Lessons · Showcase

Sarabande

Weight on the second beat

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% A sarabande is a slow triple dance whose weight falls on beat TWO.
% In a bar of twelve sixteenths — meter 3, unit 1/4 — Even spaces the
% tonic triad over three equal beats of four, while Lean drops the third
% beat and lets beat two hold to the barline; the upper voice of mm.25 in
% Bach's Sarabande from the Lute Suite BWV 997 is that bar exactly — a
% chord on one and a lone g4 from beat two to the end, over a lower voice
% that keeps moving.
 
bpm 45
meter 3
unit 1/4
key a4 min
mode diatonic
 
Even ::= | 1 _4 .5 _4 .3 _4 |
Lean ::= | 1 _4 .5 _8 |
 
Even Lean
| {.5, .2, ..7} _4 .7 _8 |
 
 
% Beat one fills with sixteenths so that beat two can be still. Fall
% drops from the sixth to the fourth, and mm.3 spends it twice — once
% into the held b4 on beat two, once out to the barline.
 
Fall ::= .6 .5 .4
Turn ::= | .4 Fall 2 _3 1 .7# Fall |
 
Turn
 
 
% Sixth is one dyad; '@~n' moves it by SCALE steps, so it walks the
% scale and takes whatever quality the scale gives it — minor, major,
% major, minor. mm.18 sounds it four times, a scale step lower each
% time, after a beat-one lead-in.
 
Sixth   ::= {.3, ..5} _2
Descent ::= | .5 _3 .6 Sixth@~3 Sixth@~2 Sixth@~1 Sixth |
 
Descent
 
 
% mm.1 opens the melody: the tonic takes three of beat one's four
% sixteenths, then Sixth fills beats two and three — once at the sixth
% step and twice at the fifth, with the leading-tone dyad g#4/b3
% between them.
 
Lead ::= | 1 _3 2 Sixth@~6 Sixth@~5 {.7#, .2} _2 Sixth@~5 |
 
Lead
 
 
% Under the tune the accompaniment states the chord on beat one and
% Pulse restrikes the tonic on two and three. A third voice sounds one
% note in the whole measure, and it lands on beat two.
 
Pulse  ::= ..1 _4*2
Ground ::= | {.5, .3, ..3} _4 Pulse |
Chime  ::= | - _4 3 - _7 |
 
{Lead, Ground, Chime}
 
 
% mm.2 swaps the roles: the upper voices hold one chord for all three
% beats while the lowest voice walks, and Step reversed and dropped
% three semitones closes it with the leading-tone lean home. The chime
% answers two octaves lower, again on beat two.
 
Step ::= ..3 _2 ..2 _2
Walk ::= | ..1 _3 ..2 ..2 _2 ..1 _2 Step~@-3 |
 
Hold ::= | {.4, .2, ..6} _12 |
 
{Walk, Hold, Chime@-24}
 
 
% The phrase entire, mm.1-4. Sigh falls a step and Close says it twice
% before two beats of silence; underneath, Chords marks beats one and
% two and leaves three to the bass, then Rise steps up to f4 while the
% melody rests.
 
Sigh  ::= .3 .2
Close ::= | Sigh*2 - _8 |
 
Chords ::= | {.2, ..6, ...7} _4 {.4, ..7#, ..1} _4 ..1 _4 |
 
Rise ::= | ..1 _4 .1 ..5 .1 .2 .3 Fall~ |
 
{Lead Walk, Ground Hold, Chime Chime@-24}
{Turn Close, Chords Rise}
 
 
% THE WHOLE SARABANDE, from here to the last bar. Seven stretches, one
% per form letter: A mm.1-8 · B mm.9-16 · A′ mm.17-21 · C mm.22-24 ·
% D mm.25-27 · D′ mm.28-32 · E mm.33-34.
%
% mm.1-8 — form A, in a minor. m.1, m.3 and m.4 are Ground, Chords and
% Rise, in the order they stand; m.2 is the chord Hold holds, written
% here as the triad it is — the diminished ii on b with its fifth in the
% bass, and a hold that fills its measure wants no barlines around it.
% Then the bass stops moving altogether: three bars of the open A struck
% on every beat, nine strikes, while the tune works above it. And one bar
% turns to the dominant — A diminished with its own fifth at the bottom
% over a low E, the leading-tone dyad b3/g#3 on beat two, and Step
% walking c3 b2 to the barline, where m.9 answers with the a below.
 
