4. Research Method
4.1 Artificial intelligence system of simulation for composer's thinking
4.1.3 Musical form style analysis of every ism composer
Beethoven has stretched the practice of functional tonality to its limit which promotes the evolution from the classic era into romanticism. His works can be generally divided into three common periods. The first period contains works prior to 1802, the last contain works after 1818, and the middle period (1802 – 1818) which is the Testament of Heiligenstadt of the watershed. The musical genre of choice for imitation for the current musical systems is focused on the middle period and only on the piano sonata. The first step in selecting the artificial intelligence is to analyze the traditional sonata form and using it as the basis to structure the sections.
Sonata Form:
Exposition: first subject transition1 second subject transition2 codetta1 Development:
Recapitulation: first subject transition3 second subject transition4 codetta2
Base on the above analysis, the musical material can be separated into 10 minor sections. Emphasizing on the hierarchical importance of each section, the artificial
intelligence network will generate the first subject and the second subject. Using the two generated subjects as the basis, the transitions and codetta will be further developed.
To further emulate composer’s inspirations, the probabilities of interval progression are arranged and fitted into a table. Using random selection to allow the relationships between consecutive-interval occurrences to be in accordance to the composer’s liking will shorten the distance in achieving close-imitation.
Interval upward probability table:
Intervallic
Table 2. The probability table of the upward interval for Beethoven style.
Interval downward probability table:
Intervallic
Table 3. The probability table of the downward interval for Beethoven style.
Nevertheless, the two dimensional progression, is only capable of representing the pitch content of a single melody. Without the concept of harmonic progression (vertical component) the imitation quality becomes pessimistic. Therefore, a large amount of classic music is analyzed for its harmonic structure and the progression is as follows: Table 4. “Row” means harmony progression; “column” means the probability of Markov Chain which can be connected with harmony progression.
The probability matrix of harmony progression connection is as follows:
I
Figure 5. The diagram of Harmonic progression Markov Chain.
Since the pitch content of the main melody is more flexible than that of the harmonic progression, when assigning harmonic and melodic progressions, rules of voice leading and first and second common-chord for modulation are designed to follow composer’s occurrence probability. The data collected are distributed among different databases and its index triggered to provide more bounding between harmonies.
The probability MARKOV chain change after analyzing more than half of the piano sonatas of Beethoven is the following table.
Probability I II III IV V VI VII I 15.909% 11.112% 25.786% 29.583% 51.111% 09.513% 36.364%
II 04.545% 12.110% 00.000% 14.286% 04.444% 11.539% 00.000%
III 02.273% 10.111% 24.214% 06.661% 02.222% 05.263% 09.091%
IV 13.636% 00.000% 00.000% 07.625% 00.000% 21.053% 00.000%
V 47.727% 21.224% 00.000% 27.559% 31.111% 10.526% 00.000%
VI 04.545% 23.220% 24.572% 06.684% 06.667% 36.842% 27.273%
VII 11.365% 22.223% 25.428% 07.602% 04.445% 05.264% 27.272%
Table 5. Beethoven’s Functional Harmony percetage in Markov Chain.
Beethoven style harmony progression connection probability matrix:
P I P II P III P IV P V P VI P VII
15.909% 11.112% 25.786% 29.583% 51.111% 09.513% 36.364%
04.545% 12.110% 00.000% 14.286% 04.444% 11.539% 00.000%
02.273% 10.111% 24.214% 06.661% 02.222% 05.263% 09.091%
13.636% 00.000% 00.000% 07.625% 00.000% 21.053% 00.000%
47.727% 21.224% 00.000% 27.559% 31.111% 10.526% 20.000%
04.545% 23.220% 24.572% 06.684% 06.667% 36.842% 27.273%
11.365% 22.223% 25.428% 07.602% 04.445% 05.264% 27.272%
P I P II P III P IV P V P VI P VII
(3)
Nocturnes style of Chopin:
Chopin is the most well known composer for his special ornamental melodies, figuration and counterpoint that are presented in his piano nocturnes, mazurkas and etudes. Chopin’s works is often regarded as an extension to the early 19th-century models and Bach’s ornamental melodies. Often there exists the blurring of tonal functions between melodies and figures while the broken chord and the contrapuntal lines provide underlying harmonic structure.
The musical genre of choice for imitation for the current musical systems is focused on Chopin’s 19 nocturnes. Nocturne is originated from the Latin word Hox, meaning the night goddess and night prayer.
The first nocturnes to be published are by pianist John Field in 1812. By year 1820 there already established certain general consistency in nocturnes, which were contributed by Field and many of his composer circles. The central idea for nocturne is to imitate the vocal style of French romance or Italian aria. This helped in the development of sustaining pedal, which allows the wide spread arpeggios to support the melody. These characteristics can be seen in Chopin’s 19 nocturnes.
