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Solfeggietto

C. P. E. Bach — one rolling idea

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% C. P. E. Bach's Solfeggietto is ONE relentless idea: a broken
% chord ROLLING in sixteenths. Two shapes carry the whole piece — the
% roll on the tonic and its answer on the dominant — and '@12' lifts
% the restatement an octave (these are the literal opening bars):
 
bpm 140
key c harm
 
Roll   ::= .3 .1 .3 .5 1 3 2 1
Answer ::= .7 .5 .7 2 5 4 3 2
 
Roll Answer Roll@12
 
 
% Bar four is a plain scale PLUNGE — and slices audition its
% pieces: the whole fall, its retrograde, the halves:
 
Fall ::= '2 '1 7 6 5 4 3 2
 
Roll Answer Roll@12 Fall
Fall[::-1] Fall[0:4] Fall[4:] Fall
 
 
% Written as SCALE STEPS from the last pitch, the roll is one
% spelling that starts wherever the harmony has wandered — and
% ANCHOR APPLICATION states it once per starting pitch: Seed(a b c)
% is 'a Seed b Seed c Seed'. 'assert' proves the two spellings play
% identically:
 
Seed ::= s-2 s2 s2 s3 s2 s-1 s-1
 
Seed(.3 3 '3)
assert Seed(.3 3 '3) == .3 Seed 3 Seed '3 Seed
 
 
% From m.9 the roll RELOCATES: the same shape spelled as intervals
% (Theme) anchored on new pitches walks the harmony into E-flat, the
% relative major. Then the texture flips — repeated top notes PEAL
% over sixths while the roll's energy idles beneath:
 
Theme ::= i4 i5 i3 i-1 i-2 i-1 i-4 i4 i3 i5 i-2 i-2 i-1
Peal  ::= '1 ''1 '1 {3, '1} @5 '1 ''1 '1 {3, '1} @4 '1 '7b '1 {3, '1} @4 '1 '7b '1
 
7b ..5 ..7b Theme
.7b .5 .7b Theme
{3, '1} @5 Peal
 
 
% The storm (mm.17-24): the roll visits F minor, then a measured
% TREMOLO — a broken octave sustained through the whole bar — sinks
% by semitone, '@-1' at a time:
 
Trem ::= {..2b _16, .2b _16}
 
'6 ..4 ..6 Theme
.6 .4 .6 Theme
Trem Trem @-1 Trem @-2
 
 
% The last build (mm.25-32): the roll compressed into LEAPING
% two-note cells — sevenths answering thirds — laddering up to the
% summit run, the highest line in the piece:
 
Ladder ::= '2 4 {1, 7b} @-2 4 '2 4 {3, 5} '2b '7b '2b {3, 5} '2b '7b '2b
Summit ::= '3 '5 ''1 '5 '7b '6 '5 '4
 
{1, 7b} 5 Ladder @2
Summit
 
 
% The whole journey in one pass: the opening page, the E-flat
% peal, the F-minor storm and sinking tremolo, the ladder to the
% summit, and the closing rush up to high C:
 
Roll Answer Roll@12 Fall Roll@~1 Answer@~1 Roll@~1 @12 Fall@~1
7b ..5 ..7b Theme {3, '1} @5 Peal
'6 ..4 ..6 Theme Trem Trem @-1 Trem @-2
{1, 7b} 5 Ladder @2 Summit
3 1 3 Theme '3 '1 '3 '5 ''1 ''3 ''2 '7 ''1 _4
 
 
% mm.1-5 — NOTE FOR NOTE from here: the piece itself, at its own
% tempo, every measure to the end. The opening page states the roll
% four times and climbs two octaves doing it — at pitch, twice at the
% octave, then two octaves up — and answers it each time: twice with
% the dominant Answer, twice with a scale coming down. That scale is
% not quite 'Fall'. The piece RAISES its sixth, a natural where the
% harmonic minor flattens it, and one override says so. Then m.5 lets
% the sixteenths go: a long E flat with C minor falling out of it, a
% long A flat with A flat major rising out of that.
 
bpm 120
meter 4
unit 1/4
key c4 harm
mode diatonic
 
Descent ::= Fall \3 {6#}
Climb   ::= Roll Answer Roll@12 Descent Roll@12 Answer@12 Roll@24 Descent@12
 
assert Descent == '2 '1 7 6# 5 4 3 2
 
Climb
  '3 _5 ''1 '5 '3 '6 _5 6 '1 '3
 
 
% mm.6-8 — the turn to G MINOR. Nothing in these three measures comes
% back anywhere in the piece, so they are written where they stand: a
% held D with B flat major falling out of it, a held G with E flat
% rising to its seventh; a four-note turn on A with the A flat under
% it, said twice, and C minor falling to that same A, said twice; then
% the dominant seventh of G broken four ways, the last of them straight
% down the chord.
 
