The melodic minor

A scale that changes with direction

% MELODIC minor is one key with two ladders, one for going up and one
% for coming down: under 'key e4 mel' the sixth and seventh degrees
% RISE on the way up and FALL on the way back. '>' picks the ascending
% form and '<' the descending: zero-duration toggles, threaded left to
% right, doing nothing outside a 'mel' key. One body covers both, since
% 'Ladder~' is the same eight rungs backwards.
 
bpm 42
instrument plain
meter 4
unit 1/4
key e4 mel
 
Ladder ::= 1 2 3 4 5 6 7 '1
 
> Ladder _2
< Ladder~ _2
> Ladder < Ladder~
 
 
% The tune from 'Melodies' comes back, not one character changed. It
% was written in degrees, so it travels. That lesson left it in E minor,
% where the Tag loses its leading tone: '.7' is a d, a whole step under
% home. Ascending is the default form, so '<' is what asks for plain
% natural minor, and '>' is what hands the leading tone back.
 
Theme  ::= 5 _2 5 6 5 4 3 _2 2 _2 1 _2 2 _4
Bridge ::= '1 _2 7 _2 6 _2 5 _2 6 5 4 3 2 _2 -*2
Tag    ::= 3 _2 2 _2 .7 _2 1 _4
 
assert < .7 == d4
assert > .7 == d#4
 
< Theme Bridge Tag
< Theme Bridge > Tag
 
 
% The Bridge falls from the octave. Turn it around ('Bridge~' reverses
% it, durations and all) and the same line climbs to it, which is where
% the ascending form belongs: 6 and 7 come back a semitone higher, so
% the last three notes are c# d# e and they pull into the octave the way
% the Tag pulls into 1. Each form is the other with its top two degrees
% bent by a semitone, and the engine will say so:
 
assert > 6 == < 6#
assert > 7 == < 7#
 
> Bridge~
> Bridge~ < Bridge > Tag
 
 
% The same phrase on the wrong ladder. Climbing on the descending form,
% the top of the line is a whole step from home and the arrival goes
% slack; falling on the ascending form, the raised 6 and 7 keep pointing
% back up against the motion. Both ladders are real scales (the
% descending form is plain natural minor) but neither one turns where
% this tune turns.
 
< Bridge~ > Bridge
> Bridge~ < Bridge
 
 
% A '{}' field inherits the direction in force where it starts and keeps
% its own changes to itself: a mark outside the brace governs the whole
% texture, a mark inside governs one voice. The bass here is the ladder
% an octave down. First both voices climb on the one form, in octaves;
% then they part company (the tune up the ascending form, the bass down
% the descending one, c# and d# over c and d) and the tritone they make
% three notes from the end opens outward to a sixth and then the octave.
 
> {Bridge~, Ladder@-12}
{> Bridge~, < Ladder~@-12}
 
 
% The forms reach the chords. 'Dia' stacks a triad out of the scale, so
% a degree changes QUALITY with the direction: climbing, 4 and 5 are
% major (5 because it holds the leading tone) and 6 is diminished;
% falling, 4 and 5 are minor and 6 is the major chord natural minor
% owns. Close puts those chords under the Tag, so the one mark that
% bends the tune's d bends the dominant's with it.
 
Close ::= .1Dia _2 ..5Dia _4 .1Dia _4
 
assert > 4Dia == aMaj
assert > 5Dia == bMaj
assert > 6Dia == 'c#Dim
assert < 4Dia == aMin
assert < 5Dia == bMin
assert < 6Dia == 'cMaj
 
> {Tag, Close}
< {Tag, Close}
 
 
% The song entire, A A B A and the Tag, and not a note of it is new. The
% tune sings alone; the bass enters only where the line changes ladders,
% in contrary motion, walking down while the Bridge climbs and back up
% while it falls; the chords come in only to close. Four phrases, and
% every turn in them is one character.
 
