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Micrologus is an educational site dedicated to the discussion of Music Theory and Music Notation, with a secondary area of interest in Music Technology.

It is named after Guido of Arezzo's treatise (c. 1025-1028), which included the earliest guide for staff notation. Guido is also credited with inventing solfège, using the hymn "Ut queant laxis", and the Guidonian Hand, a mnemonic teaching system.

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Irregular Divisions of the Beat (Tuplets)

Posted by Robert Thomas on March 30th, 2011

Any division of a unit into irregular components requires the addition of a number showing the division. The term “tuplet” is used to refer to these irregular beat divisions. Abnormal divisions of beats are shown with brackets, numbers (showing the number of notes in the resulting group by means of an Arabic number or ratio) and beams. The note values of tuplets are determined by the note-values of the regular grouping against which they are set. With three notes against two in simple time, the duplet is the regular grouping and thus the triplet grouping would use the same note values as the duplet (in 16th post 2/4 time signature, the regular duple grouping would be two quarter notes and therefore the triple grouping would also be quarter notes). When the number of notes in the irregular group is more than twice the number of the regular duplet, the next smaller note value is used (e.g., with quintuplets in 16th post 2/4 time signature, the regular duple grouping is two quarter notes and therefore the quintuplet grouping is eighth notes [5 > 2 x 2]). While triplets and quintuplets are generally understood to imply the ratios 3:2 and 5:4, respectively, other irregular groupings can and do occur. In order to facilitate ease of understanding, it is recommended that ratios be used in these cases.

26th Post 1st Tuplets Image

If a tuplet figure is beamed, the number is placed on the side of the beam opposite the note head. If there is any question as to which notes or rests are included in a tuplet, or if a tuplet figure is not beamed or only partially beamed (as may be the case when a rest or notes of mixed values are included in the tuplet), a bracket should be must be used with a number or ratio.

Brackets must enclose the entire space of all notes and rests included within the grouping (from the left side of the first note to the right side of the last note – although if the last note of the tuplet is flagged, the stem is used for the boundary, not the flag). Brackets and numbers are normally placed on the stem side of notes, but when ledger lines are used, the number and bracket appear on the note head side. Usually, the two halves of a tuplet bracket should be straight enough to appear as if they are part of the same line, with the tuplet number centered within the bracket. In cases where the figure includes both up- and down-stem notes, the tuplet is placed above the figure.

Numbers should be centered over or under the center of each grouping. The number of the tuplet is written in boldface italic type and is a little over one space tall.

Unless absolutely impossible, the tuplet number should always be outside the staff. If fingerings are marked, the tuplet number should be placed opposite the fingering numerals. If the tuplet number lies in the path of a slur, the tuplet number should be moved to the side of the note opposite the slur (that is, if the tuplet would normally be placed above the staff, place it below the staff, and vice versa). Articulation markings (except large slurs over the entire configuration) are always included inside a tuplet bracket. Care should be taken to ensure proper vertical alignment between parts when dealing with tuplets.

26th Post 2nd Tuplets Image

Nested tuplets are always placed on the same side of the figure, regardless of stem directions. When dealing with nested tuplets, the smallest values are placed closest to the notes with progressively larger groupings placed further out.

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