successive chord being linked to the preceding note by a note in common. [Scientific Basis and Build of Music, page 49]

There are two Diatonic systems in Music - the major and the minor. With the exception of one note, all the notes of the one system are identical with those of the other. The major key C has all the notes of the minor key A excepting D, the root of the minor subdominant; and the minor has all the notes of the major exception D, the top of the major dominant. These twain are one music, the masculine and feminine of a twofold unity; one system in duality rather than two systems. [Scientific Basis and Build of Music, page 50]

There are two semitones in each system, B-C and E-F. But when the notes of the two systems are being generated simultaneously, the two semitonic intervals originate separately. While the major is generating the semitone E-F, the third and fourth of the major scale, the minor is generating the semitone B-C, the second and third of the minor scale. So E-F is the semitone which belongs genetically to the major, and B-C to the minor.1 These two semitones are the two roots of
THE CHROMATIC SYSTEM,
and they are found together in what has been called the "Minor Triad," and by other names, namely, B-D-F. [Scientific Basis and Build of Music, page 50]

Some of the elements of the Chromatic System were known 200 years ago. The Diatonic scale, being called the "Natural scale," implied that the chromatic chords were consider to be artificial; but the notes of the chromatic chords, from their PROXIMITY to the notes of the tonic chord, fit to them like hand and glove. Nothing in music is more sweetly natural and pleasingly effective than such resolutions; and hence their extensive use in the hands of the Masters. The chromatic chords have close relations to the whole system of music, making the progressions of its harmonies easy and delectable, and producing effects often enchanting and elevating, as well as often subtle and profound; and while they are ever at hand at the call of the Composer, they are ever in loyal obedience to the laws of their own structure and system. When a diatonic chord precedes another diatonic chord belonging to the same scale, it has one note moving in semitonic progression;1 but when a chromatic chord precedes a diatonic chord, it may have three semitonic progressions.2 The primary chromatic chord resolves into 8 of the 24 diatonic tonic chords, with 3 semitonic progressions. These identical notes of the chromatic chord, with only some changes of names, resolve into another 8 of the 24 tonic chords, with 2 semitonic progressions and one note in common; and when they resolve into the third and last 8 of the 24 tonic chords, they move with one semitonic progression and 2 notes in common. So to the chromatic chord there are no foreign keys.3 And as it is with the first chromatic chord, so with the other two. [Scientific Basis and Build of Music, page 51]

See Also


Frequency
Interval
Key
Pitch
Scale
Tone
Triplet

Created by admin. Last Modification: Saturday October 24, 2020 05:51:10 MDT by Dale Pond.