Lessons · Advanced

Hemiola

Six beats heard as 3+3, then as 2+2+2

% A HEMIOLA is six beats that change their mind. Heard as 3+3 they are
% two bars of a waltz; heard as 2+2+2 they are three bars of a march.
% Nothing in the notes moves — the same six quarters fill the same
% twenty-four units either way — only where the weight falls. This is
% the waltz reading, the ground striking every third beat.
 
bpm 120
meter 3
unit 1/4
key g maj
 
Six   ::= 5 _4 '1 _4 7 _4 6 _4 5 _4 4 _4
Waltz ::= .1 _12 .5 _12
 
assert Six == | 5 _4 '1 _4 7 _4 | 6 _4 5 _4 4 _4 |
 
{Six, Waltz}*2
 
 
% The march reading takes the SAME rule for the tune, untouched, and
% regroups only the ground: three strokes where there were two, each
% two beats long. Play them back to back and the tune never wavers —
% what moves is the floor under it.
 
March ::= .1 _8 .4 _8 .5 _8
 
{Six, March}*2
{Six, Waltz} {Six, March}
{Six, Waltz} {Six, March}
 
 
% Written out, the regrouping is a change of METER — three bars of two
% in the time of two bars of three. The score mints a new signature
% where it happens and re-bars from there, which is how a player is
% told. The assert is the lesson in one line: rebarred, it is the same
% music.
 
meter 2
 
Barred ::= | 5 _4 '1 _4 | 7 _4 6 _4 | 5 _4 4 _4 |
Tread  ::= | .1 _8 | .4 _8 | .5 _8 |
 
assert Barred == Six
assert Tread == March
 
{Barred, Tread}*2
 
 
% Both readings AT ONCE is the vertical hemiola: the two-stroke ground
% and the three-stroke ground under one tune, colliding on the downbeat
% and nowhere else until the next. Baroque writing spends whole
% passages here, because the ear cannot settle on either reading.
 
meter 3
 
{Six, Waltz, March}*2
{Six@~2, Waltz, March}*2
{Six, Waltz, March}*2
 
 
% Where it earns its keep: the CADENCE. Four bars of plain waltz, then
% the ground stops agreeing — two beats to a stroke through the
% approach — so the tonic arrives a bar later than the meter promised.
% That delay is the whole device, and it is why a courante ends so.
 
Phrase ::= | 3 _4 4 _4 5 _4 | 6 _4 5 _4 4 _4 |
  | 3 _4 5 _4 '1 _4 | 7 _4 6 _4 5 _4 |
Under  ::= | .1 _12 | .6 _12 | .4 _12 | .5 _12 |
Close  ::= 6 _4 5 _4 4 _4 3 _4 4 _4 2 _4 1 _12
Delay  ::= .4 _8 .5 _8 .5 _8 .1 _12
 
{Phrase, Under} {Close, Delay}
{Phrase, Under} {Close, Delay}
 
 
% The whole argument in order: the waltz, its march, the two grounds
% heard together, and the cadence that walks in twos while the tune
% keeps counting in threes.
 
{Six, Waltz}*2
{Six, March}*2
{Six, Waltz, March}*2
{Phrase, Under} {Close, Delay}

% A HEMIOLA is six beats that change their mind. Heard as 3+3 they are
% two bars of a waltz; heard as 2+2+2 they are three bars of a march.
% Nothing in the notes moves — the same six quarters fill the same
% twenty-four units either way — only where the weight falls. This is
% the waltz reading, the ground striking every third beat.

bpm 120
meter 3
unit 1/4
key g maj

Six   ::= 5 _4 '1 _4 7 _4 6 _4 5 _4 4 _4
Waltz ::= .1 _12 .5 _12

assert Six == | 5 _4 '1 _4 7 _4 | 6 _4 5 _4 4 _4 |

{Six, Waltz}*2

% The march reading takes the SAME rule for the tune, untouched, and
% regroups only the ground: three strokes where there were two, each
% two beats long. Play them back to back and the tune never wavers —
% what moves is the floor under it.

March ::= .1 _8 .4 _8 .5 _8

{Six, March}*2
{Six, Waltz} {Six, March}
{Six, Waltz} {Six, March}

% Written out, the regrouping is a change of METER — three bars of two
% in the time of two bars of three. The score mints a new signature
% where it happens and re-bars from there, which is how a player is
% told. The assert is the lesson in one line: rebarred, it is the same
% music.

meter 2

Barred ::= | 5 _4 '1 _4 | 7 _4 6 _4 | 5 _4 4 _4 |
Tread  ::= | .1 _8 | .4 _8 | .5 _8 |

assert Barred == Six
assert Tread == March

{Barred, Tread}*2

% Both readings AT ONCE is the vertical hemiola: the two-stroke ground
% and the three-stroke ground under one tune, colliding on the downbeat
% and nowhere else until the next. Baroque writing spends whole
% passages here, because the ear cannot settle on either reading.

meter 3

{Six, Waltz, March}*2
{Six@~2, Waltz, March}*2
{Six, Waltz, March}*2

% Where it earns its keep: the CADENCE. Four bars of plain waltz, then
% the ground stops agreeing — two beats to a stroke through the
% approach — so the tonic arrives a bar later than the meter promised.
% That delay is the whole device, and it is why a courante ends so.

Phrase ::= | 3 _4 4 _4 5 _4 | 6 _4 5 _4 4 _4 |
  | 3 _4 5 _4 '1 _4 | 7 _4 6 _4 5 _4 |
Under  ::= | .1 _12 | .6 _12 | .4 _12 | .5 _12 |
Close  ::= 6 _4 5 _4 4 _4 3 _4 4 _4 2 _4 1 _12
Delay  ::= .4 _8 .5 _8 .5 _8 .1 _12

{Phrase, Under} {Close, Delay}
{Phrase, Under} {Close, Delay}

% The whole argument in order: the waltz, its march, the two grounds
% heard together, and the cadence that walks in twos while the tune
% keeps counting in threes.

{Six, Waltz}*2
{Six, March}*2
{Six, Waltz, March}*2
{Phrase, Under} {Close, Delay}

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

Opening…

Hemiola · Pattern Engine