assert ..2Dia$5-1-3 _12 == Hold
assert | Pulse ..1 _4 |*3 == ..1 _4*9
assert {.3, .1, ..5b} == ..1Dim$5-1-3
 
Ground
  ..2Dia$5-1-3 _12
  Chords
  Rise
  | Pulse ..1 _4 |*3
  | {.3, .1, ..5b, ...5} _4 {.2, ..7#} _4 Step |
 
 
% mm.9-16 — form B, in the relative major, and the eight bars are one
% Sequence. Rung is its unit: the upper voice answering in pairs of
% repeated sixteenths while the bass walks in eighths under it, five
% beats long, ending on the f the next bass note takes over. It does NOT
% begin on a barline — it starts halfway through m.9's second beat — so
% the five bars it spans are written flat, with no bars at all. Here the
% figure is the measure.
%
% The rung comes back a minor third lower. Two of its notes cannot
% follow it down: a minor third under its f2 and its e2 is a d2 and a
% c#2, and this piece never goes below e2. Both are taken an octave up
% instead, and the two overrides say so where the rung is restated —
% everything else falls the minor third exactly.
%
% From m.13 the sequence gives out and the bass walks to the cadence:
% Sigh and Step and their retrogrades, down to the g2 that m.16 answers
% with C major, its third in the bass.
 
Rung ::= .7 .7 ...6 _2 2b 2b ...5 _4 .5 .3 ..7 _2 ..3 _2 Step~@5
 
assert Rung[2:3]@-3 == ...4 _2
assert Rung[5:6]@-3 == ...3# _4
 
Sequence ::= ..1 _2 .5 .5 ...7 _2
  Rung
  .3 .3 ..5 _2
  Rung@-3 \2 {..4 _2} \5 {..3# _4}
  ..4 _2 Sigh~@~-3 Step~@~2 ..6 _2
  | Pulse@10/2 Sigh~ Step~@~-2 ..2 _2 |
  | Step Step~@-7 Pulse@-2/2 |
  | ..3Dia$3-5-1 _12 |
 
Sequence
 
 
% mm.17-21 — form A′: mm.1-8 return, varied, and they open on the
% relative major's own chord. Pillar is that shape — a root-position
% triad spread over four voices, its root on top as well, held the whole
% bar — and it is the shape the piece ends on, on its own tonic,
% seventeen bars from here. m.18 is Ground's bar again, a chord on one
% and one note struck on two and three, with c3 where the a2 was. Then
% the stretch cadences into the relative major: m.19 holds f#4 over a3,
% the third and fifth of the D that m.20's G major answers, and m.21
% lands on g2 and replies with b4/g4 two octaves above it.
 
Pillar ::= ..1Dia$1-3-5-1 _12
 
assert Pillar == {..1, ..3, ..5, .1} _12
assert Pillar@~2 == {..3, ..5, ..7, .3} _12
 
| Pillar@~2 |
  | {.3, ..7, ..3} _4 Pulse@3 |
  | {.6#, .1} _12 |
  | ...7Dia$3-1-5 _4 ..3 _4 ..4 _4 |
  | ...7 _6 ..2 _2 {2, .7} _4 |
 
 
% mm.22-24 — form C, on the dominant, and the key says so. Sixth comes
% back five scale steps up, which in E is the tonic over its own third;
% the bar holding it opens on D major with its fifth in the bass, and
% the bar before closes on the diminished triad of d#. Then the bass
% climbs g2 a2 b2 in whole beats and hands the dance to d minor.
 
key e4 harm
 
assert Sixth@~5 == {1, .3} _2
 
| ..6 _4 {4, 2} _2 {3, 1} _2*2 ..7Dim$5-1-3 _2 |
  | ..7bMaj$5-1-3 _2 Sixth@~5 .4 _8 |
  | ..3 _4 ..4 _4 ..5 _4 |
 
