Steps, skips & leaps

Conjunct and disjunct motion, relative pitch

% A melody moves by STEP to the next rung of the key — CONJUNCT motion —
% or by SKIP to the rung past it, or by LEAP further still, both DISJUNCT.
% This piece takes two gaps and keeps taking them: 1 to 3 is a MINOR THIRD,
% three semitones; 1 to 6 a MINOR SIXTH, eight. Skip and Leap share a rhythm
% and a shape — up, hold, step back — so nothing but the gap differs, and in
% both the step back is a semitone. Arp moves in skips alone, and a drone on
% the tonic holds under both lines so each gap is heard from one note.
 
bpm 60
meter 4
unit 1/4
key c min
 
assert 1 3 == c4 eb4
assert 1 6 == c4 ab4
 
Arp  ::= 1 _4 3 _4 5 _4 3 _4
Skip ::= 1 _4 3 _8 2 _4
Leap ::= 1 _4 6 _8 5 _4
 
{Arp Skip, .1 _32}
{Arp Leap, .1 _32}
 
 
% Relative pitch writes the MOVES instead of the arrivals: 's<n>' goes n
% rungs from the note before it, 'i<n>' n semitones. Sixth is the leap with
% no pitch of its own — five rungs up, one back — and an anchor list is
% shorthand for stating it after each anchor in turn. Five rungs is a sixth
% wherever it starts and not always the same size: eight semitones from 1, 2
% and 5, nine from the other four. Every sixth this tune takes is one of
% those three, and the drone holds under all four so the widening is heard.
 
assert Leap == 1 _4 s5 _8 s-1 _4
assert 1 s5 == 1 i8
assert 3 s5 == 3 i9
 
Sixth ::= s5 s-1
 
assert Sixth(1 2 5) == 1 Sixth 2 Sixth 5 Sixth
 
{Sixth(1 2 5) _4, .1 _36}
{Sixth(3) _4, .1 _12}
 
 
% The call. Arp climbs the tonic triad and falls back; then the leap twice,
% a rung apart — c to a-flat and d to b-flat, eight semitones each, and 1
% and 2 are the only neighbouring rungs that both carry one. A third
% statement would widen to nine, so the line steps down to Open and stops on
% 2 instead. Bass is the whole song's bass, a note to the measure, moving in
% the same two gaps: up a minor sixth, a step, then down a minor third to
% the dominant; the call takes its first four.
 
Open ::= 5 _4 4 _4 2 _8
Call ::= Arp Leap Leap@~1 Open
Bass ::= .1 _16 .6 _16 .7 _16 .5 _16 .1 _16 .3 _16 .4 _16 .5 _8 .1 _8
 
assert Leap@~1 == 2 _4 7 _8 6 _4
 
Call
{Call, Bass[:4]}
 
 
% The answer leaps where the call climbed. 'Leap@~4' is the same figure
% four rungs up — 5 to '3, the last of the key's three minor sixths and the
% top of the piece — and 'Leap~' turns it over, so the sixth falls where it
% rose. Then the small gap answers the large one, 'Skip@~3' stating it from
% 4, and Close walks down in minor thirds, f to d to b, onto the leading
% tone and home. Under it the bass climbs a minor third instead, then steps
% to the dominant and home.
 
Close  ::= 4 _2 2 _2 .7# _4 1 _8
Answer ::= Leap@~4 Leap~@~4 Skip@~3 Close
 
assert Leap@~4 == 5 _4 '3 _8 '2 _4
assert 4 2 .7# == 4 i-3 i-3
 
Answer
{Answer, Bass[4:]}
 
 
% A leap opens a gap and a step-line can walk it: Fill climbs the same
% minor sixth a rung at a time and arrives where Leap arrives, on 5, in one
% measure either way — and every other note of it, held twice as long, is
% Arp's climb, the tonic triad inside the sixth. Then the song entire: two
% leaps and a half cadence, the third leap and its mirror, and the close.
 
