Fig 1.
Data flow from multi-track MIDI files to RAMEAU intermediate processing files for subsequent generation of fingerprints, barcodes and the alignment as used for tree generation.
A. Data flow from a MIDI input file to a pcs listing (all in UTF-8 encoding format). [MID: MIDI; the input files must follow the multi-track MIDI standard (v. 1); RDL: Reduced Data Listing files provide all basic information required for analyses based on VPS files, supplying all information concerning tone = pitch (as MIDI note numbers), duration of tone for every track = voice; VPS: Vertical Pitch Set files include successive vertical pitch sets; PCS: Pitch Class Set files include the successive vertical pitch sets (as ‘Forte name/numbers’]. B. Data flow schema from a multi-track MIDI input file to a MAP fingerprint file and to SEQ barcode sequence data (to be copied or exported from the cmd window under local MS Windows).
Fig 2.
Schematic of creation of a fingerprint grid diagram of pcs n- pcs n+1 2-tuples.
[The consecutive pcs (corresponding to chordal links) are coded and plotted as ‘Forte name/numbers’ (i.e. pcs 1–1, 2–1 to 2–6, 3–1 to 3–12 etc.) of the initial pcsn = right hand value (x) and the name/number of the target pcsn+1 = high value (y)].
Fig 3.
Fingerprint grid diagrams of pcs n- pcs n+1 2-tuples and relative pcs abundances of examined compositional works.
[A: D. Buxtehude 1675−76; B: A. Bruckner, 1878; based on vertical pitch set links (tuples of consecutive vertical pitch class sets) coded as pitch class sets (pcs). Consecutive ordered pairs of pcs both being extentionally diatonic (incl. intentionally chromatic) (blue); both pcs being extentionally chromatic (i.e. non-diatonic) (red); a pcs being extentionally diatonic (incl. intentionally chromatic), followed or preceded by a pcs being extentionally chromatic (i.e. non-diatonic) (green). Bar charts of relative abundances of occurring pcs from pcs 1–1 to pcs 5–38 at the bottom.] Symphony no. 5 Symphony no. 5.
Table 1.
A, B, C. Examples of music compositional works from the Baroque era, the Viennese School and the Romantic era used for fingerprinting and the generation of quasi-phylogenies. [First 20 bars (without upbeat) of the first movement considered].
Fig 4.
Rooted quasi-phylogeny of the Baroque era and Romantic era (including Viennese School) by maximum likelihood based on barcode sequences of pcs links (2-tuples of consecutive vertical pitch class sets) as elements.
A. Sequences from individual works. B) Combined sequences per composer. [The alignments of the individual works are based on pcs cardinalities 1 to 6 (i.e. including pcs 1–1 to pcs 6–50 with 18,496 variables in individual barcode sequences and 36,992 variables in the combined sequences). The years indicate the dates of composition, and are based on the (final) year of the composition. In the case of compositions by Scarlatti and Couperin, no dates of composition could be found, so the year of the respective composer’s midlife has been chosen as a substitute. Bootstrap support values originate from ultrafast bootstrap approximation (value 1) and from SH-aLRT branch test (value 2)].