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Math Music (english version)



On Spotify: https://open.spotify.com/album/1xetPp9OV7uYNhObcvJhF3?si=GCDLJWLZR6C43uPukisf1g

Track List

1. Moebius
2. Sator
3. Forse che sì forse che no (Corale)
4. Forse che sì forse che no (Passacaglia)
5. Forse che sì forse che no (Labirinto 1)
6. Forse che sì forse che no (Labirinto 2)
7. Kairos (fuga a 4 voci)
8. OnoraronO (Canone ruotabile)
9. S-Partiti (A)
10. S-Partiti (B)
11. S-Partiti (C)
12. S-Partiti (D)
13. S-Partiti (Alba)
14. S-Partiti (Giorno)
15. S-Partiti (Sera)
16. S-Partiti (Notte)
17. Alba (1) + Giorno (2) + Sera (3) + Notte (4)
18. Vette (Melodia frattale)

Bonus tracks

19. Sator (Da suonare al contrario)
20. S-Partiti (Moduli)

1. Two-part tonal musical piece whose upper line covers one half of the surface of a Mobius strip and the lower one (in a bass key) the other. If someone wanted to try it, the game is not as simple as it may seem: when you write, you must already consider that the final product must play well (or at least in a way consistent with the laws of traditional harmony) not only if read from the bottom towards the beginning (reversible or double-faced) but also by turning the score 180° (rotatable). In fact, since the strip cannot be oriented, it is not possible to distinguish a clockwise or counterclockwise direction: if we imagined dancing a waltz along the whole tape we would find ourselves, arrived at the starting point, turning in the opposite direction from our departure. Throwing random notes here and there and applying these rules would not result in problems of execution but nothing would make sense from the point of view of classical music theory: applying this principle to dodecaphony for example, the drafting of the piece would involve many less problems because they would eliminate all harmonic consonances or resolutions of some part movements.

Bibliography:

- L’infinito circolare. Borges, Bach, Escher: tre artefici di narrazioni perpetue, in «Punto Zero», n. 11, supplemento al n. 116 di «Nexus New Times», 2015, pp. 68-75 (parziale riedizione online il 04.11.2019 https://www.nexusedizioni.it/it/CT/escher-bach-borges-il-cerchio-la-spirale-e-leterno-ritorno-5960).
- Musica per nastro di Möbius, scheda didattica per il dipartimento formazione e apprendimento, Scuola Universitaria Professionale della Svizzera Italiana (SUPSI), 30 gennaio 2019, https://www.matematicando.supsi.ch/risorse-didattiche/musica-per-il-nastro-di-mobius/
- Musica per nastro di Möbius. Regole per la costruzione di un brano tonale reversibile, bustrofedico, bifronte e scomponibile, in «MatematicaMente», n. 256, 2 luglio 2019, http://www.mathesis.verona.it/wp-content/uploads/2018/Numeri/Nume256.pdf.



2. The way I proceeded in composing the Sator is to write a ‘demountable’ melody in modular fragments that can be recomposed at will using the anagram technique; thus it follows that each letter of the magic square corresponds to a melodic fragment included in the space of a bar. The meter that I have chosen to adopt (five quarters) respects the suggestion wanted by the magic square to be a multiple of 5: in this way also the pulsations inside the single bars maintain a correspondence with the whole. Starting from these basic elements, I hooked myself to those constituting the magic square, composing a melody that was palindrome exactly like the enigmatic Latin phrase. In turn, the same bars also contain palindromic melodic fragments. To make the work more effective, I also suggested a basso continuo movement (freely countable according to the classical canons) and also, of course, palindrome. Harmonization follows the melodic development by trying to respect all the dictates of traditional harmony.




Bibliography:

- SATOR, ovvero il quadrato magico in musica, http://www.margutte.com/?p=25467, 15 gennaio 2018.
- Sator. Composizione palindroma per strumento melodico e accompagnamento, Armelin Musica, PDM377, Padova 2016.





3. The idea from which I started is not absolutely original: I did correspond, continuing a well-established tradition in the organ world, to each letter of the famous Mantuan motto a note according to the scheme A = C, B = C#, C = D, etc., thus obtaining the upper voice that distinguishes the whole choral and that of the pedal of the passacaglia. Both tracks were harmonized by adding voices, and therefore harmonic complexity and listening difficulties, along the way.




4. See previous note.

5. To actually transform the score into a labyrinth (like the one on the ceiling of the Gonzaga building) I hypothesized to make a change of letter of the motto (and therefore of note) coincide with every right-angle turn of the path, so as to create a long melodic snake that from the entrance reaches the central room, leaving the phrase suspended on the note G. The last part of the game consisted in the attempt to recreate the original labyrinthine structure on the staff: by observing the image of the ceiling reproduced on a horizontal plane, it can be seen that from the top downwards 12 lines of walkway plus the central arrival chamber (which I converted into the 13 staves) and 13 vertical walkways from left to right (transformed into 13 quarter bars at the 13 spaces). Reading this score you will get as an obvious result a random fragmentation of the motto but also an effect of great rhythmic symmetry.


