The most common tuplet is the triplet (G. triole), shown at right. Whereas normally two quarter notes are the same duration as a half note, three triplet quarter notes total that same duration, so the duration of a triplet quarter note is 2/3 the duration of a standard quarter note. Similarly, three triplet eighth notes are equal in duration to one quarter note. If several note values appear under the triplet bracket, they are all affected the same way, reduced to their original 2/3 duration.
If the notes of the triplet are beamed together, the bracket may be omitted and the number written above the beam, as shown in the second illustration. Occasionally the bracket is omitted when the notes are slurred together.
For other tuplets, the number indicates a ratio to the next lower power of two. So a quintuplet indicated with the numeral 5 means that five of the indicated note value total the duration normally occupied by four, equivalent to the second higher note value; for example, five quintuplet eighth notes total the same duration as a half note. Some numbers are used inconsistently: for example septuplets are sometimes used to mean 7 notes in the duration of 4, but other times to mean 7 notes in the duration of 8. To avoid ambiguity, composers sometimes write the ratio explicitly instead of just a single number, as shown in the third illustration.
In compound metre, even-numbered tuplets can indicate that a note value is changed in relation to the dotted version of the next higher note value. Thus, two duplet eighth notes (most often used in 6/8 meter) take the time normally totaled by three eighth notes, equal to a dotted quarter note. Four quadruplet 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 more often used in compound meters.
US Patent Issued to France Telecom on Dec. 11 for "Asymmetrical Method of Encryption or Signature Verification" (French Inventors)
Dec 18, 2012; ALEXANDRIA, Va., Dec. 18 -- United States Patent no. 8,331,556, issued on Dec. 11, was assigned to France Telecom...