I have a question about this term. I know obviously 'poly' refers to many. So, the obvious answer would be 'many rhythms'.
Is a polyrhythm, for example, a measure of 5/4 that can fit into 4/4, both sharing beat one? Or is it a measure of 5/4 played with 4/4 with the 1 beat of the 4/4 falling on the 5th beat of 5/4? I know both instances occur, and I know one is called a 'polyrhythm' and the other is called something else.
Polyrhythm would be the 5 beats in the space of four. Specifically, the 5 and 4 would have to be occurring at the same time. So beat 1 of 4/4 is the same as beat 1 of 5/4.
Polymeter is like a 5-beat meter and a 4-beat meter going on at the same time. They share the same beat value (if 5/4 and 4/4, then the beat is a quarter note), so you end up with this:
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Polyrhythm is a broad term for any 2 contrasting rhythmic patterns. I'll avoid going too deep with this because it can get pretty heavy but on a really basic level, a bar of eighth note rhythms and a bar of triplets playing simultaneously would be a polyrhythm.
The first example you gave of a bar of 5/4 fitting into a bar of 4/4 is slightly misleading because it wouldn't be a bar of 5/4 unless you were using something called metric modulation. What you are probably describing is a quarter note quintuplet. That would indeed be a polyrhythm.
Bainbridge perfectly described the second example you gave which is Polymeter.
If you really want to get into this stuff it's worth checking out Frank Zappa and pretty much any 20th/21st Century classical stuff from Stravinsky through to modern day. I'm currently writing a book on complex polyrhythms/tuplets for bass guitar. They are very rarely addressed and it's really hard to find good info. Hopefully I can shed a bit of light on them, even though there won't be too much interest.
Interesting. My only experience with (what I know to be) polyrhythms is from playing piano. Specifically, the right hand playing 8th notes while the left hand is playing triplets. I'm very interested to hear more about how this would pertain to bass guitar.
Not bass specific, but Ancient Traditions, Future Possibilities is a good book that addresses such rhythms: http://www.ancient-future.com/atfp.html
Really, looking for information on this stuff specific to bass (or any other instrument, for that matter) is a narrow-sighted way of research. The reason for this is because polymeter and polyrhythm is something that happens in polyphonic textures, and there are only a handful of individual instruments that can handle polyphony, the rest being monophonic. However, many monophonic instruments together can produce polyphony. While piano, guitar, and bass are all potentially polyphonic, guitar and bass are not (typically) individually used as such, on account of requiring two hands to produce sound in normal playing technique. Doesn't mean it's inpossible for sooo guitar/bass to manufacture polyrhythmic music, but you might want to think woth the mind of a composer/arranger when studying polyrhythm, as it commonly occurs in an ensemble. In other words, like bass and drums playing triplet latterns while guitar and keys play quintuplet patterns, or something to that effect.
I like to play two melodies or the harmony and melody with each hand. (Usually a tapping technique)I also write. So, I try to utilize separate rhythms between instruments.
Because you can tell how many repetitions of X and Y meters are required respectively in order to acheive a full cycle by their lowest common denominator. For the quoted example, a full cycle of 20 beats is required before the thing repeats. It does seem like a superfluous observation, but I suppose it is worth pointing out for those who do not readily see it.
But as music is commonly designated (since we write 4/4 and 5/4 on this forum and 4 over 4 or 5 over 4 in a proper time signature), we actually need the most common numerator, if one is stuck in that sort of terminology. (I realize that a proper time sig. does not have a true numerator and denominator.)
So, my post was a way of linking math and its lexicon to music and its lexicon. It's not always obvious how the two are intertwined yet presented differently.
Here's an example of where my post is a bit more useful, as the 4/4 and 5/4 example is fairly obvious as having the "all meet at the 1 again" after 20 beats:
King Crimson's Starless, from the Red album. The Middle section is in a moderate 13 (each time through is followed by a return to 4, but let's ignore that and focus on the 13 part). 13/4, or 13/8; doesn't matter - that's a transcription issue that is irrelevant to the point. The 13 is characterized by a sort-of minor blues, as in C min to F min to C min to G (G is where the 4/4 kicks in). It is 8 bars long. 8 x 13 = 104. The second time through the 13 patter, Bill Bruford comes in in 4/4, playing the wood block on the 1 of each 4. Thus, he's playing 26 bars of 4/4 over the 8 bars of 13. Thus truly, Bruford and the band do not all get back to hitting on the 1 until after 52 beats, since the least common denominator of 13 and 4 is 52. So, over the course of each run through the C min F min C min part, the whole band only hits one twice: on the very first beat, and on the 52nd beat. Beat 105 is where they go into 4/4 over G (probably G7).
