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thirteenth note

Hughes
The twelve key-notes, with the six notes of each as they veer round in trinities, are again written in musical clef, and the scales added. The key-note leads the scale, and, after striking the two next highest notes of the seven of the harmony, goes forward, with its four lowest, an octave higher. The seven of each harmony have been traced as the three lowest, thus meeting the three highest in three pairs, the fourth note being isolated. Notwithstanding the curious reversal of the three and four of the scale, the three lowest pair with the three highest, and the fourth with its octave. The four pairs are written at the end of each line, and it will be seen how exactly they all agree in their mode of development. Keys with sharps and keys with flats are all mingled in twelve successive notes. If we strike the twelve scales ascending as they follow each other, each thirteenth note being octave of the first note of the twelve that have developed, and first of the rising series, the seventh time the scales gradually rise into the higher series of seven octaves beyond the power of the instrument. Descending is ascending reversed. After the seven and octave of a scale have been sounded ascending, the ear seems to lead to the descending; but ten notes of any scale may be struck without the necessity of modulation; at the seventh note we find that the eleventh note in the progression of harmonics rises to meet the seventh. For instance, B, the seventh note in the scale of C, must have F#. This point will be fully entered into when examining the meeting of fifths. To trace the scale of C veering round as an example for all, we may begin with C in Diagram II., and go forward with F, G, A, and B an octave higher. If the twelve scales were traced veering round, they would be found to correspond with the twelve as written in musical clef. [Harmonies of Tones and Colours, Diagram IV - The Development of the Twelve Major Scales, page 26a]

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 same laws are followed here as in the development of the major scales. In that of A, F, the sixth note, has risen to F#, in order to meet B, which has previously sounded. In descending, the seventh note, B, falls to B♭, in order to meet F, which has also previously sounded. The notes, ascending or descending, always follow the harmony of their key-note, except when rising higher or falling lower to meet in fifths. We may here trace the twelve, the ascending scale sounding the fifth harmony higher than its key-note, and, in descending, sounding the fifth lower harmony. The four pairs of each scale are written at the end of the lines. If we strike the twelve scales as they follow in succession, the thirteenth note being the octave of the first, and leader of a higher twelve; having gained them six times, at the seventh they gradually rise (though beyond the power of a keyed instrument) into the higher series of seven octaves, and again, in descending, they fall lower, and are linked into the lower series of seven octaves. Nine notes of any ascending minor scale may be struck without the necessity of modulating beyond the fifth harmony. For example, in the scale of A, its tenth note, C#, rises to meet the sixth note, which has previously sounded. In descending, E♭, the eleventh note, meets B♭, the seventh note, which has previously sounded. The scale of A may be traced veering round by reference to Diagram IX., beginning with A, and carrying the four lowest notes an octave higher, F rising to F# in ascending, B falling to B♭ in descending. [Harmonies of Tones and Colours, Diagram XI - The Twelve Minor Keynotes with the Six Note of Each, page 36a]

TO recapitulate from the beginning, observe, firstly, the twelve major key-notes as they have developed from within themselves in succession, six tones in trinities seven times through seven octaves, each thirteenth note being the octave of the first note of the twelve that have developed, and being also the first of the higher series. We may retrace all as still sounding their tones, the key-notes leading the ear to the six notes of each harmony, the keys with sharps and those with flats being mingled. The ascending and descending scales always agree in their harmonies with the key-notes and their trinities. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]

Thirdly, the twelve minor keys as they develope in succession seven times through seven octaves, always sounding their major harmony in trinities, and, as with the majors, each thirteenth note being the octave of the first note of the twelve, and first of the following series, the keys all mingled. [Harmonies of Tones and Colours, Diagram XV - The Twelve Major and the Twelve Minor Keys, page 42a]

See Also


7.22 - Thirteenth
thirteen
thirteen keys
thirteen major mathematical scales
thirteen minor mathematical scales
thirteen pairs
thirteen scales
thirteenth
thirteenth key
thirteenth note
thirteenth note octave
thirteenth octave
thirteenth scale

Created by Dale Pond. Last Modification: Saturday March 27, 2021 03:06:20 MDT by Dale Pond.