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Fifteenth - Wikipedia

From Wikipedia, the free encyclopedia

Perfect fifteenth
Name
Abbreviation	P15
Size
Semitones	24
Interval class	0
Just interval	4:1
Cents
12-Tone equal temperament	2400
24-Tone equal temperament	2400
Just intonation	2400

In music, a fifteenth or double octave, abbreviated 15^ma, 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.^[1] 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 (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.

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

15ma notation

Like the notation 8^va for octave (Italian: ottava), 15^ma (Italian: quindicesima) 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 loco, 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.^[2]

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.^[3]

References

^ Iamblichus, Life of Pythagoras Tr. Thomas Taylor (1818) p.328
^ Music Dictionary: 1–9 at Dolmetsch Online
^ Williams, Peter (2001). "Superoctave". In Sadie, Stanley; Tyrrell, John (eds.). The New Grove Dictionary of Music and Musicians (2nd ed.). London: Macmillan Publishers. ISBN 978-1-56159-239-5.‎

Intervals

Twelve-
semitone
(post-Bach
Western)

(Numbers in brackets
are the number of
semitones in the
interval.)

Perfect	unison (0) fourth (5) fifth (7) octave (12)
Major	second (2) third (4) sixth (9) seventh (11)
Minor	second (1) third (3) sixth (8) seventh (10)
Augmented	unison (1) second (3) third (5) fourth (6) fifth (8) sixth (10) seventh (12)
Diminished	second (0) third (2) fourth (4) fifth (6) sixth (7) seventh (9) octave (11)
Compound	ninth (13 or 14) tenth (15 or 16) eleventh (17 or 18) twelfth (18 or 19) thirteenth (20 or 21) fourteenth (22 or 23) fifteenth (24)

Other
tuning
systems

24-tone equal temperament
(Numbers in brackets refer
to fractional semitones.)

Neutral	quarter tone (1⁄2) second (1+1⁄2) third (3+1⁄2) major fourth (5+1⁄2) minor fifth (6+1⁄2) sixth (8+1⁄2) seventh (10+1⁄2)

Just intonations
(Numbers in brackets
refer to pitch ratios.)

7-limit	septimal quarter tone (36:35) septimal third tone (28:27) septimal chromatic semitone (21:20) septimal diatonic semitone (15:14) supermajor second (8:7) subminor third (7:6) supermajor third (9:7) subminor fifth (7:5) supermajor fourth (10:7) subminor seventh (7:4)
Higher-limit	minor diatonic semitone (17-limit)

Other
intervals

Groups	Microtone 5-limit Comma Pseudo-octave Pythagorean interval Subminor and supermajor
Semitones	Pythagorean limma Pythagorean apotome Major limma
Quarter tones	Quarter tone Septimal quarter tone Undecimal quarter tone
Commas	Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma (27.3 cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma (13.8 cents) Kleisma (8.1 cents) Septimal kleisma (7.7 cents) Schisma (1.95 cents) Breedsma (0.72 cents) Ragisma (0.4 cents)
Measurement	Cent Centitone Millioctave Savart
Others	Wolf Ditone Semiditone Secor Incomposite interval

List of pitch intervals

v t e Musical notation
Staff	8^va 15^ma Abbreviation Bar Clef Da capo Dal segno Key signature Ledger line Mode Ossia Scale Rehearsal letter Repeat sign Tempo Time signature Transposition Transposing instrument
Musical notes	Accidental flat natural sharp Cue note Dotted note Grace note Note value beam Notehead stem Pitch Rest Tacet Tuplet Tremolo Interval Helmholtz pitch notation Letter notation Scientific pitch notation
Articulation	Accent Caesura Damping Dynamics Fermata Fingering Legato Marcato Ornament Appoggiatura Glissando Grace note Mordent Slide Trill Portato Slur Staccato Tenuto Tie Tonguing
Sheet music	History of music publishing Music engraving Music publisher Scorewriter
Other systems	Braille music Chord chart Chord diagram Eye music Figured bass Graphic notation Lead sheet Nashville Number System Numbered musical notation Klavarskribo Tablature Parsons Percussion notation Simplified Ancient Greek Chinese Ekphonetic Gamelan Kunkunshi Neume Swaralipi Shakuhachi Znamenny
Related	Mensural notation Music stand Perfect pitch Sight-reading Transcription
List of musical symbols Category:Musical notation

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