Editing Tuplet (section)

== Tuplet notation ==

=== Notation ===
Tuplets are typically notated either with a bracket or with a number above or below the [[Beam (music)|beam]] if the notes are beamed together. Sometimes, the tuplet is notated with a [[ratio]] (instead of just a number) — with the first number in the ratio indicating the number of notes in the tuplet and the second number indicating the number of normal notes they have the same duration as — or with a ratio and a note value.

:<score> {
\override Score.TimeSignature #'stencil = ##f
\new RhythmicStaff {
   \clef percussion
   \time 5/4
   \set Score.tempoHideNote = ##t \tempo 4 = 100
   \tuplet 3/2 { c8 c c }
   \once \override TupletBracket.bracket-visibility = ##t \tuplet 3/2 { c8 c c }
   \once \override TupletNumber.text = "3:2" \tuplet 3/2 { c8 c c }
   \once \override TupletNumber.text = "3:2♪" \tuplet 3/2 { c8 c c }
} }
</score>

=== Rhythm ===

==== Simple meter ====
For other tuplets, the number indicates a [[ratio]] to the next ''lower'' normal value in the prevailing meter (a [[Power of two|power of 2]] in [[simple meter]]). So a '''quintuplet''' ('''quintolet''' or '''pentuplet'''{{sfn|Cunningham|2007|loc=111}}) indicated with the numeral 5 means that five of the indicated note value total the [[duration (music)|duration]] normally occupied by four (or, as a division of a dotted note in compound time, three), equivalent to the ''second'' higher note value. For example, five quintuplet eighth notes total the same duration as a half note (or, in {{music|time|3|8}} or compound meters such as {{music|time|6|8}}, {{music|time|9|8}}, etc. time, a dotted quarter note).

:<score sound="1"> \new RhythmicStaff {
   \clef percussion
   \time 2/4
   \set Score.tempoHideNote = ##t \tempo 4 = 100
   c8 c c c
   \tuplet 5/4 { c8 c c c c }
   c2
}
</score>

Some numbers are used inconsistently: for example '''septuplets''' ('''septolets''' or '''septimoles''') usually indicate 7 notes in the [[duration (music)|duration]] of 4—or in compound meter 7 for 6—but may sometimes be used to mean 7 notes in the duration of 8.{{sfn|Read|1964|loc=183–184}} Thus, a septuplet lasting a whole note can be written with either quarter notes (7:4) or eighth notes (7:8).

:<score> \new RhythmicStaff {
   \clef percussion
   \time 4/4
   \set Score.tempoHideNote = ##t \tempo 4 = 100
   \tuplet 7/4 { c4 c c c c c c }
   \tuplet 7/8 { c8 c c c c c c }
}
</score>

To avoid ambiguity, composers sometimes write the ratio explicitly instead of just a single number. This is also done for cases like 7:11, where the validity of this practice is established by the complexity of the figure. A French alternative is to write ''pour'' ("for") or ''de'' ("of") in place of the colon, or above the bracketed "irregular" number.{{sfn|Read|1964|loc=219–221}} This reflects the French usage of, for example, "six-pour-quatre" as an alternative name for the ''sextolet''.{{sfn|Damour, Burnett, and Elwart|1838|loc=79}}{{sfn|Hubbard|1924|loc=480}}

There are disagreements about the '''sextuplet''' (pronounced with stress on the first syllable, according to Baker{{sfn|Baker|1895|loc=177}}—which is also called '''sestole''', '''sestolet''', '''sextole''', or '''sextolet'''.{{sfn|Baker|1895|loc=177}}{{sfn|Cooper|1973|loc=32}}{{sfn|Latham|2002}}{{sfn|Shedlock|1876|loc=62, 68, 87, 93}}{{sfn|Stainer and Barrett|1876|loc=395}}{{sfn|Taylor|1879–1889}}{{sfn|Taylor|2001}} This six-part division may be regarded either as a triplet with each note divided in half (2 + 2 + 2)—therefore with an accent on the first, third, and fifth notes—or else as an ordinary duple pattern with each note subdivided into triplets (3 + 3) and accented on both the first and fourth notes. This is indicated by the beaming in the example below.

