“We are thus faced with the fact that there is no end to this process we have initiated: transposition up a fifth and transposition down a fifth take us on infinite journeys, ever generating new notes, even if some of these... are tantalizingly close. The journey can be thought of as traversing a spiral... for each 30º step clockwise we spiral outwards and transpose up a fifth, while for each 30º step anti-clockwise we spiral inwards and down a fifth. Adjacent points on the same ray of the spiral differ by the Pythagorean comma.”
-Neil Bibby, Tuning & Temperament: Closing the Spiral
Pythagorean Comma ≈ √3
Adjusting the perfect fifths (≈ -0.017) to a 12-note equal temperament closes this spiral into a circle. The transition between these geometric formulations of the chromatic music scale is a Key to the harmony of numbers underpinning the architecture of Tarot & Qabalah.
Mer
KA
BA
Merkabah (Chariot)
Herakles' 11th Labor
½(√5 + 1)
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