6 Bassline Strategies

I had the privilege recently of writing bass grooves for two awesome bands, Zaska and Mescalito. When I pondered over the lines I’d composed, I noticed certain techniques recurring. Today, I’ll briefly explain each technique. Plus I’ll link to a nice example of it in the reggae, funk, jazz or hip hop repertoire.

(If you want to hear the actual lines I wrote, come see Mescalito on March 24th in the Opium Rooms supporting Vernon Jane, or on April 14th in Sweeney’s, or see Zaska’s single release on April 23rd in the Sugar Club!)

1. Space

Silence can be one of the most attractive features of a cyclical bass groove. A gap, whether for half a beat or a full bar or more, lets other parts emerge, particularly drum hits. (Cutting off a bass note right on a snare backbeat is a cliche example.)

A short gap works as punctuation, giving the groove more of a shape, and therefore, it seems to me, more physical catchiness/danceability. For example, the “Stalag” riddim (which you may know as the groove for Sister Nancy’s “Bam Bam”), here underpinning Tenor Saw‘s hit “Ring The Alarm”…

 

Strat 1 Stalag.png
The “Stalag” bassline

Here’s another awesome 1-beat-ish gap in a reggae groove (beat 3 in the 2nd bar):

 

 

Strat 2 Sly & Robbie
Robbie Shakespeare’s line on “Computer Malfunction”

Longer spaces have a call-and-answer effect, as in this afrobeat groove…

 

Strat 3 Soffry.png
Leaving space for call-and-response (I’m not certain that this is really where the 1 is, by the way…)

2. Funky Melodic Cells

Like any other musical part, a strong bassline should be melodic. In a funky context, though, the tendency is usually towards blues melody rather than diatonicism. Out of the pool of blues notes I discussed a while back, a few 3- or 4-note cells emerge that are by far the strongest for constructing basslines. For example, 1 2 b3, 1 6 b7, 5 6 8 9, and the definitive cell for funk basslines, 1 5 b7. A catchy hook (i.e. with an intriguing rhythm) made from one of these cells can easily be a strong enough bassline to carry a tune.

 

Strat 4 Holland.png
The opening bass riff on “Not For Nothing” uses the 1 6 b7 cell

 

Strat 12 Hunter
The basic groove (coming in around 0:32) played by Hunter on 8-string guitar, using the 1 5 b7 cell

Here’s an example of a hook-y bassline built off the 1 2 b3 cell followed by a sequenced, retrograded version (that is, the first three notes are then transposed up a fifth and reversed in order).

 

Strat 5 ACR
Slap riff from A Certain Ratio’s “Waterline” (0:21)

More important than the motivic derivation, though, is the space in every 2nd bar which is used for call-and-response (in the form of improvised fills). Check out that nasty double-tracked slap sound too.

Contour

Another important aspect of that line is the clear direction of movement – up and then down, quite simply. A clear, uncomplicated contour like that strengthens the riff. For instance, the ascending bassline off the classic Scofield/Metheny collaboration…

Strat 6 Swallow.png
The A section groove for “Everybody’s Party”, with an ascending contour in each bar

As an aside, I would bet that this groove and the Dave Holland groove were both originally notated using 8th notes where I have 16th notes. Jazz musicians like reading 8th notes. It’s purely a notation decision with little or no musical impact, but I think 16ths are a more accurate reflection.

Octave Jumps

Steve Swallow’s bassline ascends a minor pentatonic scale before jumping from the b7 (Eb) back down to the root (F). We can imagine a variation of the where the scalar ascent continued, so instead of a jump down a minor 7th we would have a step-wise movement to the higher F:

Strat 7 No Displacement
Steve Swallow’s groove without the octave displacement at bar 2

The played line uses octave displacement of what would otherwise be step-wise movement. Another example of this is Marcus Miller’s nifty elaboration of the classic “Red Baron” groove (composed originally by Billy Cobham).

 

Strat 8 MIller.png
Octave displacement of step-wise movement

The Meters’ “Funky Miracle”, here sampled by DJ Premier for an early Gang Starr track, features both a (pentatonic) stepwise melody and then its octave displacement.

 

Strat 9 Meters
Octave displacement of expected high Ab

Even simpler than octave displacement of step-wise movement, is a plain leap of an octave. This James Brown sample (1973’s “Blind Man Can See It”) has a downwards octave leap to the tonic note:

Strat 10 Brown
Sampled bassline used in “Funky Technician”

(Note also the clear contour and the use of space, albeit with the note ringing out rather than silence.)

Here’s an upwards octave leap from the IV note. (Fred Wesley and the Horny Horns’ “Four Play”, sampled by DJ Premier.)

Strat 11 Wesley.png
What a rugged groove! Premier’s sub-bass and scratching helps of course.

5. Circularity Via Pick-Up

Emphasising the cyclic nature of a groove creates a hypnotic, trancy effect. One way is to use a phrase that starts before beat one. I read somewhere that landing on, rather than starting from, the downbeat is a characteristic of African-derived music. That’s surely a huge generalisation, but it does tie in well to how bebop improvisation and alternate paths are based on directionality towards target chords.

Starting basslines on a pickup in this way is not a very common technique, but here’s a nice example:

 

Strat 13 Headhunters.png
Paul Jackson’s line on “God Make Me Funky” (drops around 0:50)

6. Circularity Via Dynamic Balance

This is a concept I picked up from Steve Coleman’s writings, but I’m not at all qualified to say much about it. As I see it, it’s a characteristic of African-derived rhythms such as clave… basically, the quality of having points of rest alternating with points of tension in a syncopated rhythmic cycle, producing forward motion (“dynamic”) and also a self-contained, universal circularity (“balance”). Hmmm, my prose is not really up to the task here! Anyway, do we find clave-like rhythms in the funk repertoire? Of course we do, in these classic basslines:

 

Gonna sign off here! Hope you picked up some groove wisdom from all of that. Like, follow and share!

