octave

octave

(ŏk`tĭv) [Lat.,=eighth], in music, the perfect interval 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 harmonic). The range of the male voice is roughly an octave below that of the female; men and women supposedly singing in unison actually sing in octaves.

Octave

 

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

[′äk·tiv]

(acoustics)

The interval in pitch between two tones such that one tone may be regarded as duplicating at the next higher pitch the basic musical import of the other tone; the sounds producing these tones then have a frequency ratio of 2 to 1.

(physics)

The interval between any two frequencies having a ratio of 2 to 1.

octave

The interval between two frequencies having the ratio of 2:1.

octave

1. 

a. the interval between two musical notes one of which has twice the pitch of the other and lies eight notes away from it counting inclusively along the diatonic scale

b. one of these two notes, esp the one of higher pitch

c. (as modifier): an octave leap

2. Prosody a rhythmic group of eight lines of verse

3. 

a. a feast day and the seven days following

b. the final day of this period

4. the eighth of eight basic positions in fencing

Octave

(language)

A high-level interactive language by John W. Eaton, with help from many others, like MATLAB, primarily intended for numerical computations. Octave provides a convenient command line interface for solving linear and nonlinear problems numerically.

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.

home.

ftp://ftp.che.wisc.edu/pub/octave/ or your nearest GNU archive site.

E-mail: <bug-octave@bevo.che.wisc.edu>.