Lessons · Advanced

Relative pitch machinery

Interval threading, anchors, chords, direction forms

% 'i<n>' counts SEMITONES from the LAST WRITTEN pitch, so 'i4 i3' is a
% major triad from wherever it starts and the anchor in front of it
% decides which one. Nothing after that first note names a pitch, which
% is why '@7' and '@5' carry the whole call to the dominant and the
% subdominant without a note being retyped:
 
bpm 75
instrument plain
key eb maj
 
assert 1 i4 i3 == 1 3 5
 
Fanfare ::= 1 _2 i4 i3 _2 i5 _4 i-5 _2 i-3 i-4 _4
 
Fanfare Fanfare@7 Fanfare@5 Fanfare
 
 
% The last written pitch carries ACROSS a reference, so a degree put in
% front of one is the pitch it counts from. 'Alberti' has no address of
% its own; the four degrees give it four, and one figure becomes a whole
% progression under the tune:
 
Alberti ::= i7 i-3 i3 i-7 i7 i-3 i3
Air     ::= 3 _4 5 _4 6 _4 8 _4 9 _4 7 _4 8 _8
 
1 Alberti 4 Alberti 5 Alberti 1 Alberti
{1 Alberti 4 Alberti 5 Alberti 1 Alberti, Air}
 
 
% 's<n>' counts SCALE STEPS instead, so the shape bends to fit the key.
% 'i7 i-3 i3' spells a MAJOR triad under every anchor (true on 1, 4 and
% 5, false on 2), where s takes whatever triad the key holds there, so
% the one figure climbs the whole scale and comes back down under the tune:
 
assert 2 s4 s-2 == 2 6 4
 
Walk<bass> ::= s4 s-2 s2 s-4 s4 s-2 s2
 
Walk(1 2 3 4 5 6 7 8)
{Walk(8 7 6 5 4 3 2 1), Air _2}
 
 
% A chord hands its FIRST field on, so after '{1, 3, 5}' the count runs
% from the root and not from the top note: seven semitones above it is
% degree 5. One falling figure drops out of every chord in the vamp:
 
assert {1, 3, 5} i7 == {1, 3, 5} 5
 
Fill ::= s4 s-1 s-1 s-1
 
{1, 3, 5} _4 Fill {6, 8, 10} _4 Fill
{4, 6, 8} _4 Fill {5, 7, 9} _4 Fill
 
 
% In MELODIC minor, the relative minor of the key so far, the sixth
% and seventh rise going up and fall coming down, and 's' steps obey the
% direction toggle in force. Seven tokens each way, two different sixths:
 
key c mel
 
Climb ::= > 1 s1 s1 s1 _2 s1 s1 s1 s1 _4
Fall  ::= < s-1 s-1 s-1 s-1 _2 s-1 s-1 s-1 _4
 
assert Climb == > 1 2 3 4 _2 5 6 7 8 _4
 
Climb Fall
{Climb Fall, .1 _12 .5 _11}
 
 
% Both counters in one phrase: 'Turn' is diatonic and re-anchors down
% the scale, then 'i1 i1' steps outside it and back, the raised fourth
% the key does not own, leaning onto the dominant:
 
key eb maj
 
Turn ::= s1 s-1 s-1 s1
 
Turn(8 7 6 5) 4 i1 i1 _2 {5, 7, 9} _4 {1, 3, 5, 8} _8

% 'i<n>' counts SEMITONES from the LAST WRITTEN pitch, so 'i4 i3' is a
% major triad from wherever it starts and the anchor in front of it
% decides which one. Nothing after that first note names a pitch, which
% is why '@7' and '@5' carry the whole call to the dominant and the
% subdominant without a note being retyped:

bpm 75
instrument plain
key eb maj

assert 1 i4 i3 == 1 3 5

Fanfare ::= 1 _2 i4 i3 _2 i5 _4 i-5 _2 i-3 i-4 _4

Fanfare Fanfare@7 Fanfare@5 Fanfare

% The last written pitch carries ACROSS a reference, so a degree put in
% front of one is the pitch it counts from. 'Alberti' has no address of
% its own; the four degrees give it four, and one figure becomes a whole
% progression under the tune:

Alberti ::= i7 i-3 i3 i-7 i7 i-3 i3
Air     ::= 3 _4 5 _4 6 _4 8 _4 9 _4 7 _4 8 _8

1 Alberti 4 Alberti 5 Alberti 1 Alberti
{1 Alberti 4 Alberti 5 Alberti 1 Alberti, Air}

% 's<n>' counts SCALE STEPS instead, so the shape bends to fit the key.
% 'i7 i-3 i3' spells a MAJOR triad under every anchor (true on 1, 4 and
% 5, false on 2), where s takes whatever triad the key holds there, so
% the one figure climbs the whole scale and comes back down under the tune:

assert 2 s4 s-2 == 2 6 4

Walk<bass> ::= s4 s-2 s2 s-4 s4 s-2 s2

Walk(1 2 3 4 5 6 7 8)
{Walk(8 7 6 5 4 3 2 1), Air _2}

% A chord hands its FIRST field on, so after '{1, 3, 5}' the count runs
% from the root and not from the top note: seven semitones above it is
% degree 5. One falling figure drops out of every chord in the vamp:

assert {1, 3, 5} i7 == {1, 3, 5} 5

Fill ::= s4 s-1 s-1 s-1

{1, 3, 5} _4 Fill {6, 8, 10} _4 Fill
{4, 6, 8} _4 Fill {5, 7, 9} _4 Fill

% In MELODIC minor, the relative minor of the key so far, the sixth
% and seventh rise going up and fall coming down, and 's' steps obey the
% direction toggle in force. Seven tokens each way, two different sixths:

key c mel

Climb ::= > 1 s1 s1 s1 _2 s1 s1 s1 s1 _4
Fall  ::= < s-1 s-1 s-1 s-1 _2 s-1 s-1 s-1 _4

assert Climb == > 1 2 3 4 _2 5 6 7 8 _4

Climb Fall
{Climb Fall, .1 _12 .5 _11}

% Both counters in one phrase: 'Turn' is diatonic and re-anchors down
% the scale, then 'i1 i1' steps outside it and back, the raised fourth
% the key does not own, leaning onto the dominant:

key eb maj

Turn ::= s1 s-1 s-1 s1

Turn(8 7 6 5) 4 i1 i1 _2 {5, 7, 9} _4 {1, 3, 5, 8} _8

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

Relative pitch machinery · Advanced