Saying it another way

Equivalent spellings, same sound

% A lament ground: a3 falls to e3, turns through d3, and comes home in
% nothing but halves and a closing whole. A LENGTH has many spellings —
% '_8' multiplies the unit by eight, '+7' adds seven units to it, and
% marks compose, so '_4 _2' takes it up by four and then by two.
% 'assert' schedules both sides and compares them event for event, so
% every line below is a claim this lesson has to keep.
 
bpm 72
meter 4
unit 1/4
key a4 min
 
Ground ::= .1 _8 ..7 _8 ..6 _8 ..5 _8 ..4 _8 ..5 _8 .1 _16
 
assert .1 _8 == .1 +7
assert .1 _8 == .1 _4 _2
assert .1 _16 == .1 _8 _2
assert Ground == .1 +7 ..7 +7 ..6 +7 ..5 +7 ..4 +7 ..5 +7 .1 +15
 
Ground
 
 
% Every PITCH has several names too. Head opens the tune in degrees of
% A minor; those same four notes are c5 b4 c5 e5 by letter, m72 m71 m72
% m76 by MIDI, and a walk in scale steps out of c5. Four spellings, one
% opening — and then the key moves. Only the degrees follow it: in C
% minor Head is eb5 d5 eb5 g5, while the letters keep playing the old
% four notes in a key that no longer owns them.
 
Head ::= 3 _4 2 _4 3 _4 5 _4
Tune ::= Head 6 _4 5 _4 4 _4 3 _4 4 _4 3 _4 2 _4 .7# _4 1 _16
 
assert Head == c5 _4 b4 _4 c5 _4 e5 _4
assert Head == m72 _4 m71 _4 m72 _4 m76 _4
assert Head == c5 _4 s-1 _4 s1 _4 s2 _4
 
key c5 min
assert Head == eb5 _4 d5 _4 eb5 _4 g5 _4
Head c5 _4 b4 _4 c5 _4 e5 _4
 
key a4 min
{Tune, Ground}
 
 
% A mark after a reference covers the WHOLE expansion, and each one
% names a figure that would otherwise be typed out. '~' plays Head
% backwards with its durations — the slice '[::-1]' reaches the same
% four notes on a flat line — and '@~-1' drops it one SCALE step, so the
% answer sits on degrees 2 1 2 4; '@-2' would move it two semitones and
% leave the key. Marks compose, and their order does not matter.
 
Reply ::= Head Head~ Head@~-1 Head~@~-1
 
assert Head~ == Head[::-1]
assert Head~ == 5 _4 3 _4 2 _4 3 _4
assert Head@~-1 == 2 _4 1 _4 2 _4 4 _4
assert Head@-2 == bb4 _4 a4 _4 bb4 _4 d5 _4
assert Head~@~-1 == Head@~-1~
 
{Reply, Ground}
 
 
% A chord has as many names as a note. The ground's harmony is
% i VII VI v iv V i, and every chord below could have been stacked by
% hand instead. 'Dia' asks the scale, and in A minor the scale answers
% the fifth degree with a MINOR triad — so the cadence names its major
% fifth outright, the one chord the key does not own.
 
Chords ::= 1Min _8 .7Maj _8 .6Maj _8 .5Min _8 .4Min _8 .5Maj _8 1Min _16
 
assert 1Min == {1, 3, 5}
assert 1Min == aMin
assert 1Dia == 1Min
assert .5Dia == .5Min
assert .5Maj == {.5, .7#, 2}
 
{Tune, Chords, Ground}
 
 
% A bar SCALES what lies between two '|' to exactly one measure. Where
% the content already fills the measure that is the identity; where it
% does not, the bar stretches — '| Tonic |' spreads the tonic arpeggio
% over a whole bar instead of half of one. Walk's measures hold sixteen
% units already, so its bar lines change nothing but where the eye
% rests, '|*2' is one measure written twice, and '{…}_2' gives a run of
% notes one length rather than a mark each.
 