key g4 harm
 
5 _5 '3 7b 5 '1 _4 .6 1 3 5
  4 2 2b 2 4 2 2b 2 6 4 1 2 6 4 1 2
  5 4 .7 2 '2 4 .7 2 7 4 .5 2 4 2 .7 .5
 
 
% mm.9-16 — THE WHOLE PAGE AGAIN, in G minor an octave down, and it
% needs no new name: 'Climb' under '@-12', its first note overridden by
% the B flat the line leaps up to. Then the sixteenths become BELLS. A
% bass octave is struck and held a beat and its own triad falls out of
% it; the flat seventh under it is struck, and the next key's dominant
% rises out of that; then a two-note chord is struck short with an octave
% rung over it, and every bell is said twice — the strike and its echo
% are what 'Toll' holds. Those two measures come again a fourth higher,
% which is how G minor walks down to the F minor of m.17. The bells are
% written as NOTES: they ring again at m.26 under another key, on the
% same four pitches.
 
key g4 harm
 
Toll   ::= {$1, $2}/2 -/2 $3 $4 $3 {$1, $2}/2 -/2 $3 $4 $3
Bells  ::= c5 eb4 g4 g5 b4 d4 g4 f5
Strike ::= {.1, ..1} _4 '1 5 3 1 {..7b, ...7b} _4 1 3# 5 '1
 
assert Roll == bb3 g3 bb3 d4 g4 bb4 a4 g4
 
Climb \0 {'3} @-12
  Strike Toll(Bells) Strike@5 Toll(Bells@5)
 
 
% mm.17-24 — the page a THIRD time, a fifth lower again: F minor, the
% subdominant, and still no new name — only the A flat the line leaps
% to, overridden in. m.21 then breaks that F minor into four waves,
% each beginning a chord-note lower; no single mark can say that,
% because the triad's steps through the scale are uneven, so its
% sixteen degrees stand written. After it the sixteenths stop dead: an
% octave holds a whole measure and sinks a semitone at a time, three
% measures of it. It is the octave tremolo named 'Trem' above, written
% here from its top note down — 'assert' says the two agree.
 
key c4 harm
 
assert {.2b, ..2b} _16 == Trem
 
Climb \0 {''3} @-7
  6 '4 '1 6 4 '1 6 4 1 6 4 1 .6 4 1 .6
  {.2b, ..2b} _16 {.2b, ..2b} _16 @-1
{.2b, ..2b} _16 @-2
 
 
% mm.25-32 — the last build. A C octave, the F above it, then E flat
% over G held just short of a beat while the line taps out d, e flat,
% d, c, d in staccato thirds of a unit. The bells return at m.26 on the
% SAME four pitches as m.14, struck a third of a unit where they were
% struck a half — the one difference no mark can carry, so 'Knell' is
% 'Toll' written again with the shorter strike. From m.27 they fall by
% FIFTHS: C7, F7, then that pair two semitones down (B flat 7, E flat
% 7), then A flat 7 and the diminished chord that leads home. m.30
% holds E flat over G, C minor falls out of it, the dominant octave is
% struck — and the roll is back: mm.31-32 are the opening bars again.
 
key c4 harm
 
Knell  ::= {$1, $2}/3 - _2/3 $3 $4 $3 {$1, $2}/3 - _2/3 $3 $4 $3
Fifths ::= bb4 c4 g4 e5 a4 f4 eb5 c6
 
assert Knell(eb4 c5 g4 g5 b4 d4 g4 f5) == Knell(Bells)
assert Fifths[:4]@-4 == f#4 ab3 eb4 c5
 
{.1, ..1} _4 .4 _4 {'3, .5} _23/6 -/3
  {'3, ..5}/3 -/6 '2/3 -/3 '3/3 -/3 '2/3 -/3 '1/3 -/3 '2/3 -/3
  Knell(eb4 c5 g4 g5 b4 d4 g4 f5) Knell(Fifths)
  Knell(Fifths@-2) Knell(f#4 ab3 eb4 c5 eb4 f#3 c5 c6)
  {3, .5} _8 '5 '3 '1 5 {.5, ..5} _4
  Roll \0 {3} Answer Roll@12 Descent
 
 
% mm.33-34 — the roll and its answer at the octave, and then the roll
% a fourth time two octaves up, CUT SHORT after seven notes. The last
% two are the cadence the whole piece has been rolling towards: the
% leading tone, and the C above it.
 
