Lessons · Showcase

Invention No. 8

Canon at the octave

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% Invention No. 8 is a CANON at the octave: the lower voice plays the
% upper voice's line, one measure behind it. That line is two measures
% long: the F major triad in eighths (Head), then a run falling from
% f5 to g4 (Run).
 
bpm 90
instrument hollow
meter 3
unit 1/4
key f4 maj
mode diatonic
 
Head    ::= - _2 1 _2 3 _2 1 _2 5 _2 1 _2
Run     ::= '1 _2 7 6 5 6 5 4 3 4 3 2
Subject ::= Head Run
 
Subject
 
 
% While the answer enters below it, the top voice keeps going: the
% same triad in eighths, reaching up to f5 (Arp, m.3), then a zigzag
% holding c6 against bb5 and a5 (Zig, m.4). Zig is eleven notes, so the
% a5 pickup fills out the measure.
 
Arp ::= 1 _2 3 _2 5 _2 3 _2 '1 _2 5 _2
Zig ::= '5 '4 '5 '3 '5 '4 '5 '3 '5 '4 '5
 
Subject Arp '3 Zig
 
 
% THE DEVICE, bare. A canon is one rule referenced twice with a rest
% before the second entry: '-*12' is exactly one measure here (meter 3,
% unit 1/4: twelve sixteenths), and '@-12' drops the answer an octave.
% The trailing rest gives both fields the same length, so neither voice
% is stretched to fit the other.
 
Canon ::= {Subject -*12, -*12 Subject@-12}
 
Canon
 
 
% mm.1-4, note for note: the same canon with the top voice's
% continuation written in. The lower voice is still the upper voice one
% measure late: Subject, then Arp, each carrying the same '@-12'.
 
Opening ::= {Subject Arp '3 Zig, -*12 Subject@-12 Arp@-12}
 
Opening
 
 
% The canon does not stop; the voices trade places. At m.12 the LOWER
% voice leads with the subject an eleventh down, on the dominant (a
% real transposition, so its second measure sounds b natural), and the
% upper voice answers a measure later, two octaves above it.
 
Dom  ::= Subject@-17
Swap ::= {-*12 Dom@24, Dom -*12}
 
Swap
 
 
% Between the entries the piece runs on one figure: d4 rocking against
% f3, e3 and d3 underneath it (Rock). '@~n' shifts a figure by SCALE
% steps, so every copy stays in F: the lower voice states it a step up
% and then plain across mm.19-20, and the upper voice takes it eleven
% steps up in m.15.
 
Rock    ::= .6 .1 .6 ..7 .6 .1 .6 ..6 .6
Descent ::= .2 .1 .2 Rock@~1 .1 ..7 .1 Rock
 
Descent
5 4 5 Rock@~11
 
 
% The argument in one pass, in the piece's own order: the canon at the
% octave (mm.1-4), the same canon reversed on the dominant (mm.12-14),
% the rocking figure eleven steps up (m.15) and stepping down again
% (mm.19-20), and the two measures that close the piece: the bass
% falling to f2 under the F major triad.
 
Cadence ::= .4 _2 1 _2 .3 _2 1 _2 .2 _2 .7 _2 {1 _4, .5 _4, .3 _4}
Walk    ::= ..2 ..3 ..2 ..1 ..5 ..4 ..3 ..4 ..5 _2 ...5 _2 ..1 _4
 
Opening
Swap
5 4 5 Rock@~11
Descent
{Cadence, Walk}
 
 
% THE WHOLE INVENTION: the canon run out to its end.
 
bpm 90
meter 3
unit 1/4
key f4 maj
mode diatonic
 
% The cast, every motif and chord the lead line uses:
 
M17 ::= .2 _2 .4 _2 .2 _2
M12 ::= M17 .6 _2 .2 _2
M2 ::= - _2 M12@~-1
Run ::= 7 6 5
M8 ::= Run Run@~-1
S3 ::= M8@~-2
M14 ::= '5 '4 '5 '3
M9 ::= M14 M14 '5 '4 '5
M6 ::= M9 '1
M1 ::= '3 M6 M6@~-2 M9@~-4 5b _2 2 _2
M3 ::= M8@~2 5 Run@~-1
M11 ::= 3b _2 .5b _2
S2 ::= M1 6 _2 5b _2 '1 _2 6 _2 '2 '3 M3 3 _2 M3@-5 .7 Run@~-6 .5 _2 5 5b 5 _2 .7 _2 1 _2 5 _2 .7 _2 5 _2 M11~@3
S5 ::= c5 bb4 c5 a5 c5 a5 bb4 a5 c5 a5 a4 a5 bb4 _2 g4 _2 bb4 _2
M15 ::= '2 _2 S3@5 4 5 4 3
M5 ::= .2 .1 _2 .3 _2 .5 _2 .3 _2 1 _2 .5 _2
S4 ::= .4 .3 M5 M11*3 .5 _2
S6 ::= '2 '1 '2 '4 5 '4 6 '4 7 '4 5 '4
M7 ::= 7 _2 5 _2 3 _2 5 _2
 
