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key of A

Ramsay
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]

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]

The various raisings and lowerings of notes in advancing keys, major and minor. - In each fifth of the majors ascending the top of the dominant is raised a comma. A40 in the key of C becomes A40 1/2 in the key of G; E60 in the scale of G is E60 3/4 in the scale of D; B90 in the scale of D is B91 1/8 in the scale of A. This alteration of the top of the dominant major goes on through all the twelve scales. Similarly, by the Law of Duality, each fifth in the minors descending has the root of the subdominant lowered a comma. D54 in the key of E minor is D53 1/2 in the key of A; G72 in the scale of A is G71 1/9 in the scale of D; C48 in the scale of D is C47 11/27 in the scale of G. This alteration of the root of the subdominant goes on through all the twelve minor scales. [Scientific Basis and Build of Music, page 62]

In just such a manner, only by more obvious leaps, the middle of the dominant in the advancing major scales is raised a sharp - i.e., four commas. When D27, the dominant top of the key of C, is multiplied by 5, it generates F#135; so, taking it one octave lower, F64 in C major is F#67 1/2 in the key of G. C96 in the key of G is C#101 1/4 in the key of D; G72 in the key of D is G#151 7/8 in the key of A. And this raising of the middle of the dominant goes on through all the twelve major keys. [Scientific Basis and Build of Music, page 62]

In the same way, but inversely, and still under the Law of Duality, the middle of the subdominant minor is lowered a flat. F#67 1/2 in the key of E minor is F64 in the key of A; B45 in the key of A is B♭42 2/3 in the key of D; E60 in the key of D is E♭56 8/9 in the key of G. This lowering by flats of the subdominant middle in the minors, responsive to the raising by sharps of the dominant middle in the majors, goes on through all the twelve minor keys.1 [Scientific Basis and Build of Music, page 62]

Whenever a sharp comes in in making a new key - that is, the last sharp necessary to make the new key - the middle of the chord in major keys with sharps is raised by the sharp, and the top of the same chord by a comma. Thus when pausing from the key of C to the key of G, when F is made sharp A is raised a comma. When C is made sharp in the key of D, then E is raised a comma, and you can use the first open string. When G is made sharp for the key of A, then B is raised a comma. When D is made sharp for the key of E, then F# is raised a comma; so that in the key of G you can use all the open strings except the first - that is, E. In the key of D you can use all the open strings. In the key of A you can use the first, second, and third strings open, but not the fourth, as G is sharp. In the key of E you can use the first and second open. [Scientific Basis and Build of Music, page 100]

When Leonhard Euler, the distinguished mathematician of the eighteenth century, wrote his essay on a New Theory of Music, Fuss remarks - "It has no great success, as it contained too much geometry for musicians, and too much music for geometers." There was a reason which Fuss was not seemingly able to observe, namely, that while it had hold of some very precious musical truth it also put forth some error, and error is always a hindrance to true progress. Euler did good service, however. In his letters to a German Princess on his theory of music he showed the true use of the mathematical primes 2, 3, and 5, but debarred the use of 7, saying, "Were we to introduce the number 7, the tones of an octave would be increased." It was wise in the great mathematician to hold his hand from adding other notes. It is always dangerous to offer strange fire on the altar. He very clearly set forth that while 2 has an unlimited use in producing Octaves, 3 must be limited to its use 3 times in producing Fifths. This was right, for in producing a fourth Fifth it is not a Fifth for the scale. But Euler erred in attempting to generate the semitonic scale of 12 notes by the use of the power of 5 a second time on the original materials. It produces F# right enough; for D27 by 5 gives 135, which is the number for F#. D27 is the note by which F# is produced, because D is right for this process in its unaltered condition. But when Euler proceeds further to use the prime 5 on the middles, A, E, and B, and F#, in their original and unaltered state, he quite errs, and produces all the sharpened notes too low. C# for the key of D is not got by applying 5 to A40, as it is in its birthplace; A40 has already been altered for the key of G by a comma, and is A40 1/2 before it is used for producing its third; it is A40 1/2 that, multiplied by 5, gives C#202 1/2, not C200, as Euler makes C#. Things are in the same condition with E before G# is wanted for the key of A. G# is found by 5 applied to E; not E in its original and unaltered state, E30; but as already raised a comma for the key of D, E30 3/8; so G# is not 300, as Euler has it, but 303 3/4. Euler next, by the same erroneous methods, proceeds to generate D# from B45, its birthplace number; but before D# is wanted for the key of E, B has been raised a comma, and is no longer B45, but B45 9/16, and this multiplied by 5 gives D#227 13/16, not D225, as Euler gives it. The last semitone which he generates to complete his 12 semitones is B♭; that is A#, properly speaking, for this series, and he generates it from F#135; but this already altered note, before A# is wanted for the key of B, has been again raised a comma [Scientific Basis and Build of Music, page 107]

