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Create Product Set Scale Table

Source: R/consonaR.R
prodset_scale_table.Rd

Creates a scale table from a product set definition

Usage

prodset_scale_table(prodset_def, period = 2, tonic_note_number = 60)

Arguments

prodset_def

the product set scale definition. This is a list of numeric vector. Each vector is a multiset of any number of integers. For example, the prodset_def of the 1-3-5-7 Hexany is

list(c(1, 3), c(1, 5), c(1, 7), c(3, 5), c(3, 7), c(5, 7))

period

the period of the scale - default is 2.

tonic_note_number

MIDI note number of the tonic for the scale -

  • default is middle C = 60

Value

a data.table with seven columns:

  • ratio: the ratio that defines the note, as a number between 1 and period

  • ratio_frac: the ratio as a vulgar fraction (character). The ratios for this type of scale are usually irrational, so this is an approximation, computed by fractional::fractional.

  • ratio_cents: the ratio in cents (hundredths of a semitone)

  • frequency: frequency of the note given the tonic_note_number parameter

  • bent_midi: the MIDI note number as an integer plus a fraction. For example, middle C is MIDI note number 60 and middle C sharp is 61. The quarter-tone half-way between C and C sharp would have a bent_midi value of 60.5. The name bent_midi comes from the fact that a MIDI sequencer can convert the value to a regular integer MIDI note number message and a pitch bend message.

  • interval_cents: interval between this note and the previous note

  • degree: scale degree from zero to (number of notes) - 1

Examples

(hexany <- prodset_scale_table(list(
  c(1, 3),
  c(1, 5),
  c(1, 7),
  c(3, 5),
  c(3, 7),
  c(5, 7)
)))
#> Key: <ratio>
#>       ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
#>       <num> <charFrac>       <num>     <num>     <num>          <num>  <num>
#> 1: 1.000000          1      0.0000  261.6256  60.00000             NA      0
#> 2: 1.166667        7/6    266.8709  305.2298  62.66871      266.87091      1
#> 3: 1.250000        5/4    386.3137  327.0320  63.86314      119.44281      2
#> 4: 1.458333      35/24    653.1846  381.5373  66.53185      266.87091      3
#> 5: 1.666667        5/3    884.3587  436.0426  68.84359      231.17409      4
#> 6: 1.750000        7/4    968.8259  457.8447  69.68826       84.46719      5
#> 7: 2.000000          2   1200.0000  523.2511  72.00000      231.17409      0