Lessons · Showcase

Inversion

A subject against its own reflection — 31 bars of e harmonic minor, every note a sixteenth, three voices by the end

% Two voices, one of them upside down. Every note in this piece is a
% sixteenth — 926 of them, not one longer or shorter — so nothing here is
% about rhythm. It is about a line and its reflection.
%
% The subject first. It lifts off the tonic to the fourth, turns back, and
% settles onto an oscillation between the third and the second:
 
bpm 96
meter 4
unit 1/4
key e4 harm
axis first
 
Theme ::= 1 - 3 - 4 3 2 3 2 - 1 - 3 2 3 2
 
% It is stated three times, each a third lower. Harmonic minor is not
% symmetrical, so 'a third lower' has to mean two SCALE steps rather than a
% fixed number of semitones — the shape survives, the intervals bend:
 
Descent ::= Theme Theme@~-2 Theme@~-4
 
assert Theme@~-2 == .6 - 1 - 2 1 .7 1 .7 - .6 - 1 .7 1 .7
 
% and answered by a bar of pure shake: a trill on the tonic, then the same
% trill on the third. That is the whole four-bar period.
 
Shake ::= 1 2 1 2 1 2 1 2 3 4 3 4 3 4 3 4
 
Descent Shake
 
 
% The period comes round again, and this time the cadence bar runs instead
% of trilling: continuous sixteenths rocking between neighbours, a third up
% and a third back down. It sits a seventh below the theme.
 
Weave ::= .2 .1 .2 .1 .4 .3 .4 .3 .3 .2 .3 .2 .1 .2 .1 .2
 
% And in the third bar the second voice arrives — the theme MIRRORED. '^'
% reflects a figure about its own first note ('axis first'), so the two
% voices start on the same pitch and walk away from each other in opposite
% directions. Where the theme rises a fourth to A, the mirror falls a fourth
% to B:
 
assert Theme^ == 1 - .6 - .5 .6 .7 .6 .7 - 1 - .6 .7 .6 .7
 
% The two lines meet on E twice a bar, and the file sounds that note once.
 
{Descent Weave, -*32 Theme^@~-4 Weave^@~-2}
 
 
% Now the mirror runs the whole period. Eight bars of it: the subject
% falling in thirds against its own reflection falling in thirds, cadencing
% once on the shake and once on the run.
%
% The mirror of the shake is a trill on the tonic and then one a third
% BELOW, because reflection turns the ascent into a descent:
 
assert Shake^ == 1 .7 1 .7 1 .7 1 .7 .6 .5 .6 .5 .6 .5 .6 .5
 
{Descent Shake, Descent^ Shake^}
{Descent Weave, Descent^ Weave^@~-2}
 
 
% The middle of the piece drops the mirror and spreads the RUN over three
% voices instead. The lead takes it down a third, then down a fourth again,
% while the middle voice doubles it an octave above — and on the third bar
% two octaves above, so the outer voices pull two octaves apart.
%
% Under them a third voice starts the same run half a bar late and never
% moves again: eight notes of its tail, two full turns, eight notes of its
% head, and a shake to close. That wheel is twelve bars long in the end.
 
Wheel ::= Weave[8:] Weave Weave Weave[:8] Shake@~-5
 
assert Weave[8:] == .3 .2 .3 .2 .1 .2 .1 .2
 
{Weave Weave@~-2 Weave@~-5 Shake@~-7, Weave@~7 Weave@~5 Weave@~9 Shake@~4, Wheel}
 
 
% The mirrored period returns over the wheel, twice — and the second time
% the lead SLIPS. It comes in half a bar late (on the second trill of the
% shake) and stays late for the rest of the section, so subject and mirror
% no longer meet on E at all: for four bars the piece is out of phase with
% itself.
 
{Descent Weave, Descent^ Weave^@~-2, Wheel}
{Shake[8:] Descent Weave[:8], Descent^ Weave^@~-2, Wheel}
 
 
% The climb out. The lead pairs the tail of the subject with the head of
% the run and lifts the pair a fifth; the mirror lifts its run by the same
% fifth; the wheel breaks into shakes and keeps rising. The last bar is the
% third voice alone, trilling up onto the tonic an octave above where the
% piece began.
 