Tonic ::= {.1 .3 .5 .3}_2
 
Walk ::= | Tonic {..7 .2 .4 .2}_2 |
         | {..6 .1 .3 .1 ..5 ..7 .2 ..7}_2 |
         | {..4 ..6 .1 ..6 ..5 ..7# .2 ..7#}_2 |
         | Tonic {.5 .3 .1 .1}_2 |
 
assert Tonic == .1 _2 .3 _2 .5 _2 .3 _2
assert | Tonic | == {.1 .3 .5 .3}_4
assert | Tonic Tonic | == Tonic Tonic
assert | Tonic Tonic |*2 == Tonic Tonic Tonic Tonic
 
{Tune, Walk}
 
 
% The two transpose marks agree at exactly one interval. Seven scale
% steps is an octave in a seven-note key, so '@~7' and '@12' land on the
% same pitch, nested offsets add, and '@24' is two octaves. Sent up
% there the ground becomes a descant, and because the ground IS the
% roots of the harmony every note of it is a chord tone of the Chords
% beneath while Walk keeps those same roots moving underneath.
 
assert Ground@~7 == Ground@12
assert Ground@12@12 == Ground@24
assert Ground@24 == Ground@~14
 
{Ground@24, Chords, Walk}
 
 
% Six turns of the ground and a close: the subject alone, the tune, the
% harmony filled in, the answering sequence over the walking bass, the
% ground itself as descant, the tune once more — then Close takes iv V i
% over a pedal a2. The three claims say where the pieces came from: Tune
% and Reply open on the same Head, and Close harmonises the ground's own
% last two bars.
 
Close ::= {6 _8 7# _8 '1 _16, .4Min _8 .5Maj _8 1Min _16, ..1 _32}
 
assert Tune[0:4] == Head
assert Reply[0:4] == Head
assert Ground[4:] == ..4 _8 ..5 _8 .1 _16
 
Ground
{Tune, Ground}
{Tune, Chords, Ground}
{Reply, Walk}
{Ground@24, Chords, Walk}
{Tune, Chords, Walk}
Close

% A lament ground: a3 falls to e3, turns through d3, and comes home in
% nothing but halves and a closing whole. A LENGTH has many spellings —
% '_8' multiplies the unit by eight, '+7' adds seven units to it, and
% marks compose, so '_4 _2' takes it up by four and then by two.
% 'assert' schedules both sides and compares them event for event, so
% every line below is a claim this lesson has to keep.

bpm 72
meter 4
unit 1/4
key a4 min

Ground ::= .1 _8 ..7 _8 ..6 _8 ..5 _8 ..4 _8 ..5 _8 .1 _16

assert .1 _8 == .1 +7
assert .1 _8 == .1 _4 _2
assert .1 _16 == .1 _8 _2
assert Ground == .1 +7 ..7 +7 ..6 +7 ..5 +7 ..4 +7 ..5 +7 .1 +15

Ground

% Every PITCH has several names too. Head opens the tune in degrees of
% A minor; those same four notes are c5 b4 c5 e5 by letter, m72 m71 m72
% m76 by MIDI, and a walk in scale steps out of c5. Four spellings, one
% opening — and then the key moves. Only the degrees follow it: in C
% minor Head is eb5 d5 eb5 g5, while the letters keep playing the old
% four notes in a key that no longer owns them.

Head ::= 3 _4 2 _4 3 _4 5 _4
Tune ::= Head 6 _4 5 _4 4 _4 3 _4 4 _4 3 _4 2 _4 .7# _4 1 _16

assert Head == c5 _4 b4 _4 c5 _4 e5 _4
assert Head == m72 _4 m71 _4 m72 _4 m76 _4
assert Head == c5 _4 s-1 _4 s1 _4 s2 _4

key c5 min
assert Head == eb5 _4 d5 _4 eb5 _4 g5 _4
Head c5 _4 b4 _4 c5 _4 e5 _4

key a4 min
{Tune, Ground}

% A mark after a reference covers the WHOLE expansion, and each one
% names a figure that would otherwise be typed out. '~' plays Head
% backwards with its durations — the slice '[::-1]' reaches the same
% four notes on a flat line — and '@~-1' drops it one SCALE step, so the
% answer sits on degrees 2 1 2 4; '@-2' would move it two semitones and
% leave the key. Marks compose, and their order does not matter.

