Right or wrong syncope

Question

Is the fourth note syncopated or not?

Answer 1

The example, as it stands, is ambiguous. The way this passage will be perceived is going to be heavily dependent on what (if anything) precedes it, and what follows it.

Pace Sandra-Émilie, syncopation is a bit broader and more complex than "tones entering where there is no pulse." The Wikipedia page gives some idea of just how broad the definition can be, but, if we were to put it simply, we could say that syncopation is the de-emphasis of, or elision over, the strong beats by a variety of means. Note that this means that there is an implicit or explicit background of strong beats to work against.

Suspension as Sandra-Émilie uses the term is a bit iffy: for the usual definition of suspension, a change of harmony is implied over which the note is suspended. It is hard to say that this is the case for this example.

I say that this passage is ambiguous taken out of context because a) it is a single line, so there is no accompaniment to measure the melody against, and b) we have no way of knowing what surrounds the passage. If the strong beats were clearly marked in bars leading up to this passage, then yes, this may well be the start of syncopation, because the melody will be perceived as pulling against the implicit background meter.

If this is the opening of the piece, however, then the meter of the melody is ambiguous until some event (perhaps the entrance of a regular accompaniment on a strong beat, perhaps that the melody falls back into the base meter on a strong beat) serves to establish clearly what the meter is. At that point, the listener will be able make sense of the melody's rhythm after the fact. The listener may perceive polymeter (if the unaccompanied melody tends to group its events into either a consistent cross-meter, frequently 3 in a situation like this, or an apparently shifting meter) or syncopation (if the perception of beat has just been shifted onto off-beats), so what we have starting here with the tie depends on what follows.

So, to summarise, that tied crochet's function may be metrically ambiguous, it may be the start of syncopation, it may be the start of an implied polymeter: we can't tell without more of the preceding music and more of what follows these bars. Determining musical function relies heavily on context. Ambiguity itself is one of the composer's tools of the trade: there are going to be times when we want you scratching your head about a passage until such time as we bring about an "Aha!" moment and show how everything fits into the metrical framework.

As an aside, I'd strongly suggest against emulating the use of the C clef here. For one, the regular clefs used in the usual spots allow for noticeable changes of clef when the hands move across the range of the keyboard. For another, when using the regular clefs, a wider space is possible between the staves. There are times when multiple ledger line above the bass clef or below the treble clef are a more legible notation than cross-stave notes or a momentary change of clef, especially when working with multiple voices in each stave (i.e., contrapuntal music).

Answer 2

According to G. Cooper and L.B. Meyer in The Rhythmic Structure of Music, a syncopation is "a tone which enters where there is no pulse" and which is followed, on the next beat, by a rest or a suppressed tone (a tied note). Therefore, this is not a syncopation, according to these authors.

This is what is called "suspension" because it starts on a weak beat and it continues on the next beat.