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# minor scale

noun: a diatonic scale with notes separated by whole tones except for the 2nd and 3rd and 5th and 6th.

Ramsay
Well, how are we to get the true minor scale? There is a remarkable fact, and a beautiful one, which suggests the method. Such is the economy of Nature, that from one system of proportion employed in two different ways, in the one case as periods of vibrations and in the other as quantities of strings, everything in Music's foundation is produced. It is a remarkable fact that the numbers for the lengths of the strings producing the major scale are the numbers of the vibrations producing the minor scale; and the numbers for the lengths of the strings for the minor scale are the numbers of the vibrations of the notes of the major scale. Here Nature reveals to us an inverse process for the discovery of the minor scale of notes. [Scientific Basis and Build of Music, page 31]

But let us proceed with our development, for we need another fifth, a lower one, a subdominant for our minor scale. Well, let us divide A5 by 3 and we have D1 2/3, the root of the lowest fifth; and if we divide A5 by 5 we have for our middle to this fifth F1, and this is F just as we find it at the major start, and identical in quantity in both major and minor. But let us examine the D1 2/3. It is not easy to compare D1 2/3 with D27 of the major; let us bring it up a few octaves by multiplying by 2. This will not alter its quantity, but simply give us the same quantity in a higher octave, in which we may more easily compare it with the major D1 2/3 multiplied by 2 is 3 1/3; multiplied again by 2 is 6 2/3; once more by 2 it is 13 1/3; and once more by 2 it is 26 2/3. Now we can compare it with D27 of the major, and we find this strange fact, that it is a little lower than the major D. The two D's are at the center of the dual system, but the center of the system is neither in the one D nor in the other, but as an invisible point between them, like the center of gravity in a double star; for the minor D is pushed a little below the center, and the major D is pushed a little above the center of the two modes of the system. [Scientific Basis and Build of Music, page 32]

There are joinings, however, though at a wilder limit. The system of music is not a spiral line. The minor scale is developed from the major by the law of Duality; and when this is done, D26 2/3, the root of the subdominant minor, is so near to D27, the top of the dominant major, that one note may be made to serve for both; and this joins the one extreme of the major and minor systems in this note D, which has thus duality in itself. The only other place where the dual system of major and minor stands open is at the other extreme of the two modes, between B, the top of the dominant minor, and F the root of the subdominant major; and these unjoined ends reach away till at three fifths below F, namely A?, and at three fifths above [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]

Through the whole system, in the progression of major scales with sharps and minor scales with flats, the new sharp is applied to the middle of the major dominants, and the new flat to the middle of the minor subdominants. In the progression of major scales with flats and minor scales with sharps, the new flat is applied to the root of the major subdominant, and the new sharp to the top of the minor dominant.2 [Scientific Basis and Build of Music, page 43]

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]

There is nothing too small or remote to get beyond the reach of the Law of Duality; it follows the major and minor scales through all their inverse and reciprocal progressions, and by-and-by it appears at the extremity of complex music in the shape of inverse fugue. [Scientific Basis and Build of Music, page 44]

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]

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]

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]

The triplet B, D, F, has been called the imperfect triad, because in it the two diatonic semitones, B-C and E-F, and the two minor thirds which they constitute, come together in this so-called imperfect fifth. But instead of deserving any name indicating imperfection, this most interesting triad is the Diatonic germ of the chromatic chord, and of the chromatic system of chords. Place this triad to precede the tonic chord of the key of C major, and there are two semitonic progressions. Place it to precede the tonic chord of the key of F# major, and there are three semitonic progressions. Again, if we place it to precede the tonic chord of the key of A minor, there are two semitonic progressions; but make it precede the tonic chord of E? minor, and there are three semitonic progressions. This shows that the chromatic chord has its germ in, and its outgrowth from the so-called "natural notes," that is notes without flats or sharps, notes with white keys; and that these natural notes furnish, with only the addition of either A? from the major scale or G# from the minor, a full chromatic chord for one major and one minor chord, and a secondary chromatic chord for one more in each mode. [Scientific Basis and Build of Music, page 52]

