With the fundamentals explained in the previous point I have tried to create a free form that in general wants to emphasize the virtues of scale and instruments, like the old Toccatas. It can be considered that it is formed by three parts: a first, with accelerated series that aim to present the instruments; a second that includes two melodies of slight atonal inspiration but with an important harmonic content; the third part presents a set of monotonous series accelerated as a very long chromatic scale and the piece ends with two short melodies of symmetrical character with the most extreme instruments.
This piece is based on three foundations: 1. A musical scale that is microtonal. The starting point for defining the microtonal scale has been to get the maximum number of tones that were consonants, that is, they share the greatest possible number of harmonic frequencies. To achieve this goal the number that indicates the partitions partitions of the octave of the scale must contain prime numbers. The more, the better. Examples: 2•3 = 6 parts 2•3•5 = 30 parts 2•3•5•7 =210 parts etc. My choice has been three prime numbers: 2•3•5 = 30. But I wanted to play big and get a scale with a very considerable number of partitions (to bring to a high level the advantages that this entails: great chromatism, immense combinations, many possibilities of subscales, ...). For this I have decided to double twice the 30 divisions: 2• 2•2•3•5 = 120 Thus, the octave of the defined scale has 120 divisions. These divisions are all the same and the relation between two consecutive notes is: 2 ^ (1/120) = 1.00579. This implies very subtle differences. For example, the previous note and the one after "A 440Hz" have the following frequencies: 437.46578 Hz 440 Hz 442.5488941 Hz Undoubtedly, a tough test of distinction even for the most educated ear! In monotonous series with many notes the interesting effect of "the change without noticing it" is achieved. It is achieved that in the same octave there are up to 14 consonant notes with respect to the first note, in the sense that an important number of their harmonics coincide. A possible subscale is also the twelve-tone. 2. Musical timbres from synthesizer. Working with instruments created with computer synthesizers is the most consistent way to implant a microtonal scale with so many divisions. I have defined four different instruments from an existing op code in the Csound programming language, called "prepiano". It can be considered a synthesizer of the type "physical model" that uses complex mathematics in its definition and contains an important number of configurable parameters, such as: the number of strings struck as a cluster by the hammer, stiffness of the strings, detuning between the strings, decay and release time, mass of the hammer, frequency of the striking hammer, rubber is present or not on each string, rattle is present or not on each string, etc. The four instruments used in this piece are obtained from configuring "prepiano" with four different sets of values. 3. Musical composition through programming language. Csound has been the environment where the musical composition has been developed using the programming algorithms typical of this language (i-Time, k-Time, conditional and control structures, ...).
I am Ramon Capsada Blanch. I am from Barcelona (Spain) and I am 63 years old. My academic background is scientific and, in particular, mathematics since I am a graduate in Mathematical Sciences. Professionally I have always been a teacher of mathematics. Regarding music, I do not have a higher academic education. Therefore I can qualify me as self-taught in that field, because I have acquired knowledge on one's own initiative rather than through formal instruction.