Lessons · Modifiers

Transforms

~ retrograde, ^ inversion, @ transpose, axis

% Four marks, one subject. Each hugs the item before it, and after a
% rule reference it covers the WHOLE expansion. '~' plays the phrase
% time-REVERSED with every duration riding along: the crab entry opens
% on the held tonic the subject closed on, and reversing the item list
% says the same thing.
 
bpm 60
instrument plain
meter 4
unit 1/4
key d4 min
 
Subject ::= 1 _2 5 _2 4 3 2 3 4 5 6 5 3 2 1 _2
Ground  ::= .1 _4 .5 _4 .6 _4 .5 _4
 
assert Subject~ == Subject[::-1]
 
{Subject, Ground}
{Subject~, Ground}
 
 
% '^' mirrors pitch around the inversion AXIS (degree 1 here), and it
% mirrors by SCALE STEPS, so the answer never leaves D minor: the leap
% up to the fifth becomes a leap down to the fourth below. The marks
% compose, so '~^' is the retrograde inversion, and the four forms of
% the row run subject, inversion, crab, crab inversion.
 
assert {1 _2 5 _2}^ == 1 _2 .4 _2
 
{Subject^, Ground}
{Subject~^, Ground}
{Subject Subject^ Subject~ Subject~^, Ground*4}
 
 
% '@n' shifts by SEMITONES: every interval survives exactly and the key
% does not. The real answer at the fifth turns the subject's e into b
% natural, a note D minor does not own; the third entry doubles the
% subject an octave above. Nested offsets add.
 
assert 2@7 == 6#
assert Subject@7@5 == Subject@12
 
{Subject Subject@7 Subject@12, Ground*3}
{Subject@12, Subject, Ground}
 
 
% '@~n' shifts by SCALE STEPS of the current key, so it cannot leave
% it: the tonal answer is four steps up, and where the real answer
% needed b natural it takes the bb the key already owns. The same mark
% walks the subject's head down the scale, one degree per statement.
 
Head ::= Subject[0:6]
 
assert 2@~4 == 6
assert Head@~4 == 5 _2 '2 _2 '1 7 6 7
 
{Subject Subject@~4, Ground*2}
{Head Head@~-1 Head@~-2 Head@~-3, Ground*2}
 
 
% The pivot is a setting. 'axis 3' puts it on the third: 1 and 5
% exchange, 3 holds, the tonic triad maps onto itself, so the mirror
% answers at the fifth instead of below the tonic, and the two lines
% cross. 'axis first' pivots each phrase on its OWN first note, so the
% mirror of the answer enters in unison with it and opens outward.
 
axis 3
assert {1 3 5}^ == 5 3 1
 
{Subject, Subject^, Ground}
 
axis first
assert {5 6 7 '1}^ == 5 4 3 2
 
{Subject@~4, Subject@~4^, Ground}
{Subject@~4 Subject@~4^, Ground*2}
 
 
% The exposition under the default axis: subject and tonal answer,
% then a stretto where the mirror enters eight units late, the head
% sequenced down the scale, and the retrograde inversion turning back
% into the subject, closing on the held tonic triad.
 
axis 1
 
{Subject Subject@~4, Ground*2}
{Subject Subject, - _8 Subject^ - _8, Ground*2}
{Head Head@~-1 Head@~-2 Head@~-3, Ground*2}
{Subject~^ Subject, Ground*2}
 
{1, 3, 5, .1} _8

% Four marks, one subject. Each hugs the item before it, and after a
% rule reference it covers the WHOLE expansion. '~' plays the phrase
% time-REVERSED with every duration riding along: the crab entry opens
% on the held tonic the subject closed on, and reversing the item list
% says the same thing.

bpm 60
instrument plain
meter 4
unit 1/4
key d4 min

Subject ::= 1 _2 5 _2 4 3 2 3 4 5 6 5 3 2 1 _2
Ground  ::= .1 _4 .5 _4 .6 _4 .5 _4

assert Subject~ == Subject[::-1]

{Subject, Ground}
{Subject~, Ground}

% '^' mirrors pitch around the inversion AXIS (degree 1 here), and it
% mirrors by SCALE STEPS, so the answer never leaves D minor: the leap
% up to the fifth becomes a leap down to the fourth below. The marks
% compose, so '~^' is the retrograde inversion, and the four forms of
% the row run subject, inversion, crab, crab inversion.

assert {1 _2 5 _2}^ == 1 _2 .4 _2

{Subject^, Ground}
{Subject~^, Ground}
{Subject Subject^ Subject~ Subject~^, Ground*4}

% '@n' shifts by SEMITONES: every interval survives exactly and the key
% does not. The real answer at the fifth turns the subject's e into b
% natural, a note D minor does not own; the third entry doubles the
% subject an octave above. Nested offsets add.

assert 2@7 == 6#
assert Subject@7@5 == Subject@12

{Subject Subject@7 Subject@12, Ground*3}
{Subject@12, Subject, Ground}

% '@~n' shifts by SCALE STEPS of the current key, so it cannot leave
% it: the tonal answer is four steps up, and where the real answer
% needed b natural it takes the bb the key already owns. The same mark
% walks the subject's head down the scale, one degree per statement.

Head ::= Subject[0:6]

assert 2@~4 == 6
assert Head@~4 == 5 _2 '2 _2 '1 7 6 7

{Subject Subject@~4, Ground*2}
{Head Head@~-1 Head@~-2 Head@~-3, Ground*2}

% The pivot is a setting. 'axis 3' puts it on the third: 1 and 5
% exchange, 3 holds, the tonic triad maps onto itself, so the mirror
% answers at the fifth instead of below the tonic, and the two lines
% cross. 'axis first' pivots each phrase on its OWN first note, so the
% mirror of the answer enters in unison with it and opens outward.

axis 3
assert {1 3 5}^ == 5 3 1

{Subject, Subject^, Ground}

axis first
assert {5 6 7 '1}^ == 5 4 3 2

{Subject@~4, Subject@~4^, Ground}
{Subject@~4 Subject@~4^, Ground*2}

% The exposition under the default axis: subject and tonal answer,
% then a stretto where the mirror enters eight units late, the head
% sequenced down the scale, and the retrograde inversion turning back
% into the subject, closing on the held tonic triad.

axis 1

{Subject Subject@~4, Ground*2}
{Subject Subject, - _8 Subject^ - _8, Ground*2}
{Head Head@~-1 Head@~-2 Head@~-3, Ground*2}
{Subject~^ Subject, Ground*2}

{1, 3, 5, .1} _8

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

Transforms · Modifiers