Lessons · Musicianship

Voice leading

Common tones, steps, contrary motion

% A chord is a stack of notes; a progression is three melodies at once.
% I IV V I twice. Rough is root position — what 1Dia spells — so I to IV
% lifts every voice a fourth and V to I drops every voice a fifth. Smooth
% is the same four chords, each voice taking its smallest move: 1 stays
% put from I into IV, 5 from V into I, no voice moving past one step.
 
bpm 25
key g maj
 
Rough  ::= 1Dia _2 4Dia _2 5Dia _2 1Dia _2
Smooth ::= {1, 3, 5} _2 {1, 4, 6} _2 {2, 5, 7} _2 {3, 5, '1} _2
 
assert Rough == {1, 3, 5} _2 {4, 6, '1} _2 {5, 7, '2} _2 {1, 3, 5} _2
 
Rough Smooth
 
 
% The same rule across a whole phrase — I vi IV V7 | I ii6 V7 I — written
% as four lines rather than eight stacks. Only the bass leaps, because the
% bass names the chords; Sop, Alt and Ten move one scale step or not at
% all, and eight of these thirty-two chord tones are held, never restruck.
 
Sop  ::= 5 _2 6 _4 5 _4 6 _2 7 _2 '1 _2
Alt  ::= 3 _4 4 _4 3 _2 4 _4 3 _2
Ten  ::= 1 _6 .7 _2 1 _2 2 _4 1 _2
Bass ::= .1 _2 ..6 _2 ..4 _2 ..5 _2 .1 _2 .4 _2 .5 _2 .1 _2
 
Chorale ::= {Sop, Alt, Ten, Bass}
 
Chorale
 
 
% A held note can change its meaning underneath. Alt's 4 is a chord tone
% of ii; it stays exactly where it is while the bass steps 4 to 5, and the
% same note is now the seventh of V7, which obliges it to fall one step
% onto 3. The last three chords in tempo, then broadened to twice the length.
 
Close ::= {Sop[3:], Alt[3:], Ten[3:], Bass[5:]}
 
Close Close _2
 
 
% Contrary motion is the other way voices stay clear: the top climbs, the
% bottom walks down. Exactly down here — Fall is Rise mirrored around the
% tonic an octave lower, and the assert checks that rather than taking my
% word. The wedge opens, closes on its retrograde, lands on the cadence.
 
Rise ::= 1 2 3 4 5 6 7 '1
Fall ::= .1 ..7 ..6 ..5 ..4 ..3 ..2 ..1
 
assert Fall == {Rise}^@-12
 
Wedge ::= {Rise, Fall}
 
Wedge Wedge~ Close
 
 
% An accompaniment recedes because its voices barely move. Swap the top
% line for a tune with an arch and change nothing under it — Alt, Ten and
% Bass are the same three rules — and the tune owns all the motion.
 
Tune ::= 5 6 '1 7 6 _2 7 _2 5 _2 6 _2 7 _2 '1 _2
 
Verse ::= {Tune, Alt, Ten, Bass}
 
Verse
 
 
% Not one pitch is named anywhere above; every voice is a degree. So the
% last verse lifts a whole tone on one 'key' line, the way a hymn book
% does it — chorale, verse, verse in A, and the cadence broadened to close.
 
Chorale Verse
 
key a maj
 
Verse Close _2

% A chord is a stack of notes; a progression is three melodies at once.
% I IV V I twice. Rough is root position — what 1Dia spells — so I to IV
% lifts every voice a fourth and V to I drops every voice a fifth. Smooth
% is the same four chords, each voice taking its smallest move: 1 stays
% put from I into IV, 5 from V into I, no voice moving past one step.

bpm 25
key g maj

Rough  ::= 1Dia _2 4Dia _2 5Dia _2 1Dia _2
Smooth ::= {1, 3, 5} _2 {1, 4, 6} _2 {2, 5, 7} _2 {3, 5, '1} _2

assert Rough == {1, 3, 5} _2 {4, 6, '1} _2 {5, 7, '2} _2 {1, 3, 5} _2

Rough Smooth

% The same rule across a whole phrase — I vi IV V7 | I ii6 V7 I — written
% as four lines rather than eight stacks. Only the bass leaps, because the
% bass names the chords; Sop, Alt and Ten move one scale step or not at
% all, and eight of these thirty-two chord tones are held, never restruck.

Sop  ::= 5 _2 6 _4 5 _4 6 _2 7 _2 '1 _2
Alt  ::= 3 _4 4 _4 3 _2 4 _4 3 _2
Ten  ::= 1 _6 .7 _2 1 _2 2 _4 1 _2
Bass ::= .1 _2 ..6 _2 ..4 _2 ..5 _2 .1 _2 .4 _2 .5 _2 .1 _2

Chorale ::= {Sop, Alt, Ten, Bass}

Chorale

% A held note can change its meaning underneath. Alt's 4 is a chord tone
% of ii; it stays exactly where it is while the bass steps 4 to 5, and the
% same note is now the seventh of V7, which obliges it to fall one step
% onto 3. The last three chords in tempo, then broadened to twice the length.

Close ::= {Sop[3:], Alt[3:], Ten[3:], Bass[5:]}

Close Close _2

% Contrary motion is the other way voices stay clear: the top climbs, the
% bottom walks down. Exactly down here — Fall is Rise mirrored around the
% tonic an octave lower, and the assert checks that rather than taking my
% word. The wedge opens, closes on its retrograde, lands on the cadence.

Rise ::= 1 2 3 4 5 6 7 '1
Fall ::= .1 ..7 ..6 ..5 ..4 ..3 ..2 ..1

assert Fall == {Rise}^@-12

Wedge ::= {Rise, Fall}

Wedge Wedge~ Close

% An accompaniment recedes because its voices barely move. Swap the top
% line for a tune with an arch and change nothing under it — Alt, Ten and
% Bass are the same three rules — and the tune owns all the motion.

Tune ::= 5 6 '1 7 6 _2 7 _2 5 _2 6 _2 7 _2 '1 _2

Verse ::= {Tune, Alt, Ten, Bass}

Verse

% Not one pitch is named anywhere above; every voice is a degree. So the
% last verse lifts a whole tone on one 'key' line, the way a hymn book
% does it — chorale, verse, verse in A, and the cadence broadened to close.

Chorale Verse

key a maj

Verse Close _2

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Voice leading · Pattern Engine