Lessons · Showcase

The Art of Fugue I

A subject in four voices

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% The Art of Fugue opens with one voice, alone. The subject leaps to
% the fifth and falls through the D minor triad back to the tonic, drops
% to the leading tone below it, then walks up to the fourth and back
% down to the second.
 
bpm 120
meter 4
unit 1/4
key d4 min
mode diatonic
 
Subject ::= | 1 _8 5 _8 |
  | 3 _8 1 _8 |
  | .7# _8 1 _4 2 _4 |
  | 3 _10 4 _2 3 _2 2 _2 |
Subject
 
 
% Four bars later a second voice answers at the fifth — but not by
% transposing. The subject's opening leap of a fifth comes back as a
% fourth (a to d, not a to e), and where the subject dropped to c#, the
% answer drops to g#: the leading tone of the key it is answering in.
 
Answer ::= | 5 _8 '1 _8 |
  | 7 _8 5 _8 |
  | 4# _8 5 _4 6# _4 |
  | 7 _10 '1 _2 7 _2 6 _2 |
 
Subject Answer
 
 
% Fall is the shape this fugue states most often — 36 times, three
% notes: the subject's last three, a step lower. Rise is the answer's turn
% up through g#, stated 8 times, spelled in absolute pitches because it
% plays inverted later on. Step Fall down the scale under a pair of Rises
% and you have a sequence — not a passage of this fugue, but the way a
% fugue fills the space between entries.
 
Fall ::= 3 _2 2 _2 1 _2
Rise ::= g#4 _8 a4 _4 b4 _4
 
assert Fall@~1 == 4 _2 3 _2 2 _2
assert Rise == 4# _8 5 _4 6# _4
 
Sequence ::= {Fall@~4 Fall@~3 Fall@~2 Fall@~1 Fall Fall@~-1,
  Rise@-12 Rise@-14 - _4}
Sequence
 
 
% Under the answer the first voice keeps going, with the countersubject:
% a scale up to the fifth, a drop into the register below, then Fall, the
% subject's own tail handed back, and a climb of three steps to g — which
% is Rise turned upside down and read backwards.
 
Counterb ::= .5 _2 .6# _2 .7 _2 .5 _2 3 _6 .6# _2 2 _6 Fall
Counter  ::= 1 _4 2 _4 3 _4 4 _4 5 _4 Counterb Rise~^@11
 
Opening ::= {-*64 Answer,
  Subject Counter}
Opening
 
 
% The exposition is that one line four times over, each entry four bars
% after the last and in a voice that has not sung yet: alto, then soprano
% with the answer a fifth above, then bass with the subject an octave
% below the alto, then tenor with the answer an octave below the soprano.
 
Entries ::= {-*64 Answer -*128,
  Subject -*192,
  -*192 Answer@-12,
  -*128 Subject@-12 -*64}
Entries
 
 
% All of it. Under each answer the voice that has just finished its own
% entry plays the countersubject — the alto at m.5, the bass at m.13 — but
% Bach re-cuts the bass version at both ends: one held d where the alto ran
% d e f g a up the scale, and where the alto climbed e f# g the bass
% zigzags e g f# a before its g. Only the middle, Counterb, is the alto's
% bars 6-7 an octave down.
 
Counter2 ::= .1 _8 -*12 Counterb@-12 .2 _2 .4 _2 .3# _2 .5 _2 .4 _8
 
Exposition ::= {-*64 Answer -*128,
  Subject Counter -*128,
  -*192 Answer@-12,
  -*128 Subject@-12 Counter2}
 
Exposition
 
 
% THE WHOLE FUGUE — all four voices, every entry, to the close.
 
bpm 120
meter 4
unit 1/4
key d4 min
mode diatonic
 
% The cast — every motif and chord the lead line uses:
 
