Lessons · Harmony

Progressions & cadences

Function, tension, coming home

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% Chords have jobs, and a key hands out only three. 1 6 3 are HOME: 6
% and 3 each share two of their three notes with 1, so either can stand
% in for it. 4 and 2 are the STEP AWAY. 5 and 7 are the DEMAND: both
% carry 7, the semitone under home, and neither will sit still. A
% PROGRESSION is that walk: home, away, demand, home. Take the first
% chord of each family and there is the sentence; take the second of
% each and it says the same thing, only the last chord staying put,
% because home is where a sentence has to end.
 
bpm 60
instrument swell
meter 4
key g maj
 
Tonic ::= .1Dia _4 .6Dia _4 .3Dia _4
Pre   ::= .4Dia _4 .2Dia _4
Dom   ::= .5Dia _4 .7Dia _4
 
Tonic Pre Dom Tonic[0]
 
Tonic[0] Pre[0] Dom[0] Tonic[0]
Tonic[1] Pre[1] Dom[1] Tonic[0]
 
 
% Put the roots underneath and it is audible WHY one chord follows
% another: the strongest step is a root FALLING A FIFTH. 5 to 1 is that
% fall, and so is 2 to 5, which is why 2 5 1 is the commonest sentence
% in the music. Chain the fall and it visits every chord the key owns
% and comes home: 1 4 7 3 6 2 5 1. One link is no fifth at all: 4 to 7
% is the tritone, the only one the key owns, and that is the link the
% ear hears turn.
 
assert ..1 == ..5@-7
assert ..7 == ..4@6
 
Out  ::= {..1, .1Dia} _16 {..4, .4Dia} _8 {..7, .7Dia} _8 {..3, .3Dia} _8
Back ::= {..6, .6Dia} _8 {..2, .2Dia} _8 {..5, .5Dia} _8 {..1, .1Dia} _16
 
Out Back
 
 
% The tune this lesson is about, and that walk underneath it. Arc holds
% the home family for two measures: 1, then 6, which shares g and b
% with it. Ask steps away to 4 and stops on 5: a HALF cadence, the
% comma of harmony, and nothing has finished. The tune holds '1 over
% the barline into that 5 chord, where it stands a fourth above the
% root, and falls to 7: a suspension, and a prepared one, because '1
% was a chord tone the measure before.
 
Arc ::= 1 _4 3 _4 5 _8 6 _4 5 _4 3 _8
Ask ::= 4 _4 6 _4 '1 _8 '1 _4 7 _4 5 _8
 
Open ::= {..1, .1Dia} _16 {..6, .6Dia} _16
Away ::= {..4, .4Dia} _16 {..5, .5Dia} _16
 
{Arc Ask, Open Away}
 
 
% A cadence is the last two chords. The half cadence above stopped
% without arriving; here are two that shut the phrase and one that only
% pretends to. AUTHENTIC is 5 to 1: 7 lifts the semitone into '1 and
% the door shuts. PLAGAL comes from 4 (the amen) and neither chord
% holds 7, so nothing pulls: it settles rather than arrives, and one
% note can stand still through both. DECEPTIVE keeps the demand and
% answers it with 6, home's own family: the tune lifts exactly as it
% did and tells you nothing, the bass tells you. Each shares half its
% ground with Auth (Plag lands where Auth lands, Fool sets out where
% Auth sets out) and the asserts say so. A deception finishes nothing,
% so the phrase runs on and shuts for real.
 
Lift ::= 7 _8 '1 _8
 
Auth ::= {..5, .5Dia} _8 {..1, .1Dia} _8
Plag ::= {..4, .4Dia} _8 {..1, .1Dia} _8
Fool ::= {..5, .5Dia} _8 {..6, .6Dia} _8
 
assert Plag[1] == Auth[1]
assert Fool[0] == Auth[0]
 
{Arc Lift, Open Auth}
{Arc '1 _16, Open Plag}
{Arc Lift Lift, Open Fool Auth}
 
 
% The other half of the sentence. Arc comes round exactly as it was
% (that return is what makes these eight measures a PERIOD) and Answer
% walks 4 2 .7 1 down into home while the chords go 2 5 1, which is the
% tail of the circle: Shut is the last three chords of Back. A comma at
% the fourth measure, a full stop at the eighth, and not a letter name
% anywhere: every chord in the verse is a degree.
 
