833 Cent Golden Scale (Bohlen): Difference between revisions
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Heinz Bohlen's '''833 Cents Scale''' is a combination-tone-based scale which repeats at the interval of the [[golden ratio]] (φ = 1.618...). | |||
''' | |||
== Theory == | |||
There are seven | There are seven unequal steps in the Golden Scale, for starters: | ||
: 99.27 - 136.50 - 131.14 - 99.27 - 131.14 - 136.50 - 99.27 | : 99.27 - 136.50 - 131.14 - 99.27 - 131.14 - 136.50 - 99.27 | ||
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: 99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09 | : 99.27 - 235.77 - 366.91 - 466.18 - 597.32 - 733.82 - 833.09 | ||
833.09 is the cents value of the golden ratio, on which the scale is based and at which point the scale step pattern repeats. Octaves do occur in this scale but only incidentally; many octaves are out of tune, and the scale is not an octave-repeating scale. | |||
The scale is designed to take advantage of the naturally occurring mathematical concept of '''combination tones''' in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A = 55 Hz. You have 55, 89, 144, 233, 377, 610, 987, 1597 Hz and so on. These frequencies are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered "consonant." For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're on, if you go up seven steps you'll arrive at a perfect GR. | The scale is designed to take advantage of the naturally occurring mathematical concept of '''combination tones''' in order to create a whole different breed of consonant harmony. The interval of the Golden Ratio has the peculiar quality of combining harmoniously with itself when stacked. Consider the Fibonacci Sequence, and say we're starting on A = 55 Hz. You have 55, 89, 144, 233, 377, 610, 987, 1597 Hz and so on. These frequencies are all related intrinsically by combination, and the ratios of each adjacent pitch are extremely close to the Golden Ratio. So likewise, when any number of Golden intervals are stacked you get a stable, sonorous sound which could be considered "consonant." For this reason the scale repeats at the GR and not the octave; the harmony is built around the GR and its properties. The scale is designed so that no matter what step of the scale you're on, if you go up seven steps you'll arrive at a perfect GR. | ||
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-Dave G. | -Dave G. | ||
== Music == | |||
* ''[[:File:GR_Symphony_A.mp3|Gr Symphony A]]'' by [[David_Guillot|David Guillot]] ([https://soundcloud.com/dmguillotine/gr-symphony Listen on SoundCloud]) | |||
* ''833c by Bohlen scale improv'' by [[Yin Bell]] ([https://soundcloud.com/yinbell/833c-bp-scale-improv Listen on SoundCloud]) | |||
== | == External links == | ||
* [http://www.huygens-fokker.org/bpsite/833cent.html ''An 833 Cents Scale - An experiment on harmony''] (Bohlen's original article) | |||
[[Category:7-note scales]] | |||
[[Category:Golden]] | |||
[[Category:Nonoctave]] | |||
[[Category:Bohlen]] | [[Category:Bohlen]] | ||
[[Category: | [[Category:Listen]] | ||