Rhythmic Cell Theory

[BarfanyShart]

Been filling my head with current hip-hop bass rhythms, and it gave me a theory idea at work. I'm sure it's not new, but I did the math, so here it is:

Like in harmonic cell theory where you analyze groups of notes by all of the intervals they share between them (major triad has a m3, M3, and P5, and minor triad has the same intervals, thus they are related groups of notes and work well together), you can think the same way with rhythmic patterns.

Take a bar of 4/4 in eight notes 1 + 2 + 3 + 4 + , and "count" it 0 1 2 3 4 5 6 7, so you can do math with it. Take a clave rhythm, and spell it [0,3,6]. You can re-order those same groups of rhythmic intervals around the down beat in two more sets, [0,2,5] and [0,3,5]. Then, if you don't start on the downbeat and use the same groups of intervals you get five more "modes" of this rhythmic cell [1,3,6] [2,4,7] [1,4,7] [1,4,6,] [2,5,7].

Pair one of the "root" cells with one of the modes in two bars of 4/4 and you can get [0,3,6][1,4,6,] - which is a bog-standard Trap 808 beat. But all of the root cells are Trap bass beats, and they mostly groove in two-bar patterns with the modes, because they share a common collection of spaces between notes.

Here are all of the 3-note root cells in 4/4, with all of the modes:


[0,2,5] [0,3,6] [0,3,5]

+modes [1,3,6] [2,4,7] [1,4,7] [1,4,6,] [2,5,7]



[0,3,4] [0,1,5] [0,4,7]

+modes [1,4,5] [2,5,6] [3,6,7] [1,2,6] [2,3,7]



[0,1,2] [0,1,7] [0,6,7]

+modes [1,2,3] [2,3,4] [3,4,5] [4,5,6] [5,6,7]



[0,1,3] [0,2,7] [0,5,6]

+modes [1,2,4] [2,3,5] [3,4,6] [4,5,7] [1,6,7]



[0,1,4] [0,3,7] [0,4,5]

+modes [1,2,5] [2,3,6] [3,4,7] [1,5,6] [2,6,7]



[0,1,6] [0,5,7] [0,2,3]

+modes [1,2,7] [1,3,4] [2,4,5] [3,5,6] [4,6,7]



[0,2,4] [0,2,6] [0,4,6]

+modes [1,3,5] [2,4,6] [3,5,7] [1,3,7] [1,5,7]

 

[Bob_Ross]

because they share a common collection of spaces between notes.

Indeed they do...which is one of the reasons that the early Total Serialists had such difficulty crafting their total serialist approaches into music that was obviously and audibly totally serial: Because unlike pitch class intervals, rhythmic intervals [sic] are undifferentiated when expressed as a linear subdivision. The space between the third attack of a measure and the fourth attack of a measure is audibly (and temporally) identical to the space between the fourth attack of a measure and the fifth attack of a measure, if your rhythm set is simply a uniform subdivision of the measure. Whereas the space between a G and a G# is identical intervallically as the space between a D# and an E, yet we're also easily capable of hearing those pitch classes as unique and un-identical.

Of course, the solution to ^^^that problem (for the Total Serialists at least) was to scale the rhythms so they mapped onto the ordered interval row in a more literal sense -- the distance/time between attack #3 and attack #4 would be greater or lesser than the distance/time between attack #4 and attack #5, depending on how the row was constructed -- and not just by some quantity of (for example) even 8th notes [edit: although that was one of the first solutions.]. This of course leads to wonderfully complex polyrhythms...probably not appropriate for building Trap 808 beats, but pantloads of fun for creating "organized chaos" that rewards deep listening because of an inate audible structure.

btw, cool project, thanks for sharing.

 

[BarfanyShart]

Indeed they do...which is one of the reasons that the early Total Serialists had such difficulty crafting their total serialist approaches into music that was obviously and audibly totally serial: Because unlike pitch class intervals, rhythmic intervals [sic] are undifferentiated when expressed as a linear subdivision. The space between the third attack of a measure and the fourth attack of a measure is audibly (and temporally) identical to the space between the fourth attack of a measure and the fifth attack of a measure, if your rhythm set is simply a uniform subdivision of the measure. Whereas the space between a G and a G# is identical intervallically as the space between a D# and an E, yet we're also easily capable of hearing those pitch classes as unique and un-identical.

Of course, the solution to ^^^that problem (for the Total Serialists at least) was to scale the rhythms so they mapped onto the ordered interval row in a more literal sense -- the distance/time between attack #3 and attack #4 would be greater or lesser than the distance/time between attack #4 and attack #5, depending on how the row was constructed -- and not just by some quantity of (for example) even 8th notes. This of course leads to wonderfully complex polyrhythms...probably not appropriate for building Trap 808 beats, but pantloads of fun for creating "organized chaos" that rewards deep listening because of an inate audible structure.

btw, cool project, thanks for sharing.

What you are saying about the undifferentiated nature of rhythmic intervals makes a lot of sense, because I was initially surprised that there were only 56 total variations of three-note rhythms over one bar of eight notes. I'm also delighted there are so few variations, because I can actually use this method to analyze what I'm listening to in real time, and even improvise bass grooves based on it.

In addition to pairing two one-bar cells (I'm still thinking in the context of hip hop, which is all about two-bar phrases with one down beat), I can also change the interval of the cells (make them quarters, sixteenths, or triplets instead of eighths) and then nest them within each other. A lot of the rap beats I'm listening to stretch that clave across two bars so that the [0,3,6] is describing quarter notes, and then another cell with a smaller interval is nested in the two-bar phrase somewhere to increase the complexity. The cool thing is that you can do this endlessly with the clave and it's related roots and modes and make usable Trap grooves - provided that you delete from the pattern any actions that fall on the other downbeats in the two-bar phrase (both beat 3's and beat 1 in the second measure), because those are the "avoid" beats for hip hop.

I'm guessing that any hip hop producer visually sees this pattern on their grids in the computer and intuitively understands the rhythmic relationships, but it has been interesting for me to come at it from another perspective and realize that the analysis works with cells. Berg probably didn't want his stuff to sound like Trap music, but maybe ...