key c4 maj
key f4 maj
% mm.1-3: S3 stepped through the scale · 2 voices.
F1a ::= M2@12
  | '1 _2 7 6 5 6 S3 |
  1 _2 3 _2 5 _2 3 _2 '1 _2
F1a
 
% mm.1-3: S3 stepped through the scale · 2 voices.
F4a ::= 5 _2 S2
F4a
 
 
% Part 2, from m.1
 
key c4 maj
% mm.1-3: S3 stepped through the scale · 2 voices.
F12a1 ::= | '1 _4 - _8 |
  M2@24
  | ''1 _2 M8@~7 '3 '4 '3 '2 |
F12a2 ::= S5 5 _2 '2 _2 5 _2
F12a1 F12a2
 
key f4 maj
% mm.1-3: S3 stepped through the scale · 2 voices.
F17a1 ::= M15 2 _2 M17@~9 S4[7:16]@~8 3 _2 '1 _2 6 _2 '3 _2 '1 _2
F17a1 S6
 
 
% Part 3, from m.1
 
% mm.1-3: S3 stepped through the scale · 2 voices.
F22a ::= | '1 7 '1 '3 5b '3 6b '3 6 '3 5b '3 |
  S6@-3
  | M7@~1 2 _2 '1 _2 |
F22a
 
% mm.1-3: S3 stepped through the scale · 2 voices.
F25a ::= M7 1 _2
F25a
 
 
% Part 4, from m.1
 
% mm.1-3: S3 stepped through the scale · 2 voices.
F26a ::= 7b _2 S2@-7
F26a
 
% mm.1-3: S3 stepped through the scale · 2 voices.
F34a ::= .1Dia$3-5-1 _4
F34a

% Invention No. 8 is a CANON at the octave: the lower voice plays the
% upper voice's line, one measure behind it. That line is two measures
% long: the F major triad in eighths (Head), then a run falling from
% f5 to g4 (Run).

bpm 90
instrument hollow
meter 3
unit 1/4
key f4 maj
mode diatonic

Head    ::= - _2 1 _2 3 _2 1 _2 5 _2 1 _2
Run     ::= '1 _2 7 6 5 6 5 4 3 4 3 2
Subject ::= Head Run

Subject

% While the answer enters below it, the top voice keeps going: the
% same triad in eighths, reaching up to f5 (Arp, m.3), then a zigzag
% holding c6 against bb5 and a5 (Zig, m.4). Zig is eleven notes, so the
% a5 pickup fills out the measure.

Arp ::= 1 _2 3 _2 5 _2 3 _2 '1 _2 5 _2
Zig ::= '5 '4 '5 '3 '5 '4 '5 '3 '5 '4 '5

Subject Arp '3 Zig

% THE DEVICE, bare. A canon is one rule referenced twice with a rest
% before the second entry: '-*12' is exactly one measure here (meter 3,
% unit 1/4: twelve sixteenths), and '@-12' drops the answer an octave.
% The trailing rest gives both fields the same length, so neither voice
% is stretched to fit the other.

Canon ::= {Subject -*12, -*12 Subject@-12}

Canon

% mm.1-4, note for note: the same canon with the top voice's
% continuation written in. The lower voice is still the upper voice one
% measure late: Subject, then Arp, each carrying the same '@-12'.

Opening ::= {Subject Arp '3 Zig, -*12 Subject@-12 Arp@-12}

Opening

% The canon does not stop; the voices trade places. At m.12 the LOWER
% voice leads with the subject an eleventh down, on the dominant (a
% real transposition, so its second measure sounds b natural), and the
% upper voice answers a measure later, two octaves above it.

