octave(redirected from Law of Octaves)
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octave(ŏk`tĭv) [Lat.,=eighth], in music, the perfect intervalinterval,
in music, the difference in pitch between two tones. Intervals may be measured acoustically in terms of their vibration numbers. They are more generally named according to the number of steps they contain in the diatonic scale of the piano; e.g.
..... Click the link for more information. between the 1st and 8th tones of the diatonic scale. The upper note of a perfect octave has a frequency of vibration twice that of the lower, and in modern Western notation the two have the same letter name. The octave is the first overtone (see harmonicharmonic.
1 Physical term describing the vibration in segments of a sound-producing body (see sound). A string vibrates simultaneously in its whole length and in segments of halves, thirds, fourths, etc.
..... Click the link for more information. ). The range of the male voice is roughly an octave below that of the female; men and women supposedly singing in unisonunison,
in music, tones identical in pitch produced by two or more parts or voices. In popular usage a vocal composition is said to be sung in unison even though some of the voices are separated from others by the interval of an octave.
..... Click the link for more information. actually sing in octaves.
in music. (1) An interval encompassing the eight steps of the diatonic scale or six whole tones. It is one of the perfect consonances. From the acoustical point of view, an octave is the interval between two frequencies f1 and f2, the logarithm of whose ratio to the base 2, in other words log2 (f2/f1), is equal to 1. This corresponds to the ratio of the upper cutoff frequency to the lower cutoff frequency, which equals 2(f2/f1 = 2). One octave equals 1,200 cents or 301 savarts.
(2) The eighth step of the diatonic scale.
(3) A progression of musical notes that comprises all the basic notes—C (do), D (re), E (mi), F (fa), G (sol), A (la), and B (si) —or the 12 semitones of the chromatic scale. The entire range of notes used in music encompasses seven complete octaves and two incomplete octaves. These octaves progress from the low notes of the musical range to the high notes in the following order: subcontraoctave (an incomplete octave, possessing only three upper notes—A, B flat, and B), contraoctave, great octave, small octave, one-line octave, two-line octave, three-line octave, four-line octave, and an incomplete octave (in Russian, fifth octave) consisting of the single note C.
Octave can do arithmetic for real and complex scalars and matrices, solve sets of nonlinear algebraic equations, integrate functions over finite and infinite intervals, and integrate systems of ordinary differential and differential-algebraic equations.
Octave has been compiled and tested with g++ and libg++ on a SPARCstation 2 running SunOS 4.1.2, an IBM RS/6000 running AIX 3.2.5, DEC Alpha systems running OSF/1 1.3 and 3.0, a DECstation 5000/240 running Ultrix 4.2a, and Intel 486 systems running Linux. It should work on most other Unix systems with g++ and libg++.
Octave is distributed under the GNU General Public License. It requires gnuplot, a C++ compiler and Fortran compiler or f2c translator.
Latest version: 2.0.16 (released 2000-01-30), as of 2000-06-26.
ftp://ftp.che.wisc.edu/pub/octave/ or your nearest GNU archive site.