Kite's thoughts on hi-lo notation: Difference between revisions
various small changes |
→Generalized Voicings: more small improvements |
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|+Generalized voicings for a triad in 4 voices, empty octaves allowed | |+Generalized voicings for a triad in 4 voices, empty octaves allowed | ||
!stepspan | !stepspan | ||
! colspan=" | ! colspan="3" |voicing | ||
!root position | !root position | ||
!1st inversion | !1st inversion | ||
| Line 213: | Line 213: | ||
!1-1-3 | !1-1-3 | ||
!lift-2-3 | !lift-2-3 | ||
!close over 8ve | |||
|addloR | |addloR | ||
|hiRaddlo3 | |hiRaddlo3 | ||
| Line 219: | Line 220: | ||
!1-3-1 | !1-3-1 | ||
!lift-3 drop-2 | !lift-3 drop-2 | ||
! | |||
|hi5add10 | |hi5add10 | ||
|hiRlo3addlo5 | |hiRlo3addlo5 | ||
| Line 225: | Line 227: | ||
!3-1-1 | !3-1-1 | ||
!drop-2-3 | !drop-2-3 | ||
!close under 8ve | |||
|addhi5 | |addhi5 | ||
|lo35add8 | |lo35add8 | ||
| Line 232: | Line 235: | ||
!2-2-3 | !2-2-3 | ||
!lift-3 drop-1-4 | !lift-3 drop-1-4 | ||
!open over 8ve | |||
|hi3addloR | |hi3addloR | ||
|hiR5addlo3 | |hiR5addlo3 | ||
| Line 238: | Line 242: | ||
!2-3-2 | !2-3-2 | ||
!lift-2 drop-3 | !lift-2 drop-3 | ||
! | |||
|hi10addhi5 | |hi10addhi5 | ||
|hi5lo3add8 | |hi5lo3add8 | ||
| Line 244: | Line 249: | ||
!3-2-2 | !3-2-2 | ||
!lift-1-4 drop-2 | !lift-1-4 drop-2 | ||
!open under 8ve | |||
|hi3addhi10 | |hi3addhi10 | ||
|lo3addhi5 | |lo3addhi5 | ||
|hiRlo5addhi8 | |hiRlo5addhi8 | ||
|} | |} | ||
There are 42 five-part voicings of a triad, or 150 if allowing empty octaves. | |||
=== Tetrads === | === Tetrads === | ||
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Generalized voicings are particularly useful for dim7 chords. | Generalized voicings are particularly useful for dim7 chords. | ||
There are 144 five-part voicings of a tetrad, or 240 if allowing empty octaves. | |||
=== Pentads === | === Pentads === | ||
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=== Hexads, heptads, etc. === | === Hexads, heptads, etc. === | ||
For an N-ad in N voices, there are N! possible voicings, which are grouped into (N-1)! generalized voicings, which are grouped into (N-2)<sup>2</sup> + 1 stepspans.{{Navbox notation}} | For an N-ad in N voices, there are N! possible voicings, which are grouped into (N-1)! generalized voicings, which are grouped into (N-2)<sup>2</sup> + 1 stepspans. For an N-ad in M voices (M > N), use Stirling numbers of the second kind. | ||
{{Navbox notation}} | |||