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In music, a fifteenth or double octave, abbreviated ''15ma'', is the interval between one musical note and another with one-quarter the wavelength or quadruple the frequency. It has also been referred to as the bisdiapason. The fourth harmonic, it is two 
As the fifteenth is a multiple of octaves, the human ear tends to
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 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 (''15ma'' ), and the note a fifteenth below is at 100 Hz (''15mb'' ). The ratio of frequencies of two notes a fifteenth apart is therefore 4:1.
As the fifteenth is a multiple of octaves, the human ear 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 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:
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*Stop, Kentucky, an unincorporated community in the United States
* Stop (Rogatica), a village in Rogatica, Republika Srpska, Bosnia and Herzegovina
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* Bus stop
* Truck stop, a type of rest stop for truck dri ...
a fifteenth away (notated as 2′).
15ma notation
Like the notation ''8va'' foroctave
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 ...
(), ''15ma'' () means "play two octaves higher than written." It could also mean two octaves lower, but that is usually notated ''15mb''. Either direction can be cancelled with the word ', but often a dashed line or bracket indicates the extent of the music affected.
The notations ''16va'' and ''16vb'' 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