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double tones

See double tone, Poles in Harmonies, double pole, mate-pairs, two poles


Hughes
The key-note C sounding from within itself its six tones to and fro in trinities, the tones written as notes in musical clef
—The trinities hereafter termed primaries and secondaries
—The seven of each of the twelve key notes developing their tones
—The order in which the tones meet, avoiding consecutive fifths
Dissonance is not opposition or separation
—The use of the chasms and double tones is seen
—The isolated fourths sound the twelve notes
—Each double tone developes only one perfect major harmony, with the exception of F#-G♭; F# as the key-tone sounds F♮ as E#, and G♭ as the key-tone sounds B♮ as C♭
—The primaries of the twelve key-notes are shown to sound the same tones as the secondaries of each third harmony below, but in a different order
—All harmonies are linked into each other, . 23 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

In a few remarks on "Tones and Colours," inserted in the Athenæum of February 24, 1877, I alluded to the great loss I had sustained by the sudden death of Dr. Gauntlett. I often retrace with grateful remembrance the kind manner in which he examined this scheme when it was but crude and imperfect; with a very capacious intellect, he had a warm and generous heart, causing him to think over with candour any new ideas placed before him. He was of the greatest use to me, by corroborating the points which I had gained. I remarked to him one day, "I find that, of the double tones, F# is a key-note and G♭ a root." He replied, "You must have a right foundation to work upon, or you would never have ascertained the necessity of the two poles; you have gained the double tones correctly, and the development of harmonies without limit. On this point I have always felt the failure of the laws followed by the musician." [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

The inequality of the equinoctial points is a well-known fact. It will be seen how apparent this is in the developments of harmonies. From the moment that trinities depart from unity, the balance is unequal, and the repeated endeavours after closer union cause a perpetual restlessness. May not this want of equilibrium be the life or motive power of the entire universe, with its continuous struggle after concord, even to oneness? "Closer and closer union is the soul of perfect harmony." In tracing harmonies of tones and colours, the double tones of keyed instruments will be seen to correspond with the intermediate tints and shades of colours. The twelve notes, scales, and chords in the major and minor series, the meetings by fifths, &c., all agree so exactly in their mode of development, that if a piece of music is written correctly in colours with the intermediate tints and shades, the experienced musician can, as a rule, detect errors more quickly and surely with the eye than the ear, and the correct eye, even of a non-musical person, may detect technical errors. Although the arithmetical relation has been most useful in gaining the laws, it is not here entered upon; but numbers equally meet all the intricacies both of tones and colours. The bass notes have been omitted, in order to simplify the scheme. [Harmonies of Tones and Colours, The Arabian System of Music, page 21]

THE five circles represent a musical clef on which the twelve notes of a keyed instrument are written. Six of the notes are shown to be double, i.e., sounding two tones, eighteen in all, including E#, which is only employed in the harmony of F#, all others being only higher or lower repetitions. [Harmonies of Tones and Colours, Diagram I - The Eighteen Tones of Keyed Instruments, page 22a]

We here trace the twelve harmonies developing in succession. Notice how exactly they all agree in their mode of development; also the use of the chasms between E and F, B and C. Remark also the beautiful results from the working of the double tones, especially C#-D♭, and E#-F♭, causing the seven tones of each harmony, when ascending, to rise one tone, and, descending, to reverse this movement. F#-G♭ is the only double tone which acts as F# when a key-tone, and G♭ when the root of D♭. The root of each harmony is the sixth and highest tone in each succeeding harmony, rising one octave; when it is a double tone, it sounds according to the necessity of the harmony. The intermediate tones are here coloured, showing gradual modulation. The isolated fourths (sounding sevenths) were the previously developed key-tones; these also alter when they are double tones, according to the necessity of the harmony. Beginning with B, the isolated fourth in the harmony of C, the tones sound the twelve notes of a keyed instrument, E# being F♮, and the double tones, some flats, some sharps. [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

Examine C# in musical clef as an example of double tones only developing each one major harmony. C# sounds neither B nor E, but C and C#, F and F#. [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

