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...

 There are two major tuning in Gamelan. Slendro scale note 6 1 2 3 5 6 cents 0 231 474 717 955 1208 Pelog scale note 1 2 3 4 5 6 7 1 cents 0 120 258 539 675 785 943 1206 The "scale" concept here is different from the Western. The western scale can modulate or transpose to other keys, like G major scale to D major scale, and the harmonic function. In gamelan, the scale here indicates the fixed set of notes on instruments, and does not implies modulation and harmonic concept. In my theory, I would prefer to call  Slendro "tuning" rather than "scale" to separate the concepts, though scholars use both words to refer to each other. The slendro tuning is similar to a 5-equal temperament. According to Sethares (2010), this pattern lines up with the harmonic partial when an F and G bonang play together, constructing the slendro tuning. The banang is a bell-like metallic instrument. It does not vibrate in harmonic series. That is the reason the octave is off, 12...

 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...

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...