Ramsay
B, namely G#, they come in touch of each other like the two D's. When this three fifths below F major and three fifths above B minor have been developed, the extremes A? and G#, though standing like the two D's in duality, are so near that here again one note can be made to serve both. The major series of scales and the minor series at these limits are thus by two notes which have duality in themselves hermetically sealed; but not till Nature has measured off for any one of these scales a sphere of twelve keys in which to move in perfect freedom of kinship by softly going modulations. [Scientific Basis and Build of Music, page 39]

lastly it is altered again and becomes, by the power of 3 once more, F#,#, and serves in four keys. But this carries us beyond the horizon of our musical world of twelve keys; for in B#, the top of the tonic E, we have reached our twelfth fifth, and it here coalesces with C of the seventh octave, and closes the circle. This is the way that all notes become alternately altered, either by commas and sharps in the upward genesis of scales, or by commas and flats in the downward genesis, by the alternate powers of 3 and 5. In the upward genesis in this illustration, notes by the power of 5 serve in three keys, and those by the power of 3 serve in four keys. In the minors it is just the inverse on this by the Law of Duality. But no note serves for more than either three or four keys, as the case may be. [Scientific Basis and Build of Music, page 63]

The Chromatic Scale is naturally the last to come into view, for it is not generated by a mathematical process at all. Chromatic intervals are indeed found in the scale as mathematically generated. The semitones between B-C and E-F are two chromatic intervals, and the chord which occurs between the major and the minor in the chord-scale when it begins with the minor mode is a chromatic chord, though in an uncompleted condition. But the making of the octave into a chromatic scale of twelve small or semi-tones, is the work of modulation from one key to another through the whole twelve keys in either the major or minor sphere; and this process is fully set forth in the pre-note to the chromatic treatise. [Scientific Basis and Build of Music, page 69]

This diagram shows pictorially the open in the spiral of the mathematical scales, in which, if written in sharps only, B# is seen a little, that is, a comma and the apotome minor, in advance of C, and as the first scale of the new cycle; for it is a violation of Nature's beautiful steps to call it a thirteenth scale of this order, since every scale in the order is 31 commas in advance of the preceding, whereas B# is only one comma and a small fraction in advance of C. If the scales be written in ?s and #s for convenience of signature, then G# is seen a comma and apotome in advance of A?; while the whole circle of keys advancing by fifths are each 31 commas in advance of the preceding. We may therefore cast utterly from us the idea of there being more than twelve mathematical scales, and view the so-called thirteenth as simply the first of a new round of the endless spiral of scales. There is, however, in this note a banner with the strange device, "Excelsior," for it leads us onward into ever-advancing regions of vibrations, and would at last bring us to the ultimate and invisible dynamic structure of the visible world. The tempered system of 12 keys, as in Fig. 1, is by causing the G# and A? to coalesce and be one, as the two D's are already literally one by Nature's own doing. [Scientific Basis and Build of Music, page 118]

Hughes
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 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

The modulating gamut
—One series of the twelve keys meeting by fifths through seven octaves
—Keys not mingled
—A table of the key-notes and their trinities thus meeting
—The fourths not isolated
—The table of the twelve scales meeting by fifths
—The twelve keys, trinities, scales, and chords thus meeting are written in musical clef
—The twelve meeting through seven circles, each circle representing the eighteen tones
—The keys of C and G meeting, coloured
—Retrospection of the various major developments, . . . . 29 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

The twelve keys trinities, scales, and chords are written in musical clef,..38 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

The twelve keys meeting by fifths, one series modulating through seven octaves, keys not mingled
—The twelve veering round, the intermediate notes not coloured
—The keys of A and E meeting the intermediate notes coloured in musical clef, . . . . . 39 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]

whether veering round, or advancing and retreating in musical clef. I next tried the major keys which develope flats, and I thought that G? would develope a perfect harmony, but found that it must be F#, and that in this one harmony E# must be used in place of F?; on reference, I found that thus the twelve keys developed correctly in succession, the thirteenth being the octave, or first of a higher series. [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

I had forgotten all the minor keys, except that A is the relative minor of C major; but although I had only faint hopes of success, I determined to try, and I gained the twelve keys correctly, with the thirteenth octave. I found also that E? was usually printed as a minor key-note, Nature's laws having shown that it must be D#. [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]

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]

