Converts the pitch class `pc' into an OMN pitch in the given `octave'.

Examples:

    (pc->pitch 1 4) 
     => cs4 

Expects a list of pitch class integers and returns an Opusmodus chord symbol.

Examples:

    (pcs->chord '(0 4 7)) 
     => c4e4g4 

Converts the OMN pitch `pitch' into a pitch class integer

Boulez's multiplication of chords. The intervals of `chord1' are built over every pitch of `chord2'.

Examples:

Over every pitch of the C-major triad (chord2) the fifths of chord1 is created.

    (chord-multiplication '(d4 a4) '(c4 e4 g4)) 

Notes:

Boulez, Pierre (1963) Musikdenken heute. Schott's Söhne, Mainz.

Proportional streching/shrinking of intervals.

Arguments:

• pitches: list of Opusmodus pitches

• factor (integer, float or fraction): Factor by which all but the first `pitches' are stretched or shrunk.

• round: whether or not to round the result to semitones. Must be T for now, but in future when Opusmodus supports microtonal music this might be refined.

Examples:

    (stretch-pitches '(c4 e4 g4) 2) 
      
     (stretch-pitches '(c4 e4 g4) 1.5) 
      
     (stretch-pitches '(c4 e4 g4) 2/3)   

Notes:

Boulez, Pierre (1963) Musikdenken heute. Schott's Söhne, Mainz.

Creates `number' derivates from chord following a procedure suggested by Giacomo Manzoni where the chord intervals are systematically stretched or shrunk.

Arguments:

• number (int): number of chords to generate.

• chord: list of Opusmodus pitches

• factor (integer, float or fraction): controls the interval between resulting chord pitches. If 1, the first chord interval is increased by 1 semitone, the second by 2 and so on. If 2, the first interval is increased by 2 semitones, the second by 4 etc.

Examples:

    (stretch-pitches2 5 '(c4 e4 g4) 1) 
      
     (stretch-pitches2 5 '(c4 e4 g4) 1.5) 

Notes:

Series of conferences by Giacomo Manzoni at Fiesole (Florence, Italy) School of Music from 26th of June to 1st of July, 1988.

Function for generating a chord/spectral domain. Returns all transpositions of the given spectra that fit in the given scale (i.e., all their pitch classes are contained in the scale).

Arguments:

• spectra (OMN chords): a list of untransposed spectra

• scale (OMN pitch list)

Translates a sequence of pitches into a fenv that linearily inerpolates between the pitches. Fenv values encode pitches by their corresponding MIDI note.

Variant of pitches->fenv where pitches are first translated into transposition intervals before turning them into fenvs.

Translates a fenv into a sequence of pitches. Fenv values encode pitches by their corresponding MIDI note.

Transposes pitches in sequence by their corresponding fenv value.

Arguments:

• sequence: (possibly nested) list of pitches or OMN expression

• fenv: a fenv that ranges over the full sequence; mapping of notes to fenv value by position in sequence (not temporal position); intervals are specified in semitones; intervals are rounded to their closes integer All arguments of pitch-transpose-n are supported as well.

Examples:

    (fenv-transpose-pitch '(c4 c4 g4 g4) (fenv:linear-fenv (0 0) (1 2))) 
     => (c4 cs4 gs4 a4) 

    (fenv-transpose-pitch '(c4 c4 g4 g4) (fenv:linear-fenv (0 0) (1 2)) :ambitus '(d4 a4)) 
     => (d4 eb4 gs4 a4) 

    (fenv-transpose-pitch '((q c4 e c4 g4) (h g4)) (fenv:linear-fenv (0 0) (1 2))) 
     => ((q c4 e cs4 gs4) (h a4)) 

A variant of Openmusic's `gen-rotate` for rotating individual parameters (e.g., the pitch).

Arguments:

• type (:length, :pitch, :velocity, :duration, or :articulation): the musical parameter to rotate.

• n (positive or negative int; alternatively :left or :right): how many positions to rotate.

• sequence: OMN sequence, can be nested.

Examples:

    (rotate-parameter :pitch -1 '((q f3 q ab3 e c4 bb3 ab3 g3))) 

NB: Openmusic's `pitch-rotate` does something rather different.

My version of pitch-retrograde that is working until the original is fixed for OMN expressions with flattened input.

This function is similar to the build-in function `ambitus-field', but this function only compresses or expandes a given sequence without transposing it (the originally lowest or highest pitch remains unchanged). Therefore, instead of a range only an interval is specified (by an integer).

Arguments:

• interval (int): resulting ambitus interval.

• sequence: OMN sequence, can be nested.

• direction (either :keep-low or :keep-high): whether the lowest or highest pitch is kept unchanged.

• section (list of ints or nil): sublists (bars) to process. Arg is ignored if `flat' is T.

• flat (Boolean): whether or not a flat list is processed.

• omn (Boolean): whether or not to force OMN style output.

