Everything about Fifteenth totally explained
In
music, a
fifteenth (sometimes abbreviated
15ma) is the
interval between one musical
note and another with one-quarter or quadruple the
frequency. It corresponds to two
octaves. It is the fourth
harmonic. 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) don't 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's at 1600 Hz, and the note a fifteenth below is at 100 Hz. The ratio of frequencies of two notes a fifteenth apart is therefore 4:1.
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's less likely than an octave to be judged the same pitch by non-musicians. Passages in parallel fifteenths is much less common than parallel octaves, though it does happen. In particular, sometimes an organist will use two
stops a fifteenth away (notated as 2').
Like the notation
8va for
octave,
15ma (
quindicesima) means "play two octaves higher than written." It could also mean two octaves lower, but two octaves below the low notes of the bass clef is below the range of nearly all instruments. This direction can be cancelled with the word
loco, but often a dashed line or bracket indicates the extent of the music affected.
The 16va and 16vb notations
The notation
16va is an alternative notation often found in music notation to indicate "play two octaves higher than written." Most consider this usage improper. It seems to have arisen from the folk beliefs that if one octave is 8 steps then two octaves must be 16 steps, and the suffix "va" must mean something like "play higher." Thus if
8va means "play one octave higher" then
16va must mean "play two octaves higher."
Some musicians and music publishers who well understand that two octaves is the interval of a 15th and
8va is an abbreviation for the Italian "ottava" still use the notation
16va, especially in music intended for amateurs or children, because they feel
16va is more immediately comprehensible than
15ma, especially to non-Italian speakers.
Similarly the notation
16vb is an alternative notation, considered by some to be improper but found in many printed scores, indicating "play two octaves lower than written".
Further Information
Get more info on 'Fifteenth'.
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