Lessons · Musicianship

Harmonizing a tune

One melody, five settings

% Eight bars in F, a period. Ask climbs to c and stops on 2 — the
% question — and Say answers it with Ask's own first three notes lifted
% three scale steps, touches the tune's one peak at f5, then walks home.
% Every setting below harmonizes exactly these fourteen notes.
 
bpm 42
meter 4
unit 1/4
key f maj
 
Ask ::= 1 _2 3 _2 5 _4 6 5 3 _2 2 _4
Say ::= Ask[:3]@~3 7 6 5 _2 1 _4
 
assert Say == 4 _2 6 _2 '1 _4 7 6 5 _2 1 _4
 
Tune ::= Ask Say
 
Tune
 
 
% The first setting refuses to choose: one open fifth on 1 under all
% eight bars. No chord ever changes, so no note of the tune is a chord
% tone or isn't — bar 3's d and bar 5's bb stand on identical ground.
 
Drone ::= {..1 _8, ..5 _8}
 
{Tune, Drone*4}
 
 
% The next setting adds no chords either; it moves a copy of the tune.
% '@~-2' is two SCALE steps down, a third under every note, and the key
% does the arithmetic — four of Ask's seven thirds come out minor and
% three major, though the mark never said which. '@~-5' opens it to sixths.
 
assert Ask@~-2 == .6 _2 1 _2 3 _4 4 3 1 _2 .7 _4
 
{Tune, Tune@~-2}
{Tune, Tune@~-5}
 
 
% Chords at last. 'Dia' asks the key for the triad on a degree, so Hymn
% names roots and nothing else: I I vi V, IV I V I. Bar 4 stops on V — the
% half cadence the tune already asked for — and bar 8 answers V I.
 
Hymn ::= ..1Dia _8 ..6Dia _4 ..5Dia _4 ..4Dia _4 ..1Dia _4 ..5Dia _4 ..1Dia _4
 
{Tune, Hymn}
 
 
% No chord is written anywhere here: two lines, and the harmony is
% whatever the pair of them makes. Walk and Walkb move against the tune in
% all four bars where it moves, and in the four bars where it holds a
% whole note the bass is the only thing moving.
 
Walk  ::= .1 _2 ..6 _2 ..7 _2 .1 _2 .2 _2 .3 _2 ..5 _2 ..7 _2
Walkb ::= .1 _2 ..4 _2 ..1 _2 ..3 _2 ..5 _2 ..7 _2 .1 _2 ..1 _2
 
{Ask, Walk} {Say, Walkb}
 
 
% The same fourteen notes read in D minor, the relative, and not one bar
% keeps the chord the hymn gave it: i VII, VI i, iv across two bars, VI,
% v, i. The v is minor, so nothing leans back to F — and the tune's last
% note, the tonic a moment ago, is now the third of the chord under it.
 
Minor ::= ..6Dia _4 ..5Dia _4 ..4Dia _2 ..6Dia _2 ..2Dia _8 ..4Dia _4 ..3Dia _4 ..6Dia _4
 
{Tune, Minor}

% Eight bars in F, a period. Ask climbs to c and stops on 2 — the
% question — and Say answers it with Ask's own first three notes lifted
% three scale steps, touches the tune's one peak at f5, then walks home.
% Every setting below harmonizes exactly these fourteen notes.

bpm 42
meter 4
unit 1/4
key f maj

Ask ::= 1 _2 3 _2 5 _4 6 5 3 _2 2 _4
Say ::= Ask[:3]@~3 7 6 5 _2 1 _4

assert Say == 4 _2 6 _2 '1 _4 7 6 5 _2 1 _4

Tune ::= Ask Say

Tune

% The first setting refuses to choose: one open fifth on 1 under all
% eight bars. No chord ever changes, so no note of the tune is a chord
% tone or isn't — bar 3's d and bar 5's bb stand on identical ground.

Drone ::= {..1 _8, ..5 _8}

{Tune, Drone*4}

% The next setting adds no chords either; it moves a copy of the tune.
% '@~-2' is two SCALE steps down, a third under every note, and the key
% does the arithmetic — four of Ask's seven thirds come out minor and
% three major, though the mark never said which. '@~-5' opens it to sixths.

assert Ask@~-2 == .6 _2 1 _2 3 _4 4 3 1 _2 .7 _4

{Tune, Tune@~-2}
{Tune, Tune@~-5}

% Chords at last. 'Dia' asks the key for the triad on a degree, so Hymn
% names roots and nothing else: I I vi V, IV I V I. Bar 4 stops on V — the
% half cadence the tune already asked for — and bar 8 answers V I.

Hymn ::= ..1Dia _8 ..6Dia _4 ..5Dia _4 ..4Dia _4 ..1Dia _4 ..5Dia _4 ..1Dia _4

{Tune, Hymn}

% No chord is written anywhere here: two lines, and the harmony is
% whatever the pair of them makes. Walk and Walkb move against the tune in
% all four bars where it moves, and in the four bars where it holds a
% whole note the bass is the only thing moving.

Walk  ::= .1 _2 ..6 _2 ..7 _2 .1 _2 .2 _2 .3 _2 ..5 _2 ..7 _2
Walkb ::= .1 _2 ..4 _2 ..1 _2 ..3 _2 ..5 _2 ..7 _2 .1 _2 ..1 _2

{Ask, Walk} {Say, Walkb}

% The same fourteen notes read in D minor, the relative, and not one bar
% keeps the chord the hymn gave it: i VII, VI i, iv across two bars, VI,
% v, i. The v is minor, so nothing leans back to F — and the tune's last
% note, the tonic a moment ago, is now the third of the chord under it.

Minor ::= ..6Dia _4 ..5Dia _4 ..4Dia _2 ..6Dia _2 ..2Dia _8 ..4Dia _4 ..3Dia _4 ..6Dia _4

{Tune, Minor}

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Harmonizing a tune · Pattern Engine