Lessons · Showcase

Sonata K. 11

Scarlatti: binary dance, hand-crossing leaps

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% A Scarlatti sonata is a BINARY dance: one half out to the
% dominant, one half home, both repeated. The opening gesture: up
% the octave, then the courtly turn (lifted verbatim from the
% verified grammar):
 
bpm 120
instrument plain
meter 8
unit 1/8
key c harm
 
Theme ::= 5 _2 '3 _2 5 _2 '2 _2 '1 7 '1
Theme
 
 
% The answering idea walks down by step with the raised sixth of
% the harmonic minor. 6# is the Scarlatti color:
 
ThemeB ::= '4 _2 '5 _2 '1 _2 7 _2 6# _2 5 _2
ThemeB Theme
 
 
% HAND-CROSSING, the sonata's stunt: the same line hurled two
% octaves down mid-phrase. One '@-24' is the whole acrobatic:
 
Theme {Theme}@-24 Theme
 
 
% The binary shape in miniature: A leans away, B leans home,
% and each half says itself twice, exactly as the repeat signs ask:
 
A ::= Theme ThemeB
B ::= {ThemeB}@~-2 Theme
 
A A B B
 
 
% THE SONATA, note for note: both halves at full length. Every rule
% below is a figure the piece states more than once; whatever it says in
% one place only is written where it stands.
%
% Ped is this sonata's accompaniment in one line: a CELL whose hole takes
% a melody note and answers it with the g below. Two notes poured through
% it are the whole of m.5.
% Arp: the tonic arpeggio, c g c eb g, sounded four times. Its first
% four notes an octave up are the link inside DropPair, and that is the
% slice Arp[:4], not a second rule.
% Drop: f eb d over that same g, then c b to finish; the pedal answers
% only the first two notes.
% DropPair: Drop twice with the link between them. It closes mm.1-8 and
% comes back at mm.22-23, both times ending three units short of the
% barline.
 
key c4 harm
mode diatonic
 
Ped      ::= $1 _2 5 _2
Arp      ::= 1 .5 1 3 5 _2
Drop     ::= Ped('4 '3) '2 _2 '1 7
DropPair ::= Drop Arp[:4]@12 Drop '1
 
assert Arp[:4]@12 == '1 5 '1 '3
 
 
% mm.1-8: the first paragraph, built out of the two ideas the lesson
% opened with. Answer is ThemeB with the two steps that lead into it: the
% piece never states ThemeB without them. Its last four notes are also
% the cadence of the phrase BETWEEN the two statements of Answer, an
% octave lower: the slice ThemeB[2:] under one transposition, and not a
% second name.
%
% Then m.5 states the Theme's own eb g d with the g moved to fall AFTER
% each melody note instead of before it, which is exactly what Ped
% spells, and the measure says itself twice.
%
% Nothing here begins on a barline after the opening note, so the lines
% below break at figures: the phrase, the repeated measure, the close.
 
Answer ::= '2 _2 '3 _2 ThemeB
 
assert ThemeB[2:]@-12 == 1 _2 .7 _2 .6# _2 .5 _2
assert Ped('3 '2) == Theme[1:4] 5 _2
 
5 _4 7 _7/2 6#/2 '1 _6 Answer 4 _2 3 _2 4 _2 5 _2 ThemeB[2:]@-12 Answer '2 _2
  | Ped('3 '2) '1 _2 7 6# 7 5 7 '2 |*2
  DropPair 7 '1 '2
 
 
% mm.9-14, OUT TO THE DOMINANT, and the key mark is the whole of that
% claim: g minor, the dominant's own harmonic minor. The four rules below
% are written in DEGREES, so these same names sound in g here and in c
% when the piece comes home at m.25: one figure each, not two.
%
% Tetra: four steps down from the leading tone; in c that is b ab g f.
% Halved, and restated a step or an octave lower, it is every scale in
% the sonata, and the assert builds a whole octave out of it.
% Trill: one shake on the second degree, ending on the tonic.
% TrillPair: the shake a step higher, then the shake, each one shedding
% a note as it goes. Four places name it and it sounds six times,
% as often as Tetra, which is saying something for a shake against
% a scale.
% Min3: a minor third, a quarter long. Four transpositions state it,
% and it is a minor third at every one.
 
