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Page 00000001 INTERACTIVE GENJAM: INTEGRATING REAL-TIME PERFORMANCE WITH A GENETIC ALGORITHM John A. Biles Rochester Institute of Technology 102 Lomb Memorial Drive Rochester, NY 14623-5608 http://www.it.rit.edu/~jab/ firstname.lastname@example.org Abstract This presentation will describe and demonstrate recent enhancements to GenJam, an interactive genetic algorithm jazz improviser. The most significant enhancement incorporates a pitch-to-MIDI capability, which allows GenJam to integrate human improvisations into its own improvisations. Specifically, when GenJam "trades fours" wvith a human, it listens to the human's last four measures, maps what it hears to its chromosome representation, mutates the chromosomes, and plays the result as its next four. In other words, GenJam evolves what it "hears" into what it will play in real time. Other recent enhancements are also discussed. 1 Introduction and Background GenJam is an interactive genetic algorithm that models a jazz improviser and performs as a featured soloist in the author's Virtual Quintet. Previous papers [Biles 94, Biles 96] have described GenJam's hierarchically related populations of melodic ideas, its chromosome representations for those ideas, its genetic operators for evolving new ideas, and the training of new soloists. This training is done under the guidance of a human mentor, who listens to GenJam improvise and indicates "good" or "bad" whenever so moved. The mentor's feedback is used to increment or decrement the fitness of individual melodic ideas and serves as the environment in which those ideas survive or die off. New ideas evolve by selecting the "better" ideas to be parents, breeding children using single-point crossover and musically meaningful mutation, and replacing the "worse" ideas in the population with these new children. This paper describes several recent enhancements, chief among them an interactive capability that allows GenJam to "trade fours" with a human improviser by listening to what a human plays and evolving what it thought it "heard" into what it plays in response. The subtitle of this paper, then, has two interpretations. The more obvious meaning is "the addition of real-time interactive performance to GenJam's capabilities." The more subtle meaning is "the use of genetic algorithms as a paradigm for accomplishing real-time interactivity." This second interpretation refers to the approach taken in making GenJam interactive, which was to reuse as much of GenJam's genetic infrastructure as possible. By using GenJam's existing chromosome structures, mutation operators and harmonic knowledge, we were able to build a very robust system that successfully confronts the notorious pitchtracking problems of off-the-shelf pitch-to-MIDI products. 2 Interactivity via Real-Time Evolution Figure 1 shows the high-level algorithm GenJam executes as it trades fours with a human player. The target of the pitch-to-MIDI activity is GenJam's chromosome structure for representing melodic ideas, which we term GenJam Normal Form (GJNF). Once the human's four has been mapped to GJNF, it may be mutated using any of GenJam's musically meaningful mutation operators, and the result is guaranteed to be playable over any four-bar chord sequence. By taking advantage of this highly robust representation, most of the typical pitch-to-MIDI problems evaporate, and the resulting system is highly fault-tolerant. This makes it feasible to use an off-the-shelf Human plays four bars into cheap microphone plugged into Roland GI-10 pitch-to-MIDI converter GI-10 sends MIDI events to GenJam running on host computer via Yamaha MU80 tone generator GenJam listens to MIDI events and builds chromosomes for a phrase and its four measures in GJNF Chromosomes are mutated in last 1/32 note (roughly) of human's four Mutated chromosomes are used to generate GenJam's next four as if they were part of a stored soloist Figure 1. GelJam algorithm for trading fours 232 PROCEEDINGS ICMC98
Page 00000002 pitch-to-MIDI converter, the Roland GL-l() in this case. Although the GI- 10 was desi~oned for use with a guitar, the inclusion of a microphone input allows its use with acoustic instruments like the author's trumpet. The res t of this section will focus on an exampie to help illustrate how Ge~nJam evolves a human's four into its response as it progresses through the steps in Figure 1. The example comes from measures 25-32 of Jerome Kern's All the Thzings Yout Ar~e. In the extample, the human played the first four bars of the Charlie Parker line Prince Albert over mleasures 25-28 (shown in E~igure 2). Even thougih this fotur is not spontaneous, it was chosen because it should be familiar to jazz listeners, presents some interesting rhythmic challenges for the pitch tracker. and because GenJam evolved it into a nice four played over bars 29)-32 of the tune. The four bars that the human played are notated in Figure 2 with the chords played by the rhythm section indicated for each measure. The notation in this and later fi~ures does not try to capture a swing interpretationl of the eighth notes. Fm7l Bbm'rEb Abmaj7r Figurec 2'. Pr'ince' AlbertI quote played~l overr me4asurelrs 25-28 of ~All the Th~ines You Are 'Table 1 gives the chord-scale mappings used both during the listening phase and in the playing phase. Genlam builds these maps from the