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Is there a name for a chord that is introduced one note at a time?
You can hear an example in the first couple of seconds of "Lolly, Lolly, Lolly, Get Your Adverbs Here!" on Schoolhouse Rock:
It's different from an arpeggio; I don't know that much about music theory but from looking it up, it doesn't seem exactly the same as a rolled chord or broken chord.
This technique has a few different names, a pyramid, bell, or cascade chord. It can be considered a classification of arpeggio since sometimes when arpeggios are played the notes are sustained.
Here is an excerpt from the “Arpeggio” article in Wikipedia:
A bell chord, also known colloquially as "bells", is a musical arrangement technique in which a composition has separate instruments (or multiples of the same instrument) play single notes of a chord in sequence, sustaining individual notes to form the chord. It is, in effect, an arpeggio played by several instruments sequentially. This is also known as a pyramid or cascade. It is common in barbershop music. [End excerpt]
This technique can be used in vocal music, horn arrangements and even orchestral settings. Vocally it has been used in “Twist and Shout” and “Bohemian Rhapsody” just to name a few.
An arpeggio is a chord played with the notes in ascending or descending order.
A broken chord is a chord played such that not all pitches are sounded at the same time.
In this case, it's both an arpeggio and a broken chord — both terms are appropriate to describe the music — but it also happens that each note is sung by a different voice. The multiple voices don't disqualify it as an arpeggio or broken chord.
One tends to think of arpeggios and broken chords in the context of a single instrument, but they need not be. It's also common to think of the notes of arpeggios and broken chords as happening in relatively rapid succession, but this need not be the case either.
It could be considered a rolled chord as well. Rolled notes typically are performed more rapidly, but not by definition. There is music in which chords are rolled slowly — but a slow roll is rather the exception than the rule. Nevertheless, if a slowly rolled chord is going to appear, the beginning or end of a piece is the most likely place to find it.
The term arpeggio gets used in two ways, as a type of embellishment of a chord represented by the ways line...
...and also to mean playing the tones of a chord separately in a line...
The second mean is often called arpeggiation - as a process, like in composition - and sometimes it's called broken chord.
The embellishment is normally played from bottom up, very fast, and sustaining all tones for the duration of the chord, whereas arpeggiation can order the chord tones freely into a line (tons of melodies are just the result of the arpeggiation process) so there is a clear aural difference.
The difference between the two meanings is usually understood in context. If someone were to say the opening theme to Eine kleine Nachtmusik is arpeggios, it's understood that they mean the broken chord/arpeggiation process not the wavy line embellishment.
The device at the beginning of Lolly, Lolly, Lolly, Get Your Adverbs Here! is arpeggiation, a broken chord. Even though the tones go from bottom up and are sustained it's performed fairly slow. You wouldn't notate it with a wavy line, but write out full durations with long note values.