key g4 harm
 
Tetra     ::= 7 _2 6 _2 5 _2 4 _2
Trill     ::= 2 3/2 2/2 3/2 2/2 1/2
TrillPair ::= Trill@~1 1/2 Trill .7/2
Min3      ::= {2, .7} _2
 
assert 1 == g4
assert '1 7b Tetra@~-1/2 2 1 == '1 7b 6 5 4 3 2 1
assert Trill@~8 == '3 '4/2 '3/2 '4/2 '3/2 '2/2
assert Min3 == {f#4, a4} _2
 
 
% Both halves of the sonata end the same way, and it is ONE pair of
% rules, the only reason mm.25-29 need no new material at all.
%
% Approach: the arpeggio and the trill pair, twice over, the second time
% from the fifth above. The '?' slots are a CHOICE the rule offers: this
% statement takes the derivation that leaves them silent, and m.27 pins
% the other one, which is the whole of how the return is varied.
% Descent: two octaves down onto the tonic chord, and both octaves are
% Tetra: halved a step lower, then halved an octave and a step lower.
%
% mm.9-14 entire. m.9 walks the scale down from the sixth (with the
% fourth flattened between two c's) and then circles the f# below it;
% m.10 is the arpeggio, the third and the shakes; Approach and Descent
% run three and a half measures together, so they take a line of their
% own; and the g minor chord ends the half twice over, the second time
% with its third underneath.
 
Approach ::= Arp 4 _2 TrillPair 5 3? 1 5? 3 '1? 5 '1 _2 4 _2 TrillPair
Descent  ::= 1 '1 7b Tetra@~-1/2 2 1 1 .7b Tetra@~-8/2 .2 .1 - _3 1Min _4
 
6 5 4 4b Tetra@~-3/2 2 1 .7 .6# .7 .5 .6# .7
  Arp Min3@~2 TrillPair
  Approach Descent
  1Min$3-5-1 _4 - _4
 
 
% mm.15-16: the double bar, and the second half begins by standing
% still. Two measures on c minor's own dominant, one to the line: the
% bass g alone, the chord struck twice, silence, and then a new head in
% the opening's rhythm, a long note, a note with a flick off it, and a
% long one again.
 
key c4 harm
 
.5 - _3 5Dia _4 5Dia$1-3-5-1 _4 - _4
  7 _4 '1 _7/2 7/2 '2 _6 '3 _2
 
 
% mm.17-24: the second half's long paragraph, a page of SEQUENCES, one
% measure to the line except where DropPair runs across a barline.
%
% m.17 falls through three minor thirds a step apart, and all three are
% Min3: the middle one held twice as long, which '_2' after a reference
% says. m.18 falls in melodic thirds instead (ab f, g eb, f d), each
% pair a step lower than the last, and three steps down to the tonic to
% close it. m.20 states Step three times, each statement a degree below
% the one before, and then climbs away from the bottom of the fall:
% '1 '2 '3, three notes it has not just said, going up where
% everything before them went down.
%
% From there the paragraph ends the way the first half's did: the shake
% an octave and a step higher, DropPair, and two tetrachords chained into
% one scale.
 
Step ::= '4 '3 '2 _2
 
assert Step@~-2 == '2 '1 7 _2
 
Min3@~9 Min3@~8 _2 Min3@~7 '3/2 '4/2 '3/2 '4/2 '3 '2/2 '3/2 '1 _2 5 _2
  6 _2 4 _2 5 _2 3 _2 4 _2 2 _2 3 2 1 _2
  .7 _2 .5 _2 1 _4 .5 _6 '5 _2
  Step Step@~-1 Step@~-2 '1 '2 '3 _2
  '2/2 '3/2 '4 _3 Trill@~8 '3/2 '2 _6 '3 _2
  DropPair 7b 6 5
  Tetra@~-1/2 Tetra@~-3/2 2 1 .7 1 .7 .5 .6 .7
 
 
% mm.25-29: mm.9-14 return, at home and an octave up. '@~7' is seven
% scale steps, and in a seven-note scale that is the octave, which the
% assert says outright.
%
% So the end of the sonata needs no new material at all. One measure of
% the arpeggio and the shakes, then the whole of Approach, PINNED this
% time to the derivation that fills its optional slots, so the notes the
% return adds come from the same rule that sounded without them at m.11
% and then Descent, and the tonic chord in four voices.
 
