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Tertian set

tertianSetS4.Rd

tertianSet is one of humdrumR's types of tonal data, representing Western tertian harmonies. tertianSet is a subclass of diatonicSet (and hence, struct).

This functions a generic form of tertian harmony representation, commonly used in music theory. In this representation, the root of a chord is indicated as **kern, followed by one or more quality indicators, like "CMM" (C major seventh).

Usage

tset(
  root = 0L,
  signature = 0L,
  alterations = 0L,
  cardinality = 3L,
  extension = NULL,
  inversion = 0L
)

is.tertianSet(x)

# Default S3 method
tertian(
  x,
  ...,
  Key = NULL,
  transposeArgs = list(),
  parseArgs = list(),
  inPlace = FALSE
)

Arguments

x

An atomic vector.

The x argument can be any (atomic) vectors

Key

The diatonic key used by the parser, deparser, and transposer.

Defaults to NULL, which is interpreted as C major.

Must be a diatonicSet or something coercable to diatonicSet; must be either length 1 or length(x).

transposeArgs

An optional list of arguments passed to a transpose() call.

Defaults to an empty list().

Must be a list of named arguments to transpose().

parseArgs

An optional list of arguments to the chord parser.

Defaults to an empty list().

Must be a list of named arguments to the chord parser.

inPlace

Should non-chord information be retained in the output string.

Defaults to FALSE.

Must be a singleton logical value: an on/off switch.

Details

The only structural addition, compared to diatonicSet, is the Extensions slot. This slot indicates which tertian chord members are active in the chord. There are seven possible chord members: the root, third, fifth, seventh, ninth, eleventh, and thirteenth. Every possible combination of these seven degrees is represented by a single integer, corresponding to the 7-bit representation of on/offs on the seven degrees in reverse order (13, 11, 9, 7, 5, 3, 1). For example, the integer 15 corresponds to a seventh chord: in binary, 15 is 0001111. The initial three zeros indicate that the 13th, 11th, and 9th are not part of the harmony, while the four ones indicate that the root, third, fifth, and seventh are part of the harmony. Ultimately, adding or removing a chord degree from a harmony can be achieved by adding the power of two associated with that degree:

  • Root: \(\pm 1\)

  • Third: \(\pm 2\)

  • Fifth: \(\pm 4\)

  • Seventh: \(\pm 8\)

  • Ninth: \(\pm 16\)

  • Eleventh: \(\pm 32\)

  • Thirteenth: \(\pm 64\)

tertianSet has many specific methods defined for reading/writing harmonic information.

The first quality after the root indicates the quality of the triad. Subsequent qualities, if present, indicate the quality of the 7th, 9th, 11th, and 13th respectively. Some examples:

  • M: major triad

  • Mm: dominant-seventh chord

  • MM: major-seventh chord

  • Mmm: dominant-seventh-with-flat-9 chord.

  • oo: fully-diminished-seventh chord.

Missing extensions can be indicated in their position using .. For example, E-Mm.P indicates a E-flat dominant-11th chord with no 9th. Missing members of the triad can be indicated by specifying either 5 or 3 immediately after the root, but before any quality indicators. For example, C5M indicates a C major chord with no 3rd, while G3mm indicates a G-minor-seventh chord with missing 5th.

The default quality indicators are P (perfect), M (major), m (minor), o (diminished), or + (augmented), but these can be overridden by calls to their respective arguments: for example, tertian('Cdim', diminish = 'd').

Inversions

Inversions are indicated with slash notation, with the scale degree to the right of the slash. For example, a first-inversion A major chord would be AM/3.

See also

The main way to create tertianSet S4 objects is with the tertianSet() pitch parser.

Other Tonal S4 classes: diatonicSetS4, tonalIntervalS4

Examples

romanNumerals <- c('2I', '2IV7', '1V', '2vi', '2-VI', '2iio7', '2Vb9')

tertian(romanNumerals)
#> [1] "CM"   "FMM"  "GM"   "Am"   "AbM"  "Dom"  "GbMm"
tertian(romanNumerals, Key = 'A:')
#> [1] "AM"   "DMM"  "EM"   "F#m"  "FM"   "Bom"  "EbMm"

B075 <- readHumdrum(humdrumRroot, "HumdrumData/BeethovenVariations/B075_00_05_a.krn")
#> Finding and reading files...
#> 	REpath-pattern '/home/nat/.tmp/RtmpBDgnJw/temp_libpath28db92437ebb13/humdrumR/HumdrumData/BeethovenVariations/B075_00_05_a.krn' matches 1 text files in 1 directory.
#> One file read from disk.
#> Validating one file...
#> all valid.
#> Parsing one file...
#> Assembling corpus...
#> Done!
with(B075[[,2]], tertian(Token))
#> [1] "FM"  "FM"  "CMm" "FM"  "BbM" "CMm" "FM"