Moreover, it is only from one to five, that is from C to G in ascending, which is its proper direction in the genesis, that the major in being harmonized does not admit of minor chords, but if we descend this same natural major scale of the fifth from five to one, that is from G to C, the first chord is C E G; the next chord is F A C; if this is succeeded by the minor chord A C E, there are two notes in common and one semitonic progression, as very facile step in harmony; and the following two notes are most naturally harmonized as minor chords. So modulation into the minor, even in this major scale, is very easy in descending, which is the proper direction of the minor genesis.2 In a similar way, it is only from five to one, that is from E to A in descending, which is its proper genetic direction, that the minor in being harmonized does not admit of major chords; but if we ascend this same minor scale of the fifth from one to five, the first chord is A C E, the next is E G B, and if this chord be followed by the major C E G, there are here again two notes in common and one semitonic progression; and the two notes following are then most naturally harmonized as major chords. So modulation into the major, even in this minor scale, is very natural and easy in ascending, which is the proper direction of the major genesis.3 The dominant minor and the tonic major are, like the subdominant major and the tonic minor, very intimately related in having two notes in common and one semitonic progression. [Scientific Basis and Build of Music, page 65]

It is a remarkable fact that the numbers for the lengths of strings producing the major scale are the number of the vibration of the notes of the minor scale; for example, string-length as 26 2/3 will give the vibrations for [Scientific Basis and Build of Music, page 87]

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]

The six successive major scales with sharps require 2 new notes each, and the six successive minor scales with sharps require also 2 new notes each; but one of these new notes for each minor scale is supplied from the scale of the relative major, and the other from the sub-relative major, i.e., the scale one-fifth lower than the relative. So when the major scales with sharps have been developed they furnish all the new notes needed for the minors. The six successive minor scales with flats require 2 new notes each, and the six successive major scales with flats require each 2 new notes; but one of these is supplied from the scale of the relative minor, and the other from the scale of the super-relative, i.e., the scale one fifth higher than the relative. So when the minor scales with flats are developed they furnish all the new notes require by these majors.[Scientific Basis and Build of Music, page 89]

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]

"What we have thus said about the resolving notes to the major tonic has been allowed in the case of the minor. No one ever said that the second of the minor scale resolved to the root of the tonic. Notwithstanding the importance of the tonic notes, the semitonic interval above the second of the scale decided the matter for the Law of Proximity; and no one ever said that D, the root of the subdominant minor, did not resolve to C, the center of the tonic minor, on the same terms that two notes are brought to the center of the tonic major; with this difference, that the semitonic interval is above the center in the major and below it in the minor. The other two notes which resolve into the tonic minor are on the same terms as the major; with this difference, that the semitonic interval is below the root of the tonic major and above the top of the tonic minor. And the small tone ratio 9:10 is above the top of the tonic major and below the root of the tonic minor. If it has been the case that D resolved to the root of the tonic major, then, according to the Law of Duality, there would have been another place where everything would have been the same, only in the inverse order; but, fortunately for itself, the error has no other error to keep it in countenance. This error has not been fallen into by reasoning from analogy. [Scientific Basis and Build of Music, page 99]

"Dividing the octave into twelve semitones is a near approach to the mathematical quantities, and this saves the musical artist from errors in tone - at least to any extent; but it does not save from errors in judgment. In the case of G#, for example, not one of the reasons given for the use of the sharp seventh in the minor scale is a correct one. A touch of nature makes the world akin, and a touch of the Law of Duality balances everything in music." [Scientific Basis and Build of Music, page 99]

THE 24 MAJOR AND MINOR SCALES IN sharp AND ?s AND THEIR MUTUAL PROVIDINGS.

