Musical scales

Programming with musical scales can be assisted by a collection of functions in tabr that check and manipulate musical scales, modes and key signatures.

Key signatures

For key signatures, keys lists valid key signature abbreviation strings for each key as used in tabr. There are several key_is_* functions that return a logical result regarding properties of keys:

key_is_natural()
key_is_sharp()
key_is_flat()
key_is_major()
key_is_minor()

There are also the functions, key_n_flats() and key_n_sharps(), that give the number of respective accidentals in a key signature.

keys()

#>  [1] "c"   "g"   "d"   "a"   "e"   "b"   "f#"  "c#"  "f"   "b_"  "e_"  "a_" 
#> [13] "d_"  "g_"  "c_"  "am"  "em"  "bm"  "f#m" "c#m" "g#m" "d#m" "a#m" "dm" 
#> [25] "gm"  "cm"  "fm"  "b_m" "e_m" "a_m"


key_is_flat("f")

#> [1] TRUE

key_n_flats("f")

#> [1] 1

The previous section gave an overview of noteworthy strings. While some of the functions that help enforce proper notation in R seemed like they did not offer much utility in terms of direct use, it was clear that they were integral to the robustness of other tabr functions. Now, looking at these key signature helpers, it may be tempting to dismiss their utility even more quickly because a trained musician does not need to invoke them at the command line to know what result they will return.

These functions are not provided to answer basic questions in an interactive R session so much as they are for programming. These are some of the initial building blocks on top of which more complex functions are built, including many functions in tabr. As the collection of music programming helper functions in tabr grows, it becomes easy to do more with less.

Scales

Several predefined musical scales are provided and accessible by calling various scale_* functions.

scale_chromatic
scale_diatonic
scale_minor
scale_major
scale_harmonic_minor
scale_hungarian_minor
scale_melodic_minor
scale_jazz_minor

scale_hungarian_minor(key = "am", collapse = TRUE)

#> <Noteworthy string>
#>   Format: space-delimited time
#>   Values: a, b, c d# e f g#

You can specify whether the vector result should be returned as is, for convenient vectorized programming pipelines, or collapsed to a single string in keeping with the space-delimited time syntax format common throughout tabr. Many functions in tabr accept both formats as inputs and/or offer them as outputs.

You can also specify if octave numbering should be included or stripped. Octave numbering is included by default because this maintains pitch order when the scale does not start on C. Every note in a noteworthy string has an implicit octave-3 (the octave below middle C, C4) position if not explicitly stated. Octave numbering attempts to be somewhat balanced around C3. If the result is not what is desired, it can be shifted by 12 semitones with transpose().

scale_major("f", TRUE, ignore_octave = TRUE)

#> <Noteworthy string>
#>   Format: space-delimited time
#>   Values: f g a b_ c d e

scale_major("f", TRUE, ignore_octave = FALSE)

#> <Noteworthy string>
#>   Format: space-delimited time
#>   Values: f g a b_ c' d' e'

See help("scale-helpers") for details. Depending on the scale, other arguments are available.

Modes

The seven modern modes are also available with mode_* functions or through modern_mode() by passing the mode string name. Other functions include is_mode and rotate_mode.

mode_ionian()
mode_dorian()
mode_phrygian()
mode_lydian()
mode_mixolydian()
mode_aeolian()
mode_locrian()

modes()

#> [1] "ionian"     "dorian"     "phrygian"   "lydian"     "mixolydian"
#> [6] "aeolian"    "locrian"

mode_aeolian("c")

#> <Noteworthy string>
#>   Format: vectorized time
#>   Values: c d e_ f g a_ b_

Diatonic scale chords

The scale_chords() function provides a list of diatonic scale chords based on the root note and scale chosen. It returns triads by default and can also return seventh chords.

scale_chords("b_", "major", "seventh", collapse = TRUE)

#> <Noteworthy string>
#>   Format: space-delimited time
#>   Values: <b_,dfa> <ce_gb_> <dfac'> <e_gb_d'> <fac'e_'> <gb_d'f'> <ac'e_'g'>

scale_chords("f#", "minor", "triad", collapse = TRUE)

#> <Noteworthy string>
#>   Format: space-delimited time
#>   Values: <f#ac#'> <g#bd'> <ac#'e'> <bd'f#'> <c#'e'g#'> <d'f#'a'> <e'g#'b'>

Scale degrees

The functions scale_note() and scale_degree() map between notes and degree in a given scale. For chords in a noteworthy string, only the root note is considered. For scale_degree(), if a note is not diatonic to the scale, NA is returned. NA is also used when rests occur. Octaves are ignored. For scale_note(), degrees outside the range of the scale are recycled. See below. To see if chords are fully diatonic, use is_diatonic() or the more general is_in_scale(). chord_degree() will return a list comparable to scale_degree().

x <- "c e gb'd'"
scale_degree(x)

#> [1] 1 3 2

scale_degree(x, key = "a")

#> [1] NA  5  4

scale_degree(x, key = "am")

#> [1] 3 5 4

scale_degree(x, scale = "chromatic")

