Time signatures (I prefer the word meter) are a little bit of a slippery subject when you're talking about jazz music— which may be played in a different meter or time feel than is indicated on the original chart— or when discussing any music not played from a written arrangement.
In those situations, the meter is, effectively, what is apparent from listening to it. We determine that by counting, and by determining whether there is a two-note (straight 8th) or three-note (triplet feel) subdivision. There are also stylistic conventions associated with certain meters, and broader conventions in all of music. And there are meters associated with certain rhythm section or drum grooves.
A tune like All Blues may be written in 6/8 in The Real Book, or wherever, but it's typically played with a jazz waltz feel— 3/4 time— the performed drum rhythm is effectively in 3/4. Two measures of 3/4 waltz feel = one measure of 6/8 on the lead sheet. It has that famous little vamp figure, which can be counted in 6, or as two measures of 3.
Making a drum transcription of it— where the drummer is playing a regular old jazz waltz— it would be stupid to try to write out a in 6/8 with an 8th note as the main pulse just to agree with the lead sheet. You could write it in 6/4, but to me 6/4 suggests a 2+2+2 or 4+2 phrasing. I would at least put a dashed imaginary barline in between measures.
With a drum transcription, we're giving a representation of what the drummer played, with the time signature reflecting the phrasing of the drumming performance. If a tune is written in 4/4, but the drummer plays an persistent triplet feel* through out, why not write it in 12/8?
* - Not simply swing 4/4 with a lot of triplets.
Time signatures and style indications also have certain implications for the performing musicians. 12/8 indicates a triplet feel. 8/8 means you're playing in 4/4, but they want strong 8th notes all the way through. 6/4 suggests 2+2+2, usually not 3+3. 6/8 may suggest an Afro-Cuban feel. Those may be the actual time signature of the written chart, or they may be given in the style description— like a tune written in 4/4, with “12/8 feel” indicated at the upper left of the page.
If you decide a piece is counted in 4, with a straight 8th feel, how do you decide what kind of 4? Technically it could possibly be 4/4, 4/2, 4/8, 4/16, 4/32, and so on. The answer is: it's 4/4.
I don't believe I've ever been handed a piece of music in 4/2. Usually, to me, #/2 meters suggest some fast activity in the equivalent #/4 meter. A piece with a moderato time feel, but with a lot of double time activity in the rest of the accompaniment, could be assigned a #/2 time signature.
I've also never seen a 4/8 in the field, but it suggests an interpretation of 2/4 with persistent 8th notes. For example a lot of Brazilian arrangements are written in 2/4, with 8th notes as the beat, and a lot of 16th note activity. It wouldn't be unreasonable to call that 4/8, though I've never seen it done. Sambas also emphasis the 2 of the 2/4, so maybe that's not a great idea; bossa novas, which have a 4 feel, would be better candidates for that.
4/16 and 4/32 would be used strictly for connecting complex changing meters. If you see them as the main ongoing time signature in a piece of music, it means that the composer hates you, and you should pack your drums and leave.
I'll get deeper into that topic another time— what different time signatures suggest to me as a drummer.
So there's more than one right answer, often, depending on what aspect you're considering— the paper chart, the general style of the performance, the drum groove. Sometimes there's just simple ambiguity about whether a tune is best counted in 4 or in 2. You may also have to consider rhythm activity in the accompaniment, and what other meters are used in the same piece.
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