Etude

Tonal etude for piano solo. Has a short introduction and coda, which are an elaboration of I,I or I,V or V,I in the piece tonality. The rest consists of melody plus chords, starting and ending in the same tonality, but freely modulating (unprepared changes of key, which I cannot hear anyway). The melody evolves from measure to measure, using my own technique of motif multiplication, and the chords are fitted to it. Most of the time, the melody is in the right hand and the chords in the left (surprise!), but sometimes viceversa. Most of the time the chords are blocked, but often expanded as arpeggios and simple rhythmic figures.
The instruction:
perl neotod.pl parameters
will produce a score named, e.g. gminWDC and a playable midi file gminWDC.mid. In more detail, neotod.pl executes:
perl neotoca.pl @ARGV
perl neotocb.pl
copy colophon.txt+sco.txt+befaf.txt  $nam
midi $nam
		

neotoca.pl
- parses the parameter list
  rand_1234     ton_min     size_12     regular     fit
  as supplied to neotod.pl. All the parameters are optional; their interpretation is as follows:
  
  regular
  pick one of the time signatures 8/8 9/8 12/16 16/16 18/16.
  fit
  in the introduction and coda, play 16*n sixteenth notes, for some integer n (even if the main rhythm is irregular or ternary, like 9/8 )
  size_size
  size may be 8 to 18. size < 12 generates a time signature of size/8, the others generate size/16. 12/16 may be interpretaed as 3/4 with each quarter subdivided into sixteenths, or 4/4 with each quarter subdivided into triolets; both will be usually accompanied by chords lasting one quarter each.
  The irregular time signatures 10/8 11/8 13/16 14/16 15/16 17/16 are played aksak – chords rhythm is some combination of quarters and dotted quarters (eighths and dotted eighths respectively)
  rand_seed
  seed is used to initialize the random numbers generator
  ton_tonality
  tonality may be maj, min or min9. maj specifies the major mode, and the others the minor mode. Plain min uses the melodic scale, e.g.
  A min = A B C D E F# G#
  A G F E D C B A   in descending scales
  and min9 uses freely nine notes, e.g. :
  A min9 = A B C D E F F# G G#
  
  The parameters are written on the file   colophon.txt.
- creates a pair of motives, each consisting of several notes at unison, and sets the first melody to the product of these motifs – some more unisons. It selects the tonality, C major or C minor, using the parameter ton, if available. Then it builds the bass to the first measure, and writes out the results.
- for each subsequent measure
  - creates a melody draft This is made from the previous measure, by one of the variations:
    1. replace 1st motif, rebuild product
    2. replace 2nd motif, rebuild product
    3. swap the two motives, rebuild product
    4. transpose the measure
    5. cancrizans on measure
    6. mirror on measure
    7. cancrizans mirror on measure
  - if necessary, repeats the product to fill the measure.
    If the parameter regular is set, then repeat from the first note, otherwise from some arbitrary point in the product.
  - if necessary, modulates to a new key
  - makes sure the melody belongs to the key, by changing notes if necessary ( routine tosca, i.e. to scale )
  - builds the corresponding bass
    This is done based on rhythm and current key. For time signature of, say, 9/8 there will be three chords in the bass, each lasting a dotted quarter and accompanying three eights in the melody. The chords are picked from the current key chords.
    For time signature of 16/16 there will be four chords in the bass , each lasting a quarter and accompanying four sixteenths in the melody.
    For an irregular time signature , e.g. 13/16, the bass will use an aksak rhythm, say 3+2+3+3+2 ( = 13 ), so:
    
    the first chord will last a dotted eighth accompanying the first three sixteenths in the melody;
    the second chord will last one eighth accompanying the next two sixteenths;
    the third chord will last one dotted eighth accompanying the next three sixteenths;
    etc...
    Sometimes, a special aksak rhythm is generated for the measure (even in regular rhythms) and used in the bass.
  - writes results to intermediate file inte.txt
neotocb.pl
- reads the intermediate file inte.txt
- analyze the data to set piece tonality (routine analy)
  The introduction and coda are also created here, as they are built on I and V chords of the selected tonality. This step may fail, and then the driver neotod.pl increases the random seed and restarts from neotoca.pl .
- for each measure:
  decide if the chords are played below the melody (usually) or above (with small probability).
  This sets a high and a low range, one each for the melody and accompaniment.
  emit the melody
  There is little sophistication in this step, as the melody consists in notes of given pitch, all of the same duration.
  emit the chords
  A more complex routine, as the chords may be emitted:
  
  plain, as blocked chords
  as arpeggios
  brocken: e.g. G,B,D,F 3/8 ==> two chords B,D,F 1/8 G 2/8
  preceded by rests: e.g. G,B,D,F 3/8 ==> rest 1/8 G,B,D,F 2/8
- writes the 3 intermediate files:
  
  befaf.txt
  part of the score containing introduction and coda.
  sco.txt
  score between introduction and coda
  nam.txt
  the name of the piece, e.g. name = dmajRFV. In this case, the etude starts and ends in D major; the letters following are a unique identifier, to distinguish between various etudes in D major.
  
