octave(redirected from 8va)
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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.