Maximally Even Rhythms Part 2

In the first part of this series, I defined “maximally even” rhythms. I explored what could be done with one such rhythm, the 3 3 2 grouping or “Cuban triplet”: warping it into 3:2, using different modes (different placements against the downbeat, also called rotations), and creating larger patterns from it. I also went into detail on the mathematical nature of the rhythm.

x/((x/2)-1)

This formula gives the total amount of notes and the amount of inner groups for all the divisions I’ll discuss, including the Cuban triplet.

x = 8
8/((8/2)-1) = 8/(4-1) = 8/3 (Cuban triplet groups 8 units into 3 sections)

The satisfactory divisions obtained from this formula require x to be a multiple of 4. So today we’ll be looking at:

x = 12
Division: 12/5 (6/8 clave groups 12 units into 5 sections)

x = 16
Division: 16/7 (Partido alto groups 16 units into 7 sections)

x = 20
Division: 20/9 (20 units grouped in 9 sections)

Sorry about all the numbers. Let’s start with 12/5. It has two deceptively similar solutions, one of which, 2 2 2 3 3, is lopsided because all the short notes are clumped together (and so the long ones are too, at the end). Better to intersperse the 2s and 3s, arriving at the maximally even solution: 2 3 2 2 3.

ME 1 6 8
Sectioning 12 8th notes (two bars of 6/8 time) into 5 maximally even groups

This rhythm is known to jazz musicians as 3:2 6/8 Afro-Cuban clave. The most important word there is “clave” meaning “key” rhythm of Cuban music. This rhythm can be traced back to West Africa where it is a hugely important structure in many complex drumming/dancing/music traditions. I know nothing about these, but articles like this show how musicologists have tried to describe them. Willie Anku is an important figure in this research.

 

6/8 clave can be warped from a triplet to a sixteenth grid (subdivision) to create son clave and rhumba clave. That is, the relationship of the attacks to the pulse is approximated using a new subdivision of each beat. So, notes that were on the beat (beats 1 and 4) stay on the beat.

M E 2 Warp Son
Warping (similar to quantising in a MIDI program) from 6/8 clave to son clave
M E 3 Warp Rhy.png
From 6/8 clave to son clave

Rhumba clave is closer to the 6/8 original than son clave, but this is only a mathematical detail – both versions are fundamental to Cuban music, with son clave’s more stable placement of the third attack proving crucial to how it is used. Son clave and rhumba clave, by the way, are also present in West African music. They are not maximally even divisions but they keep the strength of 6/8 clave, and indeed music built off them tends to strongly reference the triplet feel of the 6/8 clave and to warp between triplets and sixteenths.

Gerhard Kubik, who I quoted extensively in my blues discussion, pointed out that the presence of rhythms such as 6/8 clave anywhere in the world indicates a connection to Africa. This is because the mathematical nature of the pattern cannot be altered without it losing its (maximally even) properties. So, unlike words, gestures, melodies, lyrics, etc., these rhythms spread between cultures without changing in any way!

Actually I’m glad I pulled out my copy of Africa and the Blues to check that, because in it Kubik lists all the rhythms I’m discussing today as unambiguously African. His name for them is “asymmetric time-line patterns” – asymmetric because each rhythm breaks into two unequal halves, e.g. 3 and 5 for Cuban triplet or 5 and 7 for 6/8 clave.

M E 4 Asy.png

Okay, here’s a riff I’m working on at the moment with my band Mescalito, which has just reunited! (First gig on March 24th in the Opium Rooms, come on down!)

After composing the riff, I discovered that it is derived from a mode of 6/8 clave (actually its bell pattern version, bembe, where the 3s are filled in with (2 1)s), modulated into 3/4 (so 3 beats of 16ths rather than 4 beats of triplets). This modulation does not affect the cyclic strength of the pattern because it still comes back to the beat at the top of each cycle. There is no polyrhythmic off-and-then-on energy.

M E Riff 1.png
The numbers show where the original 6/8 clave fits over my riff

Let’s move on quickly to the last two rhythms in the series. The maximally even division of 16/7 comes out like this:

M E 5 Part
And this is a crucial rhythm in Afro-Brazilian music. It is called partido alto and can feature as a guitar comping pattern or as a guide for bass and drum accents. I detected a rotation of partido alto in another new Mescalito riff:

 

M E Riff 2.png
This is rotation shifts the rhythm earlier in time by one 16th – I mark where it starts with a nifty little arrow above.

Note how using mostly only two pitches mimics the low-high/kick-snare energy of a drum line. Also, one nice thing about this riff is the placement of the lower B notes. They form a neat clave-like syncopated rhythm of their own.

Partido alto can be simplified to a grouping of 6 5 5 by hitting only some of its notes.

M E 6 (5 5 6).png
Isolating a 5 5 6 rhythm in partido alto

5 5 6 is the maximally even solution of the division 16/3 – a very important result for techno, funk and other genres that might want to spread a motif three times over a bar of 4/4 in sixteenth notes. I often use it. It’s also the distinctive comping pattern of Tito Puente’s “Oye Como Va”, mapping out the first of each pair of hits.

M E 7 (5 5 6).png
Chord hits for Oye Como Va

 

Okay, to finish today’s post, let’s look at the last one in the series. I’ve never heard anyone play this rhythm, although Gerhard Kubik mentions it. I think it carries a lot of the balance and power of the others. It’s the maximally even division of 20/9.

