Lessons · Showcase

Sonata facile

Mozart K 545: Alberti bass, diatonic sequences

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% Mozart's Sonata facile (K 545) opens with the simplest materials
% in music: a singing arpeggio melody over an ALBERTI BASS. The bass
% is ONE half-measure cell (root fifth third fifth). '_2' stretches
% its four notes into eighths, '*4' repeats it in TIME beneath the
% two-measure theme:
 
bpm 132
instrument plain
key c maj
 
Theme   ::= '1 _8 '3 _4 '5 _4 7 _6 '1 '2 '1 _4 - _4
Alberti ::= {1 5 3 5}_2
Open    ::= {Theme, Alberti *4}
 
Open
 
 
% The consequent phrase climbs to the sixth and falls back by step.
% Same bass, two more measures:
 
Answer ::= '6 _8 '5 _4 ''1 _4 '5 _4 '4 _2 '3 '4 '3 _4 - _4
 
{Answer, Alberti *4}
 
 
% Alberti cells COMPOSE. Give the rule one alternative per harmony
% and the progression is selector spelling: Mozart's actual mm.1-4
% bass is I, then V6/5, IV6/4, vii°6, each resolving home:
 
unit 1/4
Cell   ::= {1 5 3 5}_2 = {2 5 4 5}_2 = {1 6 4 6}_2 = {.7 5 2 5}_2
Phrase ::= | Cell#1 Cell#1 | Cell#2 Cell#1 | Cell#3 Cell#1 | Cell#4 Cell#1 |
 
Phrase
 
 
% From m.5 the right hand is ONE rising-and-falling scale figure,
% restated a scale step lower each measure, a diatonic sequence.
% Write the figure once; '@~-1' does the restating (Mozart bends the
% tail of the later ones, but the sequence is the skeleton):
 
Run ::= 6 _2 7 '1 '2 '3 '4 '5 '6 '5 '4 '3 '2 '1 7 6
 
Run Run@~-1 Run@~-2
 
 
% The whole opening page in one line: the themes over the composed
% bass phrase, the falling sequence, and a V-I close:
 
{Theme Answer, Phrase} Run Run@~-1 Run@~-2 5Maj _2 1Maj _2
 
 
% The SECOND THEME (m.14) moves to G, the dominant: sonata form's
% standing agreement. A broken-chord question, a chromatic climb, and
% the trilled cadence that seals the exposition:
 
Rise  ::= 2 5 7 _4 - 1 3 5 '1 _4
Climb ::= 3 4 5 6 7 '2b '2 6 7 '2b '2 '3 '4 '5
Trill ::= .7 2 .7 2
 
Rise
Climb
Trill Trill .7 2 Trill .7 2
 
 
% The DEVELOPMENT (m.29) turns the lights down: minor now, and one
% falling figure SEQUENCED down the scale. Write the model once and
% let '@~-1' walk it, exactly as Mozart does:
 
Fall ::= ''2 ''1 '7 '6 '5 '4 _4 - _4
 
- '6 ''3 Fall
- '5 ''2 Fall @~-1
- '4 ''1 Fall @~-2
 
 
% The RECAPITULATION (m.42) springs this sonata's famous surprise:
% the theme returns in F (the SUBDOMINANT) before settling home.
% One diatonic shift says it; then the second theme returns pulled
% down to C ('@-5', a fourth) so the movement can end where it began:
 
{Theme @~3, Alberti @~3 *4}
{Theme, Alberti *4}
Rise @-5
Trill Trill .7 2 Trill .7 2
 
 
% The whole movement in one arc: exposition with its two themes,
% the minor-mode sequence, the subdominant return, and the close:
 
{Theme Answer, Phrase} Run Run@~-1 Run@~-2
Rise Climb Trill Trill .7 2 Trill .7 2
- '6 ''3 Fall - '5 ''2 Fall @~-1 - '4 ''1 Fall @~-2
{Theme @~3, Alberti @~3 *4} {Theme, Alberti *4} Rise @-5
Trill Trill .7 2 Trill .7 2 5Maj _2 1Maj _2 {.1, 1} _4
 