  The files colophon.txt, sco.txt, and befaf.txt will be later combined to the score called name, and then converted to the midi file name.mid. Using the example above, the end result is dmajRFV.mid.

Motif multiplication

Each note of the first motif is replaced by the second motif, transposed by that note. For the purpose of this piece, all durations, in the motives and their product, are equal, so they do not get mentioned. For example:

9 12 x 7 11 14 17 = 16 20 23 26 19 23 26 29

9 becomes 9+7 9+11 9+14 9+17 and 12 becomes 12+7 12+11 12+14 12+17. In this scheme, obviously, 0,12,24... = C, 1,13,25... = C# = D♭, ... etc, and 12 is one octave higher than 0.

Notice that both motifs above belong to C major (the notes are A C and G B D F) but the product is not in C major, because 20 = G#. If the melody is to remain in C major, it will be played

16 19 23 26 19 23 26 29 = E G B D G B D F

Alternatively, the new key will be set to A minor – one of several possibilities. In this case the melody will appear as:

16 20 23 26 20 23 26 30 = E G# B D G# B D F#

accompanied by chords of A minor.

The routine analy

This routine examines the data read from inte.txt. The measures start in either C major or C minor, then modulate freely. analy records only the mode (major or minor) and tries to find, at the end of the piece, a measure in the same mode. If found, the tonality of that measure becomes the tonality of the piece, and the etude will end with the last measure in the same tonality. If not, the program exits with an error code, to be recognized and automatically fixed by the driver.

Once the tonality has been established, analy copies the initial measures in c, suitably transposed, and prepends them to the data already in memory. If necessary, it will also transpose and append a few measures at the end of the data, so the final tonality will be heard long enough to become established.

analy then calls the routines af and bef to write the introduction and coda, which further emphasize the piece tonality.

Introduction (routine bef )

This is a straightforward presentation of the piece tonality: either the scale, or two chords: I,I or I,V or I,V7. Each of I, V or V7 may appear as a simple blocked chord, or a pair of arpeggios, one in each hand. The scale is also played simultaneously in the two hands, in the same direction or in opposite directions. For variety, rests replace some notes in the scales.

Coda (routine af )

An elaboration on the final cadence in the piece tonality: either the scale, or two chords: I,I or V,I or V7,I. Each of I, V or V7 may appear as a simple blocked chord, or a pair of arpeggios, one in each hand. The scale is also played simultaneously in the two hands, in the same direction or in opposite directions. For variety, rests replace some notes in the scales.

A pair of scales or arpeggios is followed by one final tonic chord.

Intermediate file inte.txt

0: START	0 0 0 0 x 0 0 0 0	=	0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  
cmin9 4013 8/8 2 4									tonality c minor, two beats subdivided into 4 

 60 1/8 60 1/8 60 1/8 60 1/8 60 1/8 60 1/8 60 1/8 60 1/8				eight eights unison on C=60 	
 53,57,48 4/8  53,57,48 4/8								two chords lasting one quarter each: F,A,C  F,A,C


1: new1st	7 12 x 0 0 0 0	=	7 7 7 7 12 12 12 12 				no more unison
cmin9 4013 8/8 2 4

 67 1/8 67 1/8 67 1/8 67 1/8 72 1/8 72 1/8 72 1/8 72 1/8
 55,58,50 4/8  53,56,48 4/8 


2: miror	7 12 x 0 0 0 0	=	5 5 5 5 0 0 0 0 
cmin9 4013 8/8 2 4

 65 1/8 65 1/8 65 1/8 65 1/8 60 1/8 60 1/8 60 1/8 60 1/8				melody:	F F F	F C	C C C
 50,53,57 3/8  48,53,57 2/8 53,56,48 3/8						bass:	D,F,A	C,F,A	F,Ab,C	aksak rhythm   


3: swap12	7 12 x 0 0 0 0	=	7 12 7 12 7 12 7 12 
cmin9 4013 8/8 2 4

 67 1/8 72 1/8 67 1/8 72 1/8 67 1/8 72 1/8 67 1/8 72 1/8
 48,51,55 4/8  48,51,55 4/8 

 43,47,50,53 4/8  43,47,50,53 4/8 


{	____________ new tonality ebmaj ______________ }	

4: new2nd	7 12 x 0 7 3	=	7 14 10 12 19 15 
ebmaj 1453 8/8 2 4

 74 1/8 70 1/8 72 1/8 79 1/8 75 1/8 67 1/8 74 1/8 70 1/8				melody:		D  Bb  C  G		Eb  G  D  Bb
 46,50,56 4/8  51,55,58,50 4/8								chords:		Bb,D,Ab			Eb,G,Bb,D


{	____________ new tonality cmaj ______________ }	

5: transpo	7 12 x 0 7 3	=	4 11 7 9 4 0					transpose prev. measure 3 semitones down (causes modulation from Eb major to C major)
cmaj 2741 8/8 2 4

 69 1/8 64 1/8 60 1/8 64 1/8 71 1/8 67 1/8 69 1/8 64 1/8
 57,48,52 4/8  43,47,50,53 4/8 
			.
			.

The final score

An example, with lots of commentaries, may be found here.