Changing Series in Walzer Opus 23Emmanuel Rens 

Set
1 191692800 rows. MOD= 12 MOT= 2, 16 data 
Set
2 106168320 rows. MOD= 10 MOT= 4,26 data 
Set
3 66355200 rows. MOD= 8 MOT= 6,7 data 
Set
4 66355200 rows. MOD= 6 MOT= 10,11,12,22,25 data 
Set
5 44697600 rows. MOD= 4 MOT= 9,15,17,18,24 data 
Set
6 3732480 rows. MOD= 2 MOT= 3,19,23 data 


0231510
 ord 899 (442944 rows) 

42370B1596A8 (MOT=7) listen  data 
7962A354801B (MOT=11) listen  data 
314B762A0895 (MOT=18) listen  data 
no
such row (with given interval set) 

Special
rows (symetric, derived, ..) 
Schoenberg,
Serenade op.24 (Self Transposed
listen
 dataOpposite) (MOT=2) 
017B268A5493 (MOT=4)
listen
 data 
All intervals (MOT=7) listen  data 
Harmonic (MOT=11) listen  data 
Webern, Quartet
op. 28 (Derived Set) (MOT=18) listen  data 
Webern, Chamber
Symph. op. 21 (Palindromic
Row) (MOT=23) listen  data 

0122133
ord 1523 (535680 rows) 
0A7184B56392
(MOT=2) listen  data 
71853B609A42
(MOT=4) listen  data 
24A5B9038176
(MOT=7) listen  data 
562039718B4A (MOT=11) listen  data 
816079352BA4 (MOT=18) listen  data 
3802B65A4179 (MOT=23) listen  data 

0224121
ord 886 (1505664 rows) 
5A4678B29031 (MOT=2) listen  data 
3028957AB416
(MOT=4) listen  data 
B423095617A8 (MOT=7) listen  data 
1693A02B7854 (MOT=11) listen  data 
917A052436B8 (MOT=18) listen  data 
853B69A70142 (MOT=23) listen  data 

0320511
ord 509 (211392 rows) 
827B9A651340
(MOT=16) listen  data 
6A84359127B0
(MOT=26) listen  data 
059A4621B378 (MOT=11) listen  data 
A3B789510264 (MOT=25) listen  data 
15AB08264379 (MOT=17) listen  data 
B12A37640895 (MOT=19) listen  data 

0432102
ord 246 (270144 rows) 
20689A17543B
(MOT=16) listen  data 
B9A203417865
(MOT=26) listen  data 
0B2A45786931
(MOT=6) listen  data 
421B3587609A (MOT=25) listen  data 
536209871BA4 (MOT=17) listen  data 
1B0A96458237 (MOT=19) listen  data 

0111342
ord 1672 (548352 rows) 
374810629B5A (MOT=16) listen  data 
5038916A427B
(MOT=26) listen  data 
9082713B6A54 (MOT=6) listen  data 
27B6154093A8 (MOT=25) listen  data 
6170495B238A (MOT=17) listen  data 
A27B50389164 (MOT=19) listen  data 

0820101
ord 43 (3456 rows) 
no
such row (with MOT=16) 
8764359AB012 (MOT=26) listen  data 
56021BA98734 (MOT=6) listen  data 
3456210BA879 (MOT=25) listen  data 
no
such row (with MOT=17) 
7B0A98654321 (MOT=19) listen  data 

Set
1 191692800 rows. MOD= 12 MOT= 2, 16 data 
Set
2 106168320 rows. MOD= 10 MOT= 4,26 data 
Set
3 66355200 rows. MOD= 8 MOT= 6,7 data 
Set
4 66355200 rows. MOD= 6 MOT= 10,11,12,22,25 data 
Set
5 44697600 rows. MOD= 4 MOT= 9,15,17,18,24 data 
Set
6 3732480 rows. MOD= 2 MOT= 3,19,23 data 


Chromatic (MOT=2) listen data 

1B093A276485,
All Intervals (MOT=7) listen  data 
Harmonic (MOT=11) listen  data 
Schoenberg,
Suite for piano op. 25 (MOT=24) listen  data 
Berg,
Lyric suite, All Intervals (MOT=23) listen  data 

Circle
of Fifths (MOT=2) listen  data 
1B09473A2865,
All Intervals (MOT=4) listen  data 
Bach, Praeludium I Transposed Harmonic (MOT=11) listen data 
Schoenberg,
Ode to
Napoleon op. 41, Derived Set (MOT=18) listen  data 

Selfmapped
Opposite (MOT=2) listen data 

Set
1 191692800 rows. MOD= 12 MOT= 2, 16 data 
Set
2 106168320 rows. MOD= 10 MOT= 4,26 data 
Set
3 66355200 rows. MOD= 8 MOT= 6,7 data 
Set
4 66355200 rows. MOD= 6 MOT= 10,11,12,22,25 data 
Set
5 44697600 rows. MOD= 4 MOT= 9,15,17,18,24 data 
Set
6 3732480 rows. MOD= 2 MOT= 3,19,23 data 


0231510
 ord 899 (442944 rows) 

42370B1596A8 (MOT=7) listen  data 
7962A354801B (MOT=11) listen  data 
314B762A0895 (MOT=18) listen  data 
no
such row (with given interval set) 