IF we strike the twelve keys of harmonies in trinities, scales, and chords, as written in musical clef, beginning with the lowest C in the bass clef, this first development is linked into the lower series of seven octaves by the four lower tones sounded by C. If we follow with the twelve keys six times, at the seventh time they will gradually rise into the higher series. We obtain a glimpse of the beauty arising from musical notes in the Pendulograph. How exquisite would they be if they could be represented in their natural coloured tones! — as, for instance, the chord of the scale of C in red, yellow, and blue, with the six coloured tones rising from each, and harmoniously blended into each other. [Harmonies of Tones and Colours, The Twelve Keys Rising Seven Times, page 28a]

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]

The following table shows the regularity of each seven of the twelve key-notes ascending by fifths, and the use of the two poles is again seen. The key-notes and their trinities are closely linked into each other, the three highest notes of the lower fifth key becoming the three lowest of the higher fifth key, and the four lowest becoming the four highest in an octave higher. The twelve keys, rising in each note a tone higher and descending a tone lower, cause the meetings by fifths. Having examined the table, we may strike the keys by fifths as written in the musical clef, beginning with the lowest C in [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys1, page 29]

Finally, trace the twelve keys by fifths as they veer round through the seven circles, each circle representing the eighteen tones. Beginning with C in the innermost circle ascending, C becomes the root of G, G of D, and so on. In descending, begin with C in the outermost circle (though really the first of a higher series which we have not the power of striking on instruments); F, its root, becomes the key-note, B? the root and then the key-note, and so on. The keys thus gained are written in musical clef below. [Harmonies of Tones and Colours, The Twelve Scales Meeting by Fifths, page 31a]

The keys of C and G meeting are coloured, and show the beautiful results of colours arising from gradual progression when meeting by fifths. Each key-note and its trinities have been traced as complete in itself, and all knit into each other, the seven of each rising a tone and developing seven times through seven octaves, the keys mingled. The twelve scales have been traced, developing seven times through seven octaves, all knit into each other and into the key-notes and their trinities. The chords have also been traced, each complete in itself, and all knit into each other and into the key-notes, trinities, and scales. And lastly, one series of the twelve keys, no longer mingled, but modulating into each other, have been traced, closely linked into each other by fifths through seven octaves, three keys always meeting. Mark the number of notes thus linked together, and endeavour to imagine this number of tones meeting from the various notes. [Harmonies of Tones and Colours, The Twelve Scales Meeting by Fifths, page 31a]

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 term "key" in the minor developments must be taken in the sense in which it is understood by musicians, although it will be seen that it is only the seven of the harmony that are the relative minor keys of the majors, the scales with their chords sounding other keys. The grandeur, combined with simplicity, of the laws which develope musical harmonies are strikingly exhibited in the minor keys. Although at first they appear most paradoxical, and, comparing them with the majors, we may almost say contradictory in their laws of development, when they are in some degree understood, the intricacies disappear, and the twelve keys follow each other (with the thirteenth octave), all exactly agreeing in their mode of development. I shall endeavour to trace them as much as possible in the same manner as the majors, the lowest developments of the minor keys being notes with scales and chords, the notes always sounding their major harmonies in tones. Here an apparently paradoxical question arises. If the major keys are gained by the notes sounding the major tones, how are the minor keys obtained? Strictly speaking, there are no minor key-notes: the development of a minor harmony is but a mode of succession within the octave, caused by each minor key-note employing the sharps or flats of the fourth major key-note higher; and with this essential difference, it will be seen in how many points the developments of major and minor harmonics agree. I have carefully followed the same laws, and if any capable mind examines the results, I am prepared for severe criticism. I can only express that it was impossible to gain any other results than the seven of the harmony, the ascending and the descending scale and the chords combining three different keys. [Harmonies of Tones and Colours, Diagram VIII - On the Development of the Twelve Minor Harmonies, page 32]

The roots of the Minor Chord. The difference between a Major and a Minor Chord. The chords of the 12 keys follow. The sharps or flats that vary from the seven of the harmony, in the scales written to each note. The last descending chord is here seen to be the same as the first ascending, but this repetitive chord is only written in A. [Harmonies of Tones and Colours, The Roots of the Minor Chord, page 36c]

IF we strike the twelve as written in musical clef, beginning with the lowest A in the bass clef, each key-note, with its trinities, scale, and chords, sounds three harmonics. We may follow with the twelve keys as they rise, and descend by following the keys upwards as written in musical clef, each key falling lower. [Harmonies of Tones and Colours, Diagram XIII - The Twelve Keynotes with Their Trinities, page 38a]

Secondly, we have the one series of the twelve keys as they meet by fifths through the seven octaves. The keys are no longer mingled; the scales meet by fifths in the same keys and their trinities. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]

See Also

key
twelve
Twelve keys
twelve major keys
twelve minor keys
twelve major scales
twelve minor scales
12 Major Key-notes meeting by fifths