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Götterzahlen and scale structure

Book by Richard Dumbrill · 1 quotes · Music

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Götterzahlen and scale structure Quotes

“2. If these figures express units of string lengths, then Anu is, with 60 units, the longest string, the bass note. Sin is one octave below Ištar and one above Anu. The ratios of string lengths are thus in reciprocal relation to the ratios of frequencies. It seems appropriate at this point to introduce the musical cent or centième since it is the most tangible unit of tonometry. The conversion of ratios into musical cents consists in multiplying the log to base 10 of the quotient of the division between the denominator and numerator of the ratio by the constant 3986.314. This method produces a scale composed of 1200 units in which equal semitones measure 100 cents. Thus, 1/1 = 0 cents; 2/1= 1200 cents, the octave; 9/8 = 204 cents, the Pythagorean tone; 3/4 = 498, the just fourth; 2/3 = 702, the just fifth, etc. From this we see that the gods’ respective numbers are contained in the span of the top octave. Anu, Enlil, Ea and Sin provide with the tonal infrastructure for the Babylonian scale as shown below: SIN EA ENLIL ANU 0 498 884 1200 Fundamental Fourth Sixth Octave Anu/Enlil 60/50 = 6/5 = 316 = just minor third Enlil/Ea 50/40 = 5/4 = 386 = just major third Ea/Sin 40/30 = 4/3 = 498 = just fourth Sin/Šamaš 30/20 = 3/2 = 702 = just fifth Šamaš/Bel 20/10 = 2/1 = 1200 = octave.”

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