![]() If you move around the circle clockwise you go up a Fifth with every “step” you take, if you move around the circle counterclockwise you go up a Fourth with every “step” you take. The Circle of Fifths is based on the stacking of (Perfect) Fifths, characteristic for the Pythagorean Temperament. Both clockwise and counterclockwise movements follow the Chromatic Scale (respectively up and down). The Chromatic Circle is a visualization of the Chromatic Scale and the 12-Tone Equal Temperament. The most common tone circles in Western music are the “ Chromatic Circle” and the “ Circle of Fifths“. When we look at these intervals and how they relate to one another in the musical tone circles, some geometric shapes appear. If you are interested in a more esoteric-philosophical perspective on the intervals, then read the article: “ The Function of the Intervals” on Roel’s World. Note: click on the interval names for more basic info (Wikipedia). These intervals are the: Unison, Minor Second, Major Second, Minor Third, Major Third, Fourth, Tritone, Fifth, Minor Sixth, Major Sixth, Minor Seventh, Major Seventh and Octave. In Western music theory there are 13 intervals from Tonic (unison) to Octave. ↧JUMP TO “ COUNTING CORNERS (ANGLE DEGREE TO HERTZ)“ ↧JUMP TO “ GEOMETRY OF HARMONIC PROGRESSIONS“ ↧JUMP TO “ GEOMETRY OF SYMMETRICAL SCALES“ ![]() ↧JUMP TO “ SEQUENCE OF THE FALLING FIFTHS (OR FOURTHS)” ↧JUMP TO “ THE TETRACTYS & MUSICAL INTERVAL RATIOS“ Skip “INTRODUCTION (ABOUT 12-TONE CIRCLES)” AND … This article will “zoom-in” into geometry in particular. Would it thus be too ‘far-fetched’ to say that the same “rules” apply for many – if not all – things in the universe? But in the math behind many “things” there are formulas and ratios (relationships) that are very similar, if not identical. Units like Hertz and Degrees are not the same, they have their own function and use. Now, of course tones and chords are not the same “things” as for example polygons and polygrams. In its form, rhythm and metre, the pitches of its notes (intervals) and the tempo of its pulse music can be related to the mathematical measurement of time and frequency, offering ready analogies in geometry. “Music theory has no self-evident foundation in modern mathematics yet the basis of musical sound can be described mathematically (in acoustics ) and exhibits “a remarkable array of number properties”.
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