chord profression for the tune, which it reads from- a data file. The maps ae used as lookup tables, where an evenlt in a measure chromosome is used as an index into the table, and the contents of the table is the corresponding pitch. During the listening phase, incoming MIDI pitches are searched for in the table. axnd the index of the closest match is used as the e 'ent in the chromosome. Durinlg thke playing phase, thle event f'romn the chromtosome is used as an index into the t~able, and the pitch fo~und at that location is usedf for the M~IDIf note-on message sent to the tone g~enerator. Bar Ichord [Scale] Pitches for new-note events 1-~14 25 Fm7 Hexatonic Minor (avoid 6~th) C Sb~ F C Aib Sb C S~b F G Abi S~b ~ 26 13brn7 Hexaltonic Minor (avo~id 6th) C Sb Eb F Ab Sb C Db Sib F' SiEb C1" - 217 Lh7 Hexatonic Mlixolydian (lavorid 4th) C Sb Sb F S Sb C Sb Sb F C S1~ C Sb 28 Ab~vaj7 Hexatonic Ma~jor (avoidi 4th) C: Sb S b Ab~ Sb C Sb S S~b 7 Sb C 259 DhIaj7 Hexatonic Majorr (avo~id 4th) C Sb Sb F Ab S~b C Sb Sb S FS~ b C Db 3(1) Gbt3 He. atonic Mixolvdian (avoid 4th) S3b Sb SFb Gb Ab Sb DC Sb S~b Sk rb 3 Ab Sb Sb Sb 3 1 Cm7 Hexatonic Minor (avoid 6~th) C S Sb F S Sb C S Sb S S- b C S 32 Bdim Whole/Hal~f DiIminished S S F S Ab S~b S Sbr S S F S Ab Sb Tarble I Cho~rd-scale~ mapprtingls for- mearsureus 25-32 o~-f All thre Thines You Area When listening to a four, GenJam-1 quatntizes each measure into 8 eighth-note-length windows, one window for eaich locus in1 a measure chromrosomle. Eigure 3 shows the chromosomes in GJJNF resultinc fromt GenJarn's listening to the Prin~te 'Albertt quote. Thre left column represents the phrase chromosome, which contains pointers to four m easure chromtosomes, in this case mne'sures 0)-3. The right column contains the four measure chromo~somes (0)-3), one measure per row, with eight loci corresponding to the eight windows in each row. Locus values of 0 are rest events, which are played by sendinl a note-off message to the tone generator. Locus v lues of 1.5 are hold events, which are played by sending no messages (holding the previous event-). Locus values fromn 1-14 are new-note evenrts, which' ae played by sending a note-off message followed by a note-on message. using the pitch found at the event's location in the appropriate scale, as described above. GJNF has the advantage of unifying pitch and rhythmic sctructures and results in four-bar phlrase~s that can be played in any harmonic s eting~. 0 9 tof 11 12 13 11 10f 9 It t4 14 13 14 13 12 12 tIl 12 I11 1 1 10) 11 15 12 12 141 1 5 0) 12 11 tO 9 15 0)1 Figurre 3. Chlromosome~cs in GJNr~F / nult frlom listeninr to~ the Pr~inlce Albert qmwterr PROCEEDINGS ICMC9823 233
Page 00000003 Figure 4 shows the chromosomes of Figure 3 played against the original chords of measures 25-29. Comparing Figures 2 and 4 reveals some of the inaccuracies in mapping the Prince Albert quote to GJNF. Some of these inaccuracies are due to the fact that GenJam can represent only eighth-note multiples, which is an obvious limitation in handling the triplets and sixteenth notes in the second measure of Figure 2. Fm7 Bbm6 E A0maj7 Figure 4. Traditional notation of GJNF in Figure 3 Other inaccuracies are due to pitch-tracking and quantization errors. All the "correct" pitches were transmitted by the GI-10, but they were often obscured by spurious notes, some of which were repetitions of correct notes and some of which were "chromatic passing tones" likely due to slurred articulation. A full-blown analysis of the MIDI signals sent by the GI-10 reveals that the 32 notes played by the author resulted in 53 note-on/note-off pairs, with three windows, none of which were in the measure containing the triplets and sixteenths, receiving four pairs. The heuristic used by GenJam to cope with extra notes is simply to select the last note-on that occurs in a window and to ignore note-offs in a window once a note-on has been received. The only way, then, that a rest event (0) can occur is if only a single note-off event is received in its window. If no MIDI events at all are received in a window, its corresponding locus in the measure chromosome will remain a hold event (15), which is the initialized value. In the last 30 milliseconds of the human's four, GenJam stops listening and performs musically meaningful mutations on some of the chromosomes in preparation to play them back as its next four. The available mutations on measure chromosomes include (1) reverse - play the loci in reverse order, similar to retrograde, (2) rotate - rotate the loci a random amount from 1 to 7 positions to the right, (3) invert - subtract the locus value from 15 and rescale the result to the pitch range of the original measure, and (4) transpose - raise or lower the new note events by a random amount. The available mutations on phrases include (1) reverse - play the measures in reverse order, (2) rotate - rotate the measures a random amount from I to 3 positions to the right, (3) repeat - select a random measure and repeat it, replacing the measure that would have been played with the repetition, and (4) sequence phrase - build a special phrase beginning with the last measure of the human's four, repeating that measure one or two more times and filling out the remainder of the phrase with other measures from the human's four. In the example, two random mutations were performed: (1) the phrase chromosome was rotated three positions to the right, and (2) measure 0 was transposed down two scale degrees. In addition, a heuristic was applied to the tpt\ted 1i I e'us\rm 1, ianging it to a \3 to make it a passing tone between its two neighbors, 12 and 14. The resulting chromosomes are summarized in Figure 5, where the left column is the mutated phrase chromosome and the right column is the reordered measures with the mutated loci in bold italic. 