A pseudo-octave, pseudooctave,
["Interview with Max Mathews", p.21. Author(s): C. Roads and ]Max Mathews
Max Vernon Mathews (November 13, 1926 in Columbus, Nebraska, USA – April 21, 2011 in San Francisco, CA, USA) was a pioneer of computer music.
Biography
Mathews studied electrical engineering at the California Institute of Technology and the Ma ...
. Source: ''Computer Music Journal'', Vol. 4, No. 4, (Winter, 1980), pp. 15–22. Published by: The MIT Press. or paradoxical octave
["The Paradoxes of Octave Identities", p.213. Author(s): Jenő Keuler. Source: ''Studia Musicologica Academiae Scientiarum Hungaricae'', T. 40, Fasc. 1/3, (1999), pp. 211–224. Published by: Akadémiai Kiadó.] in music is an
interval whose
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
is not 2:1 (2.3:1
or 1.9:1, for example), that of the
octave, but is perceived or treated as equivalent to this ratio, and whose pitches are considered equivalent to each other as with octave equivalency.
Stretched octave
The stretched octave, for example 2.01:1, sounds out of tune when played with true
harmonic overtones
An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...
, but in tune when played with tones whose overtones are stretched equivalently.
In
piano tuning
Piano tuning is the act of adjusting the tension of the strings of an acoustic piano so that the musical intervals between strings are in tune. The meaning of the term 'in tune', in the context of piano tuning, is not simply a particular fixed s ...
, stretched octaves are commonly encountered, where the
inharmonicity
In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency ( harmonic series).
Acoustically, a note perceived to have a singl ...
caused by string thickness and tension makes it necessary to widen every interval very slightly. See:
stretched tuning.
The octaves of
Balinese
gamelan
Gamelan () ( jv, ꦒꦩꦼꦭꦤ꧀, su, ᮌᮙᮨᮜᮔ᮪, ban, ᬕᬫᭂᬮᬦ᭄) is the traditional ensemble music of the Javanese, Sundanese, and Balinese peoples of Indonesia, made up predominantly of percussive instruments. T ...
s are never tuned 2:1, but instead are stretched or compressed in a consistent manner throughout the range of each individual gamelan, due to the physical characteristics of their instruments. Another example is the tritave of the
Bohlen–Pierce scale
The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal-tempered diatonic scale.
T ...
(3:1).
Octave stretching is less apparent on large pianos which have longer strings and hence less curvature for a given
displacement
Displacement may refer to:
Physical sciences
Mathematics and Physics
* Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
; that is one reason why orchestras go to the expense of using very long
concert grand pianos rather than shorter, less expensive
baby grand,
upright
Body relative directions (also known as egocentric coordinates) are geometrical orientations relative to a body such as a human person's.
The most common ones are: left and right; forward(s) and backward(s); up and down.
They form three pairs ...
, or
spinet pianos. Another reason is that long strings under high tension can store more acoustic
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
than can short strings, giving larger instruments more
loudness
In acoustics, loudness is the subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud". The relation of ph ...
and better sustain than similar, smaller instruments.
See also
*
Electronic tuner
In music, an electronic tuner is a device that detects and displays the pitch of musical notes played on a musical instrument. "Pitch" is the perceived fundamental frequency of a musical note, which is typically measured in Hertz. Simple tuner ...
*
Mel scale
*
Octave band
An octave band is a frequency band that spans one octave (). In this context an octave can be a factor of 2 or a factor of 100.3. 2/1 = 1200 cents ≈ 10.
Fractional octave bands such as or of an octave are widely used in engineering acoustics. ...
References
External links
"Octave Types" BillBremmer.com'.
{{DEFAULTSORT:Pseudo-Octave
Intervals (music)