Special
rows (symetric, derived, ..) 
Schoenberg,
Serenade op. 24 (Self Transposed
Opposite) (MOT=2) listen  data 
017B268A5493
(MOT=4) listen  data 
All intervals (MOT=7) listen  data 
Praeludium I, (harmonic) (MOT=11) listen  data 
Webern, Quartet
op. 28 (Derived Set) (MOT=18) listen  data 
Webern, Chamber
Symph. op. 21 (Palindromic
Row) (MOT=23) listen  data 

0122133
ord 1523 (535680 rows) 
0A7184B56392 (MOT=2) listen  data 
71853B609A42
(MOT=4) listen  data 
24A5B9038176
(MOT=7) listen  data 
562039718B4A (MOT=11) listen  data 
816079352BA4 (MOT=18) listen  data 
3802B65A4179 (MOT=23) listen  data 

0224121
ord 886 (1505664 rows) 
5A4678B29031 (MOT=2) listen  data 
3028957AB416
(MOT=4) listen  data 
B423095617A8 (MOT=7) listen  data 
1693A02B7854 (MOT=11) listen  data 
917A052436B8 (MOT=18) listen  data 
853B69A70142 (MOT=23) listen  data 

0320511
ord 509 (211392 rows) 
827B9A651340 (MOT=16) listen  data 
6A84359127B0
(MOT=26) listen  data 
059A4621B378 (MOT=11) listen  data 
A3B789510264 (MOT=25) listen  data 
15AB08264379 (MOT=17) listen  data 
B12A37640895 (MOT=19) listen  data 

0432102
ord 246 (270144 rows) 
20689A17543B (MOT=16) listen  data 
B9A203417865
(MOT=26) listen  data 
0B2A45786931
(MOT=6) listen  data 
421B3587609A (MOT=25) listen  data 
536209871BA4 (MOT=17) listen  data 
1B0A96458237 (MOT=19) listen  data 

0111342
ord 1672 (548352 rows) 
374810629B5A (MOT=16) listen  data 
5038916A427B
(MOT=26) listen  data 
9082713B6A54 (MOT=6) listen  data 
27B6154093A8 (MOT=25) listen  data 
6170495B238A (MOT=17) listen  data 
A27B50389164 (MOT=19) listen  data 

0820101
ord 43 (3456 rows) 
no
such row (with MOT=16) 
8764359AB012 (MOT=26) listen  data 
56021BA98734 (MOT=6) listen  data 
3456210BA879 (MOT=25) listen  data 
no
such row (with MOT=17) 
7B0A98654321 (MOT=19) listen  data 

Set
1 191692800 rows. MOD: 12 MOT: 2, 16 data 
Set
2 106168320 rows. MOD: 10 MOT: 4,26 data 
Set
3 66355200 rows. MOD: 8 MOT: 6,7 data 
Set
4 66355200 rows. MOD: 6 MOT: 10,11,12,22,25 data 
Set
5 44697600 rows. MOD: 4 MOT: 9,15,17,18,24 data 
Set
6 3732480 rows. MOD: 2 MOT: 3,19,23 data 


Chromatic. (MOT=2) listen data 

1B093A276485,
All Intervals Row. (MOT=7) listen  data 
Schoenberg,
Suite for piano op. 25. (MOT=24) listen  data 
Berg,
Lyric suite, All Intervals Row. (MOT=23) listen  data 

Circle
of Fifths. (MOT=2) listen  data 
1B09473A2865,
All Intervals Row. (MOT=4) listen  data 
Schoenberg, Ode to
Napoleon op. 41, Derived Set. (MOT=18) listen  data 

Selfmapped
Opposite. (MOT=2) listen data 
Praeludium I, (harmonic) (MOT=11) listen  data 
Le dodécaphonisme comme outil d'analyse  A
previous and more precise article on permutational music, coauthored
with Jérôme Palfi, in
French. 
How to read special data (↓)  A
reminder on the meaning of data formats used here. 
Degrees and Types (↓)  Distribution
of types by degrees in base 12 and type numeration (MOT). 
wop23.csd  The
Walzer Op. 23 part for Csound synthesis open software. 
dode.pl  A
Linux command line utility written in Perl, for the analysis and
generation of series (run "./dode.pl help" in a terminal window to
get usage
information). 
csdmod.pl  The
Linux command line utility written in Perl for the replacement of one
row by another in .csd files (run "./csdmod.pl help" in a terminal
window to get usage
information). 
PianoAkai_Steinway_III.sf2  The
public domain piano sound used for renderings. 
History (↓)  Record of the modifications brought to any document in this project. 
Franck
Ayres, Jr., Theory and Problems of Modern Algebra, McGrawHill Inc, New York, 1965. 
A
good manual. 
Kenneth R. Rumery, Twelve tone composition.  Detailed
examples for different types of rows. 
Emmanuel Amiot, La série dodécaphonique et ses symétries.  A
detailed overview of groups in some symetric series, with theorems and
demonstrations
(in French). 
Milton
Babbitt, Collected Essays, Princeton University Press 2003. 
Deals
with hexachords and groups. As
difficult as Babbitt can be. 
David J. Hunter and Paul T. von Hippel, How Rare Is
Symmetry in Musical 12Tone Rows?, The Mathematical Association Of
America, February 2003. 
Still
too hard and groupy for me, but row examples are nice. 
Link back to the introduction on permutations 
© Emmanuel Rens, Geneva, April 2009.  home  top 