Lessons · Musicianship

The shape of a line

One climax, leaps that recover, arcs that breathe

% A melody is a SHAPE before it is a set of notes, and the commonest
% shape is the ARCH: climb, one high point, fall. Rise reaches the
% fifth twice; Arch carries it up to '1, which sounds once and is
% never risen to again. No interval in the line is wider than a
% fourth, and that one fourth, 2 up to 5, is answered by a step down.
 
bpm 60
key a min
 
Rise ::= 1 _2 2 _2 3 _2 2 _2 5 _2 4 _2 3 _2 5 _2
Arch ::= Rise 6 _2 '1 _4 7 _2 6 _2 5 _2 3 _2 2 _2 1 _6
Bed  ::= {.1, .5} _10 {.4, .1} _8 {.6, .3} _8 {.5, .2} _6 {.1, .5} _6
 
Arch
{Arch, Bed}
 
 
% A DESCENT gives its shape away in the first two notes and spends the
% phrase making good on it. Sigh is a note, its lower neighbour, and
% back; Fall states it three times, each a scale step lower than the
% last, then walks the rest of the octave down to the tonic. Ground is
% the lament bass under it. Second time, the tune doubles an octave up.
 
Sigh   ::= '1 _4 7 _2 '1 _2
Fall   ::= Sigh Sigh@~-1 Sigh@~-2 5 _4 4 _2 3 _2 2 _4 1 _4
Ground ::= .1 _10 ..7 _10 ..6 _10 ..5 _6 .1 _4
 
assert Sigh@~-1 == 7 _4 6 _2 7 _2
 
{Fall, Ground}
{Fall, {Fall}@12, Ground}
 
 
% A WAVE has no climax: one rise-and-fall repeated, so the ear never
% gets a single highest point to hang on. Curl is that one wave, and an
% arch in miniature — shape is a matter of scale. Wave alternates Curl
% with the same curl two scale steps up, so the top note arrives twice
% and arrives the same way both times, over a bass rocking i to III.
 
Curl ::= 1 _2 3 _2 5 _2 6 _2 5 _2 3 _2 2 _2 1 _2
Wave ::= Curl Curl@~2 Curl Curl@~2
Rock ::= {.1, .5} _16 {.3, .7} _16
 
assert Curl@~2 == 3 _2 5 _2 7 _2 '1 _2 7 _2 5 _2 4 _2 3 _2
 
{Wave, Rock*2}
 
 
% Contour is a CHOICE, not a consequence of the notes. Six is one set
% of six degrees, and each tune below sounds all six of them twice, to
% the same length, over the same pedal: Arc goes out and back, Vale
% down and back, Ripple threads every other degree against the three
% it skipped. The slice marks say exactly that — three tunes, one bag
% of notes.
 
Six    ::= 1 _2 2 _2 3 _2 5 _2 6 _2 '1 _2
Arc    ::= Six Six[::-1]
Vale   ::= Six[::-1] Six
Ripple ::= Six[1::2] Six[::2]~ Six[1::2] Six[::2]~
Pedal  ::= .1 _4 .5 _4
 
{Arc, Pedal*3}
{Vale, Pedal*3}
{Ripple, Pedal*3}
 
 
% The three shapes as one piece, and not a rule in it is new: the arch
% states the tune, the lament answers with its octave descent, the wave
% turns underneath with no peak of its own, and the arch returns
% doubled at the octave to take the piece's one climax.
 
{Arch, Bed}
{Fall, Ground}
{Wave, Rock*2}
{Fall, {Fall}@12, Ground}
{Arch, {Arch}@12, Bed}

% A melody is a SHAPE before it is a set of notes, and the commonest
% shape is the ARCH: climb, one high point, fall. Rise reaches the
% fifth twice; Arch carries it up to '1, which sounds once and is
% never risen to again. No interval in the line is wider than a
% fourth, and that one fourth, 2 up to 5, is answered by a step down.

bpm 60
key a min

Rise ::= 1 _2 2 _2 3 _2 2 _2 5 _2 4 _2 3 _2 5 _2
Arch ::= Rise 6 _2 '1 _4 7 _2 6 _2 5 _2 3 _2 2 _2 1 _6
Bed  ::= {.1, .5} _10 {.4, .1} _8 {.6, .3} _8 {.5, .2} _6 {.1, .5} _6

Arch
{Arch, Bed}

% A DESCENT gives its shape away in the first two notes and spends the
% phrase making good on it. Sigh is a note, its lower neighbour, and
% back; Fall states it three times, each a scale step lower than the
% last, then walks the rest of the octave down to the tonic. Ground is
% the lament bass under it. Second time, the tune doubles an octave up.

Sigh   ::= '1 _4 7 _2 '1 _2
Fall   ::= Sigh Sigh@~-1 Sigh@~-2 5 _4 4 _2 3 _2 2 _4 1 _4
Ground ::= .1 _10 ..7 _10 ..6 _10 ..5 _6 .1 _4

assert Sigh@~-1 == 7 _4 6 _2 7 _2

{Fall, Ground}
{Fall, {Fall}@12, Ground}

% A WAVE has no climax: one rise-and-fall repeated, so the ear never
% gets a single highest point to hang on. Curl is that one wave, and an
% arch in miniature — shape is a matter of scale. Wave alternates Curl
% with the same curl two scale steps up, so the top note arrives twice
% and arrives the same way both times, over a bass rocking i to III.

Curl ::= 1 _2 3 _2 5 _2 6 _2 5 _2 3 _2 2 _2 1 _2
Wave ::= Curl Curl@~2 Curl Curl@~2
Rock ::= {.1, .5} _16 {.3, .7} _16

assert Curl@~2 == 3 _2 5 _2 7 _2 '1 _2 7 _2 5 _2 4 _2 3 _2

{Wave, Rock*2}

% Contour is a CHOICE, not a consequence of the notes. Six is one set
% of six degrees, and each tune below sounds all six of them twice, to
% the same length, over the same pedal: Arc goes out and back, Vale
% down and back, Ripple threads every other degree against the three
% it skipped. The slice marks say exactly that — three tunes, one bag
% of notes.

Six    ::= 1 _2 2 _2 3 _2 5 _2 6 _2 '1 _2
Arc    ::= Six Six[::-1]
Vale   ::= Six[::-1] Six
Ripple ::= Six[1::2] Six[::2]~ Six[1::2] Six[::2]~
Pedal  ::= .1 _4 .5 _4

{Arc, Pedal*3}
{Vale, Pedal*3}
{Ripple, Pedal*3}

% The three shapes as one piece, and not a rule in it is new: the arch
% states the tune, the lament answers with its octave descent, the wave
% turns underneath with no peak of its own, and the arch returns
% doubled at the octave to take the piece's one climax.

{Arch, Bed}
{Fall, Ground}
{Wave, Rock*2}
{Fall, {Fall}@12, Ground}
{Arch, {Arch}@12, Bed}

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

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The shape of a line · Pattern Engine