1 14 14 13 14 13 12 12 11 2 11 11 10 11 15 12 13 14 3 15 0 12 11 10 9 15 0 0 7 8 9 10 11 9 8 7 Figure 5. Mutated measure chromosomes in order used to generate GenJam's four Finally, the mutated chromosomes are played against the chords of measures 29-32, and the resulting four, in standard notation, is presented in Figure 6. Notice that the repeated 14's and 12's in measure 1 and the repeated 1l's in measure 2 became chromatic passing tones. The heuristic here is to look for eighth notes that repeat either the immediately preceding and/or succeeding pitch and alter them to be a half step above or below the next note. Dbmaj7 G13 Cm Bdim Figure 6. GenJam's four played over measures 29-32 234 PROCEEDINGS ICMC98
Page 00000004 3 Other Enhancements In earlier versions of GenJam, the initial populations of measure and phrase chromosomes were generated using a simple uniform random number generator. This produced soloists that sounded pretty dismal in early generations, and detracted from audience-mediated performance situations where the audience serves as a collective mentor to train their own soloist using feedback paddles [Biles 95]. To confront this issue, I developed a simple fractal generator, which generates initial populations that statistically resemble mature, well trained populations. This fractal generator is similar to the dice-based fractal generator proposed by Martin Gardner [Gardner 78] and is used to generate new-note events for measure chromosomes. The fractal generator uses two "dice," one with 0-7 spots and the other with 1-7 spots. Summing the dots on these dice yields numbers in the range 1-14, which is the required range for new-note events. After the first number is generated by rolling both dice, successive numbers are generated by rolling only one of the dice and alternating which die is rolled from one number to the next. The frequency distribution of these numbers is a ramp function that peaks in the middle (7 and 8), and the interval distribution for successive numbers skews toward small intervals, with an average of around 2 and a maximum interval of 7. In contrast, a uniform generator yields a frequency distribution that is flat and an interval distribution that averages about 7. Musically, we can say that the fractal generator tends to pick notes in the middle of the instrument's range, with intervals that average roughly a third and the maximum interval roughly an octave. This is typical for a mature, trained soloist, which means that the mentor(s) are more likely to hear rewardable moments in early generations, thereby speeding up the training process. Another enhancement to GenJam has been the gradual addition of more chord families to GenJam's harmonic knowledge base. As GenJam's repertoire has grown to its current size of 120 tunes, new chords have been added to handle increasingly esoteric harmonic situations. GenJam currently recognizes 17 distinct chord families, which are listed in Table 3 with their associated scales, assuming a chord root of C natural. Since GenJam is a strictly vertical player and maps chords to scales in a simple, context-free way, the scales selected are "safe" in that they avoid notes that may be "inappropriate" in some contexts. For example, the use of a hexatonic major scale with no fourth for tonic major chords avoids the decision of whether to use a natural or a Lydian fourth. Chord Scale Chord Scale CMaj7, C6, C CDEGAB C7#9 C Eb EG A Bb C7, C9, C13 CDEGABb C7b9 CDbEFGBb Cm7, Cm9, Cml1 C D Eb F G Bb CmMaj7 CDEbFGAB Cm7b5 C Eb F Gb Ab Bb Cm6 CD Eb F GA Cdim C D Eb F Gb G# A B Cm7b9 CDbEb F G A Bb C#5 C D E F# G# AB CMaj7# CD E F# GAB C7#5 C D E F# G# A# C7sus CDE F GABb C7#11 C D EF#GA Bb CMaj7sus CDEFGAB C7alt C Db D# E Gb G# Bb Table 3. Chord-scale mappings In summary, the use of GJNF as the target representation for pitch-tracking has led to a very robust interactive system. Indeed, the inevitable errors made in pitch-tracking are desirable since they serve to "develop" rather than misrepresent what the human plays. Any time you can turn a bug into a feature, you're on the right track! References [Biles 94] John A. Biles. GenJam: A Genetic Algorithm for Generating Jazz Solos. In Proceedings of the 1994 International Computer Music Co!ference, ICMA, San Francisco, 1994. [Biles 95] John A. Biles and William Eign. GenJam Populi: Training an IGA via Audience-Mediated Performance. In Proceedings of the 1995 International Computer Music Con ference, ICMA, San Francisco, 1995. [Biles 96] John A. Biles, Peter G. Anderson, Laura W. Loggi. Neural Network Fitness Functions for a Musical IGA. In Proceedings of the International ICSC Symposium on Intelligent Industrial Automation (IIA'96) and Soft Computing (SOCO'96), March 26-28, Reading, UK, ICSC Academic Press, pp. B39-B44. [Gardner 78] Martin Gardner. White and brown music, fractal curves and one-over-f fluctuations. Scientific American, 238(4), pp. 16-27, 1978. PROCEEDINGS ICMC98 235