Fifteenth

Fifteenth
Perfect fifteenth on C About this sound Play .
Perfect fifteenth
Inverse
Name
Other names
Abbreviation P15
Size
Semitones 24
Interval class 0
Just interval 4:1
Cents
Equal temperament 2400
24 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 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 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 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′).

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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Look at other dictionaries:

  • Fifteenth — Fif teenth , n. 1. One of fifteen equal parts or divisions; the quotient of a unit divided by fifteen. [1913 Webster] 2. A species of tax upon personal property formerly laid on towns, boroughs, etc., in England, being one fifteenth part of what… …   The Collaborative International Dictionary of English

  • fifteenth — [fif′teenth′] adj. [ME fiftenthe < fifteotha < fiftene: see FIFTEEN & TH2] 1. preceded by fourteen others in a series; 15th 2. designating any of the fifteen equal parts of something n. 1. the one following the fourteenth …   English World dictionary

  • Fifteenth — Fif teenth , a. [OE. fiftenthe; cf. fiftethe, AS. f[=i]fte[=o][eth]a. See {Fifteen}.] 1. Next in order after the fourteenth; the ordinal of fifteen. [1913 Webster] 2. Consisting of one of fifteen equal parts or divisions of a thing. [1913… …   The Collaborative International Dictionary of English

  • fifteenth — late 14c., from FIFTEEN (Cf. fifteen) + TH (Cf. th). By 15c. displacing forms derived from O.E. fifteoða. Cf. O.Fris. fiftuda, Du. vijftiende, Ger. fünfzehnte, O.N. fimmtandi, Goth. fimftataihunda …   Etymology dictionary

  • Fifteenth —    The fifteens or fifteenth, as it is generally called, was originally an imperial tax levied throughout the kingdom for various purposes, as wars and such like.    It was a tax of one fifteenth on movables of all kinds, and was of a similar… …   Dictionary of London

  • fifteenth — /fif teenth /, adj. 1. next after the fourteenth; being the ordinal number for 15. 2. being one of 15 equal parts. n. 3. a fifteenth part, esp. of one (1/15). 4. the fifteenth member of a series. 5. Music. the interval of two octaves. [bef. 900;… …   Universalium

  • fifteenth — fif|teenth [ fıf tinθ ] number 1. ) in the place or position counted as number 15: his fifteenth birthday 2. ) one of 15 equal parts of something: You spend about a fifteenth of your life commuting …   Usage of the words and phrases in modern English

  • fifteenth — UK [ˌfɪfˈtiːnθ] / US [fɪfˈtɪnθ] number 1) in the place or position counted as number 15 his fifteenth birthday 2) one of 15 equal parts of something You spend about a fifteenth of your life commuting …   English dictionary

  • fifteenth — fif•teenth [[t]ˈfɪfˈtinθ[/t]] adj. 1) next after the fourteenth; being the ordinal number for 15 2) being one of 15 equal parts 3) a fifteenth part, esp. of one (1/15) 4) the fifteenth member of a series • Etymology: bef. 900; ME fiftenthe (see… …   From formal English to slang

  • fifteenth — /fɪfˈtinθ/ (say fif teenth) adjective 1. next after the fourteenth. 2. being one of fifteen equal parts. –noun 3. a fifteenth part, especially of one (¹⁄₁₅). 4. the fifteenth member of a series …  

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