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 In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

, 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 A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...

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 ...

, 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

Bali Bali () is a province of Indonesia and the westernmost of the Lesser Sunda Islands. East of Java and west of Lombok, the province includes the island of Bali and a few smaller neighbouring islands, notably Nusa Penida, Nusa Lembongan, and Nu ...

nese

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. The ...

(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 piano The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

s 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 heat a ...

than can short strings, giving larger instruments more

loudness In acoustics, loudness is the subjectivity, 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 rel ...

and better sustain than similar, smaller instruments.

References

External links

"Octave Types"

BillBremmer.com
'. {{DEFAULTSORT:Pseudo-Octave Intervals (music)

Stretched octave

See also

References

External links