Lessons · Showcase

Air on the G String

A long melody over a walking bass

% Bach's Air, from the third orchestral suite (BWV 1068). Its bass
% opens walking in even eighths (eight to the measure, sixteen of
% them before it breaks stride), and one three-note cell does the
% whole descent: a step down, then the arrival struck twice. Four
% scale positions of that cell walk from e down to a.
 
bpm 72
instrument plain
meter 4
unit 1/4
key d4 maj
mode diatonic
 
Step ::= 2 _2 1 _2*2
{Step Step@~-1 Step@~-2 Step@~-3}
 
 
% mm.1-2 of the bass, note for note. Spelled with Step the cell
% overlaps its own arrival, so a measure comes out as four pitches
% struck twice each; the assert plays both spellings and compares
% them. The second measure climbs a half step at a time up to a, then
% steps back to g.
 
Walk<bass> ::= 1 _2 Step@~-1 .6 _2 Step@~-3
Bass<bass> ::= Walk .4 _2*2 .4# _2*2 .5 _2 Step@~-4
 
assert Walk == 1 _2*2 .7 _2*2 .6 _2*2 .5 _2*2
 
Bass
 
 
% The tune enters on the same downbeat and holds its first note for
% eighteen units, two units past the barline, so the melody is out of
% phase with the bass before the second measure begins. It is written
% flat, without barlines, because its phrase does not fit them. One
% unit carries two notes, where a second voice joins the tune.
 
Tune ::= '3 _18 '6 '4 {'2, '3} '1 7 '1 7 _4 5 _4
Tune
 
 
% Two rhythmic worlds in one field. { , } lays the tune beside the
% bass; both are 32 units, so neither side is stretched and the tune's
% long notes fall where they fall against the tread underneath. Hand
% the field a bass half as long and it stretches to fill the tune:
% the same walk, in quarters.
 
{Tune, Bass}
{Tune, Walk}
 
 
% mm.3-4, the tune alone. Each measure opens with a nine-unit note,
% one unit past the half measure, which is why the grid carries it a
% column into the third beat, and answers it with seven quick ones.
% The second measure is the first a step lower, same rhythm and same
% contour, with the first measure's two flatted degrees coming out
% plain.
 
Sequence ::= | '5 _9 '3 7b 6 '2 '2b '5 '4 |
             | '4 _9 '2 6 5 '1 7 '4 '3 |
Sequence
 
 
% m.5. The bass starts the walk over (Walk's first three items, note
% for note) under a phrase that has not cadenced. The melody comes
% back to its opening note and to nothing else: '3 again, held 6 units
% where it opened with 18, then pushed up to '5 and settled on '1.
 
Arch   ::= '3 _6 '4# '5 '1 _2 '1 '3 _2 '2 '2 '1
Return ::= Walk[:3] 4# 5 - _4
 
{Arch, Return}
 
 
% THE WHOLE AIR, note for note, in three stretches. And almost none
% of mm.1-8 is new material. The opening is Tune with the two places
% it read loosely written out: where the piece runs g and f# as
% sixteenths into e, Tune wrote a plain g and a doubled e over f#, and
% where the piece holds c# for three and a half units and touches b on
% the way down, Tune held c# for four. Slice Tune at those two seams
% and the rest of the tune stands untouched. mm.3-4 is Sequence, note
% for note. m.5 is Arch, opening its third-beat d into a d-e pair,
% and Arch spelled the leaning note g# where the piece spells it a
% flat: one pitch with two names, and the piece picks the one that
% leans down, which is what the assert checks. Then Turn, circling c#
% and b, reaching d and falling to a, fills mm.6-7 on its own.
 