When the major and minor scales are generated to be shown the one half in sharp and the other half in ?s, it is not necessary to carry the mathematical process through the whole 24, as when the majors are all in sharp and the minors all in ?s; because when six majors have been generated in sharp, they furnish the new notes needed by the six relative minors; and when six minors have been generated in ?s, they furnish the new notes for the six relative majors. This plate begins with the major in C and the minor in A. The notes of these two are all identical except the D, which is the sexual note, in which each is not the other, the D of the minor being a comma lower than the D of the major. Going round by the keys in sharp, we come first to E minor and G major. G major has been mathematically generated, and the relative minor E gets its F# from it; but the D of C major must also be [Scientific Basis and Build of Music, page 112]

round a common center which is lying between them, as the double stars do in the astral heavens. When this plate is reversed we have before us exactly the minor scale, and all the parts and attitudes related in exactly the inverse way, each to each, so perfect is the duality in unity of the two modes. [Scientific Basis and Build of Music, page 114]

One purpose of this plate is to show that twelve times the interval of a fifth divides the octave into twelve semitones; and each of these twelve notes is the first note of a major and a minor scale. When the same note has two names, the one has sharps and the other has flats. The number of sharps and flats taken together is always twelve. In this plate will also be observed an exhibition of the omnipresence of the chromatic chords among the twice twelve scales. The staff in the center of the plate is also used as to show the whole 24 scales. Going from the major end, the winding line, advancing by fifths, goes through all the twelve keys notes; but in order to keep all within the staff, a double expedient is resorted to. Instead of starting from C0, the line starts from the subdominant F0, that is, one key lower, and then following the line we have C1, G2, etc., B6 proceeds to G? instead of F#, but the signature-number continues still to indicate as if the keys went on in sharps up to F12, where the winding line ends. Going from the minor end, the line starts from E0 instead of A0 - that is, it starts from the dominant of A0, or one key in advance. Then following the line we have B1, F#2, etc. When we come to D#5, we proceed to B? instead of A#6, but the signature-number continues as if still in sharps up [Scientific Basis and Build of Music, page 114]

Hughes
The same laws, developing the minor scales, show that the ascending and descending scales vary from the harmony of the key-note and its trinities
—Each key developing three harmonies
—The tenth note of a minor scale modulates into a higher key, . . . . 36 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

AS an example of the twenty-four, compare A major, developing, in Diagram II., with A minor, Diagram IX., taking the notes in the order which they sound in trinities. The three notes of the primaries sounded by A minor are, first, the same root as the major; the two next are the fourth and seventh higher notes (in the major, the fifth and sixth); the secondaries only vary by the sixth and seventh notes being a tone lower than in their relative major. Observe the order in which the pairs unite; the fourth in depth, sounded seventh, isolated. A and its root do not rise from the chasms. The fundamental key-note C was seen not to be interfered with, neither is the fundamental minor key-note A; G# on the one side, and B? on the other, being the key-notes. The seven of each minor harmony embrace only seventeen tones. C major and A minor are the only two keys which sound the seven white notes of keyed instruments. The minor scale and chords of A are not included in this remark. [Harmonies of Tones and Colours, Diagram IX - The Minor Keynote A and Its Six Notes, page 34a]

