Creates a chord table for a combination product set scale based on an even number of harmonic factors.
Arguments
- scale_table
a CPS scale table based on an even number of harmonic factors. It will abort via
stop("number of harmonic factors must be even!")if it receives one with an odd number.
Value
a data.table with four columns:
chord: the chord expressed as colon-separated harmonics. A subharmonic chord is prefixed with a "~".degrees: the chord expressed as colon-separated scale degreeschord_index: the row number of the chord in the combination outputis_subharm: zero if it's harmonic, one if it's subharmonic.
The resulting data.table is sorted into harmonic-subharmonic pairs using
data.table::setkey.
Details
The algorithm used only works for a combination product set built from an even number of harmonic factors, so it aborts if it receives one with an odd number.
In the following, the symbol n)m is Erv Wilson's notation for the
number of combinations of m items taken n at a time. n_harmonics
is the number of harmonic factors, the resulting chords will have
choose <- n_harmonics / 2 + 1 notes. There will be
choose)n_harmonics "harmonic" chords and choose)n_harmonics
"sub-harmonic" chords.
Examples
# compute the tetrads of the 1-3-5-7-9-11 Eikosany
eikosany <- cps_scale_table(root_divisor = 33)
print(eikosany_chords <- cps_chord_table(eikosany))
#> chord degrees chord_index is_subharm
#> 1: 1:3:5:7 3:8:12:18 1 0
#> 2: /1:/3:/5:/7 2:7:13:17 1 1
#> 3: 1:3:5:9 4:8:11:16 2 0
#> 4: /1:/3:/5:/9 1:9:14:17 2 1
#> 5: 1:3:5:11 5:8:10:19 3 0
#> 6: /1:/3:/5:/11 0:6:15:17 3 1
#> 7: 1:3:7:9 6:11:15:18 4 0
#> 8: /1:/3:/7:/9 7:10:14:19 4 1
#> 9: 1:3:7:11 1:5:9:18 5 0
#> 10: /1:/3:/7:/11 0:4:7:16 5 1
#> 11: 1:3:9:11 2:5:11:13 6 0
#> 12: /1:/3:/9:/11 0:3:12:14 6 1
#> 13: 1:5:7:9 0:3:6:16 7 0
#> 14: /1:/5:/7:/9 2:5:9:19 7 1
#> 15: 1:5:7:11 1:3:10:14 8 0
#> 16: /1:/5:/7:/11 2:4:11:15 8 1
#> 17: 1:5:9:11 7:10:13:16 9 0
#> 18: /1:/5:/9:/11 9:12:15:18 9 1
#> 19: 1:7:9:11 1:6:13:17 10 0
#> 20: /1:/7:/9:/11 4:8:12:19 10 1
#> 21: 3:5:7:9 0:4:12:15 11 0
#> 22: /3:/5:/7:/9 1:5:10:13 11 1
#> 23: 3:5:7:11 9:12:14:19 12 0
#> 24: /3:/5:/7:/11 6:11:13:16 12 1
#> 25: 3:5:9:11 2:4:7:19 13 0
#> 26: /3:/5:/9:/11 1:3:6:18 13 1
#> 27: 3:7:9:11 2:9:15:17 14 0
#> 28: /3:/7:/9:/11 3:8:10:16 14 1
#> 29: 5:7:9:11 0:7:14:17 15 0
#> 30: /5:/7:/9:/11 5:8:11:18 15 1
#> chord degrees chord_index is_subharm
# compute the pentads of the 1-3-5-7-9-11-13-15 Hebdomekontany
hebdomekontany <- cps_scale_table(
harmonics = c(1, 3, 5, 7, 9, 11, 13, 15),
choose = 4,
root_divisor = 3 * 5 * 7
)
print(hebdomekontany_chords <- cps_chord_table(hebdomekontany))
#> chord degrees chord_index is_subharm
#> 1: 1:3:5:7:9 11:24:37:47:65 1 0
#> 2: /1:/3:/5:/7:/9 0:13:26:42:60 1 1
#> 3: 1:3:5:7:11 5:28:37:45:61 2 0
#> 4: /1:/3:/5:/7:/11 0:9:32:46:62 2 1
#> 5: 1:3:5:7:13 10:29:37:44:57 3 0
#> ---
#> 108: /5:/7:/11:/13:/15 1:11:40:47:55 54 1
#> 109: 5:9:11:13:15 0:9:27:41:60 55 0
#> 110: /5:/9:/11:/13:/15 10:28:37:47:66 55 1
#> 111: 7:9:11:13:15 0:7:26:46:63 56 0
#> 112: /7:/9:/11:/13:/15 11:30:37:44:61 56 1