M E 8 Quint.png

The 20 units can accommodate different pulses – this example uses a 4 beats of quintuplets.

But 5 beats of sixteenth notes is also possible.

What have we found in all the rhythms so far? They’re asymmetric, made of a pair of 3s separated by an odd number of 2s, and we’ve seen them all in a rotation in which the only beats landed on are 1 and 4. This relates to what Steve Coleman calls “dynamic balance”. All of these rhythms have points of rest and, at the opposite “pole” of the cycle, tension.  There is an elegant alternation of rest and tension that expresses itself in the forward motion of the rhythm.

Okay better sign off soon, though there are obviously many avenues opening up from this kind of analysis. One cool idea I want to explore more myself is creating new bell patterns by simply crashing together all or part of these rhythms. The new rhythms mightn’t be maximally even but they could retain the flow of the originals even in strange time signatures.

Last thing I’ll say is a warning. This kind of analysis is incredibly reductive because it leaves out the cultural/political/social/historical meanings of these musical structures. I’m not informed enough to deal with those, and I apologise for that! Actually, I intend to study Afro-Cuban music for a project I’m envisaging, based on exploring very large, interlocking rhythmic forms. Hopefully you’ll see some of that research in future posts (writing that should motivate me to do it!).

Thanks for reading! Please follow the blog if you like it!

Enough With The Scales

Today’s post is not research but opinion. I’ll keep it short, as I’d like it to be a starting point for discussion. You are invited to comment!

I’m going to argue that chord-scale theory, the conceptual framework used in jazz college courses world-wide, is flawed even as a teaching tool. I swallowed it whole in jazz school, and frankly I think I wasted years trying to make music according to it.

The basic idea, of matching scales to chord symbols, is useful and I’m glad I learned it early. But it can’t be your only guide. I’m with the widespread view that learning bebop is key to navigating changes. Chord-scale theory is bad at explaining what bebop and bebop-influenced players did. (Music made by people who learned chord-scale theory at jazz school, unsurprisingly, fits it better. In fairness, the theory has enabled some great music and great advances in playing.)

Is chord-scale theory a useful simplification for teaching? I believe it loses too much in return for too little understanding.

(By the way, I’m going on my memories of ensembles and courses, and books such as Mark Levine’s The Jazz Theory Book. I may not be completely fair to them. But I’m talking about the overall results of this teaching system.)

The first thing chord-scale theory misses out on is the idea of key. Jazz until the 60s (and most of it after that) was in major or minor keys (with a lot of room to manoeuvre of course). Playing in key, whether diatonically or bluesily, is a basic element of jazz improv and melody. Yet this can’t really be expressed in terms of chord-scale theory. Sure, basic chord progressions like I IV or II V I, when explained with the theory, do yield the 7 notes of a major key. But that’s an unproductive way of restating that chords can belong to a major key.

It’s not that chord-scale advocates were against the traditional view of keys and chords. Rather, they took it as given, and tried to progress from it. Unfortunately, their supplementary ideas are taught as a complete system to beginners or rock-oriented musicians who don’t understand functional harmony.

So, in the theory, chords are reduced to signposting 7-note scales/modes – supposedly a pool of equally “valid” tones. This misses out on a lot. All the inner organisation of chords is de-emphasised. That’s a massive melodic resource thrown away. The crucial functionality of dominant chords via voice-leading resolution of their tritones becomes a vague notion of “avoid notes”. The whole lovely world of functional chord relationships within a key, as well as its developments via blues and alternate paths, is defused and obscured.

To be precise for a moment… it’s valid to try make a new system to deal with e.g. extended, suspended and altered chords. But chord-scale theory fails to look in detail at directionality, acoustic effects, or any other audible aspect of those chords.

For another example, the all-important fact that melodies inescapably suggest chord progressions (which needn’t be the accompanying chord progression), is barely glimpsed in Mark Levine’s famous textbook. I went back and checked just there.

… By the way, check out this funny quote: “Why does the blues scale – with so many “wrong” notes – sound so right when played over a blues? Your guess is as good as mine.” Cheers Mark, I’m only after spending 30 quid on your book.

518mumyzhal-_sy344_bo1204203200_
His book

Sadly, this lack of specific talk on harmony means that African-American contributions may not get their due. Let me explain that. Going beyond chord-scale theory means recognising the importance of European classical concepts in jazz: tonality, chord- and non-chord tones, etc. But, observing those also forces you to observe when they don’t apply, which is often – so then you have to face African-associated forces like timbralism, pentatonicism, parallelism and alternate paths. Chord-scale theory completely flattens all this cultural/historical stuff out.

More abstractly, it doesn’t invite investigation into the underlying structures of music such as symmetry, the harmonic series and maximally even sets.

If I had to find something genuinely progressive in the theory, it’s the possibility of getting away from relating tones down to the root of a chord, and instead imagining a harmonic space to be freely divided. I like that.

Am I asking too much from a learning aid for students? Well, I think a lot of people, like I did, come to music courses without very clear ideas, searching for meaning which they sense is somewhere in the music. It’s insulting to put anything but the best ideas before anyone sincerely looking for knowledge.

I’m starting to get rather idealistic. Okay, I think chord-scale theory is popular because it is a shortcut allowing students to quickly start playing and interacting rhythmically while avoiding wrong notes, which is cool. The problem is they will probably play bad melodies.

(I did.)

What are your thoughts?

Maximally Even Rhythms Part 1

Today I’m investigating the simple maths behind some of the deepest rhythms of groove music!

The notes of a looped rhythm can be imagined as dividing up the loop into sections.

Not Displaced
A 1-bar cycle, 6 8th notes in length, evenly divided into 3 groups of 2 8th notes’ length each.