Reply ::= Head Head~ Head@~-1 Head~@~-1

assert Head~ == Head[::-1]
assert Head~ == 5 _4 3 _4 2 _4 3 _4
assert Head@~-1 == 2 _4 1 _4 2 _4 4 _4
assert Head@-2 == bb4 _4 a4 _4 bb4 _4 d5 _4
assert Head~@~-1 == Head@~-1~

{Reply, Ground}

% A chord has as many names as a note. The ground's harmony is
% i VII VI v iv V i, and every chord below could have been stacked by
% hand instead. 'Dia' asks the scale, and in A minor the scale answers
% the fifth degree with a MINOR triad — so the cadence names its major
% fifth outright, the one chord the key does not own.

Chords ::= 1Min _8 .7Maj _8 .6Maj _8 .5Min _8 .4Min _8 .5Maj _8 1Min _16

assert 1Min == {1, 3, 5}
assert 1Min == aMin
assert 1Dia == 1Min
assert .5Dia == .5Min
assert .5Maj == {.5, .7#, 2}

{Tune, Chords, Ground}

% A bar SCALES what lies between two '|' to exactly one measure. Where
% the content already fills the measure that is the identity; where it
% does not, the bar stretches — '| Tonic |' spreads the tonic arpeggio
% over a whole bar instead of half of one. Walk's measures hold sixteen
% units already, so its bar lines change nothing but where the eye
% rests, '|*2' is one measure written twice, and '{…}_2' gives a run of
% notes one length rather than a mark each.

Tonic ::= {.1 .3 .5 .3}_2

Walk ::= | Tonic {..7 .2 .4 .2}_2 |
         | {..6 .1 .3 .1 ..5 ..7 .2 ..7}_2 |
         | {..4 ..6 .1 ..6 ..5 ..7# .2 ..7#}_2 |
         | Tonic {.5 .3 .1 .1}_2 |

assert Tonic == .1 _2 .3 _2 .5 _2 .3 _2
assert | Tonic | == {.1 .3 .5 .3}_4
assert | Tonic Tonic | == Tonic Tonic
assert | Tonic Tonic |*2 == Tonic Tonic Tonic Tonic

{Tune, Walk}

% The two transpose marks agree at exactly one interval. Seven scale
% steps is an octave in a seven-note key, so '@~7' and '@12' land on the
% same pitch, nested offsets add, and '@24' is two octaves. Sent up
% there the ground becomes a descant, and because the ground IS the
% roots of the harmony every note of it is a chord tone of the Chords
% beneath while Walk keeps those same roots moving underneath.

assert Ground@~7 == Ground@12
assert Ground@12@12 == Ground@24
assert Ground@24 == Ground@~14

{Ground@24, Chords, Walk}

% Six turns of the ground and a close: the subject alone, the tune, the
% harmony filled in, the answering sequence over the walking bass, the
% ground itself as descant, the tune once more — then Close takes iv V i
% over a pedal a2. The three claims say where the pieces came from: Tune
% and Reply open on the same Head, and Close harmonises the ground's own
% last two bars.

Close ::= {6 _8 7# _8 '1 _16, .4Min _8 .5Maj _8 1Min _16, ..1 _32}

assert Tune[0:4] == Head
assert Reply[0:4] == Head
assert Ground[4:] == ..4 _8 ..5 _8 .1 _16

Ground
{Tune, Ground}
{Tune, Chords, Ground}
{Reply, Walk}
{Ground@24, Chords, Walk}
{Tune, Chords, Walk}
Close

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Saying it another way · Pattern Engine