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Table of Contents2 - Harmonies

Helmholtz's experiments on developing colours shown to agree with the scheme
—The sounds of the Falls of Niagara are in triplets or trinities
—The Arabian system divides tones into thirds
—Two trinities springing from unity apparently the germ of never-ending developments in tones and colours
—Inequality of the equinoctial points; is the want of equilibrium the motive power of the entire universe?
—The double tones of keyed instruments, the meetings by fifths, the major and minor keys, so agree with the development of colours, that a correct eye would detect errors in a piece of coloured music
Numbers not entered upon, but develope by the same laws
Bass notes omitted in order to simplify the scheme, 18

PART II.
CHAPTER IV.—DIAGRAM I.

The eighteen tones of keyed instruments veering round and in musical clef below, the twelve seen that develope major keys
—The seven colours answer to the seven white notes
—The use of the two chasms, the key-note C and its root F rising from them
—A major key-note complete in itself, embracing the eighteen tones
—In the whole process of harmony there is limit, every key-note having its point of rest, and yet it is illimitable, . . . . . . . 22

CHAPTER V.—DIAGRAM II.

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

CHAPTER VI.—DIAGRAM III.

Major key-notes developing by sevens veering round and advancing and retiring in musical clef
—The use of the two poles F#-G♭ in tones and colours
—Retrace from Chapter V. the tones in musical clef as notes, each note still sounding its tones, leading the ear to its harmony, . . 25

CHAPTER VII.—DIAGRAM IV.

The twelve major scales
—The term key-note employed in the ordinary sense of the musician
—The twelve key-notes, with the six notes of each as they veer round in trinities, are written in musical clef, and the scales added
—The reversal of the four and three of the key-note and its trinities in the seven of its scale
—The twelve keys follow each other seven times through seven octaves linked into the lower and higher series
Keys mingled
—The modulating of scales, the eleventh notes rising to higher keys, . . . . . . 26

CHAPTER VIII.—DIAGRAM V.

The chords
The fourteen roots of the chords of the twelve major keys
—A threefold major chord examined, fourfold with its octave
—The seven of each key seen to have two chords and its scale one chord, thirty-six in all, forty-eight with octaves
—The chords of the twelve keys as they follow in order are written in musical clef
Colours seen to agree, . . . 27

CHAPTER IX.—DIAGRAM VI.

The twelve keys, their trinities, scales, and chords, rising seven times through seven octaves, each thirteenth note octave of the previous twelve and first of the rising twelve
Descending, ascending reversed
Keys mingled
—The Pendulograph alluded to, . . . 28

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Created by Dale Pond. Last Modification: Thursday February 4, 2021 05:02:56 MST by Dale Pond.