Chopi Mbila Music

:: Chopi Mbila Music

Near the south eastern shore of Mozambique, the Chopi people play xylophones in large ensembles, sometimes 10 people or more, and also there are choreographed dances and whistles and flutes in concert. The xylophones, in addition to being played expertly by large, talented, and well coordinated groups, have a cool tuning. We're going to talk about it for a bit. A single one of their xylophones is called an mbila and multiple are called timbila.

The Chopi music equi-heptatonic, meaning that there are 7 notes per octaves and they're equally spaced - i.e. 7-EDO. I've heard some people claim that it's not quite 7-EDO, and I'm going to argue for a while that it totally is. 

I investigated some 7 note scales that are approximately evenly spaced, like a major scale in the temperament [P8, m3, AcA1] tuned to [2/1, 6/5, 1/1], but I don't think these are better than 7-EDO theoretically. The Chopi people explicitly try to tune their xylophones equally, and even if the frequencies are off from 7-EDO by 20 cents in either direction, that's still within normal variation of human intonation, especially when 7-EDO doesn't have pure low-limit prime harmonics besides the octave, such that you could use e.g. the 3rd or 5th harmonic to tune one of the steps.

Here's a table of tunings for one octave of mbila notes from five different Chopi communities, as reported in Hugh Tracey's "Chopi Musicians. Their music, poetry, and instruments" (1948), reproduced in Eduardo Oliveira's "Assessing the geometry and tuning properties of historical timbilas through non-destructive reverse engineering techniques", (2020). The tuning is in hertz, to the nearest 2 cents:

"Zavala": [252, 276, 304, 336, 368, 408, 456, 504] hz

"Chisiko": [256, 288, 316, 348, 384, 424, 472, 512] hz

"Mavila": [260, 284, 320, 352, 384, 424, 464, 520] hz

"Banguza": [260, 288, 316, 356, 388, 432, 472, 520] hz

"Zandamela": [276, 308, 336, 368, 408, 448, 496, 552] hz

If we divide through by the lowest frequency, we get frequency ratios over unison, which we can convert to cents and then average, giving:

[0, 176, 345, 519, 680, 854, 1027, 1200] cents

If we take octave complements, the complement scale is very close in tuning to the previous one:

[0, 173, 346, 520, 681, 855, 1024, 1200] cents

which is somewhat encouraging. The tuning between communities is not so close; for example the second scale degree ranges between:

 [157, 204, 152, 177, 190] cents

so there's like 50 cents difference, but the averages hide that, and I think that's fine. Averaging the original and the octave complement, we get

[0, 175, 346, 519, 681, 854, 1025, 1200] cents

In comparison, the 7-EDO frequency ratios are

[0, 171, 343, 514, 686, 857, 1029, 1200] cents

which only differs from the Chopi mbila tuning by like 5 cents, and that's very near the limit of human perception. So in summary: the tuning of the Chopi mbila, realtive to its tonic pitch, can vary by like 50 cents from region to region, and their tonic pitch varies from 252 hz to 276 hz by region, but when you average out the human variation, you get a scale that's basically equal to itself under octave complementation and also it's equal to 7-edo up to the precision of human hearing. Also they explicitly will tell you that they're trying to tune their scales equally and we should take that seriously. The Chopi use 7-EDO proper and not some unequal temperament that has a tempered comma in common with 7-EDO, as some microtonalists will tell you.

And this is amazing! You thought 5-limit frequencies were the bread and butter of all folk melodies, world-over? And you thought that perhaps the virtuoso middle eastern lutenists were the only people that had ever really gotten away from 5-limit melodies, at the expense of losing their harmonies? Guess again! The Chopi of Mozambique play in Seven Expletive EDO!

There are lots of xylophones across south Africa, and some of the other ones also reportedly play equi-heptatonic or equi-pentatonic scales, but this is the one I have the best evidence about and I think it's pretty solid.