Climb ::= Theme[8:] Weave[:8]@~4
 
{Climb Climb@~4 -*16, Weave^@~2 Weave^@~6 -*16, Shake@~-1 Shake@~3 Shake@~4}

% Two voices, one of them upside down. Every note in this piece is a
% sixteenth — 926 of them, not one longer or shorter — so nothing here is
% about rhythm. It is about a line and its reflection.
%
% The subject first. It lifts off the tonic to the fourth, turns back, and
% settles onto an oscillation between the third and the second:

bpm 96
meter 4
unit 1/4
key e4 harm
axis first

Theme ::= 1 - 3 - 4 3 2 3 2 - 1 - 3 2 3 2

% It is stated three times, each a third lower. Harmonic minor is not
% symmetrical, so 'a third lower' has to mean two SCALE steps rather than a
% fixed number of semitones — the shape survives, the intervals bend:

Descent ::= Theme Theme@~-2 Theme@~-4

assert Theme@~-2 == .6 - 1 - 2 1 .7 1 .7 - .6 - 1 .7 1 .7

% and answered by a bar of pure shake: a trill on the tonic, then the same
% trill on the third. That is the whole four-bar period.

Shake ::= 1 2 1 2 1 2 1 2 3 4 3 4 3 4 3 4

Descent Shake

% The period comes round again, and this time the cadence bar runs instead
% of trilling: continuous sixteenths rocking between neighbours, a third up
% and a third back down. It sits a seventh below the theme.

Weave ::= .2 .1 .2 .1 .4 .3 .4 .3 .3 .2 .3 .2 .1 .2 .1 .2

% And in the third bar the second voice arrives — the theme MIRRORED. '^'
% reflects a figure about its own first note ('axis first'), so the two
% voices start on the same pitch and walk away from each other in opposite
% directions. Where the theme rises a fourth to A, the mirror falls a fourth
% to B:

assert Theme^ == 1 - .6 - .5 .6 .7 .6 .7 - 1 - .6 .7 .6 .7

% The two lines meet on E twice a bar, and the file sounds that note once.

{Descent Weave, -*32 Theme^@~-4 Weave^@~-2}

% Now the mirror runs the whole period. Eight bars of it: the subject
% falling in thirds against its own reflection falling in thirds, cadencing
% once on the shake and once on the run.
%
% The mirror of the shake is a trill on the tonic and then one a third
% BELOW, because reflection turns the ascent into a descent:

assert Shake^ == 1 .7 1 .7 1 .7 1 .7 .6 .5 .6 .5 .6 .5 .6 .5

{Descent Shake, Descent^ Shake^}
{Descent Weave, Descent^ Weave^@~-2}

% The middle of the piece drops the mirror and spreads the RUN over three
% voices instead. The lead takes it down a third, then down a fourth again,
% while the middle voice doubles it an octave above — and on the third bar
% two octaves above, so the outer voices pull two octaves apart.
%
% Under them a third voice starts the same run half a bar late and never
% moves again: eight notes of its tail, two full turns, eight notes of its
% head, and a shake to close. That wheel is twelve bars long in the end.

Wheel ::= Weave[8:] Weave Weave Weave[:8] Shake@~-5

assert Weave[8:] == .3 .2 .3 .2 .1 .2 .1 .2

{Weave Weave@~-2 Weave@~-5 Shake@~-7, Weave@~7 Weave@~5 Weave@~9 Shake@~4, Wheel}

% The mirrored period returns over the wheel, twice — and the second time
% the lead SLIPS. It comes in half a bar late (on the second trill of the
% shake) and stays late for the rest of the section, so subject and mirror
% no longer meet on E at all: for four bars the piece is out of phase with
% itself.

{Descent Weave, Descent^ Weave^@~-2, Wheel}
{Shake[8:] Descent Weave[:8], Descent^ Weave^@~-2, Wheel}

% The climb out. The lead pairs the tail of the subject with the head of
% the run and lifts the pair a fifth; the mirror lifts its run by the same
% fifth; the wheel breaks into shakes and keeps rising. The last bar is the
% third voice alone, trilling up onto the tonic an octave above where the
% piece began.

Climb ::= Theme[8:] Weave[:8]@~4

{Climb Climb@~4 -*16, Weave^@~2 Weave^@~6 -*16, Shake@~-1 Shake@~3 Shake@~4}

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

Opening…

Inversion · Pattern Engine