 
% NOW THE MOVEMENT ITSELF, note for note: the movement's leading
% voice at full length, all 73 measures, in the names the blocks above
% have already built. Mozart's plan fits in a sentence: eight measures
% of theme and falling scales, a bridge, a singing second theme, a
% closing figure; the development turns that closing figure MINOR; and
% the recapitulation says those eight measures again in F, the
% subdominant, and has to find its way home from there.
 
bpm 132
meter 4
unit 1/4
key c4 maj
mode diatonic
 
 
% mm.1-8: the theme, its answer, and the scale figure four times, a
% step lower each time. Three names carry the page and no new one is
% needed:
 
assert Run@~-3 == e4 _2 f4 g4 a4 b4 c5 d5 e5 d5 c5 b4 a4 g4 f4 e4
 
Theme Answer Run Run@~-1 Run@~-2 Run@~-3
 
 
% mm.9-17: THE BRIDGE to the dominant, then the second theme twice
% over. Three figures carry mm.9-12 and all three come back at m.54: a
% staircase in two flights, the crest that turns it over, and a cadence
% in broken thirds. The second theme is written from C by the fifth
% ('@7') rather than under a key of its own, because a key mark stands
% only BETWEEN statements and mm.9-15 are one statement.
 
% Stair: a 15-note scale in two flights, stated twice (mm.9, 54)
Stair ::= 2 _2 3 4 5 6 7 '1# '2 6 7 '1# '2 '3 '4 '5
% Crest: its answer over the top and down, twice (mm.10, 55)
Crest ::= '6 '7 ''1 '7 '6 '5 '4 '3 '4 '5 '6 '5 '4 '3 '2 '1
% Close: the two-measure cadence in broken thirds, twice (mm.11, 56)
Close ::= 7 _2 '5 _2 '3 _2 '1 _2 '2 _2 '5 _2 '3 _2 '1 _2
  '2 _4 {7, '2, '5} _4 5 _4 - _4
% Song: the second theme, two measures, stated 4 times (mm.14, 16, 59, 61)
Song  ::= '5 _2 '3 _2 '1 _6 '2 '3 '2 _2 '1 _2 '1 _3 7 7 _4 - _8
 
assert Close[:8] == b4 _2 g5 _2 e5 _2 c5 _2 d5 _2 g5 _2 e5 _2 c5 _2
assert Song@7 == d6 _2 b5 _2 g5 _6 a5 b5 a5 _2 g5 _2 g5 _3 f#5 f#5 _4 - _8
 
Stair Crest Close - _16 Song@7
 
Song@7
 
 
% mm.18-28: the exposition's CLOSE, in G. A note struck, a breath,
% and the chord falling away under it, twice a measure, and the whole
% measure a step lower each time. The fourth statement breaks the
% pattern at its last turn: the line reaches UP to g instead of down to
% b, which is one item in the figure's own degrees, and the sequence
% mark carries the replacement down with everything else. Then the
% theme's own first measure arrives a seventh lower, on the A minor
% triad, in the half-quarter-quarter rhythm the movement opened with;
% and the section ends on the figure that becomes the whole development.
 
key g4 maj
 
% Peal: a struck note and its chord falling away, stated 8 times
% (mm.18-21 in G, mm.63-66 at home)
Peal ::= '5 _4 - '5 '3 '1 6 _4 - 6 '1 6
% Reel: a twelve-note broken chord and its turn, stated 8 times
% (mm.26, 27, 29, 30, 33, 34, 71, 72; twice of it only the first eight)
Reel ::= '1 5 '1 '3 '5 '3 '1 '3 '4 '2 7 '2
 
assert Peal \7 {'4} @~-3 == a5 _4 - a5 f#5 d5 b4 _4 - g5 d5 b4
assert Theme[:3]@~-6 == a4 _8 c5 _4 e5 _4
 
Peal Peal@~-1 Peal@~-2 Peal \7 {'4} @~-3
  Theme[:3]@~-6
  '2 _6 '3/2 '2/2 '1#/2 '2/2 '4 _2 '2 _2 '4 _2 '2 _2
  '3 _2 '1 _2 '5 _8 '4 '3 '2 '1
  '2 _16
  '1 _4 Reel '1 _4 Reel@-12
  1 _4 {5, '3} _4 {3, '1} _4 - _4
 
