Millioctave
Encyclopedia
The millioctave 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 .
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.
, 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.
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.
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
. As is expected from the prefix milli-, an octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
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 .
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
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
, 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.
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 HerschelJohn Herschel
Sir John Frederick William Herschel, 1st Baronet KH, FRS ,was an English mathematician, astronomer, chemist, and experimental photographer/inventor, who in some years also did valuable botanical work...
, who proposed a division of the octave into 1000 parts, which was published (with appropriate credit to Herschel) in George Biddell Airy
George Biddell Airy
Sir George Biddell Airy PRS KCB was an English mathematician and astronomer, Astronomer Royal from 1835 to 1881...
's book on musical acoustics.
Compared to the cent
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
, 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
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
. However, it has been criticized that it introduces a bias for the less familiar 10-tone equal temperament.