161/128: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = arithmetic mean major third, octave-reduced 161th harmonic | |||
| Name = | |||
| Color name = 23oz4 | | Color name = 23oz4 | ||
}} | }} | ||
In | In [[just intonation]], '''161/128''', the '''arithmetic mean major third''' is the frequency ratio between the 161th and the 128th harmonic. It is the [[arithmetic mean]] between the [[5/4|just major third]] and the [[81/64|Pythagorean major third]]: (5/4 + 81/64)/2 = 161/128. | ||
It is the mean between the [[5/4|just major third]] and the [[81/64|Pythagorean major third]]: (5/4 + 81/64)/2 = 161/128. | |||
It can also be calculated from the [[81/80|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128. | It can also be calculated from the [[81/80|syntonic comma]]: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128. | ||
[[Category:Third]] | |||
[[Category:Major third]] | |||
Latest revision as of 16:46, 2 March 2023
| Interval information |
octave-reduced 161th harmonic
reduced harmonic
In just intonation, 161/128, the arithmetic mean major third is the frequency ratio between the 161th and the 128th harmonic. It is the arithmetic mean between the just major third and the Pythagorean major third: (5/4 + 81/64)/2 = 161/128.
It can also be calculated from the syntonic comma: ((81/80 - 1)/2 + 1)⋅(5/4) = 161/128.