Millioctave
Physical unit | |
---|---|
Unit name | Millioctave |
Unit symbol | |
Physical quantity (s) | musical interval |
Formula symbol | |
dimension | |
In SI units | |
Named after | ancient Greek ὄκτω óktō = "eight" |
Derived from | octave |
See also: Cent , Neper , Savart |
The millioctave (mO) is an auxiliary unit of measurement for the size of musical intervals . 1000 mO correspond to an octave or 1200 cents or an interval with a frequency ratio (proportion ) of 2: 1.
The millioctave never prevailed against the cent measure. However, it is still used occasionally by authors who want to avoid the obvious association of cents with equal intervals.
definition
The following applies (see interval ):
Like the more common cent measure , the millioctave is a logarithmic measure for intervals. Therefore, one can add interval sizes in millioctaves instead of having to multiply them as with frequency ratios.
With
the result is the calculator-friendly equation:
Example:
interval Frequency ratio in millioctaves In cents 1 octave 2: 1 1000 1200 2 octaves 4: 1 2000 2400 3 octaves 8: 1 3000 3600 Fifth 3: 2 585 702 Fourth 4: 3 415 498 major third 5: 4 322 386
Conversions
- 1 mO = 1.2 cents = log _{10} (2) Savart ≈ 0.301 Savart
history
The millioctave was introduced in 1903 by the German physicist Arthur von Oettingen in his essay The dual system of harmony . As early as 1871, in On Sound and Atmospheric Vibrations with the Mathematical Elements of Music , George Biddell Airy discussed John Frederick William Herschel's proposal to divide the octave into 1000 parts.
See also
Individual evidence
- ↑ Arthur von Oettingen: The dual system of harmony . ( Memento of the original from August 24, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. In: Annalen der Naturphilosophie 1 (1902), pp. 62–75; 2 (1903/4), pp. 375-403; 3 (1904), pp. 241-269; 4 (1905), pp. 116-152 and 301-338; 5 (1906), pp. 449-503. "The millioctave is the 83rd part of a semitone and an interval so small that it can no longer be distinguished as the difference between two tones." P. 388 f.
- ↑ George Biddell Airy: On sound and atmospheric vibrations: with the mathematical elements of music . 2nd Edition. London 1871, p. 222. “We are permitted by Sir John Herschel to explain a system proposed by him which possesses that advantage. It consists in using such a modulus that the logarithm of 2 is 1000. "