Lessons · Techniques

Absolute pitch and MIDI

mode midi, m<n>, and imported material

% A bare number is a scale DEGREE only because 'mode' says so. Read
% one line of numbers twice: as degrees of g minor it climbs the tonic
% triad to the octave and comes home past the flat seventh; as
% chromatic distances from the same centre (semitones, not steps),
% the same numbers turn major with a raised fourth.
 
bpm 44
instrument plain
meter 4
unit 1/4
key g3 min
mode diatonic
 
Line ::= 1 3 5 _2 8 7 5 3 1 _2
 
Line
mode chromatic
Line
 
 
% 'mode midi' takes the key out of the reading altogether: a bare
% number is a MIDI note number, so those same numbers are notes 1 to 8
% which are four and a half octaves under the g3 they just sounded at, below
% the floor of hearing. 'm<n>' says a MIDI number in ANY mode, which is
% what makes it the anchor a claim can be pinned to. Add 54 and the
% line returns exactly as the chromatic reading: chromatic counts
% semitones up from the centre (g3 is m55), midi counts from 0.
 
mode midi
 
assert Line == m1 m3 m5 _2 m8 m7 m5 m3 m1 _2
assert Line@54 == m55 m57 m59 _2 m62 m61 m59 m57 m55 _2
 
Line@54
 
 
% Berg's Violin Concerto row is the case for absolute spelling: it is
% in no key, so a degree would start lying about it at the fourth note.
% m<n> reads the same under every mode: the document is back under
% 'mode diatonic' here and the key does not touch the row; an assert
% below checks it against the same numbers read as midi. Its head is
% eight notes stacked in thirds, every other one an open violin
% string; its tail is four whole tones.
 
mode diatonic
 
Row  ::= m55 m58 m62 m66 m69 m72 m76 m80 m83 m85 m87 m89
Head ::= Row[:8]
Tail ::= Row[8:]
 
assert Head[::2] == m55 m62 m69 m76
assert Head Tail == Row
 
Row _2
 
 
% The row's first nine notes are four triads sharing their outer
% notes: g minor, D major, A minor, E major, each starting where the
% one before it ended. That is why a row with no key in it sounds
% tonal. The head holds eight of the nine, so the last triad reaches
% one note into the tail. The chords are absolute too, and the assert
% says the chord IS the row's notes sounded together.
 
Triads ::= gMin _2 'dMaj _2 'aMin _2 ''eMaj _2
 
assert gMin == {m55, m58, m62}
assert ''eMaj == {m76, m80, m83}
 
{Head, Triads}
 
 
% The four forms are the whole technique. Absolute pitches mirror by
% SEMITONES around the axis pitch (degree 1, g3), so the inversion
% falls below the row's register, and '@34' is the plain arithmetic
% that puts it back: it enters on m89 and ends on m55, where the row
% began. Inverted, the minor-major chain of triads reads major-minor.
 
Retro  ::= Row~
Inv    ::= Row^@34
RetInv ::= Inv~
 
assert Row[::-1] == Retro
assert Inv == m89 m86 m82 m78 m75 m72 m68 m64 m61 m59 m57 m55
 
Row _2 Retro _2 Inv _2 RetInv _2
 
 
% This is what an importer writes. A MIDI file carries note numbers
% and no key, so the import sets 'mode midi' and states them bare: no
% 'm' prefix needed once the mode is midi, and no degree pretending to
% know a key that is not there. The assert is the proof that the two
% spellings are one row.
 
mode midi
 
Import ::= 55 58 62 66 69 72 76 80 83 85 87 89
 
assert Import == Row
 
Import _2
 
 
% The piece, in the mode the import left behind: the head over its
% triads, the inversion over the triads it turns major, the tail alone
% in whole tones where no triad can follow it, and the row entire.
 
