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For example, C 4 is one note above B 3, and A 5 is one note above G 5. The octave number is tied to the alphabetic character used to describe the pitch, with the division between note letters ‘B’ and ‘C’, thus: "B 3" and all of its possible variants (B, B ♭, B, B ♯, B) would properly be designated as being in octave "3".
An octave is the interval between one musical pitch and another with double or half its frequency. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1.
Notes in each include an additional prime symbol below the note's letter. The octave starting at middle C is called the "small" octave. Notes in it are written as lower case letters, so middle C itself is written c in Helmholtz notation. The next higher octave is called "one-lined". Notes in it include a prime symbol above the note's letter.
Because octave-related pitches belong to the same class, when an octave is reached, the numbers begin again at zero. This cyclical system is referred to as modular arithmetic and, in the usual case of chromatic twelve-tone scales, pitch-class numbering is "modulo 12" (customarily abbreviated "mod 12" in the music-theory literature)—that is ...
Genius (also known as the Genius Math Tool) is a free open-source numerical computing environment and programming language, [2] similar in some aspects to MATLAB, GNU Octave, Mathematica and Maple. Genius is aimed at mathematical experimentation rather than computationally intensive tasks. It is also very useful as just a calculator.
The purpose of this adjustment is to move the 12 notes within a smaller range of frequency, namely within the interval between the base note D and the D above it (a note with twice its frequency). This interval is typically called the basic octave (on a piano keyboard, an octave has only 12 keys). This dates to antiquity: in Ancient Mesopotamia ...
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Octave (aka GNU Octave) is an alternative to MATLAB. Originally conceived in 1988 by John W. Eaton as a companion software for an undergraduate textbook, Eaton later opted to modify it into a more flexible tool. Development begun in 1992 and the alpha version was released in 1993. Subsequently, version 1.0 was released a year after that in 1994.