The only exception is the double tone F#-G♭, which is a curious study. F# as a harmony takes the double tones as sharps, and F♮ is E#. G♭ is also a harmony sounding the same tones, by taking the double tones as flats, and B♮ as C♭. F# therefore takes the imperfect tone of E#, and G♭ the imperfect tone of C♭. (See here the harmony of G♭ in musical clef.) [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

We find that on a keyed instrument each primary sounds the same tones as the secondaries of each third harmony below, but in a different order, and the double tones are altered sharp or flat as the harmony requires. For example, the secondaries of B are sharps; when primaries of D♭, they are flats. In order to trace this quickly, the sharps and flats are written to each note. [Harmonies of Tones and Colours, Combinations of dissonance, rests, page 24]

This diagram represents the two last major primaries of a series of 12; 12 of a higher series follow, and the two first of a still higher series: the secondaries are written below the primaries, the sharps or flats belonging to the different harmonies are written to each note. Each primary sounds the same tones as the secondaries of each third harmony below, but in a different order; and the double tones are altered sharp or flat as the harmonies require.
By reference to previous coloured notes it will be seen that all these agree. [Harmonies of Tones and Colours, The Two Last Major Primaries, page 24e]

ON a keyed instrument only twelve are major key-notes, but as the double tones C#-D♭ and F#-G♭ are roots, there are fourteen different chords. The fourteen that are roots are written in musical clef. As an example of the major chords in the different keys, we may examine those in the key of C. A major fifth includes five out of the seven of its key; with the third or central note it is the threefold chord, or fourfold when the octave note is added. Including the silent key-notes, a threefold chord embraces eight, or, counting the double tones, not including E#, eleven. The first and second chords of the seven of the harmony are perfect major chords in the key of C; the central note of the third chord, being #C-♭D, is a discord. The first pair of fifths in the scale, with its central note, is a chord of the key; if we include the octave, the last pair of fifths, with its central note, is the same chord an octave higher than the lowest chord of the seven. Of the chords written in musical clef of the twelve keys, the octave chord is only written to C, the seven of each having two chords and the scale one, thirty-six in all, or forty-eight if the octave chords are added. Notice how the chords of each seven and the chord of its scale are altered. [Harmonies of Tones and Colours, Diagram V - The Chords of the Twelve Major Keys, page 27a]

If the chords of the twelve keys and the thirteenth octave are struck, all agree in their method of development. We see here the order in which the chords are repeated, and the working of the double tones As an example of the latter, we may trace the chords belonging to the key of D♭, and compare them with those belonging to the key of F#, also the first chord in the key of A♭. The fourth note in depth, sounded last of the seven of each harmony, has been seen as preparing for the chords; it prepares equally for the scale, and the scale for the chords, the octave chord of the scale, ascending, preparing for the latter to descend. Descending is ascending reversed. [Harmonies of Tones and Colours, Diagram V - The Chords of the Twelve Major Keys, page 27a]

When the twelve minor harmonies are traced developing in succession, we notice how exactly they all agree in their method of development, also the use of the chasms and the double tones, the seven of each harmony rising a tone when ascending, but reversing the movement in descending; keys with sharps and those with flats are mingled. The intermediate tones are here coloured, showing gradual modulation. D♭ is shown to be an imperfect minor harmony, and E♭, by employing B as C♭, is seen to be equivalent to D#. [Harmonies of Tones and Colours, Diagram IX - The Minor Keynote A and Its Six Notes, page 34a]

This diagram shews the two last minor primaries of a series of 12, with the 12 of a higher series, and the two first of a series higher still. As in the diagram of the Major, the secondaries are written below the primaries, and the sharps or flats of each harmony are written to their respective notes. With the exception that one of the primaries rises a tone higher, it will be observed that in the same way the notes of each minor primary are identical with the secondaries of each third harmony below, but in a different order; and the double tones are altered sharp or flat, as before. [Harmonies of Tones and Colours, Diagram Shews the Two Last Primaries, page 34e]

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]

See Also


double tone
mate-pairs
pair

Created by Dale Pond. Last Modification: Monday March 22, 2021 04:00:37 MDT by Dale Pond.