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The most common tuplet [9] is the triplet (German Triole, French triolet, Italian terzina or tripletta, Spanish tresillo).Whereas normally two quarter notes (crotchets) are the same duration as a half note (minim), three triplet quarter notes have that same duration, so the duration of a triplet quarter note is 2 ⁄ 3 the duration of a standard quarter note.
Tuplet A tuplet is a group of notes that would not normally fit into the rhythmic space they occupy. The example shown is a quarter-note triplet—three quarter notes are to be played in the space that would normally contain two. (To determine how many "normal" notes are being replaced by the tuplet, it is sometimes necessary to examine the ...
With a the shorter and b the longer legs of a triangle and c its hypotenuse, the Pythagoras family of triplets is defined by c − b = 1, the Plato family by c − b = 2, and the Fermat family by | a − b | = 1. The Stifel sequence produces all primitive triplets of the Pythagoras family, and the Ozanam sequence produces all primitive triples ...
A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer . For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as ...
[c] The difficulty may be seen by comparing dotted notation to tied notation: a quarter note is equivalent to 2 tied eighth notes (), a dotted quarter = 3 tied eighth notes, double dotted = 7 tied sixteenth notes (), triple dotted = 15 tied thirty-second notes (), and quadruple dotted = 31 tied sixty-fourth notes (). Although shorter notes do ...
Certainly the faster form, counted as two to a bar, is far more common for 6/8 (marches, jigs, etc.). In my experience, when composers want the slower, six-to-a-bar form, they tend to write 6/4, because it more closely resembles a pair of 3/4 bars combined. In any case, a slow tempo marking with a cautionary marking of "in six" is a good idea.—
If any of the above matrices, say A, is applied to a triple (a, b, c) T having the Pythagorean property a 2 + b 2 = c 2 to obtain a new triple (d, e, f) T = A(a, b, c) T, this new triple is also Pythagorean.
In music, a thirty-second note (American) or demisemiquaver (British) is a note played for 1 ⁄ 32 of the duration of a whole note (or semibreve).It lasts half as long as a sixteenth note (or semiquaver) and twice as long as a sixty-fourth (or hemidemisemiquaver).