6. See previous note.


7. Years ago I happened to participate in a competition whose theme, to be developed with an art form at the discretion, was summarized by the word kairós. Kairós is a Greek term that designates time in its punctuality, the right measure, the moment appropriately suitable for the individual to carry out a project or an event (equivalent to an hour). As for the motto Forse che sì forse che no, I assigned to each of the 12 notes of the chromatic scale a corresponding letter of the alphabet (A = C; B = C#; C = D; etc.) in order to be able to form a melodic sequence with the letters of the Greek word kairós (K = A; A = C; I = G#; R = E; O = D; S = F). By chance, a subject in the key of A minor was generated with these letters with which I was able to build the 4-voice fugue.



8. Wolfgang Amadeus Mozart has been attributed a composition for two violins which respects the rule of rotation of the score and which bears the evocative title of Der Spiegel (the mirror); apart from this illustrious example, I don't think there are many others, which is why I challenged myself in an attempt to build one from scratch. The method to be used is apparently simple: to produce a melody that ‘sounds good’ not only if read by turning the score upside down (and keeping the same key and the same key armor) but which becomes walking again doing itself again. All this, however – don't forget that it is a canon – must work even if played simultaneously by two performers who mirror the score. The axis of symmetry used for rotation is the line of the staff on which the note B (third line) is located: this gives the readability of the score both on one side and on the other. Defining this type of mirror canon composition, as sometimes happens to read, is not correct: in reality the specularity is maintained only from the graphic point of view between the top and bottom of the score or between the performers-readers; by superimposing the two melodic lines that will form, however, you will notice that the parts proceed first in a parallel (and not specular) way, they continue with two completely different courses to return at the end parallel. Therefore, the name suggested by me in the past of rotatable canon would be more congenial.




Bibliography:

- OnoraronO. Canone da tavolo per due strumenti melodici, Armelin Musica, PDM358, Padova 2016.
- Geometria e musica. Si può leggere uno spartito ruotandolo di 180°?, http://www.margutte.com/?p=27078, 29 maggio 2018.




9. All the pieces have been composed in such a way that at the end of each line, the next line of any piece continues its harmonious and melodic sense so as not to create abrupt jumps or aesthetic discontinuities. The mechanism is very simple: each song is composed of 16 bars divided into 4 lines on each page. Each line of the first page has the same function as each letter of the outermost wheel of a Lullian figure; each row on the second page can correspond to the innermost wheel and so on. From the rotation of the wheels, being each row independent of the others, and by combining the sequences obtained, different and original pieces are always born; in this way you can form 4x4x4x4 combinations of songs with only 4 scores.



10. See note no. 9

11. See note no. 9

12. See note no. 9

13. See note no. 9

14. See note no. 9

15. See note no. 9

16. See note no. 9










17. I chose to record a combination of the 256 possible ones (listenable at this link: https://www.youtube.com/watch?v=OMmaINuDMZE) mixing together the first line of the first piece, the second of the second and so on.




18. The procedure is very simple: having identified a correct panoramic photograph of the Alpi Cozie (Italy), I traced parallel lines equidistant both horizontally (so that the photograph became a large stave and the pitches of the notes were so clearly identifiable) both vertically (this system is useful for identifying note durations). At this point the first part of the game can be said to be almost at the end: it was enough to transcribe the melody generated by the main peaks of the Alps on pentagram paper and assign a meter to the song so that it could be read in time. Of course, that's not all: the creativity of a composer should now help make a random succession of notes difficult to catch, according to the most common aesthetic parameters. It was therefore a matter of harmonizing the melody by constructing sound chains (and they can be many and with a completely different effect) that 'bind' the melodic line to the best. Again we return to the basic concept that also fascinated Mandelbrot: through a correct harmonization somehow we manage to give an order to what was generated by chance. The result that I got, if not really pleasant, was certainly curious and you can listen to it on my youtube channel (https://www.youtube.com/watch?v=QrkoaAlGLxU).




Bibliography:

- La melodia delle Alpi Cozie, http://www.margutte.com/?p=26424, 23 marzo 2018.
- Montagne, musica e frattali. Come la musica di Villa-Lobos abbia anticipato la geometria di Mandelbrot, http://nexusedizioni.it/it/CT/montagne-musica-e-frattali-come-la-musica-di-villa-lobos-abbia-anticipato-la-geometria-di-mandelbrot-5320, 22 ottobre 2016.


19. Try to make this track play from end to beginning and you will find that both the melody and the harmony will remain unchanged. At this address you can find my performance on the piano: https://www.youtube.com/watch?v=3O9p9yGlcyc.


20. I recorded the first 4 bars (making up the first line of the score) of tracks 13, 14, 15 and 16 all interspersed with a pause. I did the same thing with bars 5-8 (making up the second line of the score) and so on. You can thus combine any fragment of the 4 of the first row with any of the second with any of the third with any of the fourth, thus generating 256 different melodies.





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