Turn ::= 7 6 6/2 7/2 '1 _3 7 6 5 _8
 
assert Arch[1] == '5b
 
Tune[:2] '4/2 '3/2 '2 Tune[4:7] 7 _7/2 6/2 Tune[8:]
  Sequence
  | Arch[:4] '1/2 '2/2 Arch[5:] |
  | Turn |*2
  | 7 _5 '1/2 7/2 6/2 7/2 5 '5 _6 7b _2 |
 
 
% mm.9-17, the middle of the Air: nine measures with no two alike.
% mm.9-11 and m.13 borrow nothing and are written where they stand;
% two small figures carry the other four. Lift is a held note
% answered by the third above it, and it opens the last three phrases:
% m.12 and m.17 on a held d, m.16 three steps lower on a. Sigh holds a
% unit longer, lifts the same third and leans back down a step; three
% of them climb by step through mm.14-15, and each hands its last note
% to the next as its first, the same overlap the bass's Step makes.
% The third one's arrival is struck again and held eight units instead
% of moving on. m.12 and m.17 go on to share the long b two notes
% later, and part company in the two notes that reach it and in how
% they leave it.
 
Lift ::= '1 _5 '3
Sigh ::= '1 _6 '3 '2
 
assert Sigh[:2] == Lift \0 {'1 _6}
assert | Sigh Sigh@~1 | == | '1 _6 '3 '2 '2 _6 '4 '3 |
 
| 6 _2 '6 _3 '5 '4 '3 '4 _9/2 '3/2 '2/2 '1/2 7 6 |
  | 6b 6 7 _3 '1 '2 _3 '3 '4 _4 '3 _2 |
  | '2 '1 7 6 7 '1/2 '2/2 '1 _2 6 _8 |
  | Lift '2 '1 '6 _6 '5 '5b |
  | '3/2 '2/2 '5 5 _2 6 _3 7/2 '1/2 7 _3 6 5 _4 |
  | Sigh Sigh@~1 |
  | Sigh@~2 '4 _8 |
  | Lift@~-3 '2 '4 '4 '2 '3 _5 '4/2 '5/2 |
  | Lift '5 '7b '6 _6 '1 _2 |
 
 
% mm.18-19, the close. The line rises c#-e-g and stands on the g for a
% whole beat, falls through b to a, climbs e-f#-g and settles back to
% e. Then it turns over the leading tone twice (b c# d, then c# d
% again) and stops on d for eight units, half the measure. Nothing is
% named here, because nothing here comes back.
 
| 7 '2 '4 _4 6 _2 5 _2 '2 '3/2 '4 _3/2 '3 _2 '2 |
  | '1/2 7/2 6 _2 7 '1 _2 7 '1 '1 _8 |

% Bach's Air, from the third orchestral suite (BWV 1068). Its bass
% opens walking in even eighths (eight to the measure, sixteen of
% them before it breaks stride), and one three-note cell does the
% whole descent: a step down, then the arrival struck twice. Four
% scale positions of that cell walk from e down to a.

bpm 72
instrument plain
meter 4
unit 1/4
key d4 maj
mode diatonic

Step ::= 2 _2 1 _2*2
{Step Step@~-1 Step@~-2 Step@~-3}

% mm.1-2 of the bass, note for note. Spelled with Step the cell
% overlaps its own arrival, so a measure comes out as four pitches
% struck twice each; the assert plays both spellings and compares
% them. The second measure climbs a half step at a time up to a, then
% steps back to g.

Walk<bass> ::= 1 _2 Step@~-1 .6 _2 Step@~-3
Bass<bass> ::= Walk .4 _2*2 .4# _2*2 .5 _2 Step@~-4

assert Walk == 1 _2*2 .7 _2*2 .6 _2*2 .5 _2*2

Bass

% The tune enters on the same downbeat and holds its first note for
% eighteen units, two units past the barline, so the melody is out of
% phase with the bass before the second measure begins. It is written
% flat, without barlines, because its phrase does not fit them. One
% unit carries two notes, where a second voice joins the tune.

Tune ::= '3 _18 '6 '4 {'2, '3} '1 7 '1 7 _4 5 _4
Tune

% Two rhythmic worlds in one field. { , } lays the tune beside the
% bass; both are 32 units, so neither side is stretched and the tune's
% long notes fall where they fall against the tread underneath. Hand
% the field a bass half as long and it stretches to fill the tune:
% the same walk, in quarters.

