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Showing posts from May, 2022

Gamelan tuning and instrumental spectra

 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

Involution in 12-note system in Western musical culture

 In pop and western classical music, from Bach to today, there are billions of pieces using the 12-note music theory system to compose. From the conservative functional harmony to the modern 4 trichords progress, things do not have big evolved in the field of diatonic. There was a big evolution from the hexatonic to the diatonic system from the middle age to the renaissance period. The transformation from meantone temperament to 12 well and equal temperament from the Baroque period, set the holy grail of 12 notes in an octave and the Twelve-tone technique (dodecaphonism) reached the maximum application of 12. Since the establishment of the 12, there has not been any big evolution. Although composers like E. Blackwood, H. Partch, W. Carlos, L. Harrison, A. Haba etc tried to make different attempts, very few gain public attention. The modern-day problem in the western music system is we are not only stuck in the 12-note system, but also stuck with the traditional functional harmony. In M

The dissonant level of triadic chords

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 Based on Sethares (2010) model to analyse the dissonant level between intervals, can also be expanded to measure the dissonant level of chords. In today's case, triadic chords, I calculated the common triads and 7th chords for comparison. Calculating the dissonant level of a chord is the sum of all the intervals in a chord (pic below). The same concept of calculating the dissonant of a note with harmonic partials. Illustration of calculating a chord Here is the calculation of the chords commonly used and sorted by the level of dissonance. The minor triad has a low dissonant level than the major. It is due to the note of the major 3rd interval is higher than the minor 3rd one. According to the equal-loudness contour, our ears are more sensitive to the higher pitch, thus, we perceive a louder tone and more dissonant. If we disregard the loudness factor of the pitch, the major and minor triad is composed with the same intervals, major 3rd, minor 3rd and perfect 5th, both of them sho

A list of Blackwood's diatonic behaviour of equal temperament

 In the succession to the previous article on Blackwood's traditional formation the relationship of a diatonic scale can be written as 5w+2h=n-TET. w, h and n must be an integer and n>w>h>0,, as the diatonic behaviour. I calculated that from 5 to 60-TET by a Python program to see which number of equal temperaments satisfy or not the diatonic behaviour. The table below is the result. If it is labelled as False, it means it does satisfy the diatonic behaviour. If it satisfies, the chart will display number of microstep of a whole tone and half tone respectively. Based on the finding below, we can see that 12-TET is the smallest amount of steps the perform the diatonic behaviour. This is the reason 12 is the most used number. The 35-TET is the last one which does not perform in diatonicly, larger than that, the number are all satisfy diatonic behaviour. The 47-TET is the smallest n-TET can perform bi-diatonic behaviour, 7 microsteps for a whole step and 6 microsteps for a wh