An Analysis of a Gamelan Slendro Tuning
The tuning of Gamelan music has been poorly understood, obstructed by cultural barriers and practical difficulties. Using a few recordings of Gamelan instruments, sampled from the Javanese Gamelan ensemble at Arizona State University, we determine the frequencies of a Gamelan musical scale, and then compare whether and equal tempered scale or a just intoned scale better explain the musical intervals. We find that the frequencies match better with a specially devised just intonation scale, than with the equal tempered alternative. The measured music intervals still deviated, and we discuss some practical and stylistic reasons for this. We do make the reservation, that our specific conclusions are constrained only the the Javanese Gamelan ensemble at Arizona State University, but using other literature on Gamelan tuning, we entertain possibilities for all tuning systems in Gamelan music culture.
I received my Bachelor of Science in Economics from the WP Carey school of business at Arizona State University. During my time at ASU I took Dr Ted Solis’ Gamelan Ensemble class twice, the first time for a necessary humanities credit and the second time for my own pleasure. I am currently not a student at ASU, but Dr Solis has been generous enough to let me participate in his fall 2015 Gamelan Ensemble class.
I was not a student of music, but I am an everyday musician and I have self studied various areas of music. I would estimate that I have read about 1,500 pages of academic music material. For this paper, Harry Partch’s ‘Genesis of a Music’ has been most insightful, providing me with a good understanding of the history, mechanics, and mathematics of tuning systems from around the world.
Gamelan is a traditional style of music from Indonesia. The word ‘Gamelan’ translated into english roughly means ‘Orchestra’, but within this paper ‘Gamelan’ will refer to the music culture itself, rather than the collection of instruments. To refer to the collection of instruments I will use ‘Gamelan orchestra’. Gamelan orchestras are percussive, and largely contain gongs and metallophones1.
Gamelan orchestras, quite unlike the ensembles in other music cultures, are each uniquely tuned. There is no Gamelan-wide tuning standard, only orchestra specific tunings. This means that one could not use a Gamelan instrument from one orchestra in a another orchestra, for the instruments would not be in tune with each other. This is in contrast with European music culture, where every instrument, regardless as to what ensemble it plays in, is tuned the same. One could say, European tuning is a culture wide standard, and Gamelan tuning is an ensemble wide standard.
In addition to the great variation of tunings between Gamelan orchestras, the tuning is exclusively done by a religious class of people in Indonesia who keep essential aspects of Gamelan orchestra production a trade secret. There is no body of work from the instrument makers explaining the theory behind Gamelan tuning.
While the tuning of Gamelan orchestras are various and mysterious, there are norms and consistencies that span Gamelan music. For example, all Gamelan instruments are are in one of two tuning systems, called Slendro and Pelog. Slendro and Pelog are distinct and separate collections of tones, unlike European scales, which are subsets of a larger collection of tones (C major being an 8 tone subset of the greater 12 tones).
Metallophones being instruments with metal bars, and Gongs being instruments with metal disks.↩
Within this paper we will examine the exact frequencies of two instruments called Sarons. The Sarons examined are both in the Slendro tuning system. Each Saron spans one octave, and are one octave apart. The higher and lower octave Sarons are called Saron Barung, and Saron Demung, respectively. Each Saron contains 6 bronze bars, notated as 1, 2, 3, 5, 6 and 1 1 2. Sarons act as the primary melodic instrument in Gamelan orchestras, and come in varieties that are in higher octaves than the Barung, and lower than the Demung.
Recordings were collected from the Javanese Gamelan instruments at Arizona State University with the help and permission of Dr. Ted Solis. Starting ten minutes before a Gamelan Ensemble class, Dr Solis and I recorded two short samples, one from the Saron Barung, and one from the Saron Demung. During each sample Dr Solis would twice play through each of the 6 bars of Slendro scale, ascending from the bottom, and letting each tone ring for about 2 seconds. After each tone, Dr Solis would silence the prior bars to ensure that each bar sounded unaccompanied by the other bars.
I used the audio software Audacity to determine the frequencies of each tone in the Slendro scale. Rather than rely on Audacitys frequency determination processes, which I have found to be unreliable, I determined each frequency by a guess and check process using my ear. For each tone in the Slendro scale, I would generate a sine wave of comparable volume, and arbitrary frequency. I repeatedly played the slendro tone, and the sine wave concurrently, while adjusting the frequency of the sine wave until it was perceptually identical to that of the slendro tone. The process was is analogous to how two violinists might tune the strings of one violinists violin, to the strings on the other violinists violin, however instead of strings, it was between a recording of a Saron, and a sine wave of a known frequency.
To detect if the Gamelan recording, and the sine wave were in tune, I would observe whether or not there was ‘beating’ between the two sounds. Beating is the auditory phenomenon of two tones very close in pitch, oscillating between being in and out of phase with each other1.
When two tones of the same frequency are in phase with each other, their amplitudes at any time t are the same, and therefore combine when sounded together. Putting aside how sound reflects in a physical environment, a listener hearing two tones with the same frequency and amplitude perceives the tone twice as load than if he heard one tone at the frequency. When two tones of the same frequency are out of phase, their amplitudes at any time t are opposite, and therefore cancel out when sounded together. A listener would hear silence if two tones of the same frequency but out of phase were sounded.
When two tones are not of the same frequency, they oscillate between being in phase with each other, and out of phase with each other. For many pairs of tones, this oscillation happens on a very short time scale. For example, 100 hertz and 150 hertz complete an oscillation between being in and out of phase every 0.02 seconds (50 hertz).↩