assert Roll[:7]@24 == eb5 c5 eb5 g5 c6 eb6 d6
 
Roll@12 Answer@12 Roll[:7]@24 '7 ''1

% C. P. E. Bach's Solfeggietto is ONE relentless idea: a broken
% chord ROLLING in sixteenths. Two shapes carry the whole piece — the
% roll on the tonic and its answer on the dominant — and '@12' lifts
% the restatement an octave (these are the literal opening bars):

bpm 140
key c harm

Roll   ::= .3 .1 .3 .5 1 3 2 1
Answer ::= .7 .5 .7 2 5 4 3 2

Roll Answer Roll@12

% Bar four is a plain scale PLUNGE — and slices audition its
% pieces: the whole fall, its retrograde, the halves:

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

Roll Answer Roll@12 Fall
Fall[::-1] Fall[0:4] Fall[4:] Fall

% Written as SCALE STEPS from the last pitch, the roll is one
% spelling that starts wherever the harmony has wandered — and
% ANCHOR APPLICATION states it once per starting pitch: Seed(a b c)
% is 'a Seed b Seed c Seed'. 'assert' proves the two spellings play
% identically:

Seed ::= s-2 s2 s2 s3 s2 s-1 s-1

Seed(.3 3 '3)
assert Seed(.3 3 '3) == .3 Seed 3 Seed '3 Seed

% From m.9 the roll RELOCATES: the same shape spelled as intervals
% (Theme) anchored on new pitches walks the harmony into E-flat, the
% relative major. Then the texture flips — repeated top notes PEAL
% over sixths while the roll's energy idles beneath:

Theme ::= i4 i5 i3 i-1 i-2 i-1 i-4 i4 i3 i5 i-2 i-2 i-1
Peal  ::= '1 ''1 '1 {3, '1} @5 '1 ''1 '1 {3, '1} @4 '1 '7b '1 {3, '1} @4 '1 '7b '1

7b ..5 ..7b Theme
.7b .5 .7b Theme
{3, '1} @5 Peal

% The storm (mm.17-24): the roll visits F minor, then a measured
% TREMOLO — a broken octave sustained through the whole bar — sinks
% by semitone, '@-1' at a time:

Trem ::= {..2b _16, .2b _16}

'6 ..4 ..6 Theme
.6 .4 .6 Theme
Trem Trem @-1 Trem @-2

% The last build (mm.25-32): the roll compressed into LEAPING
% two-note cells — sevenths answering thirds — laddering up to the
% summit run, the highest line in the piece:

Ladder ::= '2 4 {1, 7b} @-2 4 '2 4 {3, 5} '2b '7b '2b {3, 5} '2b '7b '2b
Summit ::= '3 '5 ''1 '5 '7b '6 '5 '4

{1, 7b} 5 Ladder @2
Summit

% The whole journey in one pass: the opening page, the E-flat
% peal, the F-minor storm and sinking tremolo, the ladder to the
% summit, and the closing rush up to high C:

Roll Answer Roll@12 Fall Roll@~1 Answer@~1 Roll@~1 @12 Fall@~1
7b ..5 ..7b Theme {3, '1} @5 Peal
'6 ..4 ..6 Theme Trem Trem @-1 Trem @-2
{1, 7b} 5 Ladder @2 Summit
3 1 3 Theme '3 '1 '3 '5 ''1 ''3 ''2 '7 ''1 _4

% mm.1-5 — NOTE FOR NOTE from here: the piece itself, at its own
% tempo, every measure to the end. The opening page states the roll
% four times and climbs two octaves doing it — at pitch, twice at the
% octave, then two octaves up — and answers it each time: twice with
% the dominant Answer, twice with a scale coming down. That scale is
% not quite 'Fall'. The piece RAISES its sixth, a natural where the
% harmonic minor flattens it, and one override says so. Then m.5 lets
% the sixteenths go: a long E flat with C minor falling out of it, a
% long A flat with A flat major rising out of that.

bpm 120
meter 4
unit 1/4
key c4 harm
mode diatonic

Descent ::= Fall \3 {6#}
Climb   ::= Roll Answer Roll@12 Descent Roll@12 Answer@12 Roll@24 Descent@12

assert Descent == '2 '1 7 6# 5 4 3 2

Climb
  '3 _5 ''1 '5 '3 '6 _5 6 '1 '3

% mm.6-8 — the turn to G MINOR. Nothing in these three measures comes
% back anywhere in the piece, so they are written where they stand: a
% held D with B flat major falling out of it, a held G with E flat
% rising to its seventh; a four-note turn on A with the A flat under
% it, said twice, and C minor falling to that same A, said twice; then
% the dominant seventh of G broken four ways, the last of them straight
% down the chord.

