Gamelan tuning and instrumental spectra

 There are two major tuning in Gamelan.

Slendro scale
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Pelog scale
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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, 1208 instead of 1200 in traditional western practice.

The hardest problem of studying the tuning of gamelan is each instrument has its own iconic harmonic pattern, little number of steps with an octave is impossible. I pick two iconic metallic percussion instruments, saron and gender. They are often played as melodic instruments.   Considering their harmonic spectra, both of them are quite similar. There are two ways to play gender, so 3 harmonic spectra are considered. This google sheet documented the result. Lining up 3 spectra and get an average ratio without having big divination. I found that their inharmonic spectra should better fit with the 25 TET of 1:2.1 as octave within +/- 20 cents boundary, 20 cents is not an accurate boundary. The irregular harmonic pattern is hard to get a better result in equal temperament. saron and gender use slendro tuning on some occasions. To western standards and ears, it sounds quite out of tune since the scale step does not line up with the partials of the instrument, at the same time, the explanation of the unique timbre and beating effect in gamelan music.

The pelog tuning is an unequal tuning with 7 steps. It addresses inharmonic patterns of saron and gender. The tuning steps line up quite well with the consonant ratios of saron (Sethares, 2010). Yet, the tuning of pelog is instrument by instrument, for example, different saron sounds differently region by region, thus, the tuning varies as well, same with slendro tuning.

Western musical instruments are built to fit the harmonic series, while the gamelan instruments keep the diversity of inharmonicity.

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