Lessons · Advanced

A variation set

Every machine on one theme: the capstone

% The capstone: ONE theme, and each variation is one machine from the
% lessons above. The theme is a period: the antecedent leaves the line
% open on 7 over V, the consequent closes it on 1. Both halves open
% with the same two notes, which is what the slice says. Under it runs a
% ground of I iii IV V twice, the last V resolving; every variation rides
% that same ground.
 
bpm 60
instrument plain
key g maj
 
Ant   ::= 5 _2 '1 _2 7 _2 5 _2 6 _2 '1 _2 7 _4
Con   ::= Ant[:2] 7 _2 5 _2 6 _2 4 _2 2 _2 1 _2
Theme ::= Ant Con
 
BassA  ::= .1 _4 .3 _4 .4 _4 .5 _4
BassB  ::= .1 _4 .3 _4 .4 _4 .5 _2 .1 _2
Ground<bass> ::= BassA BassB
 
assert Ant[:2] == Con[:2]
 
Theme
{Theme, Ground}
 
 
% Variation I: the SEQUENCE. Two slices of the theme are the whole
% variation: its rising pair climbs I iii IV V an octave, its falling
% pair walks back down, and the theme's own last two notes cadence. No
% pitch is written here at all, and every note lands in the chord under
% it, sixteen for sixteen.
 
Head ::= Ant[:2]
Fall ::= Con[4:6]
Var1 ::= Head Head@~2 Head@~3 Head@~4 Fall@~4 Fall@~1 Fall Con[6:]
 
assert Head Fall == 5 _2 '1 _2 6 _2 4 _2
 
Var1
{Var1, Ground}
 
 
% Variation II: the MIRROR. 'axis 5' pivots on the theme's own first
% note, so the answer enters in unison with it and opens outward: where
% the theme steps up to '1 the mirror steps down to 2, and where the
% theme falls to 1 the mirror rises to '2. A pedal holds I, V, I under
% the pair.
 
axis 5
 
Var2 ::= {Theme}^
 
assert {Ant}^ == 5 _2 2 _2 3 _2 5 _2 4 _2 2 _2 3 _4
 
Var2
{Theme, Var2, .1 _16 .5 _8 .1 _8}
 
 
% Variation III: the DOUBLE. One rule at two speeds: the theme twice
% at tempo against itself augmented an octave down, so the slow voice
% spends a whole statement on each half. The two attack together in
% octaves at the head of each half, and the slow tonic is still sounding
% under the fast one's close. The ground turns twice to cover them.
 
Var3 ::= {Theme Theme, {Theme} _2@-12}
 
assert {Ant} _2 == 5 _4 '1 _4 7 _4 5 _4 6 _4 '1 _4 7 _8
 
Var3
{Var3, Ground*2}
 
 
% Variation IV: the MINORE. Nothing is retyped. Degrees are positions
% in whatever key is in force, so one line re-reads the theme, the
% sequence and the ground in the parallel minor: 3, 6 and 7 all drop a
% semitone, the chord on 3 turns major, and the cadence walks v to i.
 
key g min
 
{Theme, Ground}
{Var1, Ground}
 
 
% The set entire: theme, the four machines in order, the minore, and
% the theme once more in the major to close. This block writes no new
% material, only the order.
 
key g maj
 
{Theme, Ground}
{Var1, Ground}
{Theme, Var2, .1 _16 .5 _8 .1 _8}
{Var3, Ground*2}
 
key g min
{Theme, Ground}
 
key g maj
{Theme, Ground}

% The capstone: ONE theme, and each variation is one machine from the
% lessons above. The theme is a period: the antecedent leaves the line
% open on 7 over V, the consequent closes it on 1. Both halves open
% with the same two notes, which is what the slice says. Under it runs a
% ground of I iii IV V twice, the last V resolving; every variation rides
% that same ground.

bpm 60
instrument plain
key g maj

Ant   ::= 5 _2 '1 _2 7 _2 5 _2 6 _2 '1 _2 7 _4
Con   ::= Ant[:2] 7 _2 5 _2 6 _2 4 _2 2 _2 1 _2
Theme ::= Ant Con

BassA  ::= .1 _4 .3 _4 .4 _4 .5 _4
BassB  ::= .1 _4 .3 _4 .4 _4 .5 _2 .1 _2
Ground<bass> ::= BassA BassB

assert Ant[:2] == Con[:2]

Theme
{Theme, Ground}

% Variation I: the SEQUENCE. Two slices of the theme are the whole
% variation: its rising pair climbs I iii IV V an octave, its falling
% pair walks back down, and the theme's own last two notes cadence. No
% pitch is written here at all, and every note lands in the chord under
% it, sixteen for sixteen.

Head ::= Ant[:2]
Fall ::= Con[4:6]
Var1 ::= Head Head@~2 Head@~3 Head@~4 Fall@~4 Fall@~1 Fall Con[6:]

assert Head Fall == 5 _2 '1 _2 6 _2 4 _2

Var1
{Var1, Ground}

% Variation II: the MIRROR. 'axis 5' pivots on the theme's own first
% note, so the answer enters in unison with it and opens outward: where
% the theme steps up to '1 the mirror steps down to 2, and where the
% theme falls to 1 the mirror rises to '2. A pedal holds I, V, I under
% the pair.

axis 5

Var2 ::= {Theme}^

assert {Ant}^ == 5 _2 2 _2 3 _2 5 _2 4 _2 2 _2 3 _4

Var2
{Theme, Var2, .1 _16 .5 _8 .1 _8}

% Variation III: the DOUBLE. One rule at two speeds: the theme twice
% at tempo against itself augmented an octave down, so the slow voice
% spends a whole statement on each half. The two attack together in
% octaves at the head of each half, and the slow tonic is still sounding
% under the fast one's close. The ground turns twice to cover them.

Var3 ::= {Theme Theme, {Theme} _2@-12}

assert {Ant} _2 == 5 _4 '1 _4 7 _4 5 _4 6 _4 '1 _4 7 _8

Var3
{Var3, Ground*2}

% Variation IV: the MINORE. Nothing is retyped. Degrees are positions
% in whatever key is in force, so one line re-reads the theme, the
% sequence and the ground in the parallel minor: 3, 6 and 7 all drop a
% semitone, the chord on 3 turns major, and the cadence walks v to i.

key g min

{Theme, Ground}
{Var1, Ground}

% The set entire: theme, the four machines in order, the minore, and
% the theme once more in the major to close. This block writes no new
% material, only the order.

key g maj

{Theme, Ground}
{Var1, Ground}
{Theme, Var2, .1 _16 .5 _8 .1 _8}
{Var3, Ground*2}

key g min
{Theme, Ground}

key g maj
{Theme, Ground}

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

A variation set · Advanced