How far does this compounding process go? The dominant seventh has the first note of the subdominant; the dominant ninth has the second; if we should add a third note, where are we? G B D F A C; here would be the dominant with the whole of the subdominant welded to it; it would have to be called the dominant eleventh, and it has brought us right through to the root of the tonic C. What would be the use of such a chord? We might, in a similar way, add the dominant to the subdominant till we should be through to the tonic on the other side; it would be G B D F A C, and so we should have reached the top of the tonic G. This process shows us, however, that there is just a certain length that we can go, and there is satisfaction in seeing exhaustively that so it is. When the beautiful becomes the useless, it ceases to be the beautiful.
The varied effect of position in chords. When a chord stands as C E G C, having its root also at the top, it has its softest, dullest, most united effect; it is undramatic, with little contrast. When it stands as E G C E, having its third at the top and bottom, it has a more ticklish, interesting, far-away effect. In reveries composers often finish thus, as if it had vanished - an unsettled effect. When it stands as G C E G, with its top at top and bottom, it has its most dominant character - loud, swelling. In the position C E G C it stands mixingly with the subdominant C E f G a C, and in this its first position its unseen filling in is chiefly from the region of gravity; hence its soft, grave, dull, heavy effect; and it passes very easily to the subdominant chord. When it stands as G C E G it stands mixingly with the dominant G b C d E G, and has its third position and most brilliant effect and uprising, for its unseen filling in is then chiefly from the region of levity; and it passes easily to the dominant chord. When in its second position, its middle position E G C E, its unseen filling in is mixingly both subdominant and dominant, E f G a b C d E; it has then its most interesting and puzzling effect; on the one hand its softest, dullest, and one-est, on the other hand its most brilliant effect, as if it would at once both sink and soar. [Scientific Basis and Build of Music, page 72]
The number of Chromatic Chords. Three chromatic chords exhaust the semitonic 12-foldness of the octave. The chromatic scale is a much more even thing than the diatonic; contrast is not its feature, and we may expect [Scientific Basis and Build of Music, page 72]
"The human ear cannot detect the triple chord of any vibration, or sounding note but every sound that is induced of any range, high or low, is governed by the same laws, as regards triple action of such that govern every sympathetic flow in Nature. Were it not for these triple vibratory conditions, change of polarity could never be effected, and consequently there could be no rotation. Thus the compounding of the triple triple, to produce the effect would give a vibration in multiplication reaching the ninth, in order to induce subservience, the enumeration which it would be folly to undertake, as the result would be a string of figures a mile in length to denote it. [Snell Manuscript - The Book, DISTURBANCE OF MAGNETIC NEEDLE, page 8]
Fig. 3 illustrates the way Nature teaches us by example how to compound so as to enable chords that are separated by the intervention of others to pass to each other. In the middle of the chord scale Nature gives the root of the one chord to the top of the other, and the top of the one to the root of the other; in compounding we are taught by this example to do the same, and the top of the separated dominant is given to the root of the [Scientific Basis and Build of Music, page 120]