Scales & keys

Whole and half steps, degrees, minor

% Every pitch below is a NUMBER: a degree, the position of a rung on a
% ladder, and 'key' decides which notes those rungs land on. The tune is
% a period: Climb rises to the octave, Turn circles it, Fall walks back
% down. The Call hangs on 2; the Answer takes the Turn one rung higher
% and comes home to 1.
 
bpm 108
instrument plain
meter 4
key c maj
 
Climb  ::= > 5 _6 6 _2 7 _4 '1 _4
Turn   ::= 7 _6 '1 _2 '2 _4 '1 _4
Fall   ::= < 7 _4 6 _4 5 _2 4 _2 3 _2 2 _2
 
Call   ::= Climb Turn Fall 1 _2 2 _2 3 _4 2 _8
Answer ::= Climb Turn@~1 Fall 1 _2 2 _2 > .7 _4 1 _8
Theme  ::= Call Answer
 
% '>' and '<' are direction marks. Three of the four ladders in this
% lesson have one form and ignore them; the fourth has two, and there
% they are the whole of it. Here they change nothing:
 
assert Climb == 5 _6 6 _2 7 _4 '1 _4
 
Theme
 
 
% The rungs are unevenly spaced: a major ladder keeps seven of the
% twelve semitones, with half steps at 3-4 and at 7-'1, which is why
% Climb's last two steps are a tone and then a semitone. The bass is
% degrees as well, so Bass says I V I V, then I vi I-IV V-I without
% naming one chord anywhere.
 
% Ton: the tonic as an Alberti bass, root fifth third fifth; the other
% three are those same four rungs stood elsewhere on the ladder
Ton  ::= .1 _2 .5 _2 .3 _2 .5 _2
Dom  ::= Ton@~-3
Six  ::= Ton@~-2
Sub  ::= Ton@~-4
 
Bass<bass> ::= Ton*2 Dom*2 Ton*2 Dom*2 Ton*2 Six*2 Ton Sub Dom Ton
 
assert 1 2 3 4 5 6 7 '1 == c4 d4 e4 f4 g4 a4 b4 c5
assert Dom == ..5 _2 .2 _2 ..7 _2 .2 _2
 
{Theme, Bass}
 
% Move the key and the whole ladder moves with it. The Call goes up a
% minor third, the Answer comes home; not one character of the tune or
% of the bass is rewritten, and neither of them knows it happened.
 
key eb maj
assert 1 2 3 4 5 6 7 '1 == eb4 f4 g4 ab4 bb4 c5 d5 eb5
 
{Call, Bass[:4]}
key c maj
{Answer, Bass[4:]}
 
 
% MINOR lowers 3, 6 and 7: the same seven rungs, three of them a
% semitone darker. 'key c min' keeps the tonic and swaps the ladder
% underneath it, so this is the parallel minor of what just played:
% the tune not touched, the bass not touched, and Dom arriving as a
% G MINOR because the ladder no longer owns a B.
 
key c min
assert 1 2 3 4 5 6 7 '1 == c4 d4 eb4 f4 g4 ab4 bb4 c5
assert Dom == g2 _2 d3 _2 bb2 _2 d3 _2
 
{Theme, Bass}
 
 
% A suffix accidental bends ONE rung and leaves the other six standing,
% and HARMONIC minor is that bend kept: 7 raised, 3 and 6 left low. The
% cadence gets its leading tone back and Dom hardens into a major V,
% but 6 to 7 is now a tone and a HALF, a step no other ladder here will
% take, and Climb walks up it while Fall walks down it.
 
key c harm
assert 1 2 3 4 5 6 7 '1 == c4 d4 eb4 f4 g4 ab4 b4 c5
assert 6 7 7b == ab4 b4 bb4
assert Dom == g2 _2 d3 _2 b2 _2 d3 _2
 
{Theme, Bass}
 
 
% MELODIC minor is two ladders in one: 6 and 7 rise a semitone on the
% way UP and stay low on the way DOWN. That is the shape of this tune,
% and it is what '>' and '<' have been marking since the first cell:
% Climb climbs through a4 and b4, Fall comes back through bb4 and ab4,
% and the Answer flips '>' on once more for its leading tone, because a
% cadence rises to the tonic however the line reached it.
 
key c mel
assert Climb == g4 _6 a4 _2 b4 _4 c5 _4
assert Fall == bb4 _4 ab4 _4 g4 _2 f4 _2 eb4 _2 d4 _2
 
{Theme, Bass}
 
 
% Four ladders, five forms of them (melodic minor counts twice) and
% one melody, not a character of it rewritten between them. Major; the
% parallel minor; then the period splits at its own seam, the Call in
% harmonic minor stepping over the tone and a half, the Answer in
% melodic minor rising raised and falling low into its leading tone;
% then home.
 
key c maj
{Theme, Bass}
key c min
{Theme, Bass}
key c harm
{Call, Bass[:4]}
key c mel
{Answer, Bass[4:]}
key c maj
{Theme, Bass}