% mm.25-27 — form D, in d minor, and its first bar is the bar this
% lesson opened with: a chord on one and a lone g4 from beat two to the
% barline, which is Lean's shape, here on d minor's ii. Then the
% dominant itself — A major with its third in the bass — under a falling
% step e4 d4 and the low a struck twice. Then Unwind: the dominant
% seventh coming apart from the top, its seventh, its fifth, its third,
% the fifth and third again, and the root under all of them. It is
% written in DEGREES because the next stretch restates it in a minor
% five scale steps down, and an interval spelling could not make that
% move.
 
key d4 harm
 
Unwind ::= .4 _2 .2 _2 ..7 _2 .2 _2 ..7 _2 ..5 _2
 
assert {..5, ..7, .2, .4} == ..5Dom7
 
| .2Min$3-5-1 _4 4 _8 |
  | ..5Maj$3-5-1 _4 2 1 Pulse@7/2 ..7 _2 |
  | Unwind |
 
 
% mm.28-32 — form D′: mm.25-27 return, varied, back in a minor, and
% Unwind comes with them five scale steps down. m.28 and m.30 keep
% m.26's bar-rhythm exactly — beat one held, a falling step in
% sixteenths on beat two, three eighths from there to the barline — and
% that falling step is Sigh at the pitch each bar wants it: d4 c4 in
% m.28, c4 b3 in m.30. Step is the same step an octave down and twice as
% slow, which is why the bass says it and the tune sighs it.
%
% Unwind is a dominant seventh both times it sounds and both times it
% resolves: the seventh on a to the d of m.28, the seventh on g to the c
% of m.30. The last two bars are Step and its retrograde walking the
% bass down to e2, the lowest note in the piece.
 
key a4 min
 
assert Step == Sigh@-12 _2
assert {...7, ..2, ..4, ..6} == ...7Dom7
 
| ..4 _4 Sigh@~1 Pulse@5/2 ..2 _2 |
  | Unwind@~-5 |
  | ..3 _4 Sigh ..5 _2 ..3 _2 ..1 _2 |
  | Step~@~2 ..4 _2 Step ..2 _2 |
  | Step ..3 _2 ...6 _2 Pulse@-5/2 |
 
% mm.33-34 — form E, two bars and the dance is over: a3 over e3 held the
% whole bar, and then Pillar on the tonic — the four-voice triad that
% opened A′ a third higher, now on a, with the weight of the bar and
% nothing after it.
 
| {.1, ..5} _12 |
  | Pillar |

% A sarabande is a slow triple dance whose weight falls on beat TWO.
% In a bar of twelve sixteenths — meter 3, unit 1/4 — Even spaces the
% tonic triad over three equal beats of four, while Lean drops the third
% beat and lets beat two hold to the barline; the upper voice of mm.25 in
% Bach's Sarabande from the Lute Suite BWV 997 is that bar exactly — a
% chord on one and a lone g4 from beat two to the end, over a lower voice
% that keeps moving.

bpm 45
meter 3
unit 1/4
key a4 min
mode diatonic

Even ::= | 1 _4 .5 _4 .3 _4 |
Lean ::= | 1 _4 .5 _8 |

Even Lean
| {.5, .2, ..7} _4 .7 _8 |

% Beat one fills with sixteenths so that beat two can be still. Fall
% drops from the sixth to the fourth, and mm.3 spends it twice — once
% into the held b4 on beat two, once out to the barline.

Fall ::= .6 .5 .4
Turn ::= | .4 Fall 2 _3 1 .7# Fall |

Turn

% Sixth is one dyad; '@~n' moves it by SCALE steps, so it walks the
% scale and takes whatever quality the scale gives it — minor, major,
% major, minor. mm.18 sounds it four times, a scale step lower each
% time, after a beat-one lead-in.

Sixth   ::= {.3, ..5} _2
Descent ::= | .5 _3 .6 Sixth@~3 Sixth@~2 Sixth@~1 Sixth |

Descent

% mm.1 opens the melody: the tonic takes three of beat one's four
% sixteenths, then Sixth fills beats two and three — once at the sixth
% step and twice at the fifth, with the leading-tone dyad g#4/b3
% between them.