assert Arp@~7 == Arp@12
 
Arp 4 _2 TrillPair
  Approach#8@~7 Descent@~7 ''1Dia$1-3-5-1 _4

% A Scarlatti sonata is a BINARY dance: one half out to the
% dominant, one half home, both repeated. The opening gesture: up
% the octave, then the courtly turn (lifted verbatim from the
% verified grammar):

bpm 120
instrument plain
meter 8
unit 1/8
key c harm

Theme ::= 5 _2 '3 _2 5 _2 '2 _2 '1 7 '1
Theme

% The answering idea walks down by step with the raised sixth of
% the harmonic minor. 6# is the Scarlatti color:

ThemeB ::= '4 _2 '5 _2 '1 _2 7 _2 6# _2 5 _2
ThemeB Theme

% HAND-CROSSING, the sonata's stunt: the same line hurled two
% octaves down mid-phrase. One '@-24' is the whole acrobatic:

Theme {Theme}@-24 Theme

% The binary shape in miniature: A leans away, B leans home,
% and each half says itself twice, exactly as the repeat signs ask:

A ::= Theme ThemeB
B ::= {ThemeB}@~-2 Theme

A A B B

% THE SONATA, note for note: both halves at full length. Every rule
% below is a figure the piece states more than once; whatever it says in
% one place only is written where it stands.
%
% Ped is this sonata's accompaniment in one line: a CELL whose hole takes
% a melody note and answers it with the g below. Two notes poured through
% it are the whole of m.5.
% Arp: the tonic arpeggio, c g c eb g, sounded four times. Its first
% four notes an octave up are the link inside DropPair, and that is the
% slice Arp[:4], not a second rule.
% Drop: f eb d over that same g, then c b to finish; the pedal answers
% only the first two notes.
% DropPair: Drop twice with the link between them. It closes mm.1-8 and
% comes back at mm.22-23, both times ending three units short of the
% barline.

key c4 harm
mode diatonic

Ped      ::= $1 _2 5 _2
Arp      ::= 1 .5 1 3 5 _2
Drop     ::= Ped('4 '3) '2 _2 '1 7
DropPair ::= Drop Arp[:4]@12 Drop '1

assert Arp[:4]@12 == '1 5 '1 '3

% mm.1-8: the first paragraph, built out of the two ideas the lesson
% opened with. Answer is ThemeB with the two steps that lead into it: the
% piece never states ThemeB without them. Its last four notes are also
% the cadence of the phrase BETWEEN the two statements of Answer, an
% octave lower: the slice ThemeB[2:] under one transposition, and not a
% second name.
%
% Then m.5 states the Theme's own eb g d with the g moved to fall AFTER
% each melody note instead of before it, which is exactly what Ped
% spells, and the measure says itself twice.
%
% Nothing here begins on a barline after the opening note, so the lines
% below break at figures: the phrase, the repeated measure, the close.

Answer ::= '2 _2 '3 _2 ThemeB

assert ThemeB[2:]@-12 == 1 _2 .7 _2 .6# _2 .5 _2
assert Ped('3 '2) == Theme[1:4] 5 _2

5 _4 7 _7/2 6#/2 '1 _6 Answer 4 _2 3 _2 4 _2 5 _2 ThemeB[2:]@-12 Answer '2 _2
  | Ped('3 '2) '1 _2 7 6# 7 5 7 '2 |*2
  DropPair 7 '1 '2

% mm.9-14, OUT TO THE DOMINANT, and the key mark is the whole of that
% claim: g minor, the dominant's own harmonic minor. The four rules below
% are written in DEGREES, so these same names sound in g here and in c
% when the piece comes home at m.25: one figure each, not two.
%
% Tetra: four steps down from the leading tone; in c that is b ab g f.
% Halved, and restated a step or an octave lower, it is every scale in
% the sonata, and the assert builds a whole octave out of it.
% Trill: one shake on the second degree, ending on the tonic.
% TrillPair: the shake a step higher, then the shake, each one shedding
% a note as it goes. Four places name it and it sounds six times,
% as often as Tetra, which is saying something for a shake against
% a scale.
% Min3: a minor third, a quarter long. Four transpositions state it,
% and it is a minor third at every one.