Polyrhythm is a great tool for some bass/drum fills in certain styles, when the fill sounds like music is slowing down/speeding while staying natural sounding and keeping the same tempo.
For example, in reggae, many fills are formed around triplet half notes (3 notes over 4/4 measure). It sounds like it slows down and then goes back to main groove. Groovy, baby!
Or in blues in 12/8, you can throw in a 6 note pattern for a transition over a 12/8 measure:
IMO, it needs to be work out with the group beforehand, and not be used too often.
There's also multi-measure polyrhythms that are more complicated and less usable.
A great wikipedia article with some hypnotizing (not kidding) vidos in it.
A good exercise (especially while stuck in traffic)-
Tap out "4" 'beats' with one(1) hand
Tap out '5" beats with the other hand.
l1e&a2e&a3e&a4e&a5e&al = "5"
l1e&a2e&a3e&a4e&a5e&al = "4"
...also, try "3"-
l1e&a2e&a3e&al = "3"
l1e&a2e&a3e&al = "4"
l1-&-2-&-3-&-4-&-5-&-6-&-l = "6"
l1-&-2-&-3-&-4-&-5-&-6-&-l = "4"
However, people sometimes overlook certain topics when they're not related to their instrument. The main rhythmic concepts that are easy to relate to a bass without being in ensemble context are odd rhythmic patterns such as tuplets, nested tuplets and metric modulation. I found it really tricky to know how to count even relatively simple rhythms like quarter note quintuplets. I know that these are not strictly polyrhythms until mixed with a differing rhythmic layer but the learning of these uncommon feels can be worked on with bass quite easily. A lot of bass players would find these rhythms completely alien. Ask someone to play an 11 across 7 beats and you'll generally get a blank look. I'd like to do some videos and the book devoted to these odd rhythms and how to conceive or play them but I get the feeling most people will think "What the hell do I need to learn that for?" I suppose it'd be nice to just put something out there though. I dig them so maybe someone else will.
It can be used even in pop: http://www.youtube.com/watch?v=cA9gUspn6gc, listen at roughly 0:55 it uses 3 over 4 beautifully.
World music (west african, hindoustani, arabic, iranian, balkan, carribean) use polyrhythmic layers (and many other unorthodox rhythms/signatures) extensively. They are integrated so seamlessly and naturally into the music, that it sounds almost too easy :-)
Where do you start?
P.S. Just in case, I've tried to find a name for the 11 - tuplet.
Could possibly be: Undectuplets, undentuplets or hendectuplets.
African music is absolutely full of polyrhythms. I think a lot of that is down to the percussive nature of the music so it naturally promotes a more rhythmic way of thinking. I've seen African percussion groups with young kids improvising complicated polyrhythms with ease but it's all done very naturally. It's not forced or played for the sake of it. Just a part of the musical language.
That said, I wouldn't ever say that any of the big name composers of the 20th Century to modern day are simply using concepts for the sake of it. Stravinsky had a vision and using polyrhythm was simply a musical tool used in sculpting that vision. Xenakis and a few of the other mathematically obsessed guys are into the conceptual side of things for the sake of it but a guy like Zappa just 'felt' odd rhythm. He knew EXACTLY what the rhythms sounded like and used them because it gave him that rinky dinky feeling.
I personally get a kick out of the feel and tension of odd rhythms against each other. It was why I was so frustrated in finding some kind of help in learning how to nail them. Some people probably hate that tension but then again I'm probably a bit of a weirdo.
It would take a while to demonstrate how to go about playing them but the best way to get started is to understand the simple maths behind them then you can work out on developing a feel for that number by knowing how close it is to other more familiar rhythms.