 
% mm.29-32: THE DEVELOPMENT, and it opens by turning that closing
% figure minor. Not a note of the figure is rewritten: 'key g4 harm'
% flats the third and keeps the f sharp, and the same Reel comes out in
% g minor. Then two measures over a diminished seventh (a quarter, a
% silence, and a scale falling out of a leap), which recur nowhere in
% the piece and so are written where they stand.
 
key g4 harm
 
assert Reel == g5 d5 g5 bb5 d6 bb5 g5 bb5 c6 a5 f#5 a5
 
1 _4 Reel '1 _4 Reel@-12
 
key c4 maj
 
5 _4 - _5 '5 '7b '6 '5 '4 '3 '2
  '1# _4 - _5 ''1# ''3 ''2 ''1# '7b '6 '5
 
 
% mm.33-40: the Reel a step up, which in C's own degrees is D MINOR
% (and, heard against m.29, the same minor figure a fourth lower).
% '@~1' does it, for the first eight notes only: the turn at the end
% wants a RAISED leading tone and no diatonic mark can raise one, so
% those four notes are written where they stand, both times. Then two
% rising scales that recur nowhere, and a four-fold sequence: a leap up
% a fifth and the scale falling back through it, each statement a step
% lower, the last bending its fourth note into the leading tone of A
% minor.
 
% Vault: a leap up a fifth and the scale falling back, 4 times (mm.37-40)
Vault ::= - '6 ''3 ''2 ''1 '7 '6 '5 '4 _4 - _4
 
assert Reel[:8]@~1 == d5 a4 d5 f5 a5 f5 d5 f5
assert Vault \4 {''1#} @~-3 == - e5 b5 a5 g#5 f5 e5 d5 c5 _4 - _4
 
'4 _4 Reel[:8]@~1 '5 '3 '1# '3
  '2 _4 Reel[:8]@~-6 5 3 1# 3
  - 2 3 4 5 6 7 '1# '2 _4 - _4
  - 7 '1 '2 '3 '4# '5# '6 '7 _4 - _4
  Vault Vault@~-1 Vault@~-2 Vault \4 {''1#} @~-3
 
 
% mm.41-50. m.41 is the retransition and it is already in F: the line
% walks down to that key's leading tone and climbs straight back up.
% Then THE RECAPITULATION, and this sonata's famous surprise: mm.1-8
% return NOTE FOR NOTE in F, the SUBDOMINANT, so the same three names
% say them again and only the key mark has changed. m.50 is the chord
% the second group arrives on.
 
key f4 maj
 
assert Theme == f5 _8 a5 _4 c6 _4 e5 _6 f5 g5 f5 _4 - _4
 
- 4 6 5 4 3 2 1 .7 1 2 3 4 5 6 7
 
Theme Answer Run Run@~-1 Run@~-2 Run@~-3
 
'3 _4 - _8 {5, '3} _4
 
 
% mm.51-58: three more of those held chords, home in C now, and then
% the bridge again: Stair with its first note halved and a d set above
% it, Crest and Close untouched.
 
key c4 maj
 
assert '2 Stair \0 {2} == d5 d4 e4 f4 g4 a4 b4 c#5 d5 a4 b4 c#5 d5 e5 f5 g5
 
{'1, '5} _4 - _8 {'1, '5} _4
  {'1, '4} _4 - _8 {7, '4} _4
  {'1, '3} _4 - _8 {'1, '3} _4
  '2 Stair \0 {2} Crest Close
  - _16
 
 
% mm.59-67: the second theme home in C, twice over; then the Peal
% sequence again, and its fourth rung takes the SAME override it took
% at m.21. The second rung jumps an octave at the tail, so seven of its
% items are sliced off and those three notes written where they stand.
% m.67 holds a d in the theme's own half-quarter-quarter rhythm.
 
assert Peal[:7]@~-1 '5 '7 '5 == f5 _4 - f5 d5 b4 g4 _4 - g5 b5 g5
 
Song*2
  Peal
  Peal[:7]@~-1 '5 '7 '5
  Peal@~5
  Peal \7 {'4} @~4
  '2 _8 '2 _4 '2 _4
 
 
% mm.68-73: m.68 is m.67 a fifth higher, the same rhythm on a held a;
% then a scale up a sixth and down a tenth, the Reel one last time in C,
% and three chords to close.
 