Examples:

    (set-ambitus 12 '(q bb4 a4 c5 b4)) 

    (set-ambitus 12 '(q bb4 a4 c5 b4) :direction :keep-low) 

If interval is a negative number, the music is inverted, while the kept highest note is now the lowest (or vice versa, depending on `direction`).

    (set-ambitus -12 '(q bb4 a4 c5 b4)) 

Special case: if interval is 0, then the original sequence is returned (instead of forcing all pitches to the same note).

    (set-ambitus 0 '(q bb4 a4 c5 b4)) 

Variant of set-ambitus that contracts or expands the existing ambitus of seq by interval

Inverts the pitches of given sequence by preserving its original overall ambitus (instead of inverting around its first pitch or some given pitch).

Examples:

    (invert-in-ambitus '(c4 e4 g4)) 
     => (g4 eb4 c4) 

Contrast: `pitch-invert' inverts around first note of `sequence'.

    (pitch-invert '(c4 e4 g4)) 
     => (c4 gs3 f3) 

Processing of full OMN sequences supported.

    (invert-in-ambitus '((q c3 ff snap+gliss q g3 cue) (-e s e3 > pizz gs3 > pizz g3 > pizz e3 > pizz eb3 > pizz gs3 p pizz) (h c4 f pizz))) 

This functions conveniently combines several common pitch variation techniques that retain a high degree of recognisability to the original input.

The input `sequence' for this function could be generated, e.g., with the function `alternate-omns' such that more remote variations are controlled with `alternate-omns' and closer variations with the present function.

Arguments:

• sequence (OMN expression that is either flat, single or double nested): input music. Double nesting is supported to allow for processing sections/motifs that consist of multiple bars.

• transposition (int, or list of ints): transposition interval of individual resulting motifs/sections

• ambitus (int, or list of ints): ambitus interval of resulting motifs. The lowest pitch of a motif is not affected by this argument, only its highest pitch, as the lowest pitch change be shifted separately with the transposition interval. Negative values result in an inversion of a motif. If 0, ambitus processing is skipped.

• invert (0, or 1, or list of such binary numbers): binary numbers indicate whether motifs are inverted or not

• append? (Boolean): whether or not nested OMN sequences should be appended instead of been combined in a list.

If you need more detailed control (e.g., a section argument for some of the variations), then simply use the original build-in function like pitch-transpose, pitch-invert and ambitus-field (or set-ambitus).

Examples:

    (setf motif '((q c3 ff snap+gliss q g3 cue) (-e s e3 > pizz gs3 > pizz g3 > pizz e3 > pizz eb3 > pizz gs3 p pizz) (h c4 f pizz))) 

    (close-variations (gen-repeat 3 (list motif)) :transposition '(0 12 2) :invert? '(0 1 0) :append? T) 

    (close-variations (gen-repeat 3 (list motif)) :transposition '(0 1 2) :ambitus '(12 11 10) :append? T) 

Increases rhythmic interest by subdividing all notes that meet the function test and turning these into a trill.

Arguments:

• sequence: nested OMN sequence (if sequence is not nested, an additional list is implicitly thrown around it)

• test: function expecting four arguments of a given note, its length, pitch, velocity and articulation.

• interval: integer specifying size and direction of trill interval (positive is up, negative is down).

• ignore-articulations: list of articulations not to repeat at inserted notes.

Examples:

    (trill-selected-notes '((q c4 e e) (q d4 e e)) (make-is-trill-length? 'e)) 
     => ((q c4 mf 1/16 c4 mf 1/16 d4 mf 1/16 c4 mf 1/16 d4 mf) (q d4 mf 1/16 d4 mf 1/16 e4 mf 1/16 d4 mf 1/16 e4 mf)) 

[Helper function for trill-selected-notes] Returns a function to be used as `test' argument for function `trill-selected-notes'. The returned function returns true for all notes of the given `length'.

Builds `chord' over or under every note in `sequence'.

Arguments:

• sequence (OMN sequence)

• chord (OMN chord or list of chords): if a list, the chords are circled through.

• position (either :top or :bottom): whether the pitches of `sequence' are the top or bottom pitch of the transposed chords.

Examples:

    (line->chord '(h c4 ten q d4 stacc e4 stacc) 'c4e4g4) 

    (line->chord '((h c4 ten) (q d4 stacc e4 stacc)) 'c4e4g4 :position :bottom :section '(0)) 

Using a list of different chords

    (line->chord '(h c4 ten q d4 stacc e4 stacc) '(c4e4g4bb4 c4e4a4 c4)) 

Transforms chords in `sequence' into single notes, extracting the chord pitch at `position' (or the closest pitch, if there is no pitch at `position').

Arguments:

• sequence (OMN seq)

• position (0-based integer)

Examples:

    (chord->line '((h c4e4g4 q) (h.)) 0) 

    BUG: What to output in case of rests -- a rest (which I would expect) or a pitch? See example above... 

