Lessons · Advanced

Bent restatements

The tonal answer, the sliding pedal: one figure, a slot, a selector

% A fugue's ANSWER restates the subject a fifth away — and, at the
% head, BENT. The Little Fugue's subject leaps from the tonic up to the
% dominant; its answer, a fifth below, leaps from the dominant up to the
% tonic — a fourth, so the music stays home. Every other note is the
% subject moved by '@~-4' — the raised seventh included, which the
% accidental carries: '.7#' walks down to '.3#', the leading tone of the
% answer's key. One note differs, and a timed optional carries both
% readings: 'x? y' derives the slot's own note or the substitute at the
% slot's exact length — the substitute FIRST, so the bare name is the
% subject and '#2' is the bent one:
 
bpm 100
meter 4
unit 1/4
key g4 min
 
Head ::= 2 _4? 1 5 _4 3 _3 2 1 _2 3 _2 2 _2 1 _2 .7# _2 2 _2 .5 _4
 
assert Head == 1 _4 5 _4 3 _3 2 1 _2 3 _2 2 _2 1 _2 .7# _2 2 _2 .5 _4
assert Head#2@~-4 == .5 _4 1 _4 .6 _3 .5 .4 _2 .6 _2 .5 _2 .4 _2 .3# _2 .5 _2 .1 _4
 
Head
Head#2@~-4
 
 
% The exposition places the answer under the subject's continuation.
% Selector and mark ride together: '#2' picks the bent reading, '@~-4'
% moves it, and the two say in four characters what the answer is —
% the subject, one note bent, a fifth below:
 
{Head 5 _2 3 _2 5 _2 .7 _2 1 _2 3 _2 2 _2 1 _2 - _12, - _28 Head#2@~-4}
 
 
% A SEQUENCE bends the same way. In the Prelude in C the middle voice
% slides down by semitones (mm.11-15): a note held through the half
% bar, then the same note a half step lower — one figure with the bend
% inside it, restated a semitone lower each bar. Where the voice holds
% its note unbent, '#2' says so, and the mark after the selector still
% covers that statement:
 
bpm 66
key c4 maj
 
Ped ::= - .7 _7 - .7 _7? .7b
 
assert Ped == - .7 _7 - .7b _7
assert Ped#2@-2 == - .6 _7 - .6 _7
 
- .7 _7 Ped Ped@-1 Ped@-2 Ped@-3 - .5 _7
 
 
% Under it the bass strikes each half bar and steps down by whole ones;
% over it the broken chords roll — the texture of the whole Prelude,
% and these five bars of it note for note. The bent figure is the line
% you hear moving:
 
Bass ::= .5 _8*4 .4 _8*4 .3 _8*2
Mid  ::= - .7 _7 Ped Ped@-1 Ped@-2 Ped@-3 - .5 _7
Top  ::= {- _2 2 5 7 2 5 7}*2 {- _2 3 5 '1# 3 5 '1#}*2 {- _2 2 6 '2 2 6 '2}*2
         {- _2 2 4 7 2 4 7}*2 {- _2 1 5 '1 1 5 '1}*2
 
{Bass, Mid, Top}
 
 
% What the two have in common is the whole idea: a figure is named
% ONCE, its bend lives inside it as a slot, and each statement chooses
% with a selector — which is exactly how the importer writes a fugue's
% answers and a prelude's pedals. Both, as the pieces have them:
 
key g4 min
{Head 5 _2 3 _2 5 _2 .7 _2 1 _2 3 _2 2 _2 1 _2 - _12, - _28 Head#2@~-4}
key c4 maj
{Bass, Mid, Top}

% A fugue's ANSWER restates the subject a fifth away — and, at the
% head, BENT. The Little Fugue's subject leaps from the tonic up to the
% dominant; its answer, a fifth below, leaps from the dominant up to the
% tonic — a fourth, so the music stays home. Every other note is the
% subject moved by '@~-4' — the raised seventh included, which the
% accidental carries: '.7#' walks down to '.3#', the leading tone of the
% answer's key. One note differs, and a timed optional carries both
% readings: 'x? y' derives the slot's own note or the substitute at the
% slot's exact length — the substitute FIRST, so the bare name is the
% subject and '#2' is the bent one:

bpm 100
meter 4
unit 1/4
key g4 min

Head ::= 2 _4? 1 5 _4 3 _3 2 1 _2 3 _2 2 _2 1 _2 .7# _2 2 _2 .5 _4

assert Head == 1 _4 5 _4 3 _3 2 1 _2 3 _2 2 _2 1 _2 .7# _2 2 _2 .5 _4
assert Head#2@~-4 == .5 _4 1 _4 .6 _3 .5 .4 _2 .6 _2 .5 _2 .4 _2 .3# _2 .5 _2 .1 _4

Head
Head#2@~-4

% The exposition places the answer under the subject's continuation.
% Selector and mark ride together: '#2' picks the bent reading, '@~-4'
% moves it, and the two say in four characters what the answer is —
% the subject, one note bent, a fifth below:

{Head 5 _2 3 _2 5 _2 .7 _2 1 _2 3 _2 2 _2 1 _2 - _12, - _28 Head#2@~-4}

% A SEQUENCE bends the same way. In the Prelude in C the middle voice
% slides down by semitones (mm.11-15): a note held through the half
% bar, then the same note a half step lower — one figure with the bend
% inside it, restated a semitone lower each bar. Where the voice holds
% its note unbent, '#2' says so, and the mark after the selector still
% covers that statement:

bpm 66
key c4 maj

Ped ::= - .7 _7 - .7 _7? .7b

assert Ped == - .7 _7 - .7b _7
assert Ped#2@-2 == - .6 _7 - .6 _7

- .7 _7 Ped Ped@-1 Ped@-2 Ped@-3 - .5 _7

% Under it the bass strikes each half bar and steps down by whole ones;
% over it the broken chords roll — the texture of the whole Prelude,
% and these five bars of it note for note. The bent figure is the line
% you hear moving:

Bass ::= .5 _8*4 .4 _8*4 .3 _8*2
Mid  ::= - .7 _7 Ped Ped@-1 Ped@-2 Ped@-3 - .5 _7
Top  ::= {- _2 2 5 7 2 5 7}*2 {- _2 3 5 '1# 3 5 '1#}*2 {- _2 2 6 '2 2 6 '2}*2
         {- _2 2 4 7 2 4 7}*2 {- _2 1 5 '1 1 5 '1}*2

{Bass, Mid, Top}

% What the two have in common is the whole idea: a figure is named
% ONCE, its bend lives inside it as a slot, and each statement chooses
% with a selector — which is exactly how the importer writes a fugue's
% answers and a prelude's pedals. Both, as the pieces have them:

key g4 min
{Head 5 _2 3 _2 5 _2 .7 _2 1 _2 3 _2 2 _2 1 _2 - _12, - _28 Head#2@~-4}
key c4 maj
{Bass, Mid, Top}

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Bent restatements · Pattern Engine