Lessons · Harmony

Changing key

The pivot chord

% A ii-V-I is the jazz sentence, and every chord in it is a seventh: a
% minor seventh on 2, a dominant seventh on 5, a major seventh at home.
% Bar four turns back on 6 so the four bars come round again. Walk is
% the bass under them, four plain quarters to the bar, reaching every
% new root by a step — f# up to g, d down to c, b down to a, c back up
% to d. Walk carries the barlines, so it goes first in the field and
% each of Changes' four chords fills one measure.
 
bpm 132
meter 4
key c maj
 
assert .2Dia7 == {.2, .4, .6, 1}
assert .5Dom7 == {.5, .7, 2, 4}
 
Changes ::= .2Dia7 .5Dom7 .1Maj7 .6Dia7
 
Walk ::= | ..2 ..6 ..4 ..4# |
         | ..5 ..4 ..3 ..2 |
         | ..1 ..3 ..5 ..7 |
         | ..6 ..5 ..3 ..1 |
 
{Walk, Changes}
 
 
% What tells one seventh chord from the next is its THIRD and its
% SEVENTH, and each of those is a step from the next chord's pair:
% Dm7's seventh c falls to G7's third b, G7's seventh f falls to
% Cmaj7's third e. Guide holds those two lines, a bar to a note. Tune
% is a melody over them, and every bar of it starts on a note Guide is
% holding — Swing pours its running notes out in pairs, long then
% short, twelve places to the bar and three to a beat.
 
Swing ::= $1 _2 $2
 
Guide ::= {| '1 | 7 | 7 | '1 |,
           | 4  | 4 | 3 | 5  |}
 
Tune ::= | Swing('1 '2 '3 '2 '1 6 4 6) |
         | Swing(7 '2 '1 7 6 5) 4 _3 |
         | 3 _6 - _3 5 _2 7 |
         | '1 _3 6 _2 '1 '2 _3 '3 _3 |
 
{Guide, Changes, Walk}
 
{Tune, Changes, Walk}
 
 
% A PIVOT is one chord two keys own, and bar four is one: Am7 is the
% chord on 6 in C and the chord on 2 in G — four pitches under two
% numbers, which is what the asserts say. So the C chorus ends on it
% and the G chorus opens on it, the same chord twice across the seam
% with not a note of it moving. Everything else is written in degrees,
% so it all goes up a fifth around that one held chord.
 
assert .6Dia7 == aMin7@-12
 
{Tune, Changes, Walk}
 
key g maj
assert .2Dia7 == aMin7@-12
 
{Tune, Changes, Walk}
 
 
% A pivot is a courtesy, not a requirement. A dominant seventh carries
% the one tritone its key owns, so two bars of ii-V state a key with
% nothing shared and nothing prepared. Here the same four bars step
% down a whole tone twice, and neither seam has a chord in common: C's
% Am7 holds an e that Bb has not got, Bb's Gm7 a d that Ab has not got.
 
key c maj
{Tune, Changes, Walk}
 
key bb3 maj
{Tune, Changes, Walk}
 
key ab3 maj
{Tune, Changes, Walk}
 
 
% Two dominant sevenths a tritone apart are built on the same pair of
% notes: G7's third b and seventh f are Db7's seventh and third, which
% is what the assert claims by swapping the two members. So either one
% can be the V of C — Pair does not move, and the root under it falls a
% fifth in the first and a half step in the second. It cuts both ways:
% that same Db7 is the V of Gb, and since Pair is written in degrees,
% 4 and 7 in Gb are cb and f — the notes 4 and 7 already were.
 
key c maj
assert .5Dom7$3-7 == .2bDom7$7-3
 
Close ::= .5Dom7 .1Maj7
Pair  ::= | {4, 7} | {3, 7} |
 
{Pair, Close}
 
{Pair, .2bDom7 Close[1:]}
 
key gb3 maj
assert .5Dom7 == {.5, .7, 2, 4}
 
{Pair, Close}
 
 
% The same twins carry Ab home. Bend Ab's own major seventh down to a
% flat one and the chord holds D7's tritone: they share c and f#, which
% is what the assert says. D7 is the dominant of C's dominant, so Ab7
% stands in for it, then G7, then home. Changes[:3] keeps the first three
% chords and puts that bend in bar four, where the chorus used to turn
% back on 6.
 
key c maj
assert .2Dom7$7-3 == .6bDom7$3-7
 
Home ::= {| '1 _3 '3b _3 '1 _3 6b _3 |
           | 7 _3 6 _3 5 _3 4 _3 |
           | 3 _6 5 _3 '1 _3 |,
           | .6bDom7 | .5Dom7 | .1Maj9 |,
           | ..6b ..5b ..3b ..1 |
           | ..5 ..4 ..3 ..2 |
           | ..1 _12 |}
 
key ab3 maj
{Tune, Changes[:3] .1Dom7, Walk}
 
key c maj
Home
 
 
% Nineteen bars, four keys, one tune. C states it; the pivot on 6 hands
% it to G with nothing moving; a ii-V drops it a whole tone twice, to Bb
% and to Ab, with nothing shared either time; and Ab's own tonic, bent to
% a seventh, carries D7's tritone and walks it home. Every key line sits
% exactly where a chord is reheard, and Bb takes the guide tones alone so
% the tune comes back new in Ab.
 
