Pythagorean means: Difference between revisions
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Created page with "{{Wikipedia| Pythagorean means }} '''Pythagorean means''' comprise: * Arithmetic mean * Logarithmic mean * Inverse-arithmetic mean In math, they are known as ar..." |
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'''Pythagorean means''' comprise: | '''Pythagorean means''' comprise: | ||
* [[Arithmetic mean]] | * [[Arithmetic mean]] | ||
* [[Inverse-arithmetic mean]] | |||
* [[Logarithmic mean]] | * [[Logarithmic mean]] | ||
In math, | In microtonal terms, the arithmetic mean is the intermediate harmonic, the inverse-arithmetic mean is the intermediate <u>sub</u>harmonic, and the logarithmic mean is the equidistant pitch by cents. Thus the three means of 1/1 and 3/2 are 5/4, 6/5 and square root (3/2) respectively. | ||
In math, the three means are known as arithmetic mean (AM), harmonic mean (HM), and geometric mean (GM) respectively. However, ''harmonic mean'' is said with respect to a length of string to be divided, and collides with the more common usage of ''harmonic'', which is said with respect to frequency. For fear of confusion, those terms are avoided and ''inverse-arithmetic mean'' is preferred instead. | |||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 06:36, 3 March 2023
Pythagorean means comprise:
In microtonal terms, the arithmetic mean is the intermediate harmonic, the inverse-arithmetic mean is the intermediate subharmonic, and the logarithmic mean is the equidistant pitch by cents. Thus the three means of 1/1 and 3/2 are 5/4, 6/5 and square root (3/2) respectively.
In math, the three means are known as arithmetic mean (AM), harmonic mean (HM), and geometric mean (GM) respectively. However, harmonic mean is said with respect to a length of string to be divided, and collides with the more common usage of harmonic, which is said with respect to frequency. For fear of confusion, those terms are avoided and inverse-arithmetic mean is preferred instead.