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Diagram XIV - The Modulating Gamut of the Twelve Minor Keys by Fifths1

CHAPTER XVII.

DIAGRAM XIV.—THE MODULATING GAMUT OF THE TWELVE MINOR KEYS BY FIFTHS IN MUSICAL CLEF, AND THE SAME VEERING ROUND THROUGH TWELVE OCTAVES: THE THREE HARMONIES SOUNDED BY EACH KEY FOLLOWING IN SUCCESSION THROUGH THE TWELVE KEYS THAT ARE MINGLED AND EVER DEVELOPING.

"There's not the smallest orb which thou behold'st,
But in his motion like an angel sings,
Still quiring to the young-eyed cherubim."—Shakespeare.

"Observations confirm this: those acquainted with scientific progress must be struck with the fact, that of late the more brilliant achievements have been made in dealing with the unseen. The microscopist, the chemist, questioning the ultimate particles of matter; those who occupy themselves with the mysteries of molecular vibration, bear the victorious wreaths of successful discovery, and show that every atom teems with wonders not less incomprehensible than those of the vast and bright far-off suns."—J. W. Reynolds, M.A.


BEGINNING with the lowest A in the bass clef, let us strike the trinities, scale, and chords, carrying each key-note a fifth higher, counting the seven belonging to its harmony. If the silent notes are included, each fifth is the eighth meeting.

Let us first examine the meeting of the key-notes and their trinities in musical clef; the isolated fourths rising through the progression of the twelve now meet, seven and seven pairing. We must notice how closely they are linked into each other, the three highest notes of the lower seven being the three lowest of the higher seven an octave higher, and the four lowest becoming the four highest an octave higher; we descend by following the keys as written in musical clef upwards.

We may also examine the table of the twelve tones gained through seven octaves: the sharp or flat is written to each note, excepting in the keys as they unite in succession. Each key-note by fifths is seen to become a root of the fifth higher key-note: thus A becomes the root of E, and so on. In descending, each root of the fifth lower seven becomes the fifth higher key-note; the key-note D has G for its root, and so on.

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Created by Dale Pond. Last Modification: Wednesday March 24, 2021 04:14:53 MDT by Dale Pond.