User:Eliora/Standard deviation: Difference between revisions
Created page with "Standard deviation is a way of assessing harmonic strength. == Null hypothesis == An interval which consists of edosteps is an irrational number, which occasionally comes cl..." |
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Therefore, counting the null hypothesis above, we assume 50% of error on edostep to be the center of our measuring, and an exact landing on the edostep by JI interval (which never happens) as infinitely away from the center of the error curve. Since it never happens, this means every interval approximation is finite number of standard deviations away. | Therefore, counting the null hypothesis above, we assume 50% of error on edostep to be the center of our measuring, and an exact landing on the edostep by JI interval (which never happens) as infinitely away from the center of the error curve. Since it never happens, this means every interval approximation is finite number of standard deviations away. | ||
This means that an edo can be said to approximate interval within one standard deviation, if the relative error is smaller than the right-tailed p-value. | |||
=== 12edo === | === 12edo === | ||
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https://www.wolframalpha.com/input?i=z-score+0.0195500086538741774&assumption=%7B%22MC%22%2C+%22%22%7D+-%3E+%7B%22Formula%22%7D&assumption=%7B%22FSVar%22%2C+%22Q%22%2C+%7B%229%22%2C+%2229%22%7D%2C+%220.0195500086538741774%22%7D+-%3E+%7B%22NormalProbabilities%22%2C+%22pr%22%7D&assumption=%22FSelect%22+-%3E+%7B%7B%22NormalProbabilities%22%7D%7D | https://www.wolframalpha.com/input?i=z-score+0.0195500086538741774&assumption=%7B%22MC%22%2C+%22%22%7D+-%3E+%7B%22Formula%22%7D&assumption=%7B%22FSVar%22%2C+%22Q%22%2C+%7B%229%22%2C+%2229%22%7D%2C+%220.0195500086538741774%22%7D+-%3E+%7B%22NormalProbabilities%22%2C+%22pr%22%7D&assumption=%22FSelect%22+-%3E+%7B%7B%22NormalProbabilities%22%7D%7D | ||
The value is '''2.063''', which means that 12edo represents the expected consonance of 3/2 with about two standard deviations away from the average dissonant irrational sound a random edostep interval will make. | The value is '''2.063''', which means that 12edo represents the expected consonance of 3/2 with about two standard deviations away from the average dissonant irrational sound a random edostep interval will make. Two standard deviations is a point of significance in many places of research, therefore [[12edo]] can be said to provide great approximation to 3/2. | ||