Answer ::= 4 _4 2 _4 .7 _8 1 _16
Shut   ::= Back[1:]
 
Verse ::= Arc Ask Arc Answer
Under ::= Open Away Open Shut
 
{Verse, Under}
 
 
% Every major key has a RELATIVE MINOR: the same seven notes with a
% different note for home. G major's 6 is E, and E minor spells e f# g
% a b c d: nothing added, nothing taken away, so the chord on 6 there
% and the chord on 1 here are one chord under two numbers. What the new
% home cannot do yet is CADENCE. Natural minor's 7 is d, a WHOLE step
% under home, so the chord on 5 comes out minor and Lift is no lift.
% Not one of these four rules is rewritten, and the door will not shut:
 
key e min
 
assert .5Dia == .5Min
 
{Arc Lift, Open Auth}
 
% 'harm' raises that 7 to d#. The chord on 5 is major again and Lift is
% a semitone again: one accidental, and it is the whole difference
% between a minor key that wanders and a minor key that closes:
 
key e harm
 
assert .5Dia == .5Maj
 
{Arc Lift, Open Auth}
 
 
% The door out of G. Raise the third of the chord on 3 and it is B
% major, and that d# is a note G major has not got: B major is the
% demand of E minor, not of G. Sound it after home and 6 stops being a
% chord in this key and becomes the next key's home: the tune sings
% the e that is about to be home, leans down through d#, and the verse
% answers with it. Then the same two rules say the whole verse again,
% dark: i VI iv V, i VI ii V i, with the step-away chord on 2
% diminished now and leaning harder. The one thing written at the use
% site is the last chord: Under without it, and a major third on the
% tonic in its place, the PICARDY, which no minor scale owns.
 
key g maj
 
assert .3Maj == {b3, d#4, f#4}
 
Turn ::= {.6 _8 .5# _8, {..3, .3Maj} _16}
 
Turn
 
key e harm
 
assert .5Dia == {b3, d#4, f#4}
 
{Verse, Under[:-1] {..1, .1Maj} _16}
 
 
% The song end to end: eight measures in G, the turn, eight in E minor,
% and home by the trick that took us out: raise a third and a home
% chord becomes somebody's demand. That Picardy, reread in G, is the
% chord on 6 with a raised third, which is the demand of 2, so the last
% measures fall by fifths the whole way, e a d g: the tail of the
% circle, entered where the minor left off. Both keys cadence for
% themselves: a comma at the fourth measure, a full stop at the eighth.
% And one amen sounds after the door is already shut.
 
key g maj
 
{Verse, Under}
Turn
 
key e harm
 
{Verse, Under[:-1] {..1, .1Maj} _16}
 
key g maj
 
{Answer 1 _16, Shut Plag}

% Chords have jobs, and a key hands out only three. 1 6 3 are HOME: 6
% and 3 each share two of their three notes with 1, so either can stand
% in for it. 4 and 2 are the STEP AWAY. 5 and 7 are the DEMAND: both
% carry 7, the semitone under home, and neither will sit still. A
% PROGRESSION is that walk: home, away, demand, home. Take the first
% chord of each family and there is the sentence; take the second of
% each and it says the same thing, only the last chord staying put,
% because home is where a sentence has to end.

bpm 60
instrument swell
meter 4
key g maj

Tonic ::= .1Dia _4 .6Dia _4 .3Dia _4
Pre   ::= .4Dia _4 .2Dia _4
Dom   ::= .5Dia _4 .7Dia _4

Tonic Pre Dom Tonic[0]

Tonic[0] Pre[0] Dom[0] Tonic[0]
Tonic[1] Pre[1] Dom[1] Tonic[0]

% Put the roots underneath and it is audible WHY one chord follows
% another: the strongest step is a root FALLING A FIFTH. 5 to 1 is that
% fall, and so is 2 to 5, which is why 2 5 1 is the commonest sentence
% in the music. Chain the fall and it visits every chord the key owns
% and comes home: 1 4 7 3 6 2 5 1. One link is no fifth at all: 4 to 7
% is the tritone, the only one the key owns, and that is the link the
% ear hears turn.

assert ..1 == ..5@-7
assert ..7 == ..4@6

Out  ::= {..1, .1Dia} _16 {..4, .4Dia} _8 {..7, .7Dia} _8 {..3, .3Dia} _8
Back ::= {..6, .6Dia} _8 {..2, .2Dia} _8 {..5, .5Dia} _8 {..1, .1Dia} _16

Out Back

% The tune this lesson is about, and that walk underneath it. Arc holds
% the home family for two measures: 1, then 6, which shares g and b
% with it. Ask steps away to 4 and stops on 5: a HALF cadence, the
% comma of harmony, and nothing has finished. The tune holds '1 over
% the barline into that 5 chord, where it stands a fourth above the
% root, and falls to 7: a suspension, and a prepared one, because '1
% was a chord tone the measure before.