{Tune, Bass}
{Tune, Walk}

% mm.3-4, the tune alone. Each measure opens with a nine-unit note,
% one unit past the half measure, which is why the grid carries it a
% column into the third beat, and answers it with seven quick ones.
% The second measure is the first a step lower, same rhythm and same
% contour, with the first measure's two flatted degrees coming out
% plain.

Sequence ::= | '5 _9 '3 7b 6 '2 '2b '5 '4 |
             | '4 _9 '2 6 5 '1 7 '4 '3 |
Sequence

% m.5. The bass starts the walk over (Walk's first three items, note
% for note) under a phrase that has not cadenced. The melody comes
% back to its opening note and to nothing else: '3 again, held 6 units
% where it opened with 18, then pushed up to '5 and settled on '1.

Arch   ::= '3 _6 '4# '5 '1 _2 '1 '3 _2 '2 '2 '1
Return ::= Walk[:3] 4# 5 - _4

{Arch, Return}

% THE WHOLE AIR, note for note, in three stretches. And almost none
% of mm.1-8 is new material. The opening is Tune with the two places
% it read loosely written out: where the piece runs g and f# as
% sixteenths into e, Tune wrote a plain g and a doubled e over f#, and
% where the piece holds c# for three and a half units and touches b on
% the way down, Tune held c# for four. Slice Tune at those two seams
% and the rest of the tune stands untouched. mm.3-4 is Sequence, note
% for note. m.5 is Arch, opening its third-beat d into a d-e pair,
% and Arch spelled the leaning note g# where the piece spells it a
% flat: one pitch with two names, and the piece picks the one that
% leans down, which is what the assert checks. Then Turn, circling c#
% and b, reaching d and falling to a, fills mm.6-7 on its own.

Turn ::= 7 6 6/2 7/2 '1 _3 7 6 5 _8

assert Arch[1] == '5b

% mm.9-17, the middle of the Air: nine measures with no two alike.
% mm.9-11 and m.13 borrow nothing and are written where they stand;
% two small figures carry the other four. Lift is a held note
% answered by the third above it, and it opens the last three phrases:
% m.12 and m.17 on a held d, m.16 three steps lower on a. Sigh holds a
% unit longer, lifts the same third and leans back down a step; three
% of them climb by step through mm.14-15, and each hands its last note
% to the next as its first, the same overlap the bass's Step makes.
% The third one's arrival is struck again and held eight units instead
% of moving on. m.12 and m.17 go on to share the long b two notes
% later, and part company in the two notes that reach it and in how
% they leave it.

Lift ::= '1 _5 '3
Sigh ::= '1 _6 '3 '2

assert Sigh[:2] == Lift \0 {'1 _6}
assert | Sigh Sigh@~1 | == | '1 _6 '3 '2 '2 _6 '4 '3 |

| 6 _2 '6 _3 '5 '4 '3 '4 _9/2 '3/2 '2/2 '1/2 7 6 |
  | 6b 6 7 _3 '1 '2 _3 '3 '4 _4 '3 _2 |
  | '2 '1 7 6 7 '1/2 '2/2 '1 _2 6 _8 |
  | Lift '2 '1 '6 _6 '5 '5b |
  | '3/2 '2/2 '5 5 _2 6 _3 7/2 '1/2 7 _3 6 5 _4 |
  | Sigh Sigh@~1 |
  | Sigh@~2 '4 _8 |
  | Lift@~-3 '2 '4 '4 '2 '3 _5 '4/2 '5/2 |
  | Lift '5 '7b '6 _6 '1 _2 |

% mm.18-19, the close. The line rises c#-e-g and stands on the g for a
% whole beat, falls through b to a, climbs e-f#-g and settles back to
% e. Then it turns over the leading tone twice (b c# d, then c# d
% again) and stops on d for eight units, half the measure. Nothing is
% named here, because nothing here comes back.

| 7 '2 '4 _4 6 _2 5 _2 '2 '3/2 '4 _3/2 '3 _2 '2 |
  | '1/2 7/2 6 _2 7 '1 _2 7 '1 '1 _8 |

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

Air on the G String · Showcase