With perfect duality of response does resolution of chords go on in the minors. When the tonic chord follows the subdominant one, they have for their note in common A, i.e., in the key of A; and the middle of the subdominant moves by semitonic progression to the top of the tonic. When the tonic chord follows the dominant one, the top of the tonic and the root of dominant E is a note in common, and the top of the dominant goes by semitonic progression to the middle of the tonic. These simple chords are thus linked together exactly with the same degree of continuity as the simple chords of the major. When the tonic chord follows the compound subdominant, this compound chord, like the compound dominant in the major, has two semitonic progressions - one to the top and one to the middle of the tonic - and they have one note in common. When the compound dominant follows the subdominant, the root of the subdominant is lent to the top of the dominant, and thus a note in common is created, and the middle of the subdominant moves by semitonic progression to the root of the dominant. When the compound subdominant follows the dominant, the top is lent to the root of the subdominant, creating a note in common between them, and the root of the dominant goes to the middle of the subdominant in semitonic progression. This is the way of Nature. The unbroken continuity of her ways is perfectly illustrated in the linked sweetness and kinship of chords in a key; or when one key passes by modulation to another key; and that through all the chords and all the keys. We shall see wondrously more of this when we come to the study and contemplation of the Chromatic System of Chords. [Scientific Basis and Build of Music, page 112]


Hughes
The twelve keys meeting by fifths, one series modulating through seven octaves, keys not mingled
—The twelve veering round, the intermediate notes not coloured
—The keys of A and E meeting the intermediate notes coloured in musical clef, . . . . . 39 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

I had forgotten all the minor keys, except that A is the relative minor of C major; but although I had only faint hopes of success, I determined to try, and I gained the twelve keys correctly, with the thirteenth octave. I found also that E♭ was usually printed as a minor key-note, Nature's laws having shown that it must be D#. [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

ALTHOUGH only twelve notes of a keyed instrument develope perfect minor harmonics, there are fifteen different chords, the double tones D#-E♭, E#-F♭, A#-B♭ all sounding as roots. The fifteen roots are written in musical clef. A major and a minor fifth embrace the same number of key-notes, but the division into threefold chords is different. In counting the twelve, a major fifth has four below the third note of its harmony, and three above it; a minor fifth has three below the third note of its harmony, and four above it. A major seventh includes twelve key-notes, a minor seventh only eleven. As an example of the minor chords in the different keys, we may first examine those in the key of A, written in musical clef. The seven of its harmony have two threefold chords, and two of its ascending scale. If we include the octave note, the highest chord of the descending scale is a repetition (sounding an octave higher) of the lowest chord of the seven in its harmony, and the second chord of the descending scale is a repetition of the first chord of its ascending scale. These two repetition chords are only written to the key of A: the chords of the other eleven keys will all be found exactly to agree with those of A in their mode of development. We may again remark on the beautiful effect which would result if the colours of the minor chords could be seen, with the tones, as they develope. [Harmonies of Tones and Colours, Diagram XII - The Chords of the Twelve Minor Keys, page 37a]

Lastly, we trace the twelve ascending by fifths as they veer round through the seven circles, each circle representing the eighteen tones, beginning with A in the innermost circle. A becomes the root of E, E of B, and so on. In descending, we begin with A in the outermost circle, though it is in fact the commencement of a higher series which we cannot strike. D, its root, becomes the fifth key-note lower, and so on. The keys of A and E are coloured, to show the result of the minor harmonies meeting by fifths. [Harmonies of Tones and Colours, Diagram XIV - The Modulating Gamut of the Twelve Minor Keys by Fifths3, page 41a]

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]

See Also


key of A
key of A flat
key of C
key of D flat
key of E
key of F
key of F sharp
key of G
progression of keys
root of the fifth higher keynote
root of the fifth keynote
The Major Keynote of C

Created by Dale Pond. Last Modification: Thursday April 15, 2021 03:42:27 MDT by Dale Pond.