Beat & meter

Pulse, tempo, measures, bars

% A PULSE is bare time — even units, nothing grouping them. 'bpm'
% counts those units per minute, so this pair of phrases runs twelve
% seconds here and exactly half that when the count doubles. Same
% notes, same order, same evenness; nothing in them yet says where a
% downbeat falls.
 
bpm 30
unit 1/16
key d4 harm
 
Chant  ::= 5 5 6 5 4 3 4 5 4 3 2 1
Answer ::= 5 '1 7 '1 5 4 3 2 1 .7 2 1
 
Chant Answer
bpm 60
Chant Answer
 
 
% METER groups the pulse, and the group is the MEASURE: '|' bars mark
% it off and what sits between two bars fills exactly one. Tread
% strikes the downbeat every three units, March every four. The tune
% is untouched — twelve units either way — and the assert says why:
% bars that already fit change no time at all. Only the grouping moves.
 
meter 3
Tread ::= | .1 -*2 | ..5 -*2 | .1 -*2 | ..5 -*2 |
 
assert Tread == .1 -*2 ..5 -*2 .1 -*2 ..5 -*2
 
{Chant, Tread} {Answer, Tread}
 
meter 4
March ::= | .1 -*3 | ..5 -*3 | .1 -*3 |
 
{Chant, March} {Answer, March}
 
 
% So the bar counts TIME, not symbols. Flourish holds four measures of
% three units and crowds three, four, five and six notes into them in
% turn — each bar quicker than the last, Tread never moving — and
% '~' plays the whole run backwards, six notes slowing to three. Six
% in three units are half-units each; the assert checks that.
 
meter 3
 
Flourish ::= | 5 '1 7 | '1 7 6 5 | '1 7 6 5 4 | 5 4 3 2 .7 1 |
 
assert | 5 4 3 2 .7 1 | == 5/ 4/ 3/ 2/ .7/ 1/
 
{Chant, Tread} {Flourish, Tread}
{Flourish~, Tread} {Answer, Tread}
 
 
% Marks ride the bar they follow, so '|*n' restates the measure it
% closes and Oom's four bars are written as two. Eight measures of
% three: I I V V, then IV IV V I, two chords a bar over the bass —
% and the tune walks down a full octave across the second strain,
% f5 to f4.
 
key f4 maj
bpm 45
 
Oom  ::= | ..1 .1Dia .1Dia |*2 | ..5 .5Dia .5Dia |*2
Oomb ::= | ..4 .4Dia .4Dia |*2 | ..5 .5Dia .5Dia | ..1 .1Dia .1Dia |
 
Tune  ::= | 5 _2 5 | 6 5 4 | 5 _2 '1 | 7 _3 |
Tuneb ::= | '1 _2 6 | 5 4 3 | 4 3 2 | 1 _3 |
 
{Tune, Oom} {Tuneb, Oomb}
 
 
% 'unit' says what the meter COUNTS: a measure is meter × 4 / unit
% units, so 6/8 and 3/4 are the same three units — six eighths or
% three quarters. Sway, which opens on Answer's first six notes, is
% identical under both; only the bass regroups, twos under 6/8 and
% threes under 3/4. Sound the two together and one bar holds a
% HEMIOLA, three against two.
 
key d4 harm
bpm 50
meter 6
unit 1/32
 
Sway   ::= | Answer[0:6] | 3 4 5 4 3 2 | .7 1 2 3 4 5 | 6 5 4 3 2 .7 |
Twos   ::= | ..1 -*2 ..1 -*2 | ..6 -*2 ..6 -*2 | ..4 -*2 ..4 -*2 | ..5 -*2 ..5 -*2 |
Threes ::= | ..1 - ..1 - ..1 - | ..6 - ..6 - ..6 - | ..4 - ..4 - ..4 - | ..5 - ..5 - ..5 - |
 
{Sway, Twos}
 
meter 3
unit 1/16
 
{Sway, Threes}
{Sway, Twos, Threes}
 
 
% Every grouping over one unchanging pulse: Chant in threes, the
% Flourish crowding those same bars, Sway's six heard as twos and
% threes at once, then Answer in fours before the tonic closes it.
% Not a note was rewritten between them — a 'meter' command did all
% the regrouping.
 
