music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

, a fifteenth or double octave, abbreviated ''15^ma'', is the interval between one

musical note In music, a note is the representation of a musical sound. Notes can represent the Pitch (music), pitch and Duration (music), duration of a sound in musical notation. A note can also represent a pitch class. Notes are the building blocks of much ...

and another with one-quarter the

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

or quadruple the

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 ...

. It has also been referred to as the bisdiapason. The fourth harmonic, it is two

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 ...

s. It is referred to as a fifteenth because, in the

diatonic Diatonic and chromatic are terms in music theory that are most often used to characterize Scale (music), scales, and are also applied to musical instruments, Interval (music), intervals, Chord (music), chords, Musical note, notes, musical sty ...

scale, there are 15 notes between them if one counts both ends (as is customary). Two octaves (based on the

Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...

word for eighth) do not make a sixteenth, but a fifteenth. In other contexts, the term ''two octaves'' is likely to be used. For example, if one note has a frequency of 400 Hz, the note a fifteenth above it is at 1600 Hz (''15^ma'' ), and the note a fifteenth below is at 100 Hz (''15^mb'' ). The ratio of frequencies of two notes a fifteenth apart is therefore 4:1. Ottava Ex

As the fifteenth is a multiple of octaves, the human

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tends to

hear Hearing, or auditory perception, is the ability to perceive sounds through an organ, such as an ear, by detecting vibrations as periodic changes in the pressure of a surrounding medium. The academic field concerned with hearing is auditory ...

both notes as being essentially "the same", as it does the octave. Like the octave, in the Western system of

music notation Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

notes a fifteenth apart are given the same name—the name of a note an octave above A is also A. However, because of the large frequency distance between the notes, it is less likely than an octave to be judged the same pitch by non-musicians. Passages in parallel fifteenths are much less common than parallel octaves. In particular, sometimes an organist will use two

stops Stop may refer to: Places *Stop, Kentucky, an unincorporated community in the United States * Stop (Rogatica), a village in Rogatica, Republika Srpska, Bosnia and Herzegovina Facilities * Bus stop * Truck stop, a type of rest stop for truck dri ...

a fifteenth away (notated as 2′).

15ma notation

Like the notation ''8^va'' for

(), ''15^ma'' () means "play two octaves higher than written." It could also mean two octaves lower, but that is usually notated ''15^mb''. Either direction can be cancelled with the word ', but often a dashed line or bracket indicates the extent of the music affected. The notations ''16^va'' and ''16^vb'' are sometimes mistakenly used instead.

Organ stop

On organs, the stops labelled "Fifteenth" ("Superoctave" or "Superoktave") are two octaves above the principal ( diapason), or an octave above stops labelled "Octave". If the principal is 8′, then the octave is 4′ and the superoctave 2′. Note that this is different from the organ coupler named "super octave", which adds notes an octave above, not two octaves above.

References

{{Musical notation Octaves Perfect intervals Compound intervals