key g4 harm

5 _5 '3 7b 5 '1 _4 .6 1 3 5
  4 2 2b 2 4 2 2b 2 6 4 1 2 6 4 1 2
  5 4 .7 2 '2 4 .7 2 7 4 .5 2 4 2 .7 .5

% mm.9-16 — THE WHOLE PAGE AGAIN, in G minor an octave down, and it
% needs no new name: 'Climb' under '@-12', its first note overridden by
% the B flat the line leaps up to. Then the sixteenths become BELLS. A
% bass octave is struck and held a beat and its own triad falls out of
% it; the flat seventh under it is struck, and the next key's dominant
% rises out of that; then a two-note chord is struck short with an octave
% rung over it, and every bell is said twice — the strike and its echo
% are what 'Toll' holds. Those two measures come again a fourth higher,
% which is how G minor walks down to the F minor of m.17. The bells are
% written as NOTES: they ring again at m.26 under another key, on the
% same four pitches.

key g4 harm

Toll   ::= {$1, $2}/2 -/2 $3 $4 $3 {$1, $2}/2 -/2 $3 $4 $3
Bells  ::= c5 eb4 g4 g5 b4 d4 g4 f5
Strike ::= {.1, ..1} _4 '1 5 3 1 {..7b, ...7b} _4 1 3# 5 '1

assert Roll == bb3 g3 bb3 d4 g4 bb4 a4 g4

Climb \0 {'3} @-12
  Strike Toll(Bells) Strike@5 Toll(Bells@5)

% mm.17-24 — the page a THIRD time, a fifth lower again: F minor, the
% subdominant, and still no new name — only the A flat the line leaps
% to, overridden in. m.21 then breaks that F minor into four waves,
% each beginning a chord-note lower; no single mark can say that,
% because the triad's steps through the scale are uneven, so its
% sixteen degrees stand written. After it the sixteenths stop dead: an
% octave holds a whole measure and sinks a semitone at a time, three
% measures of it. It is the octave tremolo named 'Trem' above, written
% here from its top note down — 'assert' says the two agree.

key c4 harm

assert {.2b, ..2b} _16 == Trem

Climb \0 {''3} @-7
  6 '4 '1 6 4 '1 6 4 1 6 4 1 .6 4 1 .6
  {.2b, ..2b} _16 {.2b, ..2b} _16 @-1
{.2b, ..2b} _16 @-2

% mm.25-32 — the last build. A C octave, the F above it, then E flat
% over G held just short of a beat while the line taps out d, e flat,
% d, c, d in staccato thirds of a unit. The bells return at m.26 on the
% SAME four pitches as m.14, struck a third of a unit where they were
% struck a half — the one difference no mark can carry, so 'Knell' is
% 'Toll' written again with the shorter strike. From m.27 they fall by
% FIFTHS: C7, F7, then that pair two semitones down (B flat 7, E flat
% 7), then A flat 7 and the diminished chord that leads home. m.30
% holds E flat over G, C minor falls out of it, the dominant octave is
% struck — and the roll is back: mm.31-32 are the opening bars again.

key c4 harm

Knell  ::= {$1, $2}/3 - _2/3 $3 $4 $3 {$1, $2}/3 - _2/3 $3 $4 $3
Fifths ::= bb4 c4 g4 e5 a4 f4 eb5 c6

assert Knell(eb4 c5 g4 g5 b4 d4 g4 f5) == Knell(Bells)
assert Fifths[:4]@-4 == f#4 ab3 eb4 c5

{.1, ..1} _4 .4 _4 {'3, .5} _23/6 -/3
  {'3, ..5}/3 -/6 '2/3 -/3 '3/3 -/3 '2/3 -/3 '1/3 -/3 '2/3 -/3
  Knell(eb4 c5 g4 g5 b4 d4 g4 f5) Knell(Fifths)
  Knell(Fifths@-2) Knell(f#4 ab3 eb4 c5 eb4 f#3 c5 c6)
  {3, .5} _8 '5 '3 '1 5 {.5, ..5} _4
  Roll \0 {3} Answer Roll@12 Descent

% mm.33-34 — the roll and its answer at the octave, and then the roll
% a fourth time two octaves up, CUT SHORT after seven notes. The last
% two are the cadence the whole piece has been rolling towards: the
% leading tone, and the C above it.

assert Roll[:7]@24 == eb5 c5 eb5 g5 c6 eb6 d6

Roll@12 Answer@12 Roll[:7]@24 '7 ''1

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Solfeggietto · Pattern Engine