M14 ::= '1 _2 5 _2
M10 ::= 7 _8 5 _8
Run2 ::= 5b _8 5 _4 7b _4
M20 ::= .1 _2 ..7 _2
M5 ::= M20@~9 1 _2
M11 ::= ..6 _6 ..4 _2
M45 ::= bb4 _6 e4 _2
M23 ::= .5 _2 .6 _4
Run ::= .7# _8 1 _4 2 _4
M12 ::= g4 _2 bb4 _2
M17 ::= bb4 _2 a4 _2
M22 ::= M10@-7/4
M3 ::= M23@~-2 .7 _10 .5 _2
S2 ::= 6 _10 M3@14 7 _4 '3 _10 M23@~10
M18 ::= '2 _6 7# _2
M25 ::= M18@~-1
M46 ::= a4 _8 d4 _4
M13 ::= M11@~12
M15 ::= 7 _8 6 _4
M47 ::= -*32
S5 ::= M5@~-6 M5@~-7 ..7# _2
M38 ::= 5 _6 7 _2
M27 ::= 3 _2 2 _6
M7 ::= 1 _6 M27 7 _2
M29 ::= 7# _2 5 _2
M43 ::= M29 M25
M28 ::= -*32
M1 ::= Run 3 _10 M20@~10
S1 ::= 5 _8 5b _8? 3 2 _8? 1 M1 2 _2
M32 ::= 3 _10 1 _2
M2 ::= '1 _2 M18 M25
M30 ::= {- _8 .5 _4 - _4}@~10 - _8
M48 ::= d4 _8 - _2
 
key g4 harm
key d4 min
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F1a1 ::= -*64
F1a2 ::= M14~ _4 M10 Run2
  | 7 _10 M5@~5 |
F1a3 ::= | 5 _2 1 _2 '1 _8 7# _4 |
F1a1 F1a2 F1a3
 
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F10a1 ::= M14 M11@~15 M45 5 _14 M23~@14 7 _10 1 _2 M11@~15 7b _8 5 _2 5b _2 5 _8
F10a2 ::= Run@~6
F10a3 ::= M12 5 _6 M17 4 _4 2 _2 M22 S2 5 _4 M25 7 _4 3 _4 6 _4 M46 M13 3 _2 '1 _2 2 _10 1 _2 M15@~-2
F10a1 F10a2 F10a3
 
 
% ——— Part 2, from m.1 ———
 
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F25a1 ::= 5 _8 - _8 M47 - _16
F25a2 ::= | 5 _8 '2 _8 |
  M10 Run2
F25a1 F25a2
 
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F32a1 ::= 7 _10 M5@~5 5 _4 - _8 5 _6 S5@17 M38@-2 2 _6 4b _2
F32a2 ::= M13 .7# _6 5 _2 M7 M7@~2 M38 7b _6 '4 _2
F32a3 ::= 7# _8
F32a1 F32a2 F32a3
 
 
% ——— Part 3, from m.1 ———
 
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F41a1 ::= '1 _4 M18 '1 _10 '2 _2
  | '3 _2 M11~@33 M5@~7 |
F41a2 ::= M43 M15 5 _4 - _4 M28
F41a3 ::= -*32
F41a4 ::= '2 _8 S1@~7
F41a5 ::= | M27~@~6 Run2@~3/2 |
  | 6 _10 M5@~3 |
  3 _8
F41a1 F41a2 F41a3 F41a4 F41a5
 
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F56a1 ::= 6 _8 5 _12 M18 M20~@26 M10@5/4 M11@~19 M5@~9 M20@~15 7# _2 M5@~5 5 _2 M32@2 M22 M32@4 M12 M32@7 M12@~2 '2b _4 '1 _4 7# _4 '5 _6 '1 _2 '4 _6 7# _2 '3 _6 M2 M15 5 _6 5 _2 M12@~4 '2 _2 M5@~8 '1 _6 M15@~3/2 M10@5/4 '2 _6 M20@~14 7b _2 7 _6 '5 _2
F56a2 ::= | '4 _2 '4b _2 M12@~7 7# _4 - _4 |
F56a1 F56a2
 
 
% ——— Part 4, from m.1 ———
 
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F71a ::= M30 '1 _18 7b _2 7# _4
F71a
 
key g4 harm
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F74a1 ::= | M18@~-4 M18@~-6 |
F74a2 ::= M48 M20~@~8 M15@~-3/2 4 _2 6 _4 M10~/4 '2 _4 '1 '2 '3 _2 5b _2 5 _24
F74a1 F74a2