Lead ::= | 1 _3 2 Sixth@~6 Sixth@~5 {.7#, .2} _2 Sixth@~5 |

Lead

% Under the tune the accompaniment states the chord on beat one and
% Pulse restrikes the tonic on two and three. A third voice sounds one
% note in the whole measure, and it lands on beat two.

Pulse  ::= ..1 _4*2
Ground ::= | {.5, .3, ..3} _4 Pulse |
Chime  ::= | - _4 3 - _7 |

{Lead, Ground, Chime}

% mm.2 swaps the roles: the upper voices hold one chord for all three
% beats while the lowest voice walks, and Step reversed and dropped
% three semitones closes it with the leading-tone lean home. The chime
% answers two octaves lower, again on beat two.

Step ::= ..3 _2 ..2 _2
Walk ::= | ..1 _3 ..2 ..2 _2 ..1 _2 Step~@-3 |

Hold ::= | {.4, .2, ..6} _12 |

{Walk, Hold, Chime@-24}

% The phrase entire, mm.1-4. Sigh falls a step and Close says it twice
% before two beats of silence; underneath, Chords marks beats one and
% two and leaves three to the bass, then Rise steps up to f4 while the
% melody rests.

Sigh  ::= .3 .2
Close ::= | Sigh*2 - _8 |

Chords ::= | {.2, ..6, ...7} _4 {.4, ..7#, ..1} _4 ..1 _4 |

Rise ::= | ..1 _4 .1 ..5 .1 .2 .3 Fall~ |

{Lead Walk, Ground Hold, Chime Chime@-24}
{Turn Close, Chords Rise}

% THE WHOLE SARABANDE, from here to the last bar. Seven stretches, one
% per form letter: A mm.1-8 · B mm.9-16 · A′ mm.17-21 · C mm.22-24 ·
% D mm.25-27 · D′ mm.28-32 · E mm.33-34.
%
% mm.1-8 — form A, in a minor. m.1, m.3 and m.4 are Ground, Chords and
% Rise, in the order they stand; m.2 is the chord Hold holds, written
% here as the triad it is — the diminished ii on b with its fifth in the
% bass, and a hold that fills its measure wants no barlines around it.
% Then the bass stops moving altogether: three bars of the open A struck
% on every beat, nine strikes, while the tune works above it. And one bar
% turns to the dominant — A diminished with its own fifth at the bottom
% over a low E, the leading-tone dyad b3/g#3 on beat two, and Step
% walking c3 b2 to the barline, where m.9 answers with the a below.

assert ..2Dia$5-1-3 _12 == Hold
assert | Pulse ..1 _4 |*3 == ..1 _4*9
assert {.3, .1, ..5b} == ..1Dim$5-1-3

Ground
  ..2Dia$5-1-3 _12
  Chords
  Rise
  | Pulse ..1 _4 |*3
  | {.3, .1, ..5b, ...5} _4 {.2, ..7#} _4 Step |

% mm.9-16 — form B, in the relative major, and the eight bars are one
% Sequence. Rung is its unit: the upper voice answering in pairs of
% repeated sixteenths while the bass walks in eighths under it, five
% beats long, ending on the f the next bass note takes over. It does NOT
% begin on a barline — it starts halfway through m.9's second beat — so
% the five bars it spans are written flat, with no bars at all. Here the
% figure is the measure.
%
% The rung comes back a minor third lower. Two of its notes cannot
% follow it down: a minor third under its f2 and its e2 is a d2 and a
% c#2, and this piece never goes below e2. Both are taken an octave up
% instead, and the two overrides say so where the rung is restated —
% everything else falls the minor third exactly.
%
% From m.13 the sequence gives out and the bass walks to the cadence:
% Sigh and Step and their retrogrades, down to the g2 that m.16 answers
% with C major, its third in the bass.