Dom  ::= Subject@-17
Swap ::= {-*12 Dom@24, Dom -*12}

Swap

% Between the entries the piece runs on one figure: d4 rocking against
% f3, e3 and d3 underneath it (Rock). '@~n' shifts a figure by SCALE
% steps, so every copy stays in F: the lower voice states it a step up
% and then plain across mm.19-20, and the upper voice takes it eleven
% steps up in m.15.

Rock    ::= .6 .1 .6 ..7 .6 .1 .6 ..6 .6
Descent ::= .2 .1 .2 Rock@~1 .1 ..7 .1 Rock

Descent
5 4 5 Rock@~11

% The argument in one pass, in the piece's own order: the canon at the
% octave (mm.1-4), the same canon reversed on the dominant (mm.12-14),
% the rocking figure eleven steps up (m.15) and stepping down again
% (mm.19-20), and the two measures that close the piece: the bass
% falling to f2 under the F major triad.

Cadence ::= .4 _2 1 _2 .3 _2 1 _2 .2 _2 .7 _2 {1 _4, .5 _4, .3 _4}
Walk    ::= ..2 ..3 ..2 ..1 ..5 ..4 ..3 ..4 ..5 _2 ...5 _2 ..1 _4

Opening
Swap
5 4 5 Rock@~11
Descent
{Cadence, Walk}

% THE WHOLE INVENTION: the canon run out to its end.

bpm 90
meter 3
unit 1/4
key f4 maj
mode diatonic

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

M17 ::= .2 _2 .4 _2 .2 _2
M12 ::= M17 .6 _2 .2 _2
M2 ::= - _2 M12@~-1
Run ::= 7 6 5
M8 ::= Run Run@~-1
S3 ::= M8@~-2
M14 ::= '5 '4 '5 '3
M9 ::= M14 M14 '5 '4 '5
M6 ::= M9 '1
M1 ::= '3 M6 M6@~-2 M9@~-4 5b _2 2 _2
M3 ::= M8@~2 5 Run@~-1
M11 ::= 3b _2 .5b _2
S2 ::= M1 6 _2 5b _2 '1 _2 6 _2 '2 '3 M3 3 _2 M3@-5 .7 Run@~-6 .5 _2 5 5b 5 _2 .7 _2 1 _2 5 _2 .7 _2 5 _2 M11~@3
S5 ::= c5 bb4 c5 a5 c5 a5 bb4 a5 c5 a5 a4 a5 bb4 _2 g4 _2 bb4 _2
M15 ::= '2 _2 S3@5 4 5 4 3
M5 ::= .2 .1 _2 .3 _2 .5 _2 .3 _2 1 _2 .5 _2
S4 ::= .4 .3 M5 M11*3 .5 _2
S6 ::= '2 '1 '2 '4 5 '4 6 '4 7 '4 5 '4
M7 ::= 7 _2 5 _2 3 _2 5 _2

key c4 maj
key f4 maj
% mm.1-3: S3 stepped through the scale · 2 voices.
F1a ::= M2@12
  | '1 _2 7 6 5 6 S3 |
  1 _2 3 _2 5 _2 3 _2 '1 _2
F1a

% mm.1-3: S3 stepped through the scale · 2 voices.
F4a ::= 5 _2 S2
F4a

% Part 2, from m.1

key c4 maj
% mm.1-3: S3 stepped through the scale · 2 voices.
F12a1 ::= | '1 _4 - _8 |
  M2@24
  | ''1 _2 M8@~7 '3 '4 '3 '2 |
F12a2 ::= S5 5 _2 '2 _2 5 _2
F12a1 F12a2

key f4 maj
% mm.1-3: S3 stepped through the scale · 2 voices.
F17a1 ::= M15 2 _2 M17@~9 S4[7:16]@~8 3 _2 '1 _2 6 _2 '3 _2 '1 _2
F17a1 S6

% Part 3, from m.1

% mm.1-3: S3 stepped through the scale · 2 voices.
F22a ::= | '1 7 '1 '3 5b '3 6b '3 6 '3 5b '3 |
  S6@-3
  | M7@~1 2 _2 '1 _2 |
F22a

% mm.1-3: S3 stepped through the scale · 2 voices.
F25a ::= M7 1 _2
F25a

% Part 4, from m.1

% mm.1-3: S3 stepped through the scale · 2 voices.
F26a ::= 7b _2 S2@-7
F26a

% mm.1-3: S3 stepped through the scale · 2 voices.
F34a ::= .1Dia$3-5-1 _4
F34a

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

Invention No. 8 · Showcase