% The Art of Fugue opens with one voice, alone. The subject leaps to
% the fifth and falls through the D minor triad back to the tonic, drops
% to the leading tone below it, then walks up to the fourth and back
% down to the second.

bpm 120
meter 4
unit 1/4
key d4 min
mode diatonic

Subject ::= | 1 _8 5 _8 |
  | 3 _8 1 _8 |
  | .7# _8 1 _4 2 _4 |
  | 3 _10 4 _2 3 _2 2 _2 |
Subject

% Four bars later a second voice answers at the fifth — but not by
% transposing. The subject's opening leap of a fifth comes back as a
% fourth (a to d, not a to e), and where the subject dropped to c#, the
% answer drops to g#: the leading tone of the key it is answering in.

Answer ::= | 5 _8 '1 _8 |
  | 7 _8 5 _8 |
  | 4# _8 5 _4 6# _4 |
  | 7 _10 '1 _2 7 _2 6 _2 |

Subject Answer

% Fall is the shape this fugue states most often — 36 times, three
% notes: the subject's last three, a step lower. Rise is the answer's turn
% up through g#, stated 8 times, spelled in absolute pitches because it
% plays inverted later on. Step Fall down the scale under a pair of Rises
% and you have a sequence — not a passage of this fugue, but the way a
% fugue fills the space between entries.

Fall ::= 3 _2 2 _2 1 _2
Rise ::= g#4 _8 a4 _4 b4 _4

assert Fall@~1 == 4 _2 3 _2 2 _2
assert Rise == 4# _8 5 _4 6# _4

Sequence ::= {Fall@~4 Fall@~3 Fall@~2 Fall@~1 Fall Fall@~-1,
  Rise@-12 Rise@-14 - _4}
Sequence

% Under the answer the first voice keeps going, with the countersubject:
% a scale up to the fifth, a drop into the register below, then Fall, the
% subject's own tail handed back, and a climb of three steps to g — which
% is Rise turned upside down and read backwards.

Counterb ::= .5 _2 .6# _2 .7 _2 .5 _2 3 _6 .6# _2 2 _6 Fall
Counter  ::= 1 _4 2 _4 3 _4 4 _4 5 _4 Counterb Rise~^@11

Opening ::= {-*64 Answer,
  Subject Counter}
Opening

% The exposition is that one line four times over, each entry four bars
% after the last and in a voice that has not sung yet: alto, then soprano
% with the answer a fifth above, then bass with the subject an octave
% below the alto, then tenor with the answer an octave below the soprano.

Entries ::= {-*64 Answer -*128,
  Subject -*192,
  -*192 Answer@-12,
  -*128 Subject@-12 -*64}
Entries

% All of it. Under each answer the voice that has just finished its own
% entry plays the countersubject — the alto at m.5, the bass at m.13 — but
% Bach re-cuts the bass version at both ends: one held d where the alto ran
% d e f g a up the scale, and where the alto climbed e f# g the bass
% zigzags e g f# a before its g. Only the middle, Counterb, is the alto's
% bars 6-7 an octave down.

Counter2 ::= .1 _8 -*12 Counterb@-12 .2 _2 .4 _2 .3# _2 .5 _2 .4 _8

Exposition ::= {-*64 Answer -*128,
  Subject Counter -*128,
  -*192 Answer@-12,
  -*128 Subject@-12 Counter2}

Exposition

% THE WHOLE FUGUE — all four voices, every entry, to the close.

bpm 120
meter 4
unit 1/4
key d4 min
mode diatonic

% The cast — every motif and chord the lead line uses:

