Searching for New Sound - Music Composition ideas

 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 reed.

To run to code, just copy and paste the code on an online python compiler, or download a python interpreter on your computer. This program automatically converts sound pressure level to loudness and calculates the dissonance level between notes with harmonics considered up to the 7th partials. First, you have to enter the fundamental frequency, the lower note you want to work with. It only accepts one frequency. There are two modes, enter 0 for drawing dissonance curve; enter 1 for calculating dissonance between two notes or even more. To calculate multiple notes (a chord), use a spacebar to separate individual frequencies. The default harmonic pattern is based on harmonic series (f,2f,3f,4f,5f,6f,7f) and sound pressure level in decibel (dBSPL) corresponds to harmonics 60, 50, 40, 40, 30, 30, 30 dBSPL respectively. You can customize the parameters in the code for inharmonic instruments like percussion, and wind. The dissonance curve drawing is based on the resolution of  2^1/120 for tw

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 octave can possibly

In order to draw the dissonant curve of a spectrum, loudness is a considered factor in the equation. The measurement of loudness in the equation is in sone. This loudness scale is based on a large number of laboratory tests in which people were asked to adjust the intensity of one pure tone until they judged it to be 'half the loudness' of another tone of the same pitch and fixed intensity. This scale is subjective based. However, the human ears respond to loudness irregularly. We are tuned to listen to the vocal range and mid-high frequency. The equal-loudness contour displays the pattern of our hearing. With the same sound pressure level (SPL), with different frequencies, the loudness we perceive is different. On the other hand, we cannot distinguish the loudness difference in high volume (high SPL); but we can sense more loudness change in lower SPL. The measurement of SPL is in Pascal and is often presented in logarithmic scale (dB), while sone is a linear scale. Sethares

 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