#> [1] 1 5 3


scale_note(1:7, "d")

#> <Noteworthy string>
#>   Format: vectorized time
#>   Values: d e f# g a b c#

scale_note(c(1:8), "dm", "harmonic minor")

#> <Noteworthy string>
#>   Format: vectorized time
#>   Values: d e f g a b_ d_ d


note_in_scale("a_ g#", "a_", strict_accidentals = FALSE)

#> [1] TRUE TRUE


x <- "r d dfa df#a f#ac#"
chord_degree(x, "d")

#> [[1]]
#> [1] NA
#> 
#> [[2]]
#> [1] 1
#> 
#> [[3]]
#> [1]  1 NA  5
#> 
#> [[4]]
#> [1] 1 3 5
#> 
#> [[5]]
#> [1] 3 5 7

is_in_scale(x, "d")

#> [1]    NA  TRUE FALSE  TRUE  TRUE

is_diatonic(x, "d")

#> [1]    NA  TRUE FALSE  TRUE  TRUE

Other functions in tabr also work with scales and some build upon functions introduced here.

Musical intervals

Musical intervals can be referenced by a name or a numeric value defining the separation of two notes. interval_semitones() returns a positive integer describing the number of semitones spanned by a common interval. It takes a name or abbreviation of a common interval as input. Essentially, any entry from any other column in the mainIntervals dataset can be used to obtain the interval in semitones. It’s a simple filter and match, but it is convenient to map between different representations of the same property in tabr without typing the extra bit of code to do so each time.

mainIntervals

#> # A tibble: 26 × 5
#>    semitones mmp            mmp_abb ad                                ad_abb
#>        <int> <chr>          <chr>   <chr>                             <chr> 
#>  1         0 perfect unison P1      diminished second                 d2    
#>  2         1 minor second   m2      augmented unison                  A1    
#>  3         2 major second   M2      diminished third                  d3    
#>  4         3 minor third    m3      augmented second                  A2    
#>  5         4 major third    M3      diminished fourth                 d4    
#>  6         5 perfect fourth P4      augmented third                   A3    
#>  7         6 tritone        TT      diminished fifth/augmented fourth d5/A4 
#>  8         7 perfect fifth  P5      diminished sixth                  d6    
#>  9         8 minor sixth    m6      augmented fifth                   A5    
#> 10         9 major sixth    M6      diminished seventh                d7    
#> # ℹ 16 more rows


interval_semitones(c("m3", "M7"))

#> [1]  3 11

Likely more useful for programming, the function pitch_interval() provides the number of semitones between two input notes. This function does not relate to specific scales, but is worth mentioning on the topic of interval helpers. It provides both magnitude and direction. The result is negative if the first note is of higher pitch than the second. It is vectorized and both inputs must have the same number of timesteps.

Chords can be reduced to their root note (lowest pitch) for comparison or forced to yield an NA interval with respect to its two adjacent timesteps (e.g., c to ceg is NA and so is ceg to c). Rests r and silent rests s also yield an NA for the interval from a prior note.

pitch_interval("a2", "c")

#> [1] 3

pitch_interval("c d e", "c c c")

#> [1]  0 -2 -4

pitch_interval("r c ceg c e g s", "a c d d f# a e")

#> [1] NA  0  2  2  2  2 NA

pitch_interval("r c ceg c e g s", "a c d d f# a e", use_root = FALSE)

#> [1] NA  0 NA  2  2  2 NA

Next is scale_interval(). This function is similar to pitch_interval() in that it takes two noteworthy strings, which together define an intervals element-wise. It is almost an inverse of interval_semitones() except that you provide notes rather than the semitone distance of their intervals. The function returns a main interval name or abbreviation from mainIntervals, depending on format. The results are name-only. They are not signed. Use pitch_interval() to obtain direction.

scale_interval("c c c c", "c, e g b")

#> [1] "P8" "M3" "P5" "M7"

scale_interval("a2", "c", format = "mmp")

#> [1] "minor third"

There are also lagged difference versions of these functions. You can adjust the lag with n. You can also retain (convenient for data frames) or trim the n leading NAs. This does not trim meaningful NAs like those resulting from rests.

pitch_diff("c d e f g a b")

#> [1] NA  2  2  1  2  2  2

pitch_diff("c d e f g a b", trim = TRUE)

#> [1] 2 2 1 2 2 2

scale_diff("c d e f g a b")

#> [1] NA   "M2" "M2" "m2" "M2" "M2" "M2"

scale_diff("c d e f g a b", n = 2)

#> [1] NA   NA   "M3" "m3" "m3" "M3" "M3"

Lagged intervals respect rest timesteps. All timestep positions including rests are retained, but the lag-n difference computation ignores them.

x <- "a, c r r r r g"
pitch_diff(x)

#> [1] NA  3 NA NA NA NA  7

scale_diff(x)

#> [1] NA   "m3" NA   NA   NA   NA   "P5"

pitch_diff(x, n = 2)

#> [1] NA NA NA NA NA NA 10

scale_diff(x, n = 2, trim = TRUE)

#> [1] NA   NA   NA   NA   "m7"