Rung ::= .7 .7 ...6 _2 2b 2b ...5 _4 .5 .3 ..7 _2 ..3 _2 Step~@5

assert Rung[2:3]@-3 == ...4 _2
assert Rung[5:6]@-3 == ...3# _4

Sequence ::= ..1 _2 .5 .5 ...7 _2
  Rung
  .3 .3 ..5 _2
  Rung@-3 \2 {..4 _2} \5 {..3# _4}
  ..4 _2 Sigh~@~-3 Step~@~2 ..6 _2
  | Pulse@10/2 Sigh~ Step~@~-2 ..2 _2 |
  | Step Step~@-7 Pulse@-2/2 |
  | ..3Dia$3-5-1 _12 |

Sequence

% mm.17-21 — form A′: mm.1-8 return, varied, and they open on the
% relative major's own chord. Pillar is that shape — a root-position
% triad spread over four voices, its root on top as well, held the whole
% bar — and it is the shape the piece ends on, on its own tonic,
% seventeen bars from here. m.18 is Ground's bar again, a chord on one
% and one note struck on two and three, with c3 where the a2 was. Then
% the stretch cadences into the relative major: m.19 holds f#4 over a3,
% the third and fifth of the D that m.20's G major answers, and m.21
% lands on g2 and replies with b4/g4 two octaves above it.

Pillar ::= ..1Dia$1-3-5-1 _12

assert Pillar == {..1, ..3, ..5, .1} _12
assert Pillar@~2 == {..3, ..5, ..7, .3} _12

| Pillar@~2 |
  | {.3, ..7, ..3} _4 Pulse@3 |
  | {.6#, .1} _12 |
  | ...7Dia$3-1-5 _4 ..3 _4 ..4 _4 |
  | ...7 _6 ..2 _2 {2, .7} _4 |

% mm.22-24 — form C, on the dominant, and the key says so. Sixth comes
% back five scale steps up, which in E is the tonic over its own third;
% the bar holding it opens on D major with its fifth in the bass, and
% the bar before closes on the diminished triad of d#. Then the bass
% climbs g2 a2 b2 in whole beats and hands the dance to d minor.

key e4 harm

assert Sixth@~5 == {1, .3} _2

| ..6 _4 {4, 2} _2 {3, 1} _2*2 ..7Dim$5-1-3 _2 |
  | ..7bMaj$5-1-3 _2 Sixth@~5 .4 _8 |
  | ..3 _4 ..4 _4 ..5 _4 |

% mm.25-27 — form D, in d minor, and its first bar is the bar this
% lesson opened with: a chord on one and a lone g4 from beat two to the
% barline, which is Lean's shape, here on d minor's ii. Then the
% dominant itself — A major with its third in the bass — under a falling
% step e4 d4 and the low a struck twice. Then Unwind: the dominant
% seventh coming apart from the top, its seventh, its fifth, its third,
% the fifth and third again, and the root under all of them. It is
% written in DEGREES because the next stretch restates it in a minor
% five scale steps down, and an interval spelling could not make that
% move.

key d4 harm

Unwind ::= .4 _2 .2 _2 ..7 _2 .2 _2 ..7 _2 ..5 _2

assert {..5, ..7, .2, .4} == ..5Dom7

% mm.28-32 — form D′: mm.25-27 return, varied, back in a minor, and
% Unwind comes with them five scale steps down. m.28 and m.30 keep
% m.26's bar-rhythm exactly — beat one held, a falling step in
% sixteenths on beat two, three eighths from there to the barline — and
% that falling step is Sigh at the pitch each bar wants it: d4 c4 in
% m.28, c4 b3 in m.30. Step is the same step an octave down and twice as
% slow, which is why the bass says it and the tune sighs it.
%
% Unwind is a dominant seventh both times it sounds and both times it
% resolves: the seventh on a to the d of m.28, the seventh on g to the c
% of m.30. The last two bars are Step and its retrograde walking the
% bass down to e2, the lowest note in the piece.

key a4 min

assert Step == Sigh@-12 _2
assert {...7, ..2, ..4, ..6} == ...7Dom7

% mm.33-34 — form E, two bars and the dance is over: a3 over e3 held the
% whole bar, and then Pillar on the tonic — the four-voice triad that
% opened A′ a third higher, now on a, with the weight of the bar and
% nothing after it.

| {.1, ..5} _12 |
  | Pillar |

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Sarabande · Pattern Engine