(There is no distinguishing feature in this cycle that makes it 6/8, by the way… unlike the rhythms we’ll be focusing on later which do have a shape. This one could equally be in 4/4 or 1/4.)

This version does the same thing, except displaced an 8th note from the pulse.

Displaced

This rhythm is even. Each of its 3 parts are equal in duration (2 8th notes). But, many divisions can’t be done evenly, for example dividing 8 8th notes into 3 sections.

In arithmetic, this division would either result in a fraction 8 / 3, with the value approx. 2.667, or need a remainder: 2 remainder 2.

ME 2 Even
Fraction: 3 groups, but the length of each group does not fit the 8th note subdivision.
ME 3 Remainder
Remainder: There are now 4 groups due to the need for a remainder of 2.

The only way to have three groups of whole 8th notes in this cycle is to have different-sized groups:

ME 4 224 125
Division of 8 notes into groups of 2 2 4 or 1 2 5

Other solutions would be 1 3 4 or 3 3 2 or 1 1 6.One of these mixed-sizes solutions has special properties, though. It is “maximally even”, meaning it’s the solution most similar to equal-sized groups. For divisions, like 8/3, that can’t be done evenly, the maximally even solution requires groupings of two different sizes. In this case, groupings of 2 and 3. So the maximally even solution to dividing 8 notes into 3 groups is…

 

ME 5 3 3 2
3 3 2 grouping AKA Cuban triplet AKA tresillo

It makes intuitive sense that the division most similar to 2.667 2.667 2.667 would involve a mixture of 2s and 3s – the whole numbers most similar to 2.667.

Is there anything musically special about this division? Well, yes. It is used almost universally in rock, pop, and dance music. Its closeness to the even division of 3:2 can confuse, and I’ve seen student musicians write down one while meaning the other. You can often hear rock, reggae or folk bands hesitate between these two rhythms, perhaps playing something between the two. More intentionally, Afro-Cuban musicians make use of this ambiguity regularly.

These examples show it’s possible to lean or warp between rhythms containing the same amount of notes per beat or bar, even if they have different subdivisions. This is because West African cultures view rhythms as divisions, not additions.

By contrast, Middle Eastern or Indian musicians would be more likely to view a Cuban triplet rhythm as a group of 3 units, followed by 3 units, followed by 2 units. That’s called additive rhythm because, conceptually, different groupings are added on to each other to form sequences. From an additive perspective, the analogue of a Cuban triplet in a triple subdivision would be use the same sequence: group of 3 notes, a group of 3, and a group of 2:

ME 6 Karnatic Style

From the West African perspective, though, the closest thing to a Cuban triplet in a triple subdivision would be the rhythm that divides 2 beats into 3 parts:

ME 1 3 over 2

So, whereas South Indian musicians excel at playing the same sequence at different speeds against a pulse (like the first example), African and African Diaspora musicians are adept at warping rhythms into a different subdivision, creating tension between the resemblance of the rhythmic shape (same average rate of notes) and the change in the flow of the subdivision (e.g. triplets feeling more rolling/circular than 16ths).

To move on: one important thing about every “maximally even” rhythm is that they are cyclical – there is no particular start or end. Like modes of a musical scale, any note can be imagined as the start of the pattern:

ME 7 3 Variants
Modes of the Cuban triplet: 3 3 2 (original), 3 2 3, 2 3 3

But unlike modes of a scale which must have a root note, cyclical rhythms needn’t have a note on beat 1, which opens up 5 more variations:

ME 8 5 Variants
5 modes of Cuban triplet that don’t land on 1.

As I unfortunately don’t have all week to write each weekly post here, I’m gonna spend the rest of today’s piece focusing only on these rhythms. In part 2 I’ll cover maximally even rhythms over 12, 16 and 20 notes, including Afro-Cuban, African and Brazilian rhythms. For now, let’s find applications for the variations of 3 3 2, and maybe make some general observations.

All of these rhythms are short, and so when I’m composing or improvising, I find they work well as a sort of basic pulsation within the groove. In a 16th-note-based style like say techno or hip hop, one or more of these rhythms can underlie all the other rhythmic activity.

In this song that my sister happened to play as I’m writing, the underlying cell is the Cuban triplet 3 3 2, but it is developed into 2-bar patterns by substituting two rests or two quarter notes.

 

ME 2 Fixed
Different rhythms in “Desire” with the times they enter

The third of those 2-bar patterns has been used in countless dance and pop-dance tunes.

In these contexts, the cymbal (and usually a 4/4 kick) provides a strong skeleton of 8th notes that the syncopated rhythms can interlock with. Interlocking is, I think, another essential component of groove music. It’s a rather large topic to try and define, but I would say that when two cyclical rhythms have some notes together and other notes a 16th note apart, they will feel interlocked. Here’s an example using a riff from my rock band, Mescalito.

Methuselah Riff
Interlocking rhythms. Notes that are together are indicated by the lines.

Onto the other variants; here’s a 3 2 3 division. This might be the least common of three variants that hit the downbeat. This example is by the Ben Prevo Band, with me on bass and Dominic Mullan playing the pattern on drums. The song is Ben Prevo’s composition, “An Udder Blue”.

 

 

ME 11 Prevo
The drum pattern on “An Udder Blue”

Check out how this example is over 4 beats of swung 8ths rather than 2 beats of straight 16ths – still 8 notes in all, divided into 3 groups. It’s important to be able to recognise fundamental rhythms no matter that they might be notated differently or felt with a half- or double-time pulse, or swung. The next example is also over 4 beats.

