complementary pairs

The three lowest of the six tones are complementary pairs with the key-note and its two highest tones. Observe the curious order in which the tones sound, avoiding consecutive fifths. First, we have the key-note and its root, or fellow; next A; then D and its root; and then E, whose root, A, has already sounded between the first and the second pair. B, the fourth and central tone in depth, sounds seventh, and, finding no fellow within the compass of the harmony developing it, is isolated. Observe also how closely a key-note and its kindred tones are linked into each other. The Primaries spring from the key-notes, the Secondaries from the Primaries; the first pair comprises a key-note and a tone of the Primaries, the other two pairs have each a tone of the Primaries and a tone of the Secondaries. The key-note, after giving out its tones in trinities, or [Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]

THE first circle on this diagram represents seven major key-notes, beginning with C on the third space in the treble clef, and sounding as their roots the seven last key-notes which have developed. The second is a continuation of the first circle. The seven previously developed key-notes are now the roots of seven higher key-notes. The intermediate notes are not coloured, but may be seen to be complementary pairs. [Harmonies of Tones and Colours, Diagram III - The Major Keynotes Developing by Sevens, page 25a]

THE twelve keys have been traced following each other seven times through seven octaves, the keys mingled, the thirteenth note being the octave, and becoming first of each rising twelve. Thus developing, the seven notes of each eighth key were complementary pairs, with the seven notes of each eighth key below, and one series of the twelve keys may be traced, all meeting in succession, not mingled. When the notes not required for each of the twelve thus meeting are kept under, the eighths of the twelve all meet by fifths, and as before, in succession, each key increases by one sharp, the keys with flats following, each decreasing by one flat; after this, the octave of the first C would follow and begin a higher series. It is most interesting to trace the fourths, no longer isolated, but meeting each other, having risen through the progression of the keys to higher harmonies. In the seven of C, B is the isolated fourth, meeting F#, the isolated fourth in the key of G, and so on. Each ascending key-note becomes the root of the fifth key-note higher; thus C becomes the root of G, &c. [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys1, page 29]

Ascending, begin with C in the innermost circle, F being its root. The Key-note C becomes the root of G, G becomes the root of D, and so on. In descending, begin with the octave Key-note C in the outermost circle. F, the root of C, becomes the fifth lower Key-note. F is the next Key-note, and becomes the root of B♭, &c. The 12 Keys in their order are written in musical clef below. Lastly, the Keys of C and G, ascending on a keyed instrument, are written in music as descending; therefore, to shew correctly notes and colours meeting, it is necessary to reverse them, and write C below G. All are seen to be complementary pairs in tones and colours. [Harmonies of Tones and Colours, Diagram VII Continued2, page 31e]

The second circle is a continuation of the first; the seven previously developed key-notes become, as before, the roots of seven higher. The uncoloured intermediate notes are in the same way complementary pairs. [Harmonies of Tones and Colours, Diagram X - Minor Keynotes Developing by Sevens, page 35a]

See Also

complementary pair
doctrine of three pair and six tones
pairs of opposition

Created by Dale Pond. Last Modification: Friday March 19, 2021 02:29:58 MDT by Dale Pond.