Template:Tone row/P

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Use[edit]

This template is intended to provide a consistent and easy display for tone rows, in all forms: prime, retrograde, inverse, retrograde inversion, and inverse retrograde; and in all transpositions.

Tone rows must be twelve tones long when using I, RI, and IR. Tones "10" and "11" may be entered as such, or as "t" and "e", and either way will be displayed as "t" and "e", except in IR, where "10" and "11" must be used. Integers or traditional letter names ("F#", etc.) may entered in the "number" parameter to indicate transposition, but may not be entered in parameters 1-12 to indicate individual tones.

For example:

 P6:
 {{Tone row|form= P|number=6|break=hexachord|0|1|2|3|4|5|10|11|8|9|6|7}}
 R6:
 {{Tone row|form= R|number=6|break=hexachord|0|1|2|3|4|5|10|11|8|9|6|7}}
 I6:
 {{Tone row|form= I|number=6|break=hexachord|0|1|2|3|4|5|10|11|8|9|6|7}}
 RI6:
 {{Tone row|form=RI|number=6|break=hexachord|0|1|2|3|4|5|10|11|8|9|6|7}}
 IR6:
 {{Tone row|form=IR|number=6|break=hexachord|0|1|2|3|4|5|10|11|8|9|6|7}}
 P6 (0 = C):
 {{Tone row|form=P sharp|number=6|break=hexachord|0|1|2|3|4|5|10|11|8|9|6|7}}

produces:

P6:
6 7 8 9 t e
4 5 2 3 0 1
R6: 1 0 3 2 5 4
e t 9 8 7 6
I6: 6 5 4 3 2 1
8 7 t 9 0 e
RI6: e 0 9 t 7 8
1 2 3 4 5 6
IR6: 1 2 e 0 9 t
3 4 5 6 7 8
[should be: 1 2 e 0 9 t 3 4 5 6 7 8] P6 (0 = C): F# G G# A A# B
E F D D# C C#

The following:
0: {{Tone row/P|number=0|0|1|2|3|4|5|10|11|8|9|6|7}}
1: {{Tone row/P|number=1|0|1|2|3|4|5|10|11|8|9|6|7}}
2: {{Tone row/P|number=2|0|1|2|3|4|5|10|11|8|9|6|7}}
3: {{Tone row/P|number=3|0|1|2|3|4|5|10|11|8|9|6|7}}
4: {{Tone row/P|number=4|0|1|2|3|4|5|10|11|8|9|6|7}}
5: {{Tone row/P|number=5|0|1|2|3|4|5|10|11|8|9|6|7}}
6: {{Tone row/P|number=6|0|1|2|3|4|5|10|11|8|9|6|7}}
7: {{Tone row/P|number=7|0|1|2|3|4|5|10|11|8|9|6|7}}
8: {{Tone row/P|number=8|0|1|2|3|4|5|10|11|8|9|6|7}}
9: {{Tone row/P|number=9|0|1|2|3|4|5|10|11|8|9|6|7}}
10: {{Tone row/P|number=10|0|1|2|3|4|5|10|11|8|9|6|7}}
11: {{Tone row/P|number=11|0|1|2|3|4|5|10|11|8|9|6|7}}
produces:

 0: 0 1 2 3 4 5 t e 8 9 6 7
 1: 1 2 3 4 5 6 e 0 9 t 7 8
 2: 2 3 4 5 6 7 0 1 t e 8 9
 3: 3 4 5 6 7 8 1 2 e 0 9 t
 4: 4 5 6 7 8 9 2 3 0 1 t e
 5: 5 6 7 8 9 t 3 4 1 2 e 0
 6: 6 7 8 9 t e 4 5 2 3 0 1
 7: 7 8 9 t e 0 5 6 3 4 1 2
 8: 8 9 t e 0 1 6 7 4 5 2 3
 9: 9 t e 0 1 2 7 8 5 6 3 4
10: t e 0 1 2 3 8 9 6 7 4 5
11: e 0 1 2 3 4 9 t 7 8 5 6

Parameters[edit]

{{Tone row |form= |break= |number= |1-12= }}

  • |form=P, R, I, RI, IR
  • |break=anything
  • |number=transposition: 0 to 11; or letter note (of 0): C to B
  • |1-12=number: 0 to 11

Formulas[edit]

  • P = {{{1|}}} {{{2|}}}...
  • R = {{{12|}}} {{{11|}}}...
  • I = 12-{{{1|}}} 12-{{{2|}}}...
  • RI = 12-{{{12|}}} 12-{{{11|}}}...
  • IR = (12-{{{12|}}})+({{{12|}}}-(12-{{{12|}}})) (12-{{{11|}}})+({{{12|}}}-(12-{{{12|}}}))...

Intervals[edit]

The intervals, the space between the notes of the row, may be figured with {{Tone row/Intervals}}.

  • {{Tone row/Intervals|0|e|7|4|2|9|3|8|t|1|5|6}}
  • e 8 9 t 7 6 5 2 3 4 1

For the interval classes, use {{Tone row/Interval classes}}.

  • {{Tone row/Interval classes|0|e|7|4|2|9|3|8|t|1|5|6}}
  • 1 4 3 2 5 6 5 2 3 4 1

See also[edit]