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Fifteenth

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Title: Fifteenth  
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Subject: Interval (music), Third (chord), Octave, Moodswinger, Octaves
Collection: Octaves, Perfect Intervals
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Fifteenth

Perfect fifteenth on C About this sound   .
Perfect fifteenth
Name
Abbreviation P15
Size
Semitones 24
Interval class 0
Just interval 4:1
Cents
Equal temperament 2400
Just intonation 2400

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. The fourth harmonic, it is two octaves. 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 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.

Example of the same two notes expressed regularly, in an 8va bracket, and in a 15ma bracket

As the fifteenth is a multiple of octaves, the human stops a fifteenth away (notated as 2′).

Like the notation 8va for octave, 15ma (Italian: quindicesima) 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 loco, but often a dashed line or bracket indicates the extent of the music affected.

The notations 16va and 16vb are sometimes mistakenly used instead.[1]

References

  1. ^ Music Dictionary: 1–9 at Dolmetsch Online
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