Searching for New Sound - Music Composition ideas

This blog article is a snippet of my article, for more info, please visit:  https://docs.google.com/document/d/1LGTcZN83AEFCCjSqfKJOCeIrQKVmdZ8BEUwbBSYOec4/edit?usp=sharing The partial pattern of most strings and wind instruments is in the pattern of harmonic series. In the harmonic series, the 2nd and 3rd partials combine in the ratio of a perfect fifth, 3/2. Stacking the fifth 12 times roughly returns to the original tone in octaves. The 12-ET is the tool to solve the Pythagorean comma. That is the background of why 12-ET fits normal instruments. The challenge right now is I need to build a partial pattern that fit 15-ET. Comparing 12-ET and 15-ET, intervals that line up with each other are major 3rd and octave. Current instruments with harmonic series partials sound really out of tune. The partials have to be rebuilt artificially.  The process of building the partial pattern First, calculate all the ratios of 15-ET. 15-ET 1 1.0473 1.0968 1.1487 1.2030 1.2599 1.3195 1.3819 1...

 In the string family, each member has a similar look to each others. People who do not have deep knowledge of music would call every string instrument a violin. The vibration of a string follows the harmonic series pattern. In the woodwind family, every instrument's shape and timbre is very unique, the spectrum may or may not follow the harmonic series. In short, to break down the shape of the woodwind instrument, there are three main types of shape: open cylindrical, close-ended cylindrical, conical.  For cylinder instruments like flute and recorder with both open ends, the spectra follow the harmonic series, ideally. The vibration stops at both ends resulting in a string with both ends fastened. But the vibration would still fade out after leaving the end, in other words, the length of vibration is slightly longer than the pipe itself, that is the topic of end correction. fn=n*(v/2L) For closing one end in cylindrical instruments like the clarinet, one end is stopped by a r...

For percussion containing wood or metal bars with free ends, the pattern of harmonic partials is irregular. Sethares (2010) calculated the pattern of the first 6 partials as:         f, 2.76f, 5.41f, 8.94f, 13.35f, and 18.65f P.1 Then, I calculated and draw the dissonant curve: The dissonant curve After that find the frequencies with consonant intervals, the green frequencies below come from the simple ratios from the harmonic pattern (P.1) and the blue one comes from the curve. The middle column is the ratios between each consonant step. consonant freq. ratio b/w each log(octave)/ log(r between) 220 259.2 1.178181818 4.126597564 302.5 1.167052469 4.380129661 329.6296296 1.089684726 7.878224355 362.3290203 1.099200399 7.154014395 432.8 avg 1.133529853 5.884741494 The main concept of finding the best number of equal temperaments is to capture all of the consonant steps as close as possible with limited steps within a reasonable range. (For example, 120 steps with an o...

 When an instrument is played, when put the sound into the spectrum analysis (Fast Fourier Transform), there are multiple tones sounding at the same time, which contributes to the timbre of each instrument. For most instruments, strings, winds, and voice, the frequencies of vibration follow the pattern of harmonic series. Different loudness of individual harmonics contributes to the unique timbre of each instrument. Harmonic series follows the pattern from the whole multiples of the fundamental frequency (f,2f,3f,4f,5f, etc). However, the inharmonic percussion instruments do not follow the harmonic series, thus, this pattern is called inharmonicity. The timbre, as Sethares (2010) describes, is gong-like or bell-like. The spectrum analysis of some iconic orchestral sounds can be found in my previous article . For percussion containing wood or metal bars with free ends, the pattern of harmonic partials is irregular. Sethares (2010) calculated the pattern of the first 6 partials as: ...

The mathematical way to measure the degree of dissonance uses the formulas suggested by Sethares (2010). The formulas below calculate the dissonant level of one pair of sine tones with loudness considered. To calculate the two notes with harmonics, calculate all pairs of sine tones and sum all individual results. The 53-TET (see the previous article ) can provide wider range of consonance and dissonace as well as the possibility in between. Sethares (2010), Appendix E a as loudness measure in sone f as freq. where f2>f1 x* =0.24 b1=3.5, b2=5.75; s1=0.021, s2=19 This temperament is played by a synthesizer developed in Pure Data. With the same instrument and loudness, all possible intervals, within the temperament, start from 440Hz to an octave above, 880Hz. The dissonant unit is only a relative measurement. The reason for using Equal Temperament of an octave instead of other tuning is that it can guarantee the octave is a perfect 2:1 ratio. It also echoes the sound design of the synt...