assert Reel@-12 == c4 g3 c4 e4 g4 e4 c4 e4 f4 d4 b3 d4
 
'6 _8 '6 _4 '6 _4
  '5 _2 '6 '7 ''1 ''2 ''3 ''2 ''1 '7 '6 '5 '4 '3 '2 '1
  '2 _16
  '1 _4 Reel '1 _4 Reel@-12
 
1 _4 {'3, '5, ''1} _4 '1 _4 - _4

% Mozart's Sonata facile (K 545) opens with the simplest materials
% in music: a singing arpeggio melody over an ALBERTI BASS. The bass
% is ONE half-measure cell (root fifth third fifth). '_2' stretches
% its four notes into eighths, '*4' repeats it in TIME beneath the
% two-measure theme:

bpm 132
instrument plain
key c maj

Theme   ::= '1 _8 '3 _4 '5 _4 7 _6 '1 '2 '1 _4 - _4
Alberti ::= {1 5 3 5}_2
Open    ::= {Theme, Alberti *4}

Open

% The consequent phrase climbs to the sixth and falls back by step.
% Same bass, two more measures:

Answer ::= '6 _8 '5 _4 ''1 _4 '5 _4 '4 _2 '3 '4 '3 _4 - _4

{Answer, Alberti *4}

% Alberti cells COMPOSE. Give the rule one alternative per harmony
% and the progression is selector spelling: Mozart's actual mm.1-4
% bass is I, then V6/5, IV6/4, vii°6, each resolving home:

unit 1/4
Cell   ::= {1 5 3 5}_2 = {2 5 4 5}_2 = {1 6 4 6}_2 = {.7 5 2 5}_2
Phrase ::= | Cell#1 Cell#1 | Cell#2 Cell#1 | Cell#3 Cell#1 | Cell#4 Cell#1 |

Phrase

% From m.5 the right hand is ONE rising-and-falling scale figure,
% restated a scale step lower each measure, a diatonic sequence.
% Write the figure once; '@~-1' does the restating (Mozart bends the
% tail of the later ones, but the sequence is the skeleton):

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

Run Run@~-1 Run@~-2

% The whole opening page in one line: the themes over the composed
% bass phrase, the falling sequence, and a V-I close:

{Theme Answer, Phrase} Run Run@~-1 Run@~-2 5Maj _2 1Maj _2

% The SECOND THEME (m.14) moves to G, the dominant: sonata form's
% standing agreement. A broken-chord question, a chromatic climb, and
% the trilled cadence that seals the exposition:

Rise  ::= 2 5 7 _4 - 1 3 5 '1 _4
Climb ::= 3 4 5 6 7 '2b '2 6 7 '2b '2 '3 '4 '5
Trill ::= .7 2 .7 2

Rise
Climb
Trill Trill .7 2 Trill .7 2

% The DEVELOPMENT (m.29) turns the lights down: minor now, and one
% falling figure SEQUENCED down the scale. Write the model once and
% let '@~-1' walk it, exactly as Mozart does:

Fall ::= ''2 ''1 '7 '6 '5 '4 _4 - _4

- '6 ''3 Fall
- '5 ''2 Fall @~-1
- '4 ''1 Fall @~-2

% The RECAPITULATION (m.42) springs this sonata's famous surprise:
% the theme returns in F (the SUBDOMINANT) before settling home.
% One diatonic shift says it; then the second theme returns pulled
% down to C ('@-5', a fourth) so the movement can end where it began:

{Theme @~3, Alberti @~3 *4}
{Theme, Alberti *4}
Rise @-5
Trill Trill .7 2 Trill .7 2

% The whole movement in one arc: exposition with its two themes,
% the minor-mode sequence, the subdominant return, and the close:

{Theme Answer, Phrase} Run Run@~-1 Run@~-2
Rise Climb Trill Trill .7 2 Trill .7 2
- '6 ''3 Fall - '5 ''2 Fall @~-1 - '4 ''1 Fall @~-2
{Theme @~3, Alberti @~3 *4} {Theme, Alberti *4} Rise @-5
Trill Trill .7 2 Trill .7 2 5Maj _2 1Maj _2 {.1, 1} _4

% NOW THE MOVEMENT ITSELF, note for note: the movement's leading
% voice at full length, all 73 measures, in the names the blocks above
% have already built. Mozart's plan fits in a sentence: eight measures
% of theme and falling scales, a bridge, a singing second theme, a
% closing figure; the development turns that closing figure MINOR; and
% the recapitulation says those eight measures again in F, the
% subdominant, and has to find its way home from there.