{Chant, Tread} {Flourish, Tread}
{Sway, Twos, Threes}
 
meter 4
{Answer, March} {1 _4, .1 _4, ..1 _4}

% A PULSE is bare time — even units, nothing grouping them. 'bpm'
% counts those units per minute, so this pair of phrases runs twelve
% seconds here and exactly half that when the count doubles. Same
% notes, same order, same evenness; nothing in them yet says where a
% downbeat falls.

bpm 30
unit 1/16
key d4 harm

Chant  ::= 5 5 6 5 4 3 4 5 4 3 2 1
Answer ::= 5 '1 7 '1 5 4 3 2 1 .7 2 1

Chant Answer
bpm 60
Chant Answer

% METER groups the pulse, and the group is the MEASURE: '|' bars mark
% it off and what sits between two bars fills exactly one. Tread
% strikes the downbeat every three units, March every four. The tune
% is untouched — twelve units either way — and the assert says why:
% bars that already fit change no time at all. Only the grouping moves.

meter 3
Tread ::= | .1 -*2 | ..5 -*2 | .1 -*2 | ..5 -*2 |

assert Tread == .1 -*2 ..5 -*2 .1 -*2 ..5 -*2

{Chant, Tread} {Answer, Tread}

meter 4
March ::= | .1 -*3 | ..5 -*3 | .1 -*3 |

{Chant, March} {Answer, March}

% So the bar counts TIME, not symbols. Flourish holds four measures of
% three units and crowds three, four, five and six notes into them in
% turn — each bar quicker than the last, Tread never moving — and
% '~' plays the whole run backwards, six notes slowing to three. Six
% in three units are half-units each; the assert checks that.

meter 3

Flourish ::= | 5 '1 7 | '1 7 6 5 | '1 7 6 5 4 | 5 4 3 2 .7 1 |

assert | 5 4 3 2 .7 1 | == 5/ 4/ 3/ 2/ .7/ 1/

{Chant, Tread} {Flourish, Tread}
{Flourish~, Tread} {Answer, Tread}

% Marks ride the bar they follow, so '|*n' restates the measure it
% closes and Oom's four bars are written as two. Eight measures of
% three: I I V V, then IV IV V I, two chords a bar over the bass —
% and the tune walks down a full octave across the second strain,
% f5 to f4.

key f4 maj
bpm 45

Tune  ::= | 5 _2 5 | 6 5 4 | 5 _2 '1 | 7 _3 |
Tuneb ::= | '1 _2 6 | 5 4 3 | 4 3 2 | 1 _3 |

{Tune, Oom} {Tuneb, Oomb}

% 'unit' says what the meter COUNTS: a measure is meter × 4 / unit
% units, so 6/8 and 3/4 are the same three units — six eighths or
% three quarters. Sway, which opens on Answer's first six notes, is
% identical under both; only the bass regroups, twos under 6/8 and
% threes under 3/4. Sound the two together and one bar holds a
% HEMIOLA, three against two.

key d4 harm
bpm 50
meter 6
unit 1/32

Sway   ::= | Answer[0:6] | 3 4 5 4 3 2 | .7 1 2 3 4 5 | 6 5 4 3 2 .7 |
Twos   ::= | ..1 -*2 ..1 -*2 | ..6 -*2 ..6 -*2 | ..4 -*2 ..4 -*2 | ..5 -*2 ..5 -*2 |
Threes ::= | ..1 - ..1 - ..1 - | ..6 - ..6 - ..6 - | ..4 - ..4 - ..4 - | ..5 - ..5 - ..5 - |

{Sway, Twos}

meter 3
unit 1/16

{Sway, Threes}
{Sway, Twos, Threes}

% Every grouping over one unchanging pulse: Chant in threes, the
% Flourish crowding those same bars, Sway's six heard as twos and
% threes at once, then Answer in fours before the tonic closes it.
% Not a note was rewritten between them — a 'meter' command did all
% the regrouping.

{Chant, Tread} {Flourish, Tread}
{Sway, Twos, Threes}

meter 4
{Answer, March} {1 _4, .1 _4, ..1 _4}

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