Pythagorean means: Difference between revisions
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added a summary and an example |
Eliminate "logarithmic mean" since it's in conflict |
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* [[Arithmetic mean]] | * [[Arithmetic mean]] | ||
* [[Inverse-arithmetic mean]] | * [[Inverse-arithmetic mean]] | ||
* [[ | * [[Geometric mean]] | ||
In microtonal terms, the arithmetic mean is the intermediate harmonic, the inverse-arithmetic mean is the intermediate <u>sub</u>harmonic, and the | In microtonal terms, the arithmetic mean is the intermediate harmonic, the inverse-arithmetic mean is the intermediate <u>sub</u>harmonic, and the geometric mean is the equidistant pitch by cents. Thus the three means of 1/1 and 3/2 are 5/4, 6/5, and sqrt (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. | 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. | ||
Revision as of 18:21, 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 geometric mean is the equidistant pitch by cents. Thus the three means of 1/1 and 3/2 are 5/4, 6/5, and sqrt (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.