bpm 132
meter 4
unit 1/4
key c4 maj
mode diatonic

% mm.1-8: the theme, its answer, and the scale figure four times, a
% step lower each time. Three names carry the page and no new one is
% needed:

assert Run@~-3 == e4 _2 f4 g4 a4 b4 c5 d5 e5 d5 c5 b4 a4 g4 f4 e4

Theme Answer Run Run@~-1 Run@~-2 Run@~-3

% mm.9-17: THE BRIDGE to the dominant, then the second theme twice
% over. Three figures carry mm.9-12 and all three come back at m.54: a
% staircase in two flights, the crest that turns it over, and a cadence
% in broken thirds. The second theme is written from C by the fifth
% ('@7') rather than under a key of its own, because a key mark stands
% only BETWEEN statements and mm.9-15 are one statement.

% Stair: a 15-note scale in two flights, stated twice (mm.9, 54)
Stair ::= 2 _2 3 4 5 6 7 '1# '2 6 7 '1# '2 '3 '4 '5
% Crest: its answer over the top and down, twice (mm.10, 55)
Crest ::= '6 '7 ''1 '7 '6 '5 '4 '3 '4 '5 '6 '5 '4 '3 '2 '1
% Close: the two-measure cadence in broken thirds, twice (mm.11, 56)
Close ::= 7 _2 '5 _2 '3 _2 '1 _2 '2 _2 '5 _2 '3 _2 '1 _2
  '2 _4 {7, '2, '5} _4 5 _4 - _4
% Song: the second theme, two measures, stated 4 times (mm.14, 16, 59, 61)
Song  ::= '5 _2 '3 _2 '1 _6 '2 '3 '2 _2 '1 _2 '1 _3 7 7 _4 - _8

assert Close[:8] == b4 _2 g5 _2 e5 _2 c5 _2 d5 _2 g5 _2 e5 _2 c5 _2
assert Song@7 == d6 _2 b5 _2 g5 _6 a5 b5 a5 _2 g5 _2 g5 _3 f#5 f#5 _4 - _8

Stair Crest Close - _16 Song@7

Song@7

% mm.18-28: the exposition's CLOSE, in G. A note struck, a breath,
% and the chord falling away under it, twice a measure, and the whole
% measure a step lower each time. The fourth statement breaks the
% pattern at its last turn: the line reaches UP to g instead of down to
% b, which is one item in the figure's own degrees, and the sequence
% mark carries the replacement down with everything else. Then the
% theme's own first measure arrives a seventh lower, on the A minor
% triad, in the half-quarter-quarter rhythm the movement opened with;
% and the section ends on the figure that becomes the whole development.

key g4 maj

% Peal: a struck note and its chord falling away, stated 8 times
% (mm.18-21 in G, mm.63-66 at home)
Peal ::= '5 _4 - '5 '3 '1 6 _4 - 6 '1 6
% Reel: a twelve-note broken chord and its turn, stated 8 times
% (mm.26, 27, 29, 30, 33, 34, 71, 72; twice of it only the first eight)
Reel ::= '1 5 '1 '3 '5 '3 '1 '3 '4 '2 7 '2

assert Peal \7 {'4} @~-3 == a5 _4 - a5 f#5 d5 b4 _4 - g5 d5 b4
assert Theme[:3]@~-6 == a4 _8 c5 _4 e5 _4

Peal Peal@~-1 Peal@~-2 Peal \7 {'4} @~-3
  Theme[:3]@~-6
  '2 _6 '3/2 '2/2 '1#/2 '2/2 '4 _2 '2 _2 '4 _2 '2 _2
  '3 _2 '1 _2 '5 _8 '4 '3 '2 '1
  '2 _16
  '1 _4 Reel '1 _4 Reel@-12
  1 _4 {5, '3} _4 {3, '1} _4 - _4

% mm.29-32: THE DEVELOPMENT, and it opens by turning that closing
% figure minor. Not a note of the figure is rewritten: 'key g4 harm'
% flats the third and keeps the f sharp, and the same Reel comes out in
% g minor. Then two measures over a diminished seventh (a quarter, a
% silence, and a scale falling out of a leap), which recur nowhere in
% the piece and so are written where they stand.