:<score> \new RhythmicStaff {
   \clef percussion
   \time 2/4
   \set Score.tempoHideNote = ##t \tempo 4 = 100
   \tuplet 6/4 { c16 \set stemRightBeamCount = #1 c \set stemLeftBeamCount = #1 c \set stemRightBeamCount = #1 c \set stemLeftBeamCount = #1 c c }
   \tuplet 6/4 { c16 c \set stemRightBeamCount = #1 c \set stemLeftBeamCount = #1 c c c }
}
</score>

Some authorities treat both groupings as equally valid forms,{{sfn|Damour, Burnett, and Elwart|1838|loc=80}}{{sfn|Köhler|1858|loc=2:52–53}}{{sfn|Latham|2002}}{{sfn|Marx|1853|loc=114}}{{sfn|Read|1964|loc=215}} while others dispute this, holding the first type to be the "true" (or "real") sextuplet, and the second type to be properly a "double triplet", which should always be written and named as such.{{sfn|Kastner|1838|loc=94}}{{sfn|Riemann|1884|loc=134–135}}{{sfn|Taylor|1879–1889|loc=3:478}} Some go so far as to call the latter, when written with a numeral 6, a "false" sextuplet.{{sfn|Baker|1895|loc=177}}{{sfn|Lobe|1881|loc=36}}{{sfn|Shedlock|1876|loc=62}} Still others, on the contrary, define the sextuplet precisely and solely as the double triplet,{{sfn|Stainer and Barrett|1876|loc=395}}{{sfn|Sembos|2006|loc=86}} and a few more, while accepting the distinction, contend that the true sextuplet has no internal subdivisions—only the first note of the group should be accented.{{sfn|Riemann|1884|loc=134}}{{sfn|Taylor|1879–1889|loc=3:478}}{{sfn|Taylor|2001}})

==== Compound meter ====
In [[compound meter (music)|compound meter]], even-numbered tuplets can indicate that a note value is changed in relation to the [[dotted note|dotted]] version of the next higher [[note value]]. Thus, two '''duplet''' [[eighth note]]s (most often used in {{music|time|6|8}} [[Metre (music)|meter]]) take the time normally totaled by three eighth notes, equal to a dotted quarter note. Four '''quadruplet''' (or '''quartole''') eighth notes would also equal a dotted quarter note. The duplet eighth note is thus exactly the same duration as a dotted eighth note, but the duplet notation is far more common in compound meters.{{sfn|Jones|1974|loc=20}}

:<score sound="1"> \new RhythmicStaff {
   \clef percussion
   \time 6/8
   \set Score.tempoHideNote = ##t \tempo 4 = 100
   c8 c c c c c
   \tuplet 2/3 { c8 c } c8. c
   \tuplet 4/3 { c8 c c c } c16. c c c
   c2.
}
</score>

A duplet in compound time is more often written as 2:3 (a dotted quarter note split into two duplet eighth notes) than 2:{{frac|1|1|2}} (a dotted quarter note split into two duplet quarter notes), even though the former is inconsistent with a quadruplet also being written as 4:3 (a dotted quarter note split into four quadruplet eighth notes).{{sfn|Anon.|1997–2000}}

=== Nested tuplets ===
On occasion, tuplets are used "inside" tuplets. These are referred to as ''nested tuplets''.

:<score sound="1"> \new RhythmicStaff {
   \clef percussion
   \time 2/4
   \set Score.tempoHideNote = ##t \tempo 4 = 68
   \once \override TupletBracket.bracket-visibility = ##t \tuplet 5/4 {c8[ \tuplet 3/2 { c16 c c] } c4 \tuplet 7/4 { c32[ c c c c c c] } } c2
}
</score>