 

ME 12 Wilkinson
The basic accents of the drumline in “Too Close”

The main accents in this d’n’b tune’s drumline (0:47) are the 2 3 3 grouping, in 8th notes. But the drumline as a whole is filled with many 16th notes. So, the energy of the maximally even division operates on one frame (8ths) with other rhythmic information in a denser frame (16ths). Take a moment if you like to feel how those interact in the song. To me, there’s a floatiness caused by the powerful but slow 1-bar cycle of the 2 3 3 (which suggests a half-time feeling, actually, and is used by itself to introduce half time at 1:53) mixed with the twitchy intricacy of the 16ths.

There’s a basic transformation that can be applied to all the maximally even rhythms I’ll talk about today and in part 2. I think of it as making a “bell pattern” out of the rhythm, because it is the technique used to turn 6/8 clave into bembe, the Cuban 6/8 bell pattern. However this is probably confusing use of language as all of these rhythms can be played on a bell. A proper name for this rhythm is cinquillo. Quite simply, the 3s in the rhythm are filled in to become (2 1). So 3 3 2 becomes 2 1 2 1 2. This is also a maximally even division of 8 into 5 parts.

ME 13 Bell
Turning the Cuban triplet into cinquillo.

Notice that this is only one note off from being a 3:2 son clave.

ME 14 Son in 16ths
The only note different between the bell pattern and son clave (notated in 16ths)

We’ll see more of how maximally even rhythms can be transformed into each other in part 2.

 

In Megadeth’s new track “The Threat Is Real”, the kick drum line at 0:59 is the same as cinquillo: 2 1 2 2 1. (The guitar chug follows this line too, with one extra note where the snare hit is.)

ME 15 Megadeth
Drumline at 0:59 of “The Threat Is Real”

I won’t try hunt up examples of all the other variants, because I think you get the idea. The main conclusions we can draw are: these rhythms can exist at half or double speed against a given pulse or subdivision; they can be warped into similar rhythms in different subdivisions (even the swung 8ths rhythm above is arguably warping, from straight 8ths into a triplet grid); they can be constituents of longer patterns like the dance-pop bassline grouping 4 4 3 3 2; and they are a very rich source because they can be spun around in all their modes, filled out and interlocked with other rhythms.

To finish, here’s a spontaneously improvised maximally even division of 8 into 3 groups – one of those that doesn’t fall on beat 1. This is from a bootleg of Mescalito playing live a few years back. I’ve included the build-up because I like how the pattern slowly asserts itself in my bassline, fully emerging at 0:48. Like the d’n’b example, this pattern is in 8ths but the rest of the band play 16ths.

 

ME 16 Mescalito Improv
Improvised bassline off mode of cinquillo

Thanks for reading! I think next week I’ll get back to my discussion of negative dominants and alternate paths, but stay tuned for a part 2 of this article where I’ll get into more maximally even rhythms in meters up to 5/4. As always, feel free to comment below!

Alternate Paths on a Blues

Today I’ll use “negative dominant” progressions to solo on a jazz blues. These ideas are from Steve Coleman – and I’m not the only one to have tried to interpret them. I had to cut them down a lot, so I recommend you read his stuff, with the warning that it is hard! After I do my best to explain the idea, I’ll show how these movements are present in typical jazz harmony, then play through entire alternate chord progressions built off them.

To understand a “negative dominant” progression, we should consider a traditional dominant to tonic cadence.

Trad 2

The tritone B F (actually tritone plus an octave in this voicing) resolves to C E, a major 3rd (plus an octave). The chord moves down a 5th (or up a 4th) – G7 to C. These resolutions are the basis of mainstream jazz harmony… but not the whole story.

Although this cadence happens all the time, spelling the notes of a plain V I progression makes a very corny melody. Jazz musicians have long avoided that sound in favour of altered and substitute chords.

Steve Coleman has characterised the harmonic/melodic techniques used by Charlie Parker to avoid the V I sound as “alternate paths” or “invisible paths”. He brilliantly uses symmetry to explain how they are the “dark side” of a normal V I. (He is also brilliant at coining names for these things, evidently.)

Symmetry emerges from mirror images.

6317943810_22fa0077ed_b

What would be a mirror image of a V I? I can “reflect” it by inverting it, for instance around the axis note D. (For the nerds, this is because the C major scale is symmetrical around the note D.) So, every note in the original progression is replaced by one equally distant to middle D…

Inv Loran Fixed.png
The process of reflecting each chord of the original progression. G7 turns into D-6, C turns into A-.

… but on the opposite side of the D axis note. Below D if it was originally above, and above D if it was originally below. E.g., the B in the G7 ends up as the high F in the D-6.

Inv Full Progs.png
Comparing the original progression with its reflection in bar 2.

What is the new progression? D-6 to A-. It has a tritone resolving to a major 3rd (B F to C E, again separated by an additional octave) but the chord moves up a fifth, not down (D-6 going to A-, not G7 going to C). And both chords are minor, not major. Steve Coleman calls this a “negative dominant” resolution to A minor.

This by itself might explain how a lot of II V licks seem to be more tonally weighted on the II- than the V7. A melody over a II V I could imply a II-6 to VI- movement (negative dominant resolution) rather than a V7 to I movement. Although the chord tones are almost the same, the mental model and the tonal gravity would be different.

Such melodic shapes can be shifted to other positions and still retain their cadential power. This is due to the phenomenon of borrowed chords, or modal interchange in jazz speak. So, instead of the negative dominant that fits in the C major scale (D-6), we could use the one that fits C minor, i.e. F-6. It still resolves down a fourth (because it’s a negative dominant), but with the distinctively pretty sound of landing on a tonic major: F-6 Cmaj. Coleman notes that this IV-6 sound is often used over a V7 chord, creating a “dominant 7th complex” notated V11b9 (G Ab B C D F). The darkening substitution of D-6 by F-6 can be re-applied to the F-6, changing F-6 to Ab-6. The resulting bVI-6 sound is also used on dominant chords forming an altered V7#5b9 chord.

So, without going any further into symmetry, we have three melodic-tonal centres that can be used as dominant chords to target a tonic chord: II-6, IV-6 and bVI-6, targeting I. Crucially, these negative dominants are present as upper structures in most functional  jazz progressions.

Often, one of these negative dominant chords will be found as an upper structure of a jazz chord, followed by one of the darker versions (e.g. II-6 followed by IV-6) as an upper structure of the next chord. So:

D- F- is present in the following functional chord progressions:
B-7b5 E7alt
B-7b5 Bb7
D-7 G7b9 (probably in the key of C)
D-7 Ealt (probably in A minor)
Fmaj7 Bb7 (probably in F major)

I’m being flexible with chord spellings – to make the point clearest I could say F6 Bb9, because clearly D- and F- are the exact upper structures of those chords. But I’m using Fmaj7 Bb7 as a shorthand for two chord types, not exact voicings. Same deal with the G7b9, it technically should be the 11b9 mentioned above.

There’s another darkening movement, which is shifting up a tritone:

D- Ab- is present in:
D-7 G7alt
D-7 Db7

As well as these darkening movements, there are the actual negative dominant resolutions to a target chord.

D- A- is in:
B-7b5 E7b9 A-
E7b9 A-
G7 Cmaj
D-7 G7 Cmaj
G7 F#-7b5
C#7alt F#-7b5

F- Cmaj is in:
D-7b5 G7b9 Cmaj
G7b9 Cmaj
F-6 Cmaj (back door, same with the next two)
Bb7 Cmaj
F-7 Bb7 Cmaj
Bb7 A-
F-7 Bb7 A-

Ab- Cmaj is in:
G7alt Cmaj
Db7 Cmaj
Ab- A- (not seen as a written chord progression but I’ll be using it later)

Okay, let’s stop with the wall of chord symbols. The take-away is: a small set of negative dominant progressions (and their associated voice-leading and cliches) can be re-used on a huge variety of jazz changes. Today I’ll use the two basic types of movement: darkening and resolving – to navigate inside and outside the harmony on a jazz blues.

2 2 Stave

My alternate pathways in the first video, with the second staff showing example bebop harmony compatible with the alternate pathways.

My alternate pathways here are inspired by the original melody of Blues For Alice (transposed to C). Then I take a somewhat strange turn in bar 9. I work from II- VI7 II-7 V7, a common decoration of a II V progression, e.g. as implied by the melody of Billie’s Bounce…

BB Lick

… but I use a C#- to target the second D-, and then straightforward negative dominants to target the E-7 of the turnaround.

3

Here there are two main ideas: bar 1 has an unexpected B- (equivalent to Bb7alt) targeting Eb-6 in bar 2, which I interpret as a C blues scale shape (because it has the notes Eb, Gb, Bb and C). This is another way to use minor shapes – as blues colours, primarily I-6 and bIII-6 against a I or IV chord. But here the Eb- (bIII-) is also functional, implying a D7alt sound going to G-.

Then I use what could be standard bebop changes to reach the bar 9: interpretable as, say, Cmaj7 F7 E-7 A7b9 (bars 7-8). But I keep up this rate of movement to arrive at a tonic chord (A- which could be Cmaj) in bar 10 rather than bar 11 as expected. I create a cyclical feel by repeating the exact pathway for the next 3 bars. Every pair of chords involves a shift up a minor 3rd, but it’s not a strict pattern because the G- D- resolution breaks it.

4
The first pathway in video no. 3.

 

5
The second pathway in video no. 3.

If you find it hard to hear how this relates to a blues, here is the same solo with bass notes added (and abominable sound quality!).

I had to slow down even more to get some juice out of these progressions. (I play the first one once and the second twice.) The first uses those blues colours again. The second uses unexpected resolutions of a minor chord to major chord a fourth below (so, the F#- is an Amaj, and the C#- is an Emaj), with that major chord changing to a minor chord. It also strictly uses only the darkening and dominant cadential movements, lending it quite a lot of momentum.

There are so many more possibilities, of course. For example, diverging from the subdominant chords in the blues, i.e. the IV in bar 5 and the II in bar 9. In my examples I stick to the original subdominants. Obviously I’m only barely scratching the surface!

I had fun coming up with and playing through these progressions. To conclude, I think the relationship of these pathways to conventional jazz harmony is crucial. I’m thinking both ways as I play. Also, obviously, the pathways are only a technique. These sequences have a rather severe sound due to the unrelenting drive of the cadences and the minor colouration – that mightn’t always be what you want.

Hope you enjoyed it! Sorry for the late post. Please comment with any related ideas, thoughts, questions or criticisms!

Thanks to Loran Witteveen for correcting my examples!

Circular Rhythm

[Edit 28/04/16 – fixed the notation of the voice-leading exercise]

A few months ago I was jamming with a trio I’m in (featuring Dylan Lynch and Max Zaska) and I improvised a riff I really liked.
Riff

It felt really inviting to play over, and Dylan coined the term “circular rhythm” for how we were freely choosing different points to accent within the cycle, not at all constrained by the barlines. I knew vaguely that this was an African-inspired approach to rhythm, and that it felt really good.

Today I’ll investigate what gives any riff or vamp this inviting, cyclical grooviness. Then I’ll look at techniques for getting very rhythmically free on the riff while still “inhabiting” it. This metaphor of the improvising musician being inside a rhythmic of harmonic form comes from Anthony Braxton’s phrase “navigating the form”.

The first nice thing about the groove is that it is compatible with two distinct divisions of the beat: 8ths (2 possible note placements per beat) or 16ths (4 possible placements).

8ths 16ths.png
2 possible underlying subdivisions

To me, these have a very different feeling, with the 8ths being smoother, more elegant, perhaps more amenable to laying back and legato playing. When soloing, I could switch between the two feelings to change the mood. Here though I just demonstrate the two one after the other.

The next nice thing I discovered is that the groove is clearly divided in groups of 3 (mostly) – a feature shared with most of the drum chants in 7 I posted about a few weeks back.

Groups 3

To come to grips with this perspective, I made a drum chant outlining the groups.

Drum Chant

…and improvised slight variations on the riff while singing it. You can see by how I’m weaving my body around that I’m feeling the rolling, triplet-ish physicality of those groups of threes! Like with those 7/4 drum chants, it was really nice to feel rhythmic independence (as drummers would call it) between my voice and hands.

A really strong technique that works nicely with this riff is rhythmic voice-leading, which I discussed already in my post on Charlie Parker’s melodies. In this video I play a bunch of different groupings that voice-lead to (i.e. land/resolve on) accents in the original riff.

Voice Leading Fixed 28 04 16
What I played in the video – groupings targeting notes of the riff

While recording that I was finding it hard to resist using two  other techniques. The first is using triplets over a 16ths groove which I do in the video below at 0:15 and 0:38. I like this because it brings out the resemblance between broken 16th rhythms and triplet rhythms – in fact, it’s really nice to “warp” between the two, playing rhythms that are in-between 16ths and triplets (0:24, 0:32). This happens a lot in both Afro-Cuban and Brazilian music.

 

The other technique is to just displace the notes of the riff like I do at 0:09 or 0:19. The distinctive Ab G notes at the start of the riff are great for this because they are so recogniseable even in different placements. This reminds me of something I heard Vijay Iyer say about being able to displace the downbeats of complex rhythmic forms – not letting the material master you. (Though obviously this is a bigger challenge in music as complicated as his!)

Finally, here’s a fun exercise that was my original idea for this post. To really face the 3 energy inherent in the riff, I tap every 3/8 – a “dotted quarter note” pulse – while nonetheless feeling the music in 4/4.

That’s all for today. Think I’m gonna post on Saturdays from now on, I never seem to make Friday. At some stage soon I want to talk about the political and cultural questions around being a white European studying music derived from and associated with African American communities. Also I want to interview some of the black musicians active in Dublin. But next week will probably be about lyrics.

Leave comments, on Facebook or even better here. Cheers!

Fun In Seven

A bunch of nice drum chants in 7/4 popped into my head while I was hiking around Powerscourt Waterfall last week. So today I’ll show various applications for them, and talk about a basic force in syncopation: maximally even rhythms.

Here I’m singing one of my drum chants while improvising over “Like Someone In Love” (one repetition of the chant per bar of the original song). The chant uses the grouping 2 3 3 3 3.

Drum Chants In 7 - 2 3 3 3 3

What’s fun about this is that it really exposed weaknesses in my rhythmic conception. I noticed I was playing notes without knowing exactly where they were placed. Normally I would rely on my foot tapping to get back in time. But now that I was busy singing the drum chant, these vague notes made the whole thing collapse. To avoid this, I had to clearly imagine phrases before they were played, and also rely much more on my muscle memory to let my fingers solve the problems. Both of these techniques required a lot of relaxation and focus. I’ll be trying this again for sure.

Here I took the shape of the drum chant – its rhythm and use of a high and low tone – and turned it into a bassline consisting of two moving guide tones through the A sections of “What Is This Thing Called Love”. The grouping this time is 3 2 2.

Drum Chants In 7 - 3 2 2
In the B section of “What Is This Thing Called Love” I use a grouping of 3 2 2 2 3 2 (or 5 4 5) as a variation. I made that into a chant of its own.

Drum Chants In 7 - 5 4 5 2

Then I turned that into a bassline and used it for some slow metronome practice, in different placements.

Finally, I took the distinctive “short short short long” part of the previous rhythm…

Drum Chants In 7 - S S S L

… and arranged it three times across two bars of 7.

Drum Chants In 7 - Long

The long notes (the Ls) now mark out a large-scale grouping of 9 10 9. There’s an important similarity between the last few drum chants: they all split 7 beats into three “maximally even” parts.
With 7 beats, the maximally even grouping is 3 2 2 (or a mode of that such as 2 3 2).
With 14 beats (or 7 beats divided into 8th notes), the maximally even grouping is 5 4 5 (or a mode).
With 28 beats (or 7 beats divided into 16th notes, or 14 beats divided into 8th notes), the maximally even division is 9 10 9 (or a mode).

Maximally even divisions are crucial in syncopation: 12/8 clave, for instance, is a maximally even division of 12 notes into 5 parts (2 3 2 2 3). For that matter, the major scale itself is a maximally even division of 12 chromatic notes into 7 parts (2 2 1 2 2 2 1). The principle is that the “odd ones out”, e.g. the 1s in the major scale, should be spread as far as possible away from each other. So a 2 2 1 1 2 2 2 scale wouldn’t be maximally even because the 1s are beside each other. For an example of a maximally even rhythmic division in 4/4 swing, check out the vamps in my band’s version of I Remember You. Stream it here.

To develop my 9 10 9 drum chant, I smoothly subdivided the 9s and 10s to make a cymbal pattern (3 3 3) (3 4 3) (3 3 3).

Drum Chants In 7 - CYmbal

As you can hear, it sounds very much like a simple triplet pattern, with a barely noticeable skip:

Then I wanted to add a cowbell but realised it would need a three-armed drummer. So I turned the rhythm of the original chant into a blues scale bassline (much like the one I used for the metronome practice above), with drums playing a “long seven” kick pulse and the cymbal and bell parts.

Drum Chants In 7 - Re-Orchestrated

Here’s a video of me smiling smugly as I play all the parts:

Hope you enjoyed that. Let me know if you’ve any thoughts or if anything should’ve been presented differently. And merry Christmas to those of you celebrating it!

Some Of My Best Friends Are Syncopations

Recognising the rhythmic shapes in syncopated music is not a skill that I’ve heard talked about much. I only became aware of it in the last year or so – before that, I only consciously did it with repeated riffs or drum patterns. Now I’ve started applying it to melodies, improvised lines and rapping.

Today I’ll write about using this perspective on some iconic Charlie Parker melodies. These (basic) analyses were first used in a workshop I gave for for The Jazzlab. This post is massively inspired by Steve Coleman’s incredibly knowledgeable discussion of Charlie Parker’s music.

Parker’s melodies were like prototype improvisations and have many of the same features as his solos. They’re incredibly rhythmically vital. I boiled them down to their rhythmic skeletons by isolating the accents – highest notes, lowest notes, isolated notes, and notes beginning and ending phrases.

Anthro Start Reduction Cropped
Isolating the accents of the opening phrase of Anthropology

This is a simple thing to do, although there are always multiple possible interpretations.  I soon noticed that in many places, the melodies reduce down to about one accent per half-bar.

 

Anthro Bridge Blocks of 4 Cropped
The accents in the bridge of Anthropology are either on beats 1 or 3, or anticipating or delaying those beats

This is interesting because it reminds me of the highly swinging comping patterns pianists use, for example Wynton Kelly on Freddie Freeloader.

Freddie Freeloader Piano Cropped
Comping rhythms from 2:14 on Freddie Freeloader (1st two trumpet choruses)

Of course, Freddie Freeloader is less than half the tempo of Anthropology. But I think that just illustrates how swing stays structurally similar at a wide scale of tempos. And I think this half-bar level of rhythmic activity is essential to swing, together with 8th note lead lines and quarter note walking bass. It’s also a fantastic way to see the ebb and flow of rest and dynamism, i.e. on- and off-beat energy. For example, in the first A of Charlie Parker’s Confirmation, the first off-beat creates motion which then receives emphasis (“Confirmation”?) from three on-the-beat hits, but resists the strong resting point of bar 3 by anticipating it. The rest of the A section is mostly unresolved, creating a strong desire for the downbeat which comes at the top of the 2nd A section.

 

 

Confirmation A
1st A section of Confirmation

I found patterns at the one-bar scale, among the most common of which were:

 

3 3 Pattern
From bars 2, 6, 15, 22 & 30 of Confirmation
3 5 Pattern
From bars 9 & 10 of Billie’s Bounce

The pattern in Billie’s Bounce could also be interpreted as a grouping of 3 3 2, which is an archetypal syncopation.

 

3 3 2
3 3 2 grouping

I like using the name “Cuban triplet” for it, but it is found pretty much everywhere – cakewalk to heavy metal, reggaeton to rock’n’roll. All of these one-bar syncopations could be described as the interaction of groups of 3 with a one-bar frame.

 

At the two-bar scale there are a bunch of lovely patterns. Many of these are at the exact same half-bar level of rhythmic activity that I talked about, but viewing them in a 2-bar frame makes them more recogniseable. Drummers and pianists use these 2-bar shapes as comping cliches.

Last A of Confirmation Cropped
The last A section of Confirmation starts with this rhythm

 

 

 

 

3-4 of Anthropology
Bars 3-4 of Anthropology use this rhythm

I suspect the 2-bar frame is a more meaningful division in swing than the single bar. One really important thing about two-bar syncopations is that they often resemble claves. The rhythm above is close to a 2:3 rhumba clave, while bars 5-6 of Relaxin’ At Camarillo resemble a 2:3 son clave.

5-6 of Relaxin' Cropped
From bars 5-6 of Relaxin’ At Camarillo

These examples are within a note or two of replicating a clave. However, Steve Coleman points out that very many of Charlie Parker’s phrasings using groups of 3 have a clave-like energy of shifting yet balanced accents, even if they don’t immediately resemble the classic Afro-Cuban rhythms.

I’ll finish with quick examples of two more phenomena that Coleman identified in Parker’s music.

The first is rhythmic voice-leading. This, like voice-leading in tonal music, is a way of smoothly connecting one point with another. It involves using repeated identical groupings to target a particular rhythmic placement.

5-7 Billie's Bounce Cropped
Rhythmic voice-leading in bars 5-7 of Billie’s Bounce

Here, groups of 2 target the anticipation of bar 6, then groups of 3 target beat 2 of bar 7. Groups of 4, 5, etc. can also be used. However, this is not the same concept as polyrhythm, polymetre or modulation (though these also use repeated groupings). The crucial difference is that the groupings do not set up an independent layer, but a path from one point to another. They have directionality. I feel this distinction wasn’t conveyed when I learnt about groupings in jazz school.

Finally, Charlie Parker’s melodies use palindromic energy. This is a huge topic, full of beauty, but I’ll just give some quick examples of sequences of groupings that are the same going backwards or forwards.

Anthropology 4 bars
Palindromic accents at the start of Anthropology: 4 3 4 3 3 3 4 3 4
Confirmation Start Palindrome
Palindromic accents at the start of Confirmation: 4 4 3 3 4 3 3 4 4

I hope you found something interesting in this post, and maybe got another perspective on syncopated rhythm. I think this way of seeing/feeling underlying structures is incredibly powerful for improvising, composing and analysing. Again, please comment!