MORTON FELDMAN Composition for violin (1984) (an excerpt from the unpublished original score is included with kind permission by © UNIVERSAL EDITION A.G., Wien, and with special thanks to the Trustees of the Morton Feldman Estate)
INTONATION by Marc Sabat
2004
MORTON FELDMAN
256/225:
! ve"
!
u f" 21/16
f
16/9
o<""
e" e"
f" f"
f0f""
16/9
n" f"
15/8
2x diminished 5th
n"" n ! 5th
nn""
f f""
9/8
2x augmented 3rd
3/2
n<"
n v" 1x augmented 3rd
n<"
e" v"
>v" u "
nn" 4th
11/6
major 7th
n" f " 7/4
<" n"
vn ""
1x augmented 6th
32/21
vn""
!
15/8
n" e"
9m u""
1x diminished 6th
21/16
64/35
13/8
2x augmented 5th
f4f"
21/16
11/8
eV"
E" e"
2x diminished 8ve
n v" E v""
3x diminished 4th
on "
ee""
52/45
u0v"
12/7
1x diminished 7th
1x augmented 3rd
27/20
! vn""
eV"
11/8
major 2nd
n" e" vE""
g4g"
2x augmented 3rd
major 7th
13/8
2x augmented 5th
16/11
!
minor 7th
minor 7th
! ve ""
35/24
3x augmented 3rd
1x augmented 3rd
! nn""
8/7
E v"
1x diminished 3rd
! e v"
: Composition for violin (1984) INTERVAL TUNINGS
4/3
n" v"
n" 32/15 u"
minor 9th
ve"" 2x diminished 6th
4f f""
16/11
Composition for violin (excerpt in original notation) Morton Feldman, ©1984 Universal Edition A.G., Wien
1 ) * . ) ! ! +) ! 1 ) * ) ) * 0 ! ! ! * , ) # % ) ' + . ! ! ! ! ! ! ! ! ! ! ! ! ! ! * ) + ) / ! ! ( !" + ! , ! ! *) ! ! !$ *) * ! !& * ) ! * *)0) ! ! +. +) ! ! !" ) *) ! ! 1 ) * . 1 , . ! !! !! / ) *+)) !! !! !!&% ) !! !! !" +*) !! ,+) !! !!$# *+. !! !!&% +. !! '" ( ! ! / *.0 !! !! ! !!" / +) ! *) *) ) ! * 0 ! !! *-) ,) ! ! ! ,. ! +) !! * ) ) ' % ' ! ! ! ! ! / / / ! !" ) *) ! !" / ) *+)) !! !! !! / ) *+)) !! !! ( !" *.0 !! ! !& * ) ! * *)0) ! !" *) ! ! ! *) *) 1 ) ) * . ! ! * 0 ! ! # +. ! ! 1 ) * ) , . + ) ! ' % ) ! ! ! ! ! ! ! ! ! ! ! / / / ! !" * 0 ! ! ! * ) ! * * )0) ! !$ * ( ! . ! ! ! ) *) ! ! !& +) ! ! ! +. * ) ! " 1 ) * . 1 ) -) ! ! !! !!!" / ) *+)) !! !! !! * ,*)) !! !! &% ( ! !!" * ,*)) ! !! ! ! +*) !! ,+) !! !!'" / *.0 !! !! !!&% ) + ) ! !! !! +. *) 1! ) , . ! * 0 ! !' ) ) ! +) ! ! ! ,. * ) % # $ + + . . * .0 !! !!&% + ) ! !! !" ! ! ! ! ! ! ! ! / / * ) + ) ! ! + ! , ! !$ * ! !$ ( !& *) ! * *)0) ! !" ) *) ! ! !" *) , ) ! 1 * . . , . ! , . !! ( ! !!" /* )) *+)) !! !! ! !$$ . ** .0 + !! !!!" / !! !!'" / + )) * )) +)) !! !!!" *-),*)) ! !! !!&% ,+)) !! ** )0 !! !! !!$$ +.. sord.
3
8
3
6:5
15
6:5
6:5
22
3
29
6:5
36
43
3
3
6:5
3
3
Composition for violin (tuned excerpt notated in The Helmholtz-Ellis JI Pitch Notation)
Morton Feldman, ©1984 Universal Edition A.G., Wien INTONATION by Marc Sabat, 9.1.2004
)-
'" )) f)) ! ! <) !! <) ) * >v > ! ( ! ! + ee*, ! ! !! ! !!" + * !! !! + f)) 0f f)) ! ! !! !!&% ) <) ! !! !!!" u f) ! ! o<)) !! !!$# f) * ! !' ) ) ! < ) ! ! ) f ' % ! ! ! + + ( !" .*, !! ! !& f ) ! f f f),) ! !" v f ! > * ' % ) v ! ! ' % ) ! f ) ) n < ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ) + + ) f 0f ( !" * ! ! ! <) ! ! # * * 0v > !! ( ! !!" + f)) 0f f)) ! ! !! ! !$$ * f f*, u !! !!!" + * !! !!'" + <)) f)) o) !! !!!" 4f f)
! !