< Theme Theme
{> Bridge~, < Ladder~@-12} {< Bridge, > Ladder@-12}
< Theme
> {Tag, Close}

% MELODIC minor is one key with two ladders, one for going up and one
% for coming down: under 'key e4 mel' the sixth and seventh degrees
% RISE on the way up and FALL on the way back. '>' picks the ascending
% form and '<' the descending: zero-duration toggles, threaded left to
% right, doing nothing outside a 'mel' key. One body covers both, since
% 'Ladder~' is the same eight rungs backwards.

bpm 42
instrument plain
meter 4
unit 1/4
key e4 mel

Ladder ::= 1 2 3 4 5 6 7 '1

> Ladder _2
< Ladder~ _2
> Ladder < Ladder~

% The tune from 'Melodies' comes back, not one character changed. It
% was written in degrees, so it travels. That lesson left it in E minor,
% where the Tag loses its leading tone: '.7' is a d, a whole step under
% home. Ascending is the default form, so '<' is what asks for plain
% natural minor, and '>' is what hands the leading tone back.

Theme  ::= 5 _2 5 6 5 4 3 _2 2 _2 1 _2 2 _4
Bridge ::= '1 _2 7 _2 6 _2 5 _2 6 5 4 3 2 _2 -*2
Tag    ::= 3 _2 2 _2 .7 _2 1 _4

assert < .7 == d4
assert > .7 == d#4

< Theme Bridge Tag
< Theme Bridge > Tag

% The Bridge falls from the octave. Turn it around ('Bridge~' reverses
% it, durations and all) and the same line climbs to it, which is where
% the ascending form belongs: 6 and 7 come back a semitone higher, so
% the last three notes are c# d# e and they pull into the octave the way
% the Tag pulls into 1. Each form is the other with its top two degrees
% bent by a semitone, and the engine will say so:

assert > 6 == < 6#
assert > 7 == < 7#

> Bridge~
> Bridge~ < Bridge > Tag

% The same phrase on the wrong ladder. Climbing on the descending form,
% the top of the line is a whole step from home and the arrival goes
% slack; falling on the ascending form, the raised 6 and 7 keep pointing
% back up against the motion. Both ladders are real scales (the
% descending form is plain natural minor) but neither one turns where
% this tune turns.

< Bridge~ > Bridge
> Bridge~ < Bridge

% A '{}' field inherits the direction in force where it starts and keeps
% its own changes to itself: a mark outside the brace governs the whole
% texture, a mark inside governs one voice. The bass here is the ladder
% an octave down. First both voices climb on the one form, in octaves;
% then they part company (the tune up the ascending form, the bass down
% the descending one, c# and d# over c and d) and the tritone they make
% three notes from the end opens outward to a sixth and then the octave.

> {Bridge~, Ladder@-12}
{> Bridge~, < Ladder~@-12}

% The forms reach the chords. 'Dia' stacks a triad out of the scale, so
% a degree changes QUALITY with the direction: climbing, 4 and 5 are
% major (5 because it holds the leading tone) and 6 is diminished;
% falling, 4 and 5 are minor and 6 is the major chord natural minor
% owns. Close puts those chords under the Tag, so the one mark that
% bends the tune's d bends the dominant's with it.

Close ::= .1Dia _2 ..5Dia _4 .1Dia _4

assert > 4Dia == aMaj
assert > 5Dia == bMaj
assert > 6Dia == 'c#Dim
assert < 4Dia == aMin
assert < 5Dia == bMin
assert < 6Dia == 'cMaj

> {Tag, Close}
< {Tag, Close}

% The song entire, A A B A and the Tag, and not a note of it is new. The
% tune sings alone; the bass enters only where the line changes ladders,
% in contrary motion, walking down while the Bridge climbs and back up
% while it falls; the chords come in only to close. Four phrases, and
% every turn in them is one character.

< Theme Theme
{> Bridge~, < Ladder~@-12} {< Bridge, > Ladder@-12}
< Theme
> {Tag, Close}

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The melodic minor · Melody