I read from https://www.boundless.com/users/232513/textbooks/understanding-basic-music-theory/notation-1/time-8/pickup-notes-and-measures-54-13529/ that there are exceptions to the rule that there always must be the correct amount of beats in a measure that correspond to a time signature. For example, three beats per measure if the time signature is 3/4.

They mention that one exception to this rule is the pickup bar, but there are also other "less common exceptions that are not discussed here[on the website]". What are these other exceptions?

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    Didn't think there were any other exceptions! – Tim Aug 9 '15 at 9:06
  • I think the proper term usage for pickup measure is upbeat or Anacrusis. I doubt whether people are easily going to understand that term. – Neil Meyer Aug 9 '15 at 10:21
  • I wouldn't argue with Anacrusis as the "correct" term, but I don't think many English speakers use it regularly nowadays. "Upbeat" is not necessarily correct, because a pickup bar might be three and a half beats out of four. "Pickup bar" (or "measure") is the term used by market-leading computer notation software like Sibelius and Finale. – user19146 Aug 9 '15 at 13:51
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    Note that "Anacrusis" can also mean "a phrase that does not start on the first beat of the bar" anywhere in a piece, even when there is a conventional time signature, bar lines, and no pickup bar. – user19146 Aug 9 '15 at 14:11
  • Anacrusis is any first bar that doesn't contain its full complement in time. – Tim Aug 9 '15 at 16:45

The only other exception I can think of is something like rubato grace notes that have no count. Here's an example from Chopin's Nocturnes, Op. 27: chopin

As for standard music notation, no other notable exceptions really come to mind.

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  • Yes, that was something I was also thinking about! :P – michaeljan Aug 9 '15 at 9:20
  • Or a cadenza, which more or less includes your grace note run here. – Carl Witthoft Aug 9 '15 at 10:45

There is no "rule" that says music must have a fixed and repetitive rhythmic structure, indicated by a time signature, that can be mapped onto "bars" and "beats". If there is no repetitive rhythm at all, there would be no time signature, and bar lines might be used simply as a visual aid to help several performers to find the same place. That is not a modern invention - it was commonly used in music up to the 16th century, except for dance music which by its nature usually has a repetitive rhythm.

There is no standard notation that means "This section in the middle of a score has no time signature", except for using smaller note heads as in @pianowolf's example. If there are "the wrong number of notes in a bar", you just have to apply common sense to decide whether that is a typo, something like a missing triplet marking, or a section of the piece without a time signature.

A long cadenza (for example in a concerto) might consist mostly of barred music with a time signature, though there might be some parts of it without a time signature.

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If we are willing to consider performance as opposed to notation, then ornamentation may provide an example. Although ornaments are notated according to the time signature, their performance may introduce an extra beats into a measure.

For example, I recently developed a fondness for Chopin, and when I listen to someone like Rubinstein play Chopin he can often appear to introduce an extra beat into a measure by adding elaboration to an ornament. This may just be an instance of rubato. My ear and my formal understanding of music is not yet very sophisticated.

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There is the possibility of a "rubato" phrase where any number of notes can be written into one "measure/bar". Theoretically this can happen anywhere in a score and may require some type of "cue" to indicate either returning to a tempo/time constraint or establishing one. Example: clarinet intro in Gershwin's

  • Rhapsody in Blue
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Some common ways that the number of beats will not add up to the time signature:

(1) the final measure of a piece with a pickup measure will often be deficient (add the last measure + the pickup measure and you will get a full measure).

(2) mid-measure repeat signs; usually caused by pickup notes. For instance, a repeat sign after beat 2 of a minuet. One can argue whether the two sides of the repeat sign together constitute a full measure (they are usually numbered as such) but in many computer encodings they will be classified as two measures.

(3) when tuplets are not explicitly marked they will often appear to not fit the time signature; whether this is a case that fits the question can again be debated, but (as in the end of Schumann Carnival where 3/4 suddenly has 4 beats in some measures) they can create problems nonetheless.

(4) Some composers have used "close enough" notes to simplify rhythms which would otherwise use many ties. Donald Byrd has collected several of these at http://homes.soic.indiana.edu/donbyrd/InterestingMusicNotation.html. For instance the Brahms Capriccio in D here: http://homes.soic.indiana.edu/donbyrd/InterestingMusicNotation_files/Brahms_CapriccioDtHalfCtxt.jpg

(5) Depending on how you read the notes, several of the examples in Julian Hook's "How to Perform Impossible Rhythms" may qualify. http://www.mtosmt.org/issues/mto.11.17.4/mto.11.17.4.hook.html

(6) Cadenzas and other such events as noted by others

(7) In "Mensurstricht" and other formats for transcribing early music, it is common to avoid the use of ties as much as possible. So for instance, in 2/4 a four-beat note might be written as a whole note with the next measure left blank rather than as two tied half notes.

(8) Conversely, it was common into the 19th century to write a quarter note tied across the barline to an eighth note as a quarter note with a single dot written on the other side of the bar line (the Bach Gesellschaft edition available on line does this often). Thus the next measure can appear to be short an eighth note.

(9) Feathered beams (https://musescore.org/sites/musescore.org/files/issues/feathered%20beams.jpg e.g.) often result in an indeterminate number of beats in a measure that can only be resolved by context.

(10) Cutaway scores (e.g.: http://www.musica-ferrum.com/shop_files/images/slyorig_1c9c27eb9dc7018746d86c890bd4fc3e.png) will often have measures that do not add up to the right number of beats. The remaining beats are assumed to be rests.

(11) Brian Ferneyhough and other new complexity composers often use non-power-of-two time signatures (2/6) for instance which give an implied tuplet mark, but whose notes do not add up to the "correct" number of beats without it.

There are all sorts of other notations (two-note tremolos, extreme voice layers, etc.) that can be perceived as looking like they don't add up to the right number of beats, but are generally accepted as having the correct number.

Almost all of these (except 1, 2, 3, and 6) are pretty rare and obscure, which is probably why the original website did not list them, but the questioner did ask about less common exceptions. :-)

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I agree with alephzero that there's no rule saying music need have a repeating rhythmic structure...but written music notation will not "break" the "adding arithmetic" of the time signature. UNLESS of course it explicitly TELLS you that it's breaking out. A pickup measure technically doesn't break the arithmetic either...by convention, it's understood that there are rests at the beginning of the measure, and by convention, as a space saving technique, the initial rests are omitted.

Additionally, though a piece of music is written in 4/4, there's no prescribed reason that the "one" beat (or any beat for that matter) should have priority emphasis or indicate anything about the feel of the music.

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