Lessons · Harmony

Colour without function

Modal harmony

% Harmony ARRIVES because of one semitone. In G the seventh degree is
% f#, a half step under home, and the chord on 5 carries it as its
% third — so 5Dia leans on 1Dia and nothing else will answer it. Bend
% that one note flat and the chord on 5 turns minor: '\2' is an
% OVERRIDE, which replaces one item of a rule where it is used, so
% Slack is Cadence over the same four roots with the lean taken out of
% it — and it no longer arrives. That lean is FUNCTION, and this whole
% lesson is the harmony left when you do without it.
 
bpm 90
meter 4
unit 1/4
key g maj
 
Cadence ::= .1Dia .4Dia .5Dia .1Dia
Slack   ::= Cadence \2 .5Min
 
assert .5Dia == {.5, .7, 2}
assert .5Min == {.5, .7b, 2}
assert Slack == .1Dia .4Dia .5Min .1Dia
 
Cadence _8
 
Slack*2 _8
 
 
% A MODE is this key with one degree bent, and the language has no word
% for one — there is no 'key g mixo' — so the bend is written where it
% sounds. Tune states 7 twice, at items 2 and 5, counting from zero the
% way a slice does; MIXOLYDIAN is Tune with both of them flat and
% nothing else touched, the second braced because it carries its own
% length. Nothing demands home now, so home is STATED instead of
% proved: a drone on 1 and 5, holding under both readings of the tune.
 
Drone ::= {..1, ..5} _16
 
Tune ::= | 5 6 7 '1 |
         | '1 _2 7 _2 |
         | 6 5 4 _2 |
         | 2 3 5 _2 |
 
Mixo ::= Tune \2 7b \5 {7b _2}
 
assert Tune[2] == 7
assert Mixo[2] == 7b
 
{Tune, Drone*4}
 
{Mixo, Drone*4}
 
 
% A bent degree reaches every chord that CONTAINS it and no other. f
% natural is the third of the chord on 5, which went minor in the first
% block, and it is the root of a major chord on 7b, a whole step below
% home — the extra dot puts that degree under .1 rather than a seventh
% above it — and G major cannot build that chord at all. Those two are
% the colour. Three major chords, no dominant among them, and the vamp
% circles where the cadence closed:
 
assert ..7bMaj == {..7b, .2, .4}
 
Vamp ::= .1Dia ..7bMaj .4Dia .1Dia
 
{Mixo, Vamp _16, Drone*4}*2
 
 
% The other two colours bend the MINOR scale — same tonic, new parent.
% Minor's chord on 4 is minor because its third is degree 6, eb. Raise
% that one degree to 6#, e natural, and iv turns into IV: Dorian is
% Minor with one item swapped, so the only chord that moves between the
% two phrases below is the second. A minor key with a major fourth is
% DORIAN:
 
key g min
 
Minor  ::= .1Dia .4Dia .1Dia .5Dia
Dorian ::= Minor \1 .4Maj
 
assert .4Maj == {.4, .6#, 1}
assert Dorian == .1Dia .4Maj .1Dia .5Dia
 
Minor _8
 
Dorian _8
 
 
% The dorian vamp is those two chords rocking, i and IV, with nothing
% on 5 to spoil it. The air sings 6# over the major fourth each time it
% comes round, and ends on 4 over that same chord rather than on home —
% so it is the drone underneath that says which note is home:
 
Ground ::= .1Dia .4Maj
 
Air ::= | 5 3 4 5 |
        | 6# _2 5 _2 |
        | 3 4 5 '1 |
        | 6# 5 4 _2 |
 
{Air, Ground*2 _16, Drone*4}*2
 
 
% The third bend points DOWN, and it is the one colour here that
% closes. 2b is ab, a half step ABOVE home, and the major chord it
% roots leans onto 1 the way the dominant leaned up into it. Natural
% minor walks 4 3 2 1 with a diminished chord on 2 — that is Descent —
% and Phrygian is the same walk with that one item swapped. This one
% arrives, and it needs no drone to hold it up: it has a semitone of
% its own, and no leading tone anywhere:
 