% Every pitch below is a NUMBER: a degree, the position of a rung on a
% ladder, and 'key' decides which notes those rungs land on. The tune is
% a period: Climb rises to the octave, Turn circles it, Fall walks back
% down. The Call hangs on 2; the Answer takes the Turn one rung higher
% and comes home to 1.

bpm 108
instrument plain
meter 4
key c maj

Climb  ::= > 5 _6 6 _2 7 _4 '1 _4
Turn   ::= 7 _6 '1 _2 '2 _4 '1 _4
Fall   ::= < 7 _4 6 _4 5 _2 4 _2 3 _2 2 _2

Call   ::= Climb Turn Fall 1 _2 2 _2 3 _4 2 _8
Answer ::= Climb Turn@~1 Fall 1 _2 2 _2 > .7 _4 1 _8
Theme  ::= Call Answer

% '>' and '<' are direction marks. Three of the four ladders in this
% lesson have one form and ignore them; the fourth has two, and there
% they are the whole of it. Here they change nothing:

assert Climb == 5 _6 6 _2 7 _4 '1 _4

Theme

% The rungs are unevenly spaced: a major ladder keeps seven of the
% twelve semitones, with half steps at 3-4 and at 7-'1, which is why
% Climb's last two steps are a tone and then a semitone. The bass is
% degrees as well, so Bass says I V I V, then I vi I-IV V-I without
% naming one chord anywhere.

% Ton: the tonic as an Alberti bass, root fifth third fifth; the other
% three are those same four rungs stood elsewhere on the ladder
Ton  ::= .1 _2 .5 _2 .3 _2 .5 _2
Dom  ::= Ton@~-3
Six  ::= Ton@~-2
Sub  ::= Ton@~-4

Bass<bass> ::= Ton*2 Dom*2 Ton*2 Dom*2 Ton*2 Six*2 Ton Sub Dom Ton

assert 1 2 3 4 5 6 7 '1 == c4 d4 e4 f4 g4 a4 b4 c5
assert Dom == ..5 _2 .2 _2 ..7 _2 .2 _2

{Theme, Bass}

% Move the key and the whole ladder moves with it. The Call goes up a
% minor third, the Answer comes home; not one character of the tune or
% of the bass is rewritten, and neither of them knows it happened.

key eb maj
assert 1 2 3 4 5 6 7 '1 == eb4 f4 g4 ab4 bb4 c5 d5 eb5

{Call, Bass[:4]}
key c maj
{Answer, Bass[4:]}

% MINOR lowers 3, 6 and 7: the same seven rungs, three of them a
% semitone darker. 'key c min' keeps the tonic and swaps the ladder
% underneath it, so this is the parallel minor of what just played:
% the tune not touched, the bass not touched, and Dom arriving as a
% G MINOR because the ladder no longer owns a B.

key c min
assert 1 2 3 4 5 6 7 '1 == c4 d4 eb4 f4 g4 ab4 bb4 c5
assert Dom == g2 _2 d3 _2 bb2 _2 d3 _2

{Theme, Bass}

% A suffix accidental bends ONE rung and leaves the other six standing,
% and HARMONIC minor is that bend kept: 7 raised, 3 and 6 left low. The
% cadence gets its leading tone back and Dom hardens into a major V,
% but 6 to 7 is now a tone and a HALF, a step no other ladder here will
% take, and Climb walks up it while Fall walks down it.

key c harm
assert 1 2 3 4 5 6 7 '1 == c4 d4 eb4 f4 g4 ab4 b4 c5
assert 6 7 7b == ab4 b4 bb4
assert Dom == g2 _2 d3 _2 b2 _2 d3 _2

{Theme, Bass}

% MELODIC minor is two ladders in one: 6 and 7 rise a semitone on the
% way UP and stay low on the way DOWN. That is the shape of this tune,
% and it is what '>' and '<' have been marking since the first cell:
% Climb climbs through a4 and b4, Fall comes back through bb4 and ab4,
% and the Answer flips '>' on once more for its leading tone, because a
% cadence rises to the tonic however the line reached it.

key c mel
assert Climb == g4 _6 a4 _2 b4 _4 c5 _4
assert Fall == bb4 _4 ab4 _4 g4 _2 f4 _2 eb4 _2 d4 _2

{Theme, Bass}

% Four ladders, five forms of them (melodic minor counts twice) and
% one melody, not a character of it rewritten between them. Major; the
% parallel minor; then the period splits at its own seam, the Call in
% harmonic minor stepping over the tone and a half, the Answer in
% melodic minor rising raised and falling low into its leading tone;
% then home.

key c maj
{Theme, Bass}
key c min
{Theme, Bass}
key c harm
{Call, Bass[:4]}
key c mel
{Answer, Bass[4:]}
key c maj
{Theme, Bass}

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

Scales & keys · Melody