key c maj
{Tune, Changes, Walk}
 
key g maj
{Tune, Changes, Walk}
 
key bb3 maj
{Guide, Changes, Walk}
 
key ab3 maj
{Tune, Changes[:3] .1Dom7, Walk}
 
key c maj
Home

% A ii-V-I is the jazz sentence, and every chord in it is a seventh: a
% minor seventh on 2, a dominant seventh on 5, a major seventh at home.
% Bar four turns back on 6 so the four bars come round again. Walk is
% the bass under them, four plain quarters to the bar, reaching every
% new root by a step — f# up to g, d down to c, b down to a, c back up
% to d. Walk carries the barlines, so it goes first in the field and
% each of Changes' four chords fills one measure.

bpm 132
meter 4
key c maj

assert .2Dia7 == {.2, .4, .6, 1}
assert .5Dom7 == {.5, .7, 2, 4}

Changes ::= .2Dia7 .5Dom7 .1Maj7 .6Dia7

Walk ::= | ..2 ..6 ..4 ..4# |
         | ..5 ..4 ..3 ..2 |
         | ..1 ..3 ..5 ..7 |
         | ..6 ..5 ..3 ..1 |

{Walk, Changes}

% What tells one seventh chord from the next is its THIRD and its
% SEVENTH, and each of those is a step from the next chord's pair:
% Dm7's seventh c falls to G7's third b, G7's seventh f falls to
% Cmaj7's third e. Guide holds those two lines, a bar to a note. Tune
% is a melody over them, and every bar of it starts on a note Guide is
% holding — Swing pours its running notes out in pairs, long then
% short, twelve places to the bar and three to a beat.

Swing ::= $1 _2 $2

Guide ::= {| '1 | 7 | 7 | '1 |,
           | 4  | 4 | 3 | 5  |}

{Guide, Changes, Walk}

{Tune, Changes, Walk}

% A PIVOT is one chord two keys own, and bar four is one: Am7 is the
% chord on 6 in C and the chord on 2 in G — four pitches under two
% numbers, which is what the asserts say. So the C chorus ends on it
% and the G chorus opens on it, the same chord twice across the seam
% with not a note of it moving. Everything else is written in degrees,
% so it all goes up a fifth around that one held chord.

assert .6Dia7 == aMin7@-12

{Tune, Changes, Walk}

key g maj
assert .2Dia7 == aMin7@-12

{Tune, Changes, Walk}

% A pivot is a courtesy, not a requirement. A dominant seventh carries
% the one tritone its key owns, so two bars of ii-V state a key with
% nothing shared and nothing prepared. Here the same four bars step
% down a whole tone twice, and neither seam has a chord in common: C's
% Am7 holds an e that Bb has not got, Bb's Gm7 a d that Ab has not got.

key c maj
{Tune, Changes, Walk}

key bb3 maj
{Tune, Changes, Walk}

key ab3 maj
{Tune, Changes, Walk}

% Two dominant sevenths a tritone apart are built on the same pair of
% notes: G7's third b and seventh f are Db7's seventh and third, which
% is what the assert claims by swapping the two members. So either one
% can be the V of C — Pair does not move, and the root under it falls a
% fifth in the first and a half step in the second. It cuts both ways:
% that same Db7 is the V of Gb, and since Pair is written in degrees,
% 4 and 7 in Gb are cb and f — the notes 4 and 7 already were.

key c maj
assert .5Dom7$3-7 == .2bDom7$7-3

Close ::= .5Dom7 .1Maj7
Pair  ::= | {4, 7} | {3, 7} |

{Pair, Close}

{Pair, .2bDom7 Close[1:]}

key gb3 maj
assert .5Dom7 == {.5, .7, 2, 4}

{Pair, Close}

% The same twins carry Ab home. Bend Ab's own major seventh down to a
% flat one and the chord holds D7's tritone: they share c and f#, which
% is what the assert says. D7 is the dominant of C's dominant, so Ab7
% stands in for it, then G7, then home. Changes[:3] keeps the first three
% chords and puts that bend in bar four, where the chorus used to turn
% back on 6.

key c maj
assert .2Dom7$7-3 == .6bDom7$3-7

Home ::= {| '1 _3 '3b _3 '1 _3 6b _3 |
           | 7 _3 6 _3 5 _3 4 _3 |
           | 3 _6 5 _3 '1 _3 |,
           | .6bDom7 | .5Dom7 | .1Maj9 |,
           | ..6b ..5b ..3b ..1 |
           | ..5 ..4 ..3 ..2 |
           | ..1 _12 |}

key ab3 maj
{Tune, Changes[:3] .1Dom7, Walk}

key c maj
Home

% Nineteen bars, four keys, one tune. C states it; the pivot on 6 hands
% it to G with nothing moving; a ii-V drops it a whole tone twice, to Bb
% and to Ab, with nothing shared either time; and Ab's own tonic, bent to
% a seventh, carries D7's tritone and walks it home. Every key line sits
% exactly where a chord is reheard, and Bb takes the guide tones alone so
% the tune comes back new in Ab.

key c maj
{Tune, Changes, Walk}

key g maj
{Tune, Changes, Walk}

key bb3 maj
{Guide, Changes, Walk}

key ab3 maj
{Tune, Changes[:3] .1Dom7, Walk}

key c maj
Home

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