Octave Topics

• atonal theory
• pitch class
• mammalian brain
• equivalency
• human ear
• biological basis
• n times
• octaves
• whole number
• early music
• web telia
• thalamus
• set theory
• counterpoint
• neural networks
• 1s
• neurons
• 400 hz
• 50 hz

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Octave, Octave

To emphasize that it is one of the perfect intervals, the octave is sometimes designated P8 ; the other perfect intervals, the unison, perfect fourth, and perfect fifth, are designated PU, P4, and P5.

The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 2 n times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 50 Hz and 400 Hz are one and two octaves away from 100 Hz because they are (or 2  −1 ) and 4 (or 2 2 ) times the frequency, respectively. However, 300 Hz is not a whole number octave above 100 Hz, despite being a harmonic of 100 Hz.

The human ear tends to hear both notes as being essentially "the same". For this reason, notes an octave apart are given the same note name in the Western system of music notationthe name of a note an octave above A is also A. This is called octave equivalency , and is closely related to harmonics. This is similar to enharmonic equivalency, and less so transpositional equivalency and, less still, inversional equivalency, the latter of which is generally used only in counterpoint, musical set theory, or atonal theory. Thus all Cs, or all 1s (if C = 0), in any octave are part of the same pitch class. Octave equivalency is a part of most musics, but is far from universal in "primitive" and early music (e.g., Nettl, 1956; Sachs & Kunst, 1962). However, monkeys experience octave equivalency, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain http://web.telia.com/~u57011259/eng7.htm and the perception of octave equivalency in self-organizing neural networks can form through exposure to pitched notes, without any tutoring, this being derived from the acoustical structure of those notes (Bharucha 2003, cited in Fineberg 2006).

The use of such intervals is rare, as there is frequently a more preferable enharmonic notation available, but these categories of octaves must be acknowledged in any full understanding of the role and meaning of octaves more generally in music.

In the diatonic scale, and the other standard heptatonic scales of Western music, there are 7 notes; if one counts both ends (see Fencepost error) there are 8 notes, hence the name "octave", from the Latin octavus , from octo (meaning "eight"). Other scales may have a different number of notes covering the range of an octave, such as the chromatic scale with 12 notes or Arabic classical scale with 17, 19, or even 24 notes, but the word "octave" is still used.

This effect may have to be created by the musician. However, some instruments are purposely tuned or designed to produce this effect, for example, the twelve-string guitar and the octave harmonica.

This is technically a misnomer, and is described here: five-octave vocal range. It is important to remember when hearing this description that a piano has octaves total.

Sometimes 8va will also be used to indicate a passage is to be played an octave lower , although the similar notation 8vb ( ottava bassa ) is more common. Similarly, 15ma ( quindicesima ) means "play two octaves higher than written" and 15mb ( quindicesima bassa ) means "play two octaves lower than written." Col 8 or c. 8va stands for coll'ottava and means "play the notes in the passage together with the notes in the notated octaves". Any of these directions can be cancelled with the word loco , but often a dashed line or bracket indicates the extent of the music affected.

Source: Wikipedia > Octave