# Harmonograph

11 10 WholeTones anD halfTones the fourth and fifth get their names Pythagoras hammers hide a set of relationships dominated by octaves 21, fifths 32 and fourths 43. The fifth and fourth combine to make an octave 32 x 43 21, and the difference between them 32 43 is called a wholetone, value 98. A natural pattern quickly evolves, producing seven discrete nodes or notes from the starting tone or tonic, separated by two halftones and five wholetones, like the sun, moon and five planets of the ancient world. The interval of the fifth 32, the leap to the dominant, naturally divides into a major third and minor third 32 54 x 65, the major third essentially consisting of two wholetones, and the minor third of a wholetone and a halftone. The thirds can be placed major before minor to give the major scale shown in the third row opposite, or in other ways. Depending on your harmonic moves, or melody, different tunings appear, for example two perfect wholetones 98 x 98 8164 are not in fact the perfect major third 54, but are slightly sharp as 8180 the syntonic or synoptic comma, the Indian sruti, or comma of Didymus, more of which later. Simple ratios, the octave and fifth, have given rise to a basic scale, a pattern of wholetones and halftones and, depending on where in the The basic manifestation of the scale. In Pythagorean tuning all wholetones are exactly 98, creating the leimma halftone of 256243 between its major third 8164 and the perfect fourth 43. The sixth and the seventh are defined as successive perfect wholetones above the fifth. In Diatonic tuning the major third is perfect at 54, which squeezes the second wholetone to 109 a minor wholetone, leaving 1615 as the diatonic halftone up to the fourth. The diatonic sixth is 53, a major third above the fourth, a minor wholetone above the fifth. The diatonic seventh 158 is a major wholetone above that, a major third above the fifth and a halftone below the octave.