InvTriads ::= ''bbMaj _2 ''ebMin _2 'g#Maj _2 'c#Min _2
InvHead   ::= Head^@34
 
{Head, Triads} _2
{InvHead, InvTriads} _2
Tail _2 Tail~ _2
Row _2

% A bare number is a scale DEGREE only because 'mode' says so. Read
% one line of numbers twice: as degrees of g minor it climbs the tonic
% triad to the octave and comes home past the flat seventh; as
% chromatic distances from the same centre (semitones, not steps),
% the same numbers turn major with a raised fourth.

bpm 44
instrument plain
meter 4
unit 1/4
key g3 min
mode diatonic

Line ::= 1 3 5 _2 8 7 5 3 1 _2

Line
mode chromatic
Line

% 'mode midi' takes the key out of the reading altogether: a bare
% number is a MIDI note number, so those same numbers are notes 1 to 8
% which are four and a half octaves under the g3 they just sounded at, below
% the floor of hearing. 'm<n>' says a MIDI number in ANY mode, which is
% what makes it the anchor a claim can be pinned to. Add 54 and the
% line returns exactly as the chromatic reading: chromatic counts
% semitones up from the centre (g3 is m55), midi counts from 0.

mode midi

assert Line == m1 m3 m5 _2 m8 m7 m5 m3 m1 _2
assert Line@54 == m55 m57 m59 _2 m62 m61 m59 m57 m55 _2

Line@54

% Berg's Violin Concerto row is the case for absolute spelling: it is
% in no key, so a degree would start lying about it at the fourth note.
% m<n> reads the same under every mode: the document is back under
% 'mode diatonic' here and the key does not touch the row; an assert
% below checks it against the same numbers read as midi. Its head is
% eight notes stacked in thirds, every other one an open violin
% string; its tail is four whole tones.

mode diatonic

Row  ::= m55 m58 m62 m66 m69 m72 m76 m80 m83 m85 m87 m89
Head ::= Row[:8]
Tail ::= Row[8:]

assert Head[::2] == m55 m62 m69 m76
assert Head Tail == Row

Row _2

% The row's first nine notes are four triads sharing their outer
% notes: g minor, D major, A minor, E major, each starting where the
% one before it ended. That is why a row with no key in it sounds
% tonal. The head holds eight of the nine, so the last triad reaches
% one note into the tail. The chords are absolute too, and the assert
% says the chord IS the row's notes sounded together.

Triads ::= gMin _2 'dMaj _2 'aMin _2 ''eMaj _2

assert gMin == {m55, m58, m62}
assert ''eMaj == {m76, m80, m83}

{Head, Triads}

% The four forms are the whole technique. Absolute pitches mirror by
% SEMITONES around the axis pitch (degree 1, g3), so the inversion
% falls below the row's register, and '@34' is the plain arithmetic
% that puts it back: it enters on m89 and ends on m55, where the row
% began. Inverted, the minor-major chain of triads reads major-minor.

Retro  ::= Row~
Inv    ::= Row^@34
RetInv ::= Inv~

assert Row[::-1] == Retro
assert Inv == m89 m86 m82 m78 m75 m72 m68 m64 m61 m59 m57 m55

Row _2 Retro _2 Inv _2 RetInv _2

% This is what an importer writes. A MIDI file carries note numbers
% and no key, so the import sets 'mode midi' and states them bare: no
% 'm' prefix needed once the mode is midi, and no degree pretending to
% know a key that is not there. The assert is the proof that the two
% spellings are one row.

mode midi

Import ::= 55 58 62 66 69 72 76 80 83 85 87 89

assert Import == Row

Import _2

% The piece, in the mode the import left behind: the head over its
% triads, the inversion over the triads it turns major, the tail alone
% in whole tones where no triad can follow it, and the row entire.

InvTriads ::= ''bbMaj _2 ''ebMin _2 'g#Maj _2 'c#Min _2
InvHead   ::= Head^@34

{Head, Triads} _2
{InvHead, InvTriads} _2
Tail _2 Tail~ _2
Row _2

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Absolute pitch and MIDI · Techniques