THE same laws are followed here as in the development of the major scales. In that of A, F, the sixth note, has risen to F#, in order to meet B, which has previously sounded. In descending, the seventh note, B, falls to B?, in order to meet F, which has also previously sounded. The notes, ascending or descending, always follow the harmony of their key-note, except when rising higher or falling lower to meet in fifths. We may here trace the twelve, the ascending scale sounding the fifth harmony higher than its key-note, and, in descending, sounding the fifth lower harmony. The four pairs of each scale are written at the end of the lines. If we strike the twelve scales as they follow in succession, the thirteenth note being the octave of the first, and leader of a higher twelve; having gained them six times, at the seventh they gradually rise (though beyond the power of a keyed instrument) into the higher series of seven octaves, and again, in descending, they fall lower, and are linked into the lower series of seven octaves. Nine notes of any ascending minor scale may be struck without the necessity of modulating beyond the fifth harmony. For example, in the scale of A, its tenth note, C#, rises to meet the sixth note, which has previously sounded. In descending, E?, the eleventh note, meets B?, the seventh note, which has previously sounded. The scale of A may be traced veering round by reference to Diagram IX., beginning with A, and carrying the four lowest notes an octave higher, F rising to F# in ascending, B falling to B? in descending. [Harmonies of Tones and Colours, Diagram XI - The Twelve Minor Keynotes with the Six Note of Each, page 36a]

Supplementary Remarks and Diagrams on the Errors in the Minor Scales as developed by Evolution in "Tones and Colours."
[Harmonies of Tones and Colours, Supplementary Remarks and Diagrams, page 53]

"I esteem myself fortunate in being introduced to you, and becoming acquainted with your beautiful work on 'Tones and Colours.' I have, to the best of my ability, worked out your idea, by writing down in music the various discords in use amongst musicians, and resolving them according to the laws of Harmony, and I find in all cases the perfect triad agrees with what you term the trinities in colours. The way in which you find the whole circle of Major and Minor keys by pairs in colours is deeply interesting, and must be true. The only point of divergence between your system and that recognised by all musicians is the ascending Minor Scale. No musically trained ear can tolerate the seventh note being a whole tone from the eighth. The Minor second in the lower octave descending is very beautiful, and it is strange how all composers feel a desire to use it. To mention one case out of hundreds, I may cite Rossini's well-known air, 'La Danza.'
"Yours faithfully,
"W. CHALMERS MASTERS." [Harmonies of Tones and Colours, Supplementary Remarks and Diagrams, page 53]

I was aware that my explanation of the Minor Scales was erroneous. I now see the beautiful Scriptural type which shows how they develope, rising or falling in perfect harmony. I hope to explain this clearly, and I think that any who have doubted my having gained these laws from the Scriptures will then see their mistake. [Harmonies of Tones and Colours, Supplementary Remarks and Diagrams, page 53]

The Minor Scales are the type of Creation developing, when no Sabbath (or Rest) was required; and we now see this re-echoed throughout the world around us, nothing resting on the Sabbath. A Minor Scale, therefore, cannot sound the [Harmonies of Tones and Colours, Supplementary Remarks and Diagrams, page 53]

The Minor Scales are the type of Creation developing, when no Sabbath (or Rest) was required; and we now see this re-echoed throughout the world around us, nothing resting on the Sabbath. A Minor Scale, therefore, cannot sound the [Harmonies of Tones and Colours, Supplementary Remarks and Diagrams, page 53]

In the Minor Scale, the Trinities and Scale develope five pairs; the last pair become the fifth higher key-note and its root, consequently the sixth pair would develope the higher key.[Harmonies of Tones and Colours, The Seven of each Harmony with its Scale, page 59]

The same laws are followed here as in the development of the Major Scales, except that the Minor Scales only develope five notes. [Harmonies of Tones and Colours, The Seven of each Harmony with its Scale, page 59]

The Minor Gamut modulating in the meeting of fifths through seven octaves. We may here trace the twelve, each fifth note becoming the higher key-note. But the sixth and seventh notes of the scale are discords. For example, in the key of A, the sixth note, F?, is a discord with the second note, B?; and the seventh note cannot be sounded as G# falling into the eighth, without being a discord with the third note, C?. No octave can be sounded in the Minor Scale, as it has risen into the fifth higher key of E. [Harmonies of Tones and Colours, The Minor Gamut Modulating in the Meeting of Fifths61, page 65]

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Created by Dale Pond. Last Modification: Thursday April 15, 2021 03:39:15 MDT by Dale Pond.