Arc ::= 1 _4 3 _4 5 _8 6 _4 5 _4 3 _8
Ask ::= 4 _4 6 _4 '1 _8 '1 _4 7 _4 5 _8

Open ::= {..1, .1Dia} _16 {..6, .6Dia} _16
Away ::= {..4, .4Dia} _16 {..5, .5Dia} _16

{Arc Ask, Open Away}

% A cadence is the last two chords. The half cadence above stopped
% without arriving; here are two that shut the phrase and one that only
% pretends to. AUTHENTIC is 5 to 1: 7 lifts the semitone into '1 and
% the door shuts. PLAGAL comes from 4 (the amen) and neither chord
% holds 7, so nothing pulls: it settles rather than arrives, and one
% note can stand still through both. DECEPTIVE keeps the demand and
% answers it with 6, home's own family: the tune lifts exactly as it
% did and tells you nothing, the bass tells you. Each shares half its
% ground with Auth (Plag lands where Auth lands, Fool sets out where
% Auth sets out) and the asserts say so. A deception finishes nothing,
% so the phrase runs on and shuts for real.

Lift ::= 7 _8 '1 _8

Auth ::= {..5, .5Dia} _8 {..1, .1Dia} _8
Plag ::= {..4, .4Dia} _8 {..1, .1Dia} _8
Fool ::= {..5, .5Dia} _8 {..6, .6Dia} _8

assert Plag[1] == Auth[1]
assert Fool[0] == Auth[0]

{Arc Lift, Open Auth}
{Arc '1 _16, Open Plag}
{Arc Lift Lift, Open Fool Auth}

% The other half of the sentence. Arc comes round exactly as it was
% (that return is what makes these eight measures a PERIOD) and Answer
% walks 4 2 .7 1 down into home while the chords go 2 5 1, which is the
% tail of the circle: Shut is the last three chords of Back. A comma at
% the fourth measure, a full stop at the eighth, and not a letter name
% anywhere: every chord in the verse is a degree.

Answer ::= 4 _4 2 _4 .7 _8 1 _16
Shut   ::= Back[1:]

Verse ::= Arc Ask Arc Answer
Under ::= Open Away Open Shut

{Verse, Under}

% Every major key has a RELATIVE MINOR: the same seven notes with a
% different note for home. G major's 6 is E, and E minor spells e f# g
% a b c d: nothing added, nothing taken away, so the chord on 6 there
% and the chord on 1 here are one chord under two numbers. What the new
% home cannot do yet is CADENCE. Natural minor's 7 is d, a WHOLE step
% under home, so the chord on 5 comes out minor and Lift is no lift.
% Not one of these four rules is rewritten, and the door will not shut:

key e min

assert .5Dia == .5Min

{Arc Lift, Open Auth}

% 'harm' raises that 7 to d#. The chord on 5 is major again and Lift is
% a semitone again: one accidental, and it is the whole difference
% between a minor key that wanders and a minor key that closes:

key e harm

assert .5Dia == .5Maj

{Arc Lift, Open Auth}

% The door out of G. Raise the third of the chord on 3 and it is B
% major, and that d# is a note G major has not got: B major is the
% demand of E minor, not of G. Sound it after home and 6 stops being a
% chord in this key and becomes the next key's home: the tune sings
% the e that is about to be home, leans down through d#, and the verse
% answers with it. Then the same two rules say the whole verse again,
% dark: i VI iv V, i VI ii V i, with the step-away chord on 2
% diminished now and leaning harder. The one thing written at the use
% site is the last chord: Under without it, and a major third on the
% tonic in its place, the PICARDY, which no minor scale owns.

key g maj

assert .3Maj == {b3, d#4, f#4}

Turn ::= {.6 _8 .5# _8, {..3, .3Maj} _16}

Turn

key e harm

assert .5Dia == {b3, d#4, f#4}

{Verse, Under[:-1] {..1, .1Maj} _16}

% The song end to end: eight measures in G, the turn, eight in E minor,
% and home by the trick that took us out: raise a third and a home
% chord becomes somebody's demand. That Picardy, reread in G, is the
% chord on 6 with a raised third, which is the demand of 2, so the last
% measures fall by fifths the whole way, e a d g: the tail of the
% circle, entered where the minor left off. Both keys cadence for
% themselves: a comma at the fourth measure, a full stop at the eighth.
% And one amen sounds after the door is already shut.

key g maj

{Verse, Under}
Turn

key e harm

{Verse, Under[:-1] {..1, .1Maj} _16}

key g maj

{Answer 1 _16, Shut Plag}

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

Progressions & cadences · Harmony