music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

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

musical note In music, notes are distinct and isolatable sounds that act as the most basic building blocks for nearly all of music. This musical analysis#Discretization, discretization facilitates performance, comprehension, and musical analysis, analysis. No ...

and another with one-quarter the

wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

or quadruple the

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

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

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

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

diatonic Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair ...

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 (''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 ear tends to hear both notes as being essentially "the same", as it does the octave. Like the octave, in the Western system of

music notation Musical notation is any system used to visually represent music. Systems of notation generally represent the elements of a piece of music that are considered important for its performance in the context of a given musical tradition. The proces ...

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 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