M14 ::= '1 _2 5 _2
M10 ::= 7 _8 5 _8
Run2 ::= 5b _8 5 _4 7b _4
M20 ::= .1 _2 ..7 _2
M5 ::= M20@~9 1 _2
M11 ::= ..6 _6 ..4 _2
M45 ::= bb4 _6 e4 _2
M23 ::= .5 _2 .6 _4
Run ::= .7# _8 1 _4 2 _4
M12 ::= g4 _2 bb4 _2
M17 ::= bb4 _2 a4 _2
M22 ::= M10@-7/4
M3 ::= M23@~-2 .7 _10 .5 _2
S2 ::= 6 _10 M3@14 7 _4 '3 _10 M23@~10
M18 ::= '2 _6 7# _2
M25 ::= M18@~-1
M46 ::= a4 _8 d4 _4
M13 ::= M11@~12
M15 ::= 7 _8 6 _4
M47 ::= -*32
S5 ::= M5@~-6 M5@~-7 ..7# _2
M38 ::= 5 _6 7 _2
M27 ::= 3 _2 2 _6
M7 ::= 1 _6 M27 7 _2
M29 ::= 7# _2 5 _2
M43 ::= M29 M25
M28 ::= -*32
M1 ::= Run 3 _10 M20@~10
S1 ::= 5 _8 5b _8? 3 2 _8? 1 M1 2 _2
M32 ::= 3 _10 1 _2
M2 ::= '1 _2 M18 M25
M30 ::= {- _8 .5 _4 - _4}@~10 - _8
M48 ::= d4 _8 - _2

key g4 harm
key d4 min
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F1a1 ::= -*64
F1a2 ::= M14~ _4 M10 Run2
  | 7 _10 M5@~5 |
F1a3 ::= | 5 _2 1 _2 '1 _8 7# _4 |
F1a1 F1a2 F1a3

% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F10a1 ::= M14 M11@~15 M45 5 _14 M23~@14 7 _10 1 _2 M11@~15 7b _8 5 _2 5b _2 5 _8
F10a2 ::= Run@~6
F10a3 ::= M12 5 _6 M17 4 _4 2 _2 M22 S2 5 _4 M25 7 _4 3 _4 6 _4 M46 M13 3 _2 '1 _2 2 _10 1 _2 M15@~-2
F10a1 F10a2 F10a3

% ——— Part 2, from m.1 ———

% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F25a1 ::= 5 _8 - _8 M47 - _16
F25a2 ::= | 5 _8 '2 _8 |
  M10 Run2
F25a1 F25a2

% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F32a1 ::= 7 _10 M5@~5 5 _4 - _8 5 _6 S5@17 M38@-2 2 _6 4b _2
F32a2 ::= M13 .7# _6 5 _2 M7 M7@~2 M38 7b _6 '4 _2
F32a3 ::= 7# _8
F32a1 F32a2 F32a3

% ——— Part 3, from m.1 ———

% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F41a1 ::= '1 _4 M18 '1 _10 '2 _2
  | '3 _2 M11~@33 M5@~7 |
F41a2 ::= M43 M15 5 _4 - _4 M28
F41a3 ::= -*32
F41a4 ::= '2 _8 S1@~7
F41a5 ::= | M27~@~6 Run2@~3/2 |
  | 6 _10 M5@~3 |
  3 _8
F41a1 F41a2 F41a3 F41a4 F41a5

% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F56a1 ::= 6 _8 5 _12 M18 M20~@26 M10@5/4 M11@~19 M5@~9 M20@~15 7# _2 M5@~5 5 _2 M32@2 M22 M32@4 M12 M32@7 M12@~2 '2b _4 '1 _4 7# _4 '5 _6 '1 _2 '4 _6 7# _2 '3 _6 M2 M15 5 _6 5 _2 M12@~4 '2 _2 M5@~8 '1 _6 M15@~3/2 M10@5/4 '2 _6 M20@~14 7b _2 7 _6 '5 _2
F56a2 ::= | '4 _2 '4b _2 M12@~7 7# _4 - _4 |
F56a1 F56a2

% ——— Part 4, from m.1 ———

% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F71a ::= M30 '1 _18 7b _2 7# _4
F71a

key g4 harm
% mm.1-9 — Run2; M5 stepped through the scale, in retrograde, augmented; M14 in retrograde, augmented · 3 voices.
F74a1 ::= | M18@~-4 M18@~-6 |
F74a2 ::= M48 M20~@~8 M15@~-3/2 4 _2 6 _4 M10~/4 '2 _4 '1 '2 '3 _2 5b _2 5 _24
F74a1 F74a2

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

Opening…

The Art of Fugue I · Pattern Engine