After the tempo there are eighth notes that are equal to a quarter note and an eighth note with a '3' on top. What does that mean?
The 3 on top of a set of notes indicates a triplet. Triplet eighth notes would play three eighth notes in the time that you would normally have two. You may also see other divisions such as 5 and 7. Often the triplet number will have a bracket, but in some transcriptions there is just the number.
In some styles of music the eighth notes are not played with an even rhythm, such as "swing" and Hornpipes. The first eighth note will be held longer than the second. In some transcriptions an attempt is made to indicate the swung feel by using dotted rhythms, but the dotted rhythm isn't exactly what the feel is, and continuous use of dotted rhythm or triplets can make the music hard to read.
There is a common practice to transcribe the eighth notes in straight, even rhythm and make note that they should be played swung.
The notation in the example is showing that the first eighth note should be longer than the second, indicating a swing feel.
Using the triplet notation to indicate a piece should be swung is fairly common. In some cases the piece will just say "Swing" and expect the musician knows what that means. Occasionally you have to know the style of the piece to know that it is swung, as no indication is given.
Hornpipes are similar, that they are usually written in straight eighths, and it is expected that the musician will add the hornpipe rhythm.
2This is almost certainly swing, especially with the playfully note.– JosiahFeb 19, 2017 at 23:38
It seems to be pretty literal. For the duration of the instructions, a notated pair of eights are to be played with the first note as 2/3 of a quarter note and the second as 1/3. (Normally an eighth is 1/2 a quarter note.) Personally, I'd have written out the triplet, mostly to avoid such questions.
1It is a triplet isn't it? Feb 19, 2017 at 22:24
@theonlygusti No, it isn't a triplet, it's swing. Have a listen to some slow Basie if you think that swing = triplet. It isn't. Feb 20, 2017 at 9:27
@EJP but ttw says that he'd have "written out the triplet" - this confused me because I thought that what can be seen on the score is already triplet notation Feb 20, 2017 at 12:08
1The original post indicated an actual triplet feel written into the music. For swing, I'd just write two eighth notes and indicated "swing" in the performance instructions. Swing feel is a bit different from triplet feel (at least it seems to me when I hear each one). Swing is a bit more flexible and some interpretation is left to the performer. Triplets (ought to) really mean thirds.– ttwFeb 20, 2017 at 14:00
@ttw It's more complicated than this. Even in swing, you have different "swingness". When the duration of the eights is approximately 2:1, it's usually denoted using the triplet notation in the tempo marking, or by writing "Medium Swing".– yo'Feb 4, 2018 at 21:35
I would need more context regarding the specific example, but in many pop arrangements, this would indicate that the eight notes are to be "swung" not played "straight". I was just playing an arrangement last week which employed both "straight" and "swung" eighth notes. I also think there is a slight difference between eighth notes that are swung and the triplet rhythmic pattern employing a quarter note and an eighth note in one beat: in traditional music notation (e.g., in "classical" compositions)a meter such as 3/8, 6/8, 9/8 or 12/8 would be used if the composer wanted that ratio.
Literally it is an instruction to play pairs of 8th notes as triplets. In practice it is often used to mean 'Swing'. Don't. Swing isn't triplets. If you want triplets write triplets, or use 12/8 time. If you want swing write straight 8s and 'Swing'. Both live musicians and Finale/Sibelius know what to do.
As a drummer, I find this useful for figuring out the amount of swing - this is more of a light swing rather than a dot plus 16th. The same could be accomplished with text but in most intermediate music this seems to be the convention.– JosiahFeb 19, 2017 at 23:42
I've thought about this long, and hard. To me - and I play in swing bands - the beat is split into counts of 3, with the first part being twice as long as the third. That has to be equivalent to a triplet feel, and often at the top of a piece, that's exactly what's written. I call it the 'Humpty Dumpty' rhythm, for obvious reasons. So, where have I been going wrong for decades? Swing is 4/4 translated into 12/8, with any approriate tempo change. Right or wrong? It's certainly not dotted quaver/semi.– TimFeb 20, 2017 at 12:52
Swing is not mathematically fixed. At slower tempos it can be closer to a dotted rhythm. At faster ones it gets closer to triplets. It's different to a triplet shuffle. 'If I have to explain it, you don't get it'. There's some truth in that cliché :-) I think I can confidently state that the person who wrote that 'metric modulation' notation wasn't trying to be precise about the degree of swing required.– LaurenceFeb 21, 2017 at 0:45
1And I can also confidently state that in @Tim's swing band, he isn't laying down strict triplets. At least, he shouldn't be. That wouldn't swing.– LaurenceFeb 22, 2017 at 17:50