As a basic example, an eighth note triplet has a certain feel. In terms of speed it is somewhere between an eighth note and sixteenth notes. You can feel the difference in pace by just alternating between them. Eighth and Sixteenth notes have a kind of 'square' feeling and triplets are more of a rolling, circular feel.
If you go one step further, an eighth note quintuplet is between an eight note and an eight note triplet. Think eight note is 4, quintuplet is 5, triplet is 6.
A eighth note septuplet (7) is next and in between a triplet and a sixteenth note.
Try playing a single note pedalling between these rhythms. Eighth note, eighth note quintuplet, eighth note triplet (sextuplet), eighth note septuplet, sixteenth note. The speed of the notes gets quicker with each grouping.
That's one level of accuracy. The next level up is 9,11,13,15. They are between the rhythmic groupings I just mentioned before (4,5,6,7,8).
Once you've nailed all these groupings at both eighth and quarter note level, you can move to putting them in the space of other beat groupings. eg. 5 in the space of 3 (5:3).
11 in the space of 7 just takes this concept a bit further but it's the same principle and method for getting used to the feel.
David Ocker (Frank Zappa's copyist) helped me out loads in getting used to the feel of these. He'd played a clarinet feature in one of Zappa's tough orchestral pieces (Moe and Herbs Vacation) with the London Symphony Orchestra and explained how to count the 15's and 17's he'd been given. Ironically, the piece started as a duet for bass and drums. So I guess it kind of relates things to bass.
Basically, 15 in the space of 16 (or 8 as it should be written) is felt as slowed down sixteenths. (Sixteenths would be 16:16).
That probably all sounds very complicated or possibly even nonsensical without demonstrating it but hopefully you get the idea.
I'm big fan of György Ligeti with his complex polyrhythms, or Karlheinz Stockhausen, or Samuel Barber.
The following link should be interesting to you:
A Pedagogical and Analytical Study of Dušan Bogdanović’s Polyrhythmic and Polymetric Studies for Guitar
As an added extra here is a little chart I made for a dissertation I wrote on the music of Frank Zappa. I described it in terms of rhythmic layers of accuracy. Each different layer requires a little more accuracy. The first number of the ratio can be simplified as being a division of a whole bar. The second number is a little like the denominator of a time signature and I use that as a guide for the rhythmic accuracy layer. The ratio is often used for labelling the rhythms in written music.
1:1 - Whole Note
2:2 - Half Note
3:2 - Half note Triplet
4:4 - Quarter Note
5:4 - Quarter Note Quintuplet
6:4 - Quarter Note Triplet
7:4 - Quarter Note Septuplet
8:8 - Eighth Note
9:8 - Eight note nonuplet
10:8 - Eight note quintuplet
11:8 - Eight note 11-tuplet
12:8 - Eighth note triplet
13:8 - Eighth note 13-tuplet
14:8 - Eighth note Septuplet
15:8 - Eight note 15-tuplet
16:16 - 16th note
17:16 - 16th note 17-tuplet
18:16 - 16th note nonuplet
19:16 - 16th note 19-tuplet
20:16 - 16th Quintuplet
21:16 - 16th note 21-tuplet
22:16 - 16th note 11-tuplet
23:16 - 16th note 23-tuplet
24:16 - 16th note triplet
25:16 - 16th note 25-tuplet
26:16 - 16th note 13-tuplet
27:16 - 16th note 27-tuplet
28:16 - 16th note Septuplet
29:16 - 16th note 29-tuplet
30:16 - 16th note 15-tuplet
31:16 - 16th note 31-tuplet
32:32 - 32nd note
Notice how I half the tuplets where I can so you can see what family they originate from. Quintuplets have the same kind of feel whether quarter, half, 8th or 16th note in nature. Same with triplets, septuplets etc. Also notice as the 2nd number of the ratio goes up, the closer and harder it is to differentiate between the adjacent rhythms in the chart. If you were to play through each of these ratios in order from the top you would hear a gradual increase in superimposed tempo over the background until you finished with 32nd notes. The only reason I wrote up to 32nd notes is because 16th note triplets, quintuplets and septuplets are relatively common and in between the 16:16 and 32:32 ratios. I'm fully aware 31:32 rhythms are about as common as pink dog sh*t.
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