key g4 harm

Tetra     ::= 7 _2 6 _2 5 _2 4 _2
Trill     ::= 2 3/2 2/2 3/2 2/2 1/2
TrillPair ::= Trill@~1 1/2 Trill .7/2
Min3      ::= {2, .7} _2

assert 1 == g4
assert '1 7b Tetra@~-1/2 2 1 == '1 7b 6 5 4 3 2 1
assert Trill@~8 == '3 '4/2 '3/2 '4/2 '3/2 '2/2
assert Min3 == {f#4, a4} _2

% Both halves of the sonata end the same way, and it is ONE pair of
% rules, the only reason mm.25-29 need no new material at all.
%
% Approach: the arpeggio and the trill pair, twice over, the second time
% from the fifth above. The '?' slots are a CHOICE the rule offers: this
% statement takes the derivation that leaves them silent, and m.27 pins
% the other one, which is the whole of how the return is varied.
% Descent: two octaves down onto the tonic chord, and both octaves are
% Tetra: halved a step lower, then halved an octave and a step lower.
%
% mm.9-14 entire. m.9 walks the scale down from the sixth (with the
% fourth flattened between two c's) and then circles the f# below it;
% m.10 is the arpeggio, the third and the shakes; Approach and Descent
% run three and a half measures together, so they take a line of their
% own; and the g minor chord ends the half twice over, the second time
% with its third underneath.

Approach ::= Arp 4 _2 TrillPair 5 3? 1 5? 3 '1? 5 '1 _2 4 _2 TrillPair
Descent  ::= 1 '1 7b Tetra@~-1/2 2 1 1 .7b Tetra@~-8/2 .2 .1 - _3 1Min _4

6 5 4 4b Tetra@~-3/2 2 1 .7 .6# .7 .5 .6# .7
  Arp Min3@~2 TrillPair
  Approach Descent
  1Min$3-5-1 _4 - _4

% mm.15-16: the double bar, and the second half begins by standing
% still. Two measures on c minor's own dominant, one to the line: the
% bass g alone, the chord struck twice, silence, and then a new head in
% the opening's rhythm, a long note, a note with a flick off it, and a
% long one again.

key c4 harm

.5 - _3 5Dia _4 5Dia$1-3-5-1 _4 - _4
  7 _4 '1 _7/2 7/2 '2 _6 '3 _2

% mm.17-24: the second half's long paragraph, a page of SEQUENCES, one
% measure to the line except where DropPair runs across a barline.
%
% m.17 falls through three minor thirds a step apart, and all three are
% Min3: the middle one held twice as long, which '_2' after a reference
% says. m.18 falls in melodic thirds instead (ab f, g eb, f d), each
% pair a step lower than the last, and three steps down to the tonic to
% close it. m.20 states Step three times, each statement a degree below
% the one before, and then climbs away from the bottom of the fall:
% '1 '2 '3, three notes it has not just said, going up where
% everything before them went down.
%
% From there the paragraph ends the way the first half's did: the shake
% an octave and a step higher, DropPair, and two tetrachords chained into
% one scale.

Step ::= '4 '3 '2 _2

assert Step@~-2 == '2 '1 7 _2

Min3@~9 Min3@~8 _2 Min3@~7 '3/2 '4/2 '3/2 '4/2 '3 '2/2 '3/2 '1 _2 5 _2
  6 _2 4 _2 5 _2 3 _2 4 _2 2 _2 3 2 1 _2
  .7 _2 .5 _2 1 _4 .5 _6 '5 _2
  Step Step@~-1 Step@~-2 '1 '2 '3 _2
  '2/2 '3/2 '4 _3 Trill@~8 '3/2 '2 _6 '3 _2
  DropPair 7b 6 5
  Tetra@~-1/2 Tetra@~-3/2 2 1 .7 1 .7 .5 .6 .7

% mm.25-29: mm.9-14 return, at home and an octave up. '@~7' is seven
% scale steps, and in a seven-note scale that is the octave, which the
% assert says outright.
%
% So the end of the sonata needs no new material at all. One measure of
% the arpeggio and the shakes, then the whole of Approach, PINNED this
% time to the derivation that fills its optional slots, so the notes the
% return adds come from the same rule that sounded without them at m.11
% and then Descent, and the tonic chord in four voices.

assert Arp@~7 == Arp@12

Arp 4 _2 TrillPair
  Approach#8@~7 Descent@~7 ''1Dia$1-3-5-1 _4

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Sonata K. 11 · Showcase