Variant of built-in function `ambitus-field': this function compresses or expanded the pitch range of the given `sequence', and the boundaries how much this compression/expansion happens can be changed over time with fenvs or value lists. This is a useful function for shaping musical results.

Note that a change of ambitus values happens only per sublist (bar), which is not really a restriction, as multiple pitches are required to fill a given range.

If you plan to harmonically revise your music (e.g., with `tonality-map') then you obviously better apply this function before the harmonic revision.

Arguments:

• sequence (nested OMN expression)

• ambitus-low (fenv or list of integers or pitches): specifies the evolving lower boundary

• ambitus-range (fenv, int or list of ints): specifies the evolving distance between the lower and upper boundary

• chord-ambitus (integer): max interval between lowest and highest tone of chords to restrict chords to playable range for keyboard player.

If the argument section is given, then only `(length section)' samples are taken from ambitus-low ambitus-range (if these are fenvs). In other words, in that case the fenv does not range across the full `sequence', but only the selected sections.

Examples:

Static ambitus-range

    (ambitus-field-fenv (gen-repeat 4 '((q c4 e4 g4))) 
     		    (fenv:linear-fenv (0 0) (1 12)) 12) 

Evolving range

    (ambitus-field-fenv (gen-repeat 4 '((q c4 e4 g4))) 
     		    (fenv:linear-fenv (0 0) (1 12)) 
     		    (fenv:linear-fenv (0 12) (1 4))) 

Note that the spread of chords is adapted to the given range

    (ambitus-field-fenv (gen-repeat 4 '((q c4e4g4 b4))) 
     		    (fenv:linear-fenv (0 0) (1 12)) 12) 

    (ambitus-field-fenv (gen-repeat 4 '((q c4e4g4 b4))) 
     		    (fenv:linear-fenv (0 0) (1 12)) 7) 

However, the spread intervals within chords is automatically adapted to stay within a keyboard players hands.

    (ambitus-field-fenv (gen-repeat 4 '((q c4e4g4 b4))) 
     		    (fenv:linear-fenv (0 0) (1 12)) 25) 

This setting can be adjusted with the argument `chord-ambitus'

    (ambitus-field-fenv (gen-repeat 4 '((q c4e4g4 b4))) 
     		    (fenv:linear-fenv (0 0) (1 12)) 
     		    25 :chord-ambitus 15) 

Expects an OMN sequence (or a different format, see below), and returns a *flat* list of floats representing the associated melodic accent value of each pitch as defined by the Thomassen model.

Arguments:

• format (keyword): sets the format of `sequence'.

  • :omn - full OMN sequence, possibly nested (though the result will be flat)

  • :pitch - list of OMN pitches, possibly nested

  • :midi - list of MIDI note numbers

Note that no accent values are available for the first two and the last pitch, therefor nil is return for those pitches.

Notes:

Hack: Quick evaluation: strong melodic accents have an accent value greater than 0.4.

• Thomassen, J. M. (1982) Melodic accent: Experiments and a tentative model. The Journal of the Acoustical Society of America. 71 (6), 1596–1605.

• Huron, D. & Royal, M. (1996) What is melodic accent? Converging evidence from musical practice. Music Perception. 489–516.

Return the given major or minor triad in root position.

Arguments:

• triad (OPMO chord): a major or minor triad of exactly three pitches in any position

Examples:

    (triad-in-root-position 'e4g4c5) 

=> c4e4g4

NOTE: Result currently always in close position.

    (triad-in-root-position 'e3a4c6) 

=> a2c3e3

BUG: Currently the pitch order must be in some rotated from of root, third, fifth. The following is currently not supported.

    (triad-in-root-position 'a2e5c6) 

=> c4e4g4

Change the chord type of a give triad to the specified chord type.

Arguments:

• triad (OPMO chord): a major or minor triad of exactly three pitches in any position

• chord-form (list): a chord name symbol or a chord form as expected by expand-chord: (chord &key variant rotate add remove mod assoc seed row)

• preserve-quality? (Boolean): not only the root, but also the third of the triad is preserved.

Examples:

Change a minor chord into an added sixth major chord

    (chord-over-triad-root 'eb4g4c5 6) 

=> c4e4g4a4

Change a minor chord into an added sixth minor chord (preserve its third)

    (chord-over-triad-root 'eb4g4c5 6 :preserve-quality? T) 

=> c4eb4g4a4

Added chord form keys are supported

    (chord-over-triad-root 'eb4g4c5 '(6 :rotate 1)) 

=> e4g4a4c5

Arguments:

• pitch (OMN pitch): pitch to start from.

• interval+chord-form (list of int and chord-form): progression interval from previous chord and Opusmodus chord-form ;; ;; TODO: later also support symbols, e.g., for Schoenberg's chart of regions ;; - transition (fraction or int) ;; - chord-form (list): a chord name symbol or a chord form as expected by expand-chord: (chord &key variant rotate add remove mod assoc seed row)