833 cents scale

The 833 cents scale is a musical tuning and scale proposed by Heinz Bohlen[clarification needed] based on combination tones, an interval of 833.09 cents, and, coincidentally, the Fibonacci sequence.

Other music theorists such as Walter O'Connell, in his 1993 "The Tonality of the Golden Section",[3] and Lorne Temes in 1970,[4] appear to have also created this scale prior to Bohlen's discovery of it.

"It is by the way unimportant which interval we choose as a starting point for the above exercise; the result is always 833 cent.

Bohlen describes a symmetrical seven tone scale, with the pitches of steps 0, 1, 3, 4, & 6 derived from the stack of golden ratio intervals.

Playⓘ This is comparable to the derivation of the major scale from a stack of perfect fifths (FCGDAEB = CDEFGAB).

The repetition of frequencies and the coincidence of higher steps with consonances such as the perfect fifth and octave may be seen (the step number of intervals that coincide with the stack of golden ratios are in bold, while the ratios of repeated intervals are in bold): The scale contains .83333 × 12 steps per octave (≈10).

[5] While ideally untempered, the scale may be approximated by 36 equal temperament, one advantage being that 36-TET includes traditional 12-TET.