Golden ratio: Difference between revisions

Line 5:

The golden ratio can be used as a frequency multiplier or as a pitch fraction; in the former case it is known as [[acoustic phi]] and in the latter case it is known as [[logarithmic phi]]. [[Lemba]] is particularly notable for approximating both simply and accurately simultaneously, at a generator + a period for acoustic and 2 generators for logarithmic, making it an excellent choice for experimenting with phi based composition. [[Triforce]] is also essentially based on dividing the 1/3 octave period into logarithmic phi sized fractions.

The phith root of phi (<math>\sqrt[\varphi]{\varphi}</math> or approximately 514.878 cents) is another useful interval for generating golden scales. Similarly to logarithmic phi ~~(<math>\sqrt[2~~]~~{\varphi}</math>)~~, <math>\sqrt[\varphi]{\varphi}</math> can be used as a generator interval to produce MOS scales whose sizes are Fibonacci numbers, where the equave is the acoustic phi instead of the octave. In this way it is a useful generator if you wish to avoid octaves and maximize the golden properties of the resulting scale.

The phith root of phi (<math>\sqrt[\varphi]{\varphi}</math> or approximately 514.878 cents) is another useful interval for generating golden scales. Similarly to [[logarithmic phi]], <math>\sqrt[\varphi]{\varphi}</math> can be used as a generator interval to produce MOS scales whose sizes are Fibonacci numbers, where the equave is the acoustic phi instead of the octave. In this way it is a useful generator if you wish to avoid octaves and maximize the golden properties of the resulting scale.

[[Category:Golden ratio| ]]

[[Category:Theory]]

@@ Line 5: / Line 5: @@
 The golden ratio can be used as a frequency multiplier or as a pitch fraction; in the former case it is known as [[acoustic phi]] and in the latter case it is known as [[logarithmic phi]]. [[Lemba]] is particularly notable for approximating both simply and accurately simultaneously, at a generator + a period for acoustic and 2 generators for logarithmic, making it an excellent choice for experimenting with phi based composition. [[Triforce]] is also essentially based on dividing the 1/3 octave period into logarithmic phi sized fractions.
-The phith root of phi (<math>\sqrt[\varphi]{\varphi}</math> or approximately 514.878 cents) is another useful interval for generating golden scales. Similarly to logarithmic phi (<math>\sqrt[2]{\varphi}</math>), <math>\sqrt[\varphi]{\varphi}</math> can be used as a generator interval to produce MOS scales whose sizes are Fibonacci numbers, where the equave is the acoustic phi instead of the octave. In this way it is a useful generator if you wish to avoid octaves and maximize the golden properties of the resulting scale.
+The phith root of phi (<math>\sqrt[\varphi]{\varphi}</math> or approximately 514.878 cents) is another useful interval for generating golden scales. Similarly to [[logarithmic phi]], <math>\sqrt[\varphi]{\varphi}</math> can be used as a generator interval to produce MOS scales whose sizes are Fibonacci numbers, where the equave is the acoustic phi instead of the octave. In this way it is a useful generator if you wish to avoid octaves and maximize the golden properties of the resulting scale.
 [[Category:Golden ratio| ]]
 [[Category:Theory]]