Other characteristics of Chopin nocturnes are: 1. Range and interval contour of the vocal styles melodies are expanded when adapting it to instrumental styles. 2 Instrumental style melodies contain both regular and irregular meter syncopations. 3.
Despite the changes, instrumental style melodies are still capable of maintaining its vocal quality.
The current system, under the Chopin mode, place heavy emphasize on
harmonies. The same approach applies in analyzing Chopin’s nocturnes and generating the algorithms for Markov Chains. The system will use Markov Chain to select the probabilities of harmonic structure and correlating it with a corresponding melody.
The probability MARKOV chain change after analyzing nocturnes of Chopin is the following table.
Probability I II III IV V VI VII
I 25.000% 07.143% 20.000% 33.333% 16.667% 00.000% 20.000%
II 25.000% 28.571% 00.000% 11.111% 33.333% 20.000% 00.000%
III 08.300% 07.143% 20.000% 11.111% 08.333% 10.000% 20.000%
IV 08.300% 07.143% 00.000% 11.111% 00.000% 10.000% 00.000%
V 08.400% 35.714% 00.000% 11.112% 16.667% 20.000% 20.000%
VI 16.700% 07.143% 40.000% 11.111% 16.667% 20.000% 20.000%
VII 08.300% 07.143% 20.000% 11.111% 08.333% 20.000% 20.000%
Table 6. Chopin’s Functional Harmony percetage in Markov Chain.
Nocturnes style of Chopin harmony progression connection probability matrix:
P I
The probability table of upward interval:
Table 7. The probability table of the upward interval for Chopin style.
The probability table of upward interval:
Intervallic
Table 8. The probability table of the downward interval for Chopin style.
Debussy style :
Debussy’s harmony is a fusion between modality and tonality. Besides using the common modes, Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian, Pentatonic, whole-tone, and octatonic scales are also frequently used. They provide oriental flavor and tonal ambiguities especially if two are juxtaposed together.
One of the major differences between Debussy’s music and other composers’ is the structure. Debussy relied on poetry to support his musical structure. The phrases, form tends to be more fluid and adventurous.
Debussy’s melodic phrases are often fragmented and irregularly developed.
Tonal colors are often supported by the interval of 7th and 9th and often they move in parallel motion. Interval of perfect 5th is also a favorite choice to provide an oriental color style.
The current system, under the Debussy mode, emphasizes on the blurring of the tonalities. In order to achieve this Sieve theory is used to filter out unwanted intervals such as major and minor thirds, which suggest major or minor tonality. Intervals such as perfect 5th and 7th will be used more abundantly.
Equation of pentatonic of Movable Do System:
Random<=127 mod 12
RC 0 2 4 7 9 Pitch C D E G A
Table 9. Pentatonic Sieve table.
Figure 6. A part of MAX/MSP Sieve.
This MAX sieve contains the pentatonic scale. It will output the RC (residual class) 0, 2, 4, 7, and 9. All other numbers in RC will be filtered out from the right outlet.
Equation of septatonic of Movable “Do” System:
Random<=127 mod 12
RC 0 2 4 6 7 9 11 Pitch C D E #F G A B
Table 10. septatonic Sieve table.
Equation of whole tone scale of Movable “Do” System:
Random<=127 mod 12
RC 0 2 4 6 8 10
Pitch C D E #F #G #A
Table 11. Whole tone scale sieve table.
The harmonic structure is constructed with Markov Chain algorithms, which imitates the qualities of impressionism.
After analyzing a large scale of piano works by Debussy, the Markov Chain probability tables are as follows:
Probability I II III IV V VI VII
I 13.333% 28.571% 09.091% 06.667% 14.286% 16.667% 07.692%
II 20.000% 07.143% 36.364% 13.333% 21.429% 25.000% 15.385%
III 06.667% 07.143% 09.091% 20.000% 07.143% 08.333% 15.385%
IV 06.667% 00.000% 27.273% 13.333% 14.286% 25.000% 00.000%
V 13.333% 42.857% 00.000% 26.667% 07.143% 08.333% 30.769%
VI 26.667% 07.143% 09.091% 06.667% 07.143% 08.333% 07.692%
VII 13.333% 07.143% 09.090% 13.333% 28.570% 08.334% 23.077%
Table 12. Debussy’s Functional Harmony percentage in Markov Chain.
Chopin style harmony progression connection probability matrix:
P I
The probability table of the upward inteval:
Table 13. The probability table of the upward interval for Debussy style.
The probability table of the downward inteval:
Intervallic
Table 14. The probability table of the downward interval for Debussy style.