Fill ::= 1 _2 2 _2 3 _2 4 _2 5 _2 6 _2
 
assert Fill[::2] _2 == Arp[:3]
 
Leap
Fill 5 _4
{Call Answer, Bass}

% A melody moves by STEP to the next rung of the key — CONJUNCT motion —
% or by SKIP to the rung past it, or by LEAP further still, both DISJUNCT.
% This piece takes two gaps and keeps taking them: 1 to 3 is a MINOR THIRD,
% three semitones; 1 to 6 a MINOR SIXTH, eight. Skip and Leap share a rhythm
% and a shape — up, hold, step back — so nothing but the gap differs, and in
% both the step back is a semitone. Arp moves in skips alone, and a drone on
% the tonic holds under both lines so each gap is heard from one note.

bpm 60
meter 4
unit 1/4
key c min

assert 1 3 == c4 eb4
assert 1 6 == c4 ab4

Arp  ::= 1 _4 3 _4 5 _4 3 _4
Skip ::= 1 _4 3 _8 2 _4
Leap ::= 1 _4 6 _8 5 _4

{Arp Skip, .1 _32}
{Arp Leap, .1 _32}

% Relative pitch writes the MOVES instead of the arrivals: 's<n>' goes n
% rungs from the note before it, 'i<n>' n semitones. Sixth is the leap with
% no pitch of its own — five rungs up, one back — and an anchor list is
% shorthand for stating it after each anchor in turn. Five rungs is a sixth
% wherever it starts and not always the same size: eight semitones from 1, 2
% and 5, nine from the other four. Every sixth this tune takes is one of
% those three, and the drone holds under all four so the widening is heard.

assert Leap == 1 _4 s5 _8 s-1 _4
assert 1 s5 == 1 i8
assert 3 s5 == 3 i9

Sixth ::= s5 s-1

assert Sixth(1 2 5) == 1 Sixth 2 Sixth 5 Sixth

{Sixth(1 2 5) _4, .1 _36}
{Sixth(3) _4, .1 _12}

% The call. Arp climbs the tonic triad and falls back; then the leap twice,
% a rung apart — c to a-flat and d to b-flat, eight semitones each, and 1
% and 2 are the only neighbouring rungs that both carry one. A third
% statement would widen to nine, so the line steps down to Open and stops on
% 2 instead. Bass is the whole song's bass, a note to the measure, moving in
% the same two gaps: up a minor sixth, a step, then down a minor third to
% the dominant; the call takes its first four.

Open ::= 5 _4 4 _4 2 _8
Call ::= Arp Leap Leap@~1 Open
Bass ::= .1 _16 .6 _16 .7 _16 .5 _16 .1 _16 .3 _16 .4 _16 .5 _8 .1 _8

assert Leap@~1 == 2 _4 7 _8 6 _4

Call
{Call, Bass[:4]}

% The answer leaps where the call climbed. 'Leap@~4' is the same figure
% four rungs up — 5 to '3, the last of the key's three minor sixths and the
% top of the piece — and 'Leap~' turns it over, so the sixth falls where it
% rose. Then the small gap answers the large one, 'Skip@~3' stating it from
% 4, and Close walks down in minor thirds, f to d to b, onto the leading
% tone and home. Under it the bass climbs a minor third instead, then steps
% to the dominant and home.

Close  ::= 4 _2 2 _2 .7# _4 1 _8
Answer ::= Leap@~4 Leap~@~4 Skip@~3 Close

assert Leap@~4 == 5 _4 '3 _8 '2 _4
assert 4 2 .7# == 4 i-3 i-3

Answer
{Answer, Bass[4:]}

% A leap opens a gap and a step-line can walk it: Fill climbs the same
% minor sixth a rung at a time and arrives where Leap arrives, on 5, in one
% measure either way — and every other note of it, held twice as long, is
% Arp's climb, the tonic triad inside the sixth. Then the song entire: two
% leaps and a half cadence, the third leap and its mirror, and the close.

Fill ::= 1 _2 2 _2 3 _2 4 _2 5 _2 6 _2

assert Fill[::2] _2 == Arp[:3]

Leap
Fill 5 _4
{Call Answer, Bass}

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Steps, skips & leaps · Pattern Engine