Searching for New Sound - Music Composition ideas

Equal temperament, dividing an octave into 12 equal semitones has a lot of advantages. Composers can compose with all 12 keys and freely modulate to each other. However, it is disconnected from nature. It disrupted the simple ratios of third and fifth that harmonics naturally vibrating. The harmony constructed with ET is sounded slightly out of tune. Claude Vivier (1948-1983) was a Quebecois composer. His music emphasis on tone color. His writing focus on a melody by the most special of him is harmonized his melody by harmonic series. See the chord at m.24. The chord (m.24) is built from the 7th, 8th, 9th, 10th, 12th overtones of G2  (the D of 11th is omitted in the chord) He spread out the notes to smoothen the quality. However, he quantized the notes to quarter tone, it is not super accurate to the actual harmonic series. These are the overtones notated for absolute accuracy. (the digit cents. 1 cent = 1/100 of a semitone) Putting the digit on the score is not very user-friendly for

When you try to compose in a random style, writing melody with random notes or spelling chords with random notes, after you compose for a few measures you may start to find a pattern is forming itself. You can try it but It is extremely difficult. How about we pass it to the computer, in theory, a computer can generate truly random numbers but we need to set a boundary to it. For instance, we don't want the frequency or the midi note number is beyond the human audible range. In this case, to ensure the numbers are useable, we will design a pseudorandom system that satisfies one or more statistical tests for randomness but is produced by a definite mathematical procedure. This is a pure data patch that I made. The program would randomly select the notes for the gamelan scale. The fun effect is the melody is randomly generated by the program there shouldn't be any pattern. But the longer you listen to it, your brain starts to organize patterns. Very cool for a composer, just sit

If you try to understand what is equal temperament (ET) and go to Wikipedia, the article says which we divide the octave into 12 equal parts (so far so good and easy to understand) and with a ratio equal to the 12th root of 2 (12√2 ≈ 1.05946). The problem is how can we use a household calculator or the app on our phone to calculate the 12th root of 2, let alone in the age without a calculator that Chu-Tsaiyu in 1584 was the first person who calculated the ratio of ET in China. Chu only wrote the answer/result only but we can only guess his process.  Back to square 1, we divide the octave with 12 equal ratios (r), the distance between two semitones. When 12 semitone distances sum up, we arrive at the octave of the original tone. We know that an octave is the original frequency double itself. Right now hands on your calculator. Step 1, calculate the square root of 2. Step 2, calculate the square root of the answer of step 1. Step 3, calculate the cube root of the answer of step 2. There