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Harmonograph

34 The fourTh 43 with thirds, sixths and sevenths By now it will be evident that each harmony displays its own distinct aesthetic character. Unison is simple and assertive. The octave introduces an emphatic flourish, and the fifth, while still fairly simple, has added elegance. With the fourth, the pattern becomes more complicated, though the design is still recognisable without counting the loops. The upper diagram opposite shows the fourth in open phase, the lower in closed phase. An increasing sophistication becomes apparent, and some of the closed phase and nearmiss variants have a strange exotic quality. Introducing the perfect thirds of diatonic tuning increases the complexity. The major third 54 is found below the fourth, the interval between them, a diatonic halftone, working out as 43 54 1615. A fourth and a major third 43 x 54 produce the major sixth, 53, a minor third 65 below the octave and a minor wholetone 109 above the fifth. Likewise, a fourth and a minor third 43 x 65 create the minor sixth 85, a major third 54 below the octave and a halftone 1615 above the fifth. A fifth and a major third 32 x 54 produce the major seventh, 158, while a fifth and a minor third 32 x 65 give the minor seventh, 95. These are the elements of the diatonic, or just, scale see page 50.
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