Text: Septochromatic Gothic #2 http://www.elvenminstrel.com/tolkien/tuningsme.htm Chromatic Scale Degree Ratio Cents 1 1/1 0.000 2 21/20 84.467 3 448/40 5174.692 4 32/27 294.135 5 56/45 378.602 6 4/3 498.045 7 7/5 582.512 8 3/2 701.955 9 63/40 786.422 10 224/135 876.647 11 16/9 996.090 12 28/15 1080.557 Diatonic scales are intended. This tuning is closely related to Pythagorean; in fact, some modes are purely so. The unique feature is that each whole tone (9:8) interval is divided into the pair 21:20 and 15:14. This yeilds a large number of unique modes from only three generating intervals (the other of which is 256:243). According to Gothic music theory student Margo Schulter, this tuning follows a principle of Gothic music but takes it even further: the leading tones are intervalically smaller, which is more extreme. Here, the classic Gothic tuning system ("Pythagorean"), which used only multiples of the prime number 3, is colored by the introduction of semitone intervals using primes 5 and 7; thus "septo-chromatic." Septochromatic Gothic #1, incidentally, divides each 9:8 first by 15:14 (ascending), leaving 21:20 remaining, whereas #2 divides 9:8 first by 21:20, leaving 15:14 remaining. #2 seemed to me to provide more modes with Middle-earthish colors (totally a subjective judgement, of course).

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