Gamelan tuning

Why can two gamelan orchestras built in neighbouring villages never be played together?

Two villages a few kilometres apart each own a gamelan — a set of tuned bronze metallophones, kettle gongs and hanging gongs. Both play the same repertoire, in the same idiom, from the same tradition. Bring an instrument from one to the other and it will not fit: the tones land in the wrong places, and the shimmer the ensemble depends on turns into a wobble.

The reflex is to call one of them out of tune — but which, and against what? A violinist arriving in a strange orchestra tunes to the oboe and joins in within seconds. What is different here, and is the difference a failure of standardisation or the right answer to the problem these musicians have?

Begin with the instruments, because the physics constrains everything after. The pitch of a bronze bar or kettle gong is set by its mass, dimensions and stiffness; the smith adjusts it with hammer and file, and then it is finished. A player has no pegs, no slide, no embouchure, no reed. Whatever agreement happens must happen at manufacture, and cannot be renegotiated in the hall.

Ask next what the smith is tuning to. Here is the first surprise: there is no external reference to hit. The set is tuned to itself — the tones placed so the intervals within it sound right to maker and patron, the whole then named and treated as a single object. Instruments are not stock parts drawn against a specification; they are members of one commissioned set.

Does that leave the intervals free? Largely, within a tradition. Javanese and Balinese practice use two systems: slendro, five tones to the octave, and pelog, seven unequal ones. Slendro is often called roughly equidistant, and it is worth seeing what that would mean. The cent is defined so an octave is 1200 of them, so five equal steps would be 240 cents each. An equal-tempered whole tone is 200 cents and a minor third 300, so a 240-cent step sits between two things a piano can play and equals neither. The sharper point is that no real gamelan is exactly equidistant, and measured sets differ by far more than an orchestra's tuning disputes. Those deviations are part of a set's character, not errors in it.

Now the second surprise, which makes swapping instruments hopeless rather than awkward. Many gamelan, Balinese sets especially, are tuned in deliberately mismatched pairs: two instruments meant to play the same part are set slightly apart in pitch, so sounding them together produces beating — the pulsing that two near-equal frequencies create, at a rate equal to their difference. Bars at 440 and 443 cycles per second pulse three times a second. That shimmer, called ombak, "wave", is not tolerated but specified.

So an incoming instrument must land on this set's tone positions; and if it belongs to a pair, it must be mistuned from its partner by this set's amount, in this set's direction. Two independent conditions, both fixed in metal, neither adjustable.

That answers the mechanical question. The interesting one is why no standard ever arose — and standardisation pays only where parties must interoperate. These two gamelan never play together: the repertoire has no piece calling for it, and each set belongs to a place. No cost is incurred by the difference, and there is a benefit, since a set with its own tuning is recognisably itself.

The comparison first. This looks like the same problem as Concert pitch standard, and at one level it is: fixed-pitch instruments needing to agree. The fixed point of difference is the size of the group that must interoperate. Orchestral practice had a real coordination failure to solve, because players, repertoire and instruments circulated between ensembles and across borders, so the cost of disagreement was continuously paid. In gamelan the interoperating unit is the single set, so the efficient number of standards is one per set — and a shared anchor frequency would not even help, because the sets differ in their intervals and not only in where they start.

Second, the beating is physics and the taste for it is not. Two tones a few cycles apart genuinely pulse at their difference, for reasons Musical consonance works through; that happens to any ear. What is conventional is which rate counts as beautiful, and that a controlled mistuning is part of being in tune. A listener raised on one set often reports a neighbouring set as slightly wrong — familiarity talking, not a judgement about the metal.

Third, the honest limits. Published interval measurements show large variation, but I will not quote cent values from memory: reported figures vary by researcher, region, and which instrument was measured, and I will not date when the systems took their present form. There are also reported cases of gamelan tuned to external references — sets built for conservatories, recording, or playing alongside Western instruments — which fits the argument rather than breaking it: the standard appears exactly where interoperation is suddenly required.

What would show the account is wrong? Swap instruments between sets and you should find tone positions displaced and pair beat rates at the wrong frequency, measurable in cents and cycles per second; and wherever ensembles have had to play together, convergence should appear. The refuting observation: sets across a region agreeing within a few cents, instruments moving freely between them — which would make the barrier a social convention about ownership rather than anything acoustic.

• How gamelan built for conservatories and cross-cultural work choose a reference, and what those sets give up.
• Why octaves in some sets are reported as deliberately stretched, and what that does to the beating.

Every term the collection defines is gathered in the glossary.