- Millioctave
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The millioctave (mO) is a unit of measurement for musical intervals. As is expected from the prefix milli-, an octave is defined as 1000 millioctaves. From this it follows that one millioctave is equal to the ratio 21/1000, the 1000th root of 2, or approximately 1.0006934 (
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Given two frequencies a and b, the measurement of the interval between them in millioctaves can be calculated by
Likewise, if you know a note b and the number n of millioctaves in the interval, then the other note a may be calculated by:
Like the more common cent, the millioctave is a linear measure of intervals, and thus the size of intervals can be calculated by adding their millioctave values, instead of multiplication, which is necessary for calculations of frequencies.
A millioctave is exactly 1.2 cents.
Contents
History and use
The millioctave was introduced by the German physicist Arthur von Oettingen in his book Das duale Harmoniesystem (1913). The invention goes back to John Herschel, who proposed a division of the octave into 1000 parts, which was published (with appropriate credit to Herschel) in George Biddell Airy's book on musical acoustics[1].
Compared to the cent, the millioctave has not been as popular. It is, however, occasionally used by authors who wish to avoid the close association between the cent and equal temperament. However, it has been criticized that it introduces a bias for the less familiar 10-tone equal temperament.[2]
See also
Notes
- ^ Airy, George Biddell (1871). On Sound and Atmospheric Vibrations with the Mathematical Elements of Music. London: Macmillan & Co.. pp. 222. "We are permitted by Sir John Herschel to explain a system proposed by him... It consists in using such a modulus that the logarithm of 2 is 1000."
- ^ Huygens-Fokker Foundation. "Logarithmic Interval Measures". Archived from the original on 2007-02-14. http://web.archive.org/web/20070214012515/http://www.xs4all.nl/~huygensf/doc/measures.html. Retrieved 2007-06-13.
External links
Musical tunings Measurement Pitch · Cent · Millioctave · Savart · Interval · Pitch class · Consonance and dissonance · List of musical intervals · List of meantone intervalsJust intonation Euler–Fokker genus · Harmonic Scale · Harry Partch's 43-tone scale · Hexany · Pythagorean tuning · Scale of harmonicsTemperaments IrregularTraditional non-Western Chinese musicology · Dastgah · Maqam (Arabian maqam · Makam · Mugham · Muqam) · Octoechos · Pelog · Raga (Carnatic rāga) · Slendro · TetrachordNon-octave Intervals (list) Numbers in brackets are the number of semitones in the interval.
Fractional semitones are approximate.Twelve-semitone
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MeasurementOthersCategories:- Units of measure
- Intervals
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