Lessons · Advanced

The mirror system

Axes, mirror answers, reflect-before-transpose

% '^' mirrors pitch by SCALE STEPS around the inversion AXIS, and
% the axis is a setting: it starts at degree 1, the tonal center.
% Under it every step above the tonic becomes the same step below,
% so the answer to this rising subject falls to a close on 1.
 
bpm 72
key g min
 
Subject ::= 5 _2 5 6 7 '1 _2 7 6 5 4 3 _2 2 1 _4
 
assert { 1 2 3 4 5 }^ == 1 .7 .6 .5 .4
 
Subject {Subject}^
{Subject {Subject}^, .1 _18 .5 _18}
 
 
% 'axis 3' moves the pivot to the third: 1 and 5 exchange, 3 holds,
% and the tonic triad maps onto itself. The same mirror now overlaps
% the subject's register instead of lying under it, and the answer
% closes on 5 — the fugal mirror answer.
 
axis 3
 
Mirror ::= {Subject}^
 
assert { 1 3 5 }^ == 5 3 1
 
{Subject Mirror, .5 _18 .1 _18}
{Subject, Mirror@-12} {Mirror, Subject@-12}
 
 
% The axis is read BEFORE any transposition: '{Fig}^@~2' mirrors
% around degree 1 first and only then walks the mirrored figure two
% steps up. So a rising figure sequenced upward has a mirror that
% falls, and the '@~' marks carry that falling shape down the scale.
 
axis 1
 
Fig  ::= 1 2 3 5 _2
Rise ::= Fig Fig@~1 Fig@~2 Fig@~3
Fall ::= {Fig}^ {Fig}^@~-1 {Fig}^@~-2 {Fig}^@~-3
 
assert {Fig}^@~2 == 3 2 1 .6 _2
 
{Rise Fall, .1 _10 .3 _10 .5 _10 .1 _10}
 
 
% 'axis first' fixes no degree — each mirrored phrase pivots on its
% OWN first pitched note. The answer therefore enters in unison with
% the subject and opens outward from it, and it tracks the subject
% to any transposition without the axis being reset.
 
axis first
 
assert {Subject}^ == 5 _2 5 4 3 2 _2 3 4 5 6 7 _2 '1 '2 _4
 
Subject {Subject}^
{Subject@~2 {Subject@~2}^, .1 _9 .4 _9 .5 _9 .1 _9}
 
 
% One subject, one rule, three axes. Nothing else changes across
% these three lines — 'Mirror' reads whichever axis is in force —
% and the answer moves with the pivot: below the subject and
% cadencing on 1, overlapping it and closing on 5, then in unison
% with it and rising.
 
axis 1
{Subject, Mirror}
 
axis 3
{Subject, Mirror}
 
axis first
{Subject, Mirror}
 
{1, .1} _8

% '^' mirrors pitch by SCALE STEPS around the inversion AXIS, and
% the axis is a setting: it starts at degree 1, the tonal center.
% Under it every step above the tonic becomes the same step below,
% so the answer to this rising subject falls to a close on 1.

bpm 72
key g min

Subject ::= 5 _2 5 6 7 '1 _2 7 6 5 4 3 _2 2 1 _4

assert { 1 2 3 4 5 }^ == 1 .7 .6 .5 .4

Subject {Subject}^
{Subject {Subject}^, .1 _18 .5 _18}

% 'axis 3' moves the pivot to the third: 1 and 5 exchange, 3 holds,
% and the tonic triad maps onto itself. The same mirror now overlaps
% the subject's register instead of lying under it, and the answer
% closes on 5 — the fugal mirror answer.

axis 3

Mirror ::= {Subject}^

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

{Subject Mirror, .5 _18 .1 _18}
{Subject, Mirror@-12} {Mirror, Subject@-12}

% The axis is read BEFORE any transposition: '{Fig}^@~2' mirrors
% around degree 1 first and only then walks the mirrored figure two
% steps up. So a rising figure sequenced upward has a mirror that
% falls, and the '@~' marks carry that falling shape down the scale.

axis 1

Fig  ::= 1 2 3 5 _2
Rise ::= Fig Fig@~1 Fig@~2 Fig@~3
Fall ::= {Fig}^ {Fig}^@~-1 {Fig}^@~-2 {Fig}^@~-3

assert {Fig}^@~2 == 3 2 1 .6 _2

{Rise Fall, .1 _10 .3 _10 .5 _10 .1 _10}

% 'axis first' fixes no degree — each mirrored phrase pivots on its
% OWN first pitched note. The answer therefore enters in unison with
% the subject and opens outward from it, and it tracks the subject
% to any transposition without the axis being reset.

axis first

assert {Subject}^ == 5 _2 5 4 3 2 _2 3 4 5 6 7 _2 '1 '2 _4

Subject {Subject}^
{Subject@~2 {Subject@~2}^, .1 _9 .4 _9 .5 _9 .1 _9}

% One subject, one rule, three axes. Nothing else changes across
% these three lines — 'Mirror' reads whichever axis is in force —
% and the answer moves with the pivot: below the subject and
% cadencing on 1, overlapping it and closing on 5, then in unison
% with it and rising.

axis 1
{Subject, Mirror}

axis 3
{Subject, Mirror}

axis first
{Subject, Mirror}

{1, .1} _8

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The mirror system · Pattern Engine