_4th_,—Out of these five entire tones, and two semitones, is formed the diatonic scale, _ut_, _re_, _mi_, _fa_, _sol_, _la_, and _si_; and, in like manner, out of the five entire or tonic colours, and the two demi-colours, are formed the gradation of colours, _blue_, _green_, _yellow_, _aurora_, _red_, _violet_, and _violant_; for the _blue_ leads to _green_, which is _demi-blue_; the _yellow_ to _aurora_, which is _gilded yellow_; the _aurora_ leads to _red_, the _red_ to _violet_, which is two-thirds of _red_, and one-third of _blue_; and the _violet_ to _violant_, which has more _blue_ than _red_. _5th_,— The entire tones divide themselves into semitones; and the five entire tones of the scale or gamut, comprehending in this the two natural semitones, make twelve semitones, viz., _ut_ natural, _ut_ dieze, _re_, _re_ dieze, _mi_, _fa_, _fa_ dieze, _sol_, _sol_ dieze, _la_, _la_ dieze, and _si_. In like manner there are twelve demi-colours, or demi-tints, and there can be neither more nor less, according to the opinion of painters themselves, and as may be demonstrated by other means. These colours are _blue_, _sea-green_, _green_, _olive_, _yellow_, _aurora_, _orange_, _red_, _crimson_, _violet_, _agathe_, and _violant_. _Blue_ leads to _sea-green_, which is a _greenish blue_; _sea-green_ leads to _green_; _green_ to _olive_, which is a _yellowish green_; _olive_ to _yellow_; _yellow_ to _aurora_; _aurora_ to _orange_; _orange_ to _red_, the colour of fire; _red_ to _crimson_, which is _red_ mixed with a little _blue_; _crimson_ to _violet_, which is still more _blue_; _violet_ to _agathe_, or _bluish violet_; and _agathe_ to _violant_. _6th_,—The progression of sounds is in a circle, setting out from _ut_, and returning back: thus, _ut_, _mi_, _sol_, _ut_, or _ut_, _re_, _mi_, _fa_, _sol_, _la_, _si_, _ut_. This is called an octave, when the last _ut_ is one-half more acute than the first. The colours also have their progression in a circle. _7th_,—After an octave, _ut_, _re_, _mi_, _fa_, _sol_, _la_, _si_, there recommences a new one, which is one-half more acute, and the whole circle of music produces several octaves.