View source for Fifteenth

{{about|the music interval}}
[[Image:Perfect fifteenth on C.png|thumb|right|Perfect fifteenth on C {{audio|Perfect fifteenth on C.mid|Play}}.]]
{{Infobox Interval
|main_interval_name = Perfect fifteenth
|inverse =
|complement =
|other_names =
|abbreviation = P15
|semitones = 24
|interval_class = 0
|just_interval = 4:1
|cents_equal_temperament = 2400
|cents_24T_equal_temperament = 2400
|cents_just_intonation = 2400
}}
In [[music]], a '''fifteenth''' or '''double octave''', abbreviated '''''15<sup>ma</sup>''''', is the [[interval (music)|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.<ref>[[Iamblichus]], ''[https://books.google.com/books?id=J_BZAAAAcAAJ Life of Pythagoras]'' Tr. [[w:Thomas Taylor (neoplatonist)|Thomas Taylor]] (1818) p.328</ref> The fourth harmonic, it is two [[octave]]s. It is referred to as a fifteenth because, in the [[diatonic]] scale, there are 15 notes between them if one counts both ends (as is customary). Two octaves (based on the [[Italian language|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&nbsp;[[Hertz|Hz]], the note a fifteenth above it is at 1600&nbsp;Hz (''15<sup>ma</sup>''&thinsp;), and the note a fifteenth below is at 100&nbsp;Hz (''15<sup>mb</sup>''&thinsp;). The ratio of frequencies of two notes a fifteenth apart is therefore 4:1.

[[File:Ottava Ex.svg|thumb|left|Example of the same two notes expressed regularly, in an 8<sup>va</sup> bracket, and in a 15<sup>ma</sup> bracket]]
As the fifteenth is a multiple of octaves, the human [[ear]] tends to [[Hearing (sense)|hear]] both notes as being essentially "the same", as it does the octave. Like the octave, in the Western system of [[Musical notation|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 [[organ stop|stops]] a fifteenth away (notated as 2′).

==15ma notation==
Like the notation ''8<sup>va</sup>'' for [[octave]] ({{Langx|it|ottava}}), ''15<sup>ma</sup>'' ({{Langx|it|quindicesima}}) means "play two octaves higher than written." It could also mean two octaves lower, but that is usually notated ''15<sup>mb</sup>''. Either direction can be cancelled with the word ''{{lang|it|loco}}'', but often a dashed line or bracket indicates the extent of the music affected.

The notations ''16<sup>va</sup>'' and ''16<sup>vb</sup>'' are sometimes mistakenly used instead.<ref>[http://www.dolmetsch.com/defs0.htm Music Dictionary: 1–9] at Dolmetsch Online</ref>

==Organ stop==
On organs, the stops labelled "Fifteenth" ("Superoctave" or "Superoktave") are two octaves above the principal ([[diapason (pipe organ)|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.<ref>{{Cite Grove |last=Williams |first=Peter |title=Superoctave}}</ref>

==References==
<references />

{{Intervals}}
{{Musical notation}}

[[Category:Octaves]]
[[Category:Perfect intervals]]
[[Category:Compound intervals]]