Descent  ::= .4Dia .3Dia .2Dia .1Dia
Phrygian ::= Descent \2 .2bMaj
 
Fall ::= | 4 5 4 3 |
         | 4 3 2b 1 |
 
Descent _8
 
{Fall, Phrygian _8}*2
 
 
% The three colours in one turn — 7b bent off the major, 6# and 2b off
% the minor, one degree each — and G is home in all three. The drone
% holds the first two up because nothing in them arrives; the third
% arrives on its own, and the drone comes back only under the chord it
% lands on:
 
key g maj
{Mixo, Vamp _16, Drone*4}
 
key g min
{Air, Ground*2 _16, Drone*4}
 
{Fall, Phrygian _8}*2
{.1Dia _16, Drone}

% Harmony ARRIVES because of one semitone. In G the seventh degree is
% f#, a half step under home, and the chord on 5 carries it as its
% third — so 5Dia leans on 1Dia and nothing else will answer it. Bend
% that one note flat and the chord on 5 turns minor: '\2' is an
% OVERRIDE, which replaces one item of a rule where it is used, so
% Slack is Cadence over the same four roots with the lean taken out of
% it — and it no longer arrives. That lean is FUNCTION, and this whole
% lesson is the harmony left when you do without it.

bpm 90
meter 4
unit 1/4
key g maj

Cadence ::= .1Dia .4Dia .5Dia .1Dia
Slack   ::= Cadence \2 .5Min

assert .5Dia == {.5, .7, 2}
assert .5Min == {.5, .7b, 2}
assert Slack == .1Dia .4Dia .5Min .1Dia

Cadence _8

Slack*2 _8

% A MODE is this key with one degree bent, and the language has no word
% for one — there is no 'key g mixo' — so the bend is written where it
% sounds. Tune states 7 twice, at items 2 and 5, counting from zero the
% way a slice does; MIXOLYDIAN is Tune with both of them flat and
% nothing else touched, the second braced because it carries its own
% length. Nothing demands home now, so home is STATED instead of
% proved: a drone on 1 and 5, holding under both readings of the tune.

Drone ::= {..1, ..5} _16

Tune ::= | 5 6 7 '1 |
         | '1 _2 7 _2 |
         | 6 5 4 _2 |
         | 2 3 5 _2 |

Mixo ::= Tune \2 7b \5 {7b _2}

assert Tune[2] == 7
assert Mixo[2] == 7b

{Tune, Drone*4}

{Mixo, Drone*4}

% A bent degree reaches every chord that CONTAINS it and no other. f
% natural is the third of the chord on 5, which went minor in the first
% block, and it is the root of a major chord on 7b, a whole step below
% home — the extra dot puts that degree under .1 rather than a seventh
% above it — and G major cannot build that chord at all. Those two are
% the colour. Three major chords, no dominant among them, and the vamp
% circles where the cadence closed:

assert ..7bMaj == {..7b, .2, .4}

Vamp ::= .1Dia ..7bMaj .4Dia .1Dia

{Mixo, Vamp _16, Drone*4}*2

% The other two colours bend the MINOR scale — same tonic, new parent.
% Minor's chord on 4 is minor because its third is degree 6, eb. Raise
% that one degree to 6#, e natural, and iv turns into IV: Dorian is
% Minor with one item swapped, so the only chord that moves between the
% two phrases below is the second. A minor key with a major fourth is
% DORIAN:

key g min

Minor  ::= .1Dia .4Dia .1Dia .5Dia
Dorian ::= Minor \1 .4Maj

assert .4Maj == {.4, .6#, 1}
assert Dorian == .1Dia .4Maj .1Dia .5Dia

Minor _8

Dorian _8

% The dorian vamp is those two chords rocking, i and IV, with nothing
% on 5 to spoil it. The air sings 6# over the major fourth each time it
% comes round, and ends on 4 over that same chord rather than on home —
% so it is the drone underneath that says which note is home:

Ground ::= .1Dia .4Maj

Air ::= | 5 3 4 5 |
        | 6# _2 5 _2 |
        | 3 4 5 '1 |
        | 6# 5 4 _2 |

{Air, Ground*2 _16, Drone*4}*2

% The third bend points DOWN, and it is the one colour here that
% closes. 2b is ab, a half step ABOVE home, and the major chord it
% roots leans onto 1 the way the dominant leaned up into it. Natural
% minor walks 4 3 2 1 with a diminished chord on 2 — that is Descent —
% and Phrygian is the same walk with that one item swapped. This one
% arrives, and it needs no drone to hold it up: it has a semitone of
% its own, and no leading tone anywhere:

Descent  ::= .4Dia .3Dia .2Dia .1Dia
Phrygian ::= Descent \2 .2bMaj

Fall ::= | 4 5 4 3 |
         | 4 3 2b 1 |

Descent _8

{Fall, Phrygian _8}*2

% The three colours in one turn — 7b bent off the major, 6# and 2b off
% the minor, one degree each — and G is home in all three. The drone
% holds the first two up because nothing in them arrives; the third
% arrives on its own, and the drone comes back only under the chord it
% lands on:

key g maj
{Mixo, Vamp _16, Drone*4}

key g min
{Air, Ground*2 _16, Drone*4}

{Fall, Phrygian _8}*2
{.1Dia _16, Drone}

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