key g4 harm

assert Reel == g5 d5 g5 bb5 d6 bb5 g5 bb5 c6 a5 f#5 a5

1 _4 Reel '1 _4 Reel@-12

key c4 maj

5 _4 - _5 '5 '7b '6 '5 '4 '3 '2
  '1# _4 - _5 ''1# ''3 ''2 ''1# '7b '6 '5

% mm.33-40: the Reel a step up, which in C's own degrees is D MINOR
% (and, heard against m.29, the same minor figure a fourth lower).
% '@~1' does it, for the first eight notes only: the turn at the end
% wants a RAISED leading tone and no diatonic mark can raise one, so
% those four notes are written where they stand, both times. Then two
% rising scales that recur nowhere, and a four-fold sequence: a leap up
% a fifth and the scale falling back through it, each statement a step
% lower, the last bending its fourth note into the leading tone of A
% minor.

% Vault: a leap up a fifth and the scale falling back, 4 times (mm.37-40)
Vault ::= - '6 ''3 ''2 ''1 '7 '6 '5 '4 _4 - _4

assert Reel[:8]@~1 == d5 a4 d5 f5 a5 f5 d5 f5
assert Vault \4 {''1#} @~-3 == - e5 b5 a5 g#5 f5 e5 d5 c5 _4 - _4

'4 _4 Reel[:8]@~1 '5 '3 '1# '3
  '2 _4 Reel[:8]@~-6 5 3 1# 3
  - 2 3 4 5 6 7 '1# '2 _4 - _4
  - 7 '1 '2 '3 '4# '5# '6 '7 _4 - _4
  Vault Vault@~-1 Vault@~-2 Vault \4 {''1#} @~-3

% mm.41-50. m.41 is the retransition and it is already in F: the line
% walks down to that key's leading tone and climbs straight back up.
% Then THE RECAPITULATION, and this sonata's famous surprise: mm.1-8
% return NOTE FOR NOTE in F, the SUBDOMINANT, so the same three names
% say them again and only the key mark has changed. m.50 is the chord
% the second group arrives on.

key f4 maj

assert Theme == f5 _8 a5 _4 c6 _4 e5 _6 f5 g5 f5 _4 - _4

- 4 6 5 4 3 2 1 .7 1 2 3 4 5 6 7

Theme Answer Run Run@~-1 Run@~-2 Run@~-3

'3 _4 - _8 {5, '3} _4

% mm.51-58: three more of those held chords, home in C now, and then
% the bridge again: Stair with its first note halved and a d set above
% it, Crest and Close untouched.

key c4 maj

assert '2 Stair \0 {2} == d5 d4 e4 f4 g4 a4 b4 c#5 d5 a4 b4 c#5 d5 e5 f5 g5

{'1, '5} _4 - _8 {'1, '5} _4
  {'1, '4} _4 - _8 {7, '4} _4
  {'1, '3} _4 - _8 {'1, '3} _4
  '2 Stair \0 {2} Crest Close
  - _16

% mm.59-67: the second theme home in C, twice over; then the Peal
% sequence again, and its fourth rung takes the SAME override it took
% at m.21. The second rung jumps an octave at the tail, so seven of its
% items are sliced off and those three notes written where they stand.
% m.67 holds a d in the theme's own half-quarter-quarter rhythm.

assert Peal[:7]@~-1 '5 '7 '5 == f5 _4 - f5 d5 b4 g4 _4 - g5 b5 g5

Song*2
  Peal
  Peal[:7]@~-1 '5 '7 '5
  Peal@~5
  Peal \7 {'4} @~4
  '2 _8 '2 _4 '2 _4

% mm.68-73: m.68 is m.67 a fifth higher, the same rhythm on a held a;
% then a scale up a sixth and down a tenth, the Reel one last time in C,
% and three chords to close.

assert Reel@-12 == c4 g3 c4 e4 g4 e4 c4 e4 f4 d4 b3 d4

'6 _8 '6 _4 '6 _4
  '5 _2 '6 '7 ''1 ''2 ''3 ''2 ''1 '7 '6 '5 '4 '3 '2 '1
  '2 _16
  '1 _4 Reel '1 _4 Reel@-12

1 _4 {'3, '5, ''1} _4 '1 _4 - _4

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

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