8
)f ) ! ! ff f),, ! ! !!$#
>v* ! ! !! u *
6:5
)-
!! !! !
! ! ! ! !
3
15
6:5
22
3
29
6:5
36
43
6:5
3
6:5
3
3
3
The Extended Helmholtz-Ellis JI Pitch Notation microtonal accidentals designed by Marc Sabat and Wolfgang von Schweinitz, 2004
3-LIMIT (PYTHAGOREAN) INTERVALS
E e n v V
FUNCTION OF THE ACCIDENTALS notate 35 pitches from the series of untempered perfect fifths (3/2) perfect fifth (3/2); perfect fourth (4/3); major wholetone (9/8)
!
± 702.0 cents;
5-LIMIT (PTOLEMAIC) INTERVALS
DdmuU FfowW CcltT GgpxX BbksS HhqyY
notate an alteration by one syntonic comma (81/80) ± 21.5 cents; major third (5/4); minor third (6/5); major sixth (5/3); minor sixth (8/5); minor wholetone (10/9) !
notate an alteration by two syntonic commas (81/80)·(81/80) augmented fifth (25/16); diminished fourth (32/25)
!
± 43.0 cents;
notate an alteration by three syntonic commas (81/80)·(81/80)·(81/80) minor diesis (128/125)
!
± 64.5 cents;
7-LIMIT (SEPTIMAL) INTERVALS
<
>
• <<
¶ >>
or
or
notate an alteration by one septimal comma (64/63) ± 27.3 cents; natural seventh (7/4); septimal wholetone (8/7); septimal diminished fifth (7/5); septimal tritone (10/7); septimal minor third (7/6); septimal quartertone (36/35) !
notate an alteration by two septimal commas (64/63)·(64/63) septimal sixthtone (49/48)
!
± 54.5 cents;
11-LIMIT (UNDECIMAL) INTERVALS
4
5
notate an alteration by one undecimal quartertone (33/32) ± 53.3 cents; undecimal augmented fourth (11/8); undecimal diminished fifth (16/11)
9
notate an alteration by one tridecimal thirdtone (27/26) ± 65.3 cents; tridecimal neutral sixth (13/8); tridecimal neutral third (16/13)
!
13-LIMIT (TRIDECIMAL) INTERVALS
0
!
PRIMES IN THE HARMONIC SERIES OCTAVE 16 - 32 (5-limit signs are given relative to “A”; to be adjusted accordingly)
:f /n ^v o! ¥5
;u \n ±e "m µ4
notate an alteration of the 5-limit accidental by one 17-limit schisma (16/17)·(16/15) = (256/255) Galileo’s “equal-tempered” semitone (18/17); 17-limit diminshed seventh chord 10:12:14:17
notate an alteration by one 19-limit schisma (19/16)·(27/32) = (513/512) 19-limit minor third (19/16); 19-limit minor triad 16:19:24
notate an alteration by one 23-limit comma (23/16)·(8/9)·(8/9)·(8/9) raised leading tone (23/12)
!
!
!
± 6.8 cents;
± 3.4 cents;
± 16.5 cents;
notate an alteration of the 5-limit accidental by one 29-limit comma (29/16)·(5/9) = (145/144)
!
± 12.0 cents
notate an alteration of the 11-limit accidental by one 31-limit schisma (32/31)·(32/33) = (1024/1023)
!
± 1.7 cents
PRIMES IN THE HARMONIC SERIES OCTAVE 32 - 64 (5-limit signs are given relative to “A”; to be adjusted accordingly)
4 {w}
#
%
v
'
5 {d}
$
&
v ªe æe ¡u ¬f ) ƒ * + u f or
(
or
notate an alteration of the 11-limit accidental by one 37-limit schisma (36/37)·(33/32) = (297/296)
± 5.8 cents
notate an alteration of the 5-limit accidental by one 41-limit schisma (32/41)·(81/64)·(81/80) = (6561/6560)
notate an alteration by one 43-limit comma (43/32)·(3/4) = (129/128)
!
notate an alteration of the 5-limit accidental by one 53-limit comma (32/53)·(5/3) = (160/159)
!
!
notate an alteration of the 7-limit accidental by one 61-limit schisma (61/32)·(21/40) = (1281/1280)
NOTE ABOUT CENTS INDICATIONS: optional cents indications may be placed above or below the respective accidentals and are always understood in reference to Equal Tempered semitones, as implied by the Pythagorean accidentals
± 0.3 cents
!
± 0.8 cents
± 10.9 cents
notate an alteration of the 13-limit accidental by one 59-limit schisma (32/59)·(24/13) = (768/767)
notate the respective Equal Tempered Semitone; may be combined with a cents indication to notate any pitch
!
± 13.5 cents
notate an alteration of the 7-limit accidental by one 47-limit schisma (32/47)·(48/49)·(3/2) = (2304/2303)
IRRATIONAL AND TEMPERED INTERVALS:
A a j z Z
!
± 2.3 cents
!
± 1.4 cents
