Millioktava

Millioktava ( mO ) is a dimensionless logarithmic unit of the ratio of two frequencies or a musical interval . 1000 millictavs are equal to an octave . The two frequencies a and b with a difference of one milli octave relate as

a / b = 2 ^1/1000 = 1.0006934 ...

If the frequencies of two sounds ( a ) and ( b ) are known, then the number of millictaves ( m ) in the interval between them is calculated by the formulas:

m=1000\log _{2}\left({\frac {a}{b}}\right)\approx 3322\log _{10}\left({\frac {a}{b}}\right)

{\ displaystyle m = 1000 \ log _ {2} \ left ({\ frac {a} {b}} \ right) \ approx 3322 \ log _ {10} \ left ({\ frac {a} {b}} \ right)}

m = 1000 \ log_2 \ left (\ frac {a} {b} \ right) \ approx 3322 \ log_ {10} \ left (\ frac {a} {b} \ right)

If the sound frequency ( b ) and the interval in millictaves ( m ) are known, then the frequency of the second sound is calculated as follows:

a=b\times 2^{\frac {m}{1000}}

{\ displaystyle a = b \ times 2 ^ {\ frac {m} {1000}}}

a = b \ times 2 ^ \ frac {m} {1000}

The term "millioktava" was first found in the book of the German physicist and music theorist A. Oettingen Das duale Harmoniesystem (1913) ^[1] . The division of the octave into 1000 parts, proposed back in the 19th century by the English physicist J. Herschel , is the basis of a 10-tone uniformly temperament system that has not received further development in modern music.

Notes

↑ Arthur von Oettingen , Das duale Harmoniesystem, Leipzig, 1913

[1] Arthur von Oettingen , Das duale Harmoniesystem, Leipzig, 1913

Millioktava

See also

Notes

More articles: