Lessons · Harmony

Inversions and the bass

The same chord, a different bass

% A triad is three notes, and its INVERSION is which of the three lies
% LOWEST. The chord symbol says it outright: '$' lists the members from
% the bottom up, so 1Dia$3 is that same triad with its third underneath
% and 1Dia$5 with its fifth. The names are figures counted off that bass
% (a sixth and a third over the third, a sixth and a fourth over the
% fifth) and nothing up there changes its letter.
 
bpm 100
instrument swell
meter 4
key c3 min
 
Root    ::= 1Dia
Six     ::= 1Dia$3
SixFour ::= 1Dia$5
 
assert Six == {3, 5, '1}
assert SixFour == {5, '1, '3}
 
{Root _4 Six _4 SixFour _4 Six _4, .1 _4 .3 _4 .5 _4 .3 _4}
{Root, .1} _16
 
 
% A funk arrangement is built from the bass up, so the rhythm gets
% written first. Tresillo is half a bar with three holes in it (on the
% beat, on the 'a', on the next '&'), three sixteenths, three, then two.
% Six arguments fill it twice, so one line is one bar.
%
% Pour the tonic triad through those holes and the bass walks root,
% third, fifth, octave and back down. Hold the chord over it: the three
% notes on top never move, and the bass renames them six times a bar:
% root position, first inversion, second, and home.
 
Tresillo ::= $1 -*2 $2 -*2 $3 -
Arp      ::= Tresillo(.1 .3 .5 1 .5 .3)
 
assert Arp == .1 -*2 .3 -*2 .5 - 1 -*2 .5 -*2 .3 -
 
Arp*2
{Arp, Root _16}*2
 
 
% Now the other way round: hold the BASS and move the chords. All three
% chords of this vamp own the note C (Cm is 1 3 5, Fm is 4 6 1, Ab is
% 6 1 3) so '$5' hands the fourth chord its fifth for a bass and '$3'
% the sixth chord its third, and C sits under all three. Two of them are
% inversions, the riff never leaves home, and the top voice travels two
% semitones in four bars: g ab ab g. Chop is half a bar of comping stated
% twice, so one argument is one bar.
 
Riff ::= Tresillo(.1 .1 .5 .1 .5 1)
Chop ::= {-*2 $1 - $1 _2 -*2}*2
Vamp ::= Chop(1Dia .4Dia$5 .6Dia$3 1Dia)
 
assert .4Dia$5 == {1, 4, 6}
assert .6Dia$3 == {1, 3, 6}
 
{Riff*4, Vamp}
 
 
% The same three chords with their own roots back underneath. '@~3' and
% '@~5' shift the riff three and five scale steps, so one figure still
% covers all three, but the bass leaps a fourth and a third now, and the
% top voice travels sixteen semitones where it travelled two: g c eb g.
% Not a note of the harmony changed. The floor did.
 
Roots ::= Chop(1Dia 4Dia 6Dia 1Dia)
 
{Riff Riff@~3 Riff@~5 Riff, Roots}
{Riff*4, Vamp}
 
 
% Horns on top, and a turnaround in the fourth bar: the bass takes the
% arpeggio back and the horns answer their own bar backwards, which is
% all '~' means. The hook itself never changes note: over Cm those three
% are the fifth, the seventh and the octave, over Fm the ninth, the
% eleventh and the fifth, over Ab the seventh, the ninth and the third.
% One line, three readings, and the bass is what decides.
 
Horn ::= -*4 '5 '7 - ''1 -*3 '7 - '5 -*2
 
{Riff*4, Vamp, Horn*4}
{Riff*3 Arp, Vamp, Horn*3 Horn~}
 
 
% The one job an inversion holds down in a cadence. Over the bass .5 the
% SixFour stands a fourth and a sixth above it and neither note can stay:
% both fall a step into 5Dom7, which owns the b that c minor does not,
% and 5Dom7 shuts the door on Root. A six-four over the dominant is a
% lean, never a chord to stop on.
 
Land ::= {SixFour, .5} _8 {5Dom7, .5} _8 {Root, .1} _16
 
{Riff*3 Arp, Vamp} Land
 
 
% All of it in order: the riff bare, the chord over it, the vamp, the
% horns and their turnaround, one pass with the roots underneath to hear
% what the pedal was worth, and a whole step up for the last chorus:
% nothing above names a pitch, so the lift costs one line.
 
Riff*2
{Riff, Root _16}*2
{Riff*4, Vamp}
{Riff*3 Arp, Vamp, Horn*3 Horn~}
{Riff Riff@~3 Riff@~5 Riff, Roots}
 
key d3 min
 
{Riff*4, Vamp, Horn*4}
{Riff*3 Arp, Vamp, Horn*3 Horn~}
{Arp, Root _16}*2
 
Land

% A triad is three notes, and its INVERSION is which of the three lies
% LOWEST. The chord symbol says it outright: '$' lists the members from
% the bottom up, so 1Dia$3 is that same triad with its third underneath
% and 1Dia$5 with its fifth. The names are figures counted off that bass
% (a sixth and a third over the third, a sixth and a fourth over the
% fifth) and nothing up there changes its letter.

bpm 100
instrument swell
meter 4
key c3 min

Root    ::= 1Dia
Six     ::= 1Dia$3
SixFour ::= 1Dia$5

assert Six == {3, 5, '1}
assert SixFour == {5, '1, '3}

{Root _4 Six _4 SixFour _4 Six _4, .1 _4 .3 _4 .5 _4 .3 _4}
{Root, .1} _16

% A funk arrangement is built from the bass up, so the rhythm gets
% written first. Tresillo is half a bar with three holes in it (on the
% beat, on the 'a', on the next '&'), three sixteenths, three, then two.
% Six arguments fill it twice, so one line is one bar.
%
% Pour the tonic triad through those holes and the bass walks root,
% third, fifth, octave and back down. Hold the chord over it: the three
% notes on top never move, and the bass renames them six times a bar:
% root position, first inversion, second, and home.

Tresillo ::= $1 -*2 $2 -*2 $3 -
Arp      ::= Tresillo(.1 .3 .5 1 .5 .3)

assert Arp == .1 -*2 .3 -*2 .5 - 1 -*2 .5 -*2 .3 -

Arp*2
{Arp, Root _16}*2

% Now the other way round: hold the BASS and move the chords. All three
% chords of this vamp own the note C (Cm is 1 3 5, Fm is 4 6 1, Ab is
% 6 1 3) so '$5' hands the fourth chord its fifth for a bass and '$3'
% the sixth chord its third, and C sits under all three. Two of them are
% inversions, the riff never leaves home, and the top voice travels two
% semitones in four bars: g ab ab g. Chop is half a bar of comping stated
% twice, so one argument is one bar.

Riff ::= Tresillo(.1 .1 .5 .1 .5 1)
Chop ::= {-*2 $1 - $1 _2 -*2}*2
Vamp ::= Chop(1Dia .4Dia$5 .6Dia$3 1Dia)

assert .4Dia$5 == {1, 4, 6}
assert .6Dia$3 == {1, 3, 6}

{Riff*4, Vamp}

% The same three chords with their own roots back underneath. '@~3' and
% '@~5' shift the riff three and five scale steps, so one figure still
% covers all three, but the bass leaps a fourth and a third now, and the
% top voice travels sixteen semitones where it travelled two: g c eb g.
% Not a note of the harmony changed. The floor did.

Roots ::= Chop(1Dia 4Dia 6Dia 1Dia)

{Riff Riff@~3 Riff@~5 Riff, Roots}
{Riff*4, Vamp}

% Horns on top, and a turnaround in the fourth bar: the bass takes the
% arpeggio back and the horns answer their own bar backwards, which is
% all '~' means. The hook itself never changes note: over Cm those three
% are the fifth, the seventh and the octave, over Fm the ninth, the
% eleventh and the fifth, over Ab the seventh, the ninth and the third.
% One line, three readings, and the bass is what decides.

Horn ::= -*4 '5 '7 - ''1 -*3 '7 - '5 -*2

{Riff*4, Vamp, Horn*4}
{Riff*3 Arp, Vamp, Horn*3 Horn~}

% The one job an inversion holds down in a cadence. Over the bass .5 the
% SixFour stands a fourth and a sixth above it and neither note can stay:
% both fall a step into 5Dom7, which owns the b that c minor does not,
% and 5Dom7 shuts the door on Root. A six-four over the dominant is a
% lean, never a chord to stop on.

Land ::= {SixFour, .5} _8 {5Dom7, .5} _8 {Root, .1} _16

{Riff*3 Arp, Vamp} Land

% All of it in order: the riff bare, the chord over it, the vamp, the
% horns and their turnaround, one pass with the roots underneath to hear
% what the pedal was worth, and a whole step up for the last chorus:
% nothing above names a pitch, so the lift costs one line.

Riff*2
{Riff, Root _16}*2
{Riff*4, Vamp}
{Riff*3 Arp, Vamp, Horn*3 Horn~}
{Riff Riff@~3 Riff@~5 Riff, Roots}

key d3 min

{Riff*4, Vamp, Horn*4}
{Riff*3 Arp, Vamp, Horn*3 Horn~}
{Arp, Root _16}*2

Land

running…edit it and it re-runs as you type

Inversions and the bass · Harmony