Georgian Folk Music

:: Georgian Folk Music

The country of Georgia has some great weird folk music. It often has pretty complex vocal polyphony. The music is microtonal (and was even more microtonal before recent western influence). Some people will tell you it's based on a nearly equal heptatonic scale, i.e. it tends toward 7-EDO. It doesn't sound like 7-EDO to me, but I haven't heard very much. Maybe I'm listening to the wrong sources.

So what is it? How is it tuned? I don't know. Let's figure it out.

Based on some spectral measurements in "Erkomaishvili Dataset: A Curated Corpus of Traditional Georgian Vocal Music for Computational Musicology" by (Rosenzweig, Scherbaum, Shugliashvili, Arifi-Müller, and Müller, 2020), I'd say a reasonable first start at describing the music would be a scale like this:

[P1, M2, AsGrm3, P4, P5, M6, AsGrm7, P8] # [1/1, 10/9, 11/9, 4/3, 3/2, 5/3, 11/6, 2/1]

In relative degrees this is

[10/9, 11/10, 12/11] * 9/8 * [10/9, 11/10, 12/11]

with the repeated tetrachord sized like

[182c, 165c, 151c]

The scale, from the spectral analysis, clearly has a lower major second and major sixth than Pythagorean, and I've simply used the just 5-limit tunings here. The scale also has neutral 3rds and 7ths. That's my first stab at it. Let's see what other have to say.

"The Georgian Musical System" (Malkhaz Erkvanidze, 2016) describes a Georgian scale that also has a repeated tetrachord structure. My introduction to Georgian folk music was a video of Malkhaz Erkvanidze singing in and directing a trio (https://www.youtube.com/watch?v=FVxD6NB8-CI) so I'm quite curious what he has to say about the genre.

The tetrachord he presents looks like this in cents:

[172c, 154c, 172c]

Let's call this G for the Georgian tetrachord. This is a really weird tetrachord, especially since Georgians use harmonic instruments. If they had inharmonic bells and gongs it wouldn't be so crazy, but they sing, and they play strings and flutes and other harmonic instruments.

Let's try to figure out a just explanation for the tetrachord. The Georgian tetrachord looks like 7-EDO in-so-much as all of its steps are multiple of 171 cents, which the outer two intervals definitely are, but the middle step is not, and also the Erkvanidze source claims that in some scales the tetrachord appears twice alongside the usual Pythagorean acute major second at 9/8, so that we get an octave scale. How about these for just explanations:

[21/19, 12/11, 209/189] _ [173c, 151c, 174c]

[32/29, 35/32, 116/105] _ [170c, 155c, 172c]

I haven't worked much with 19-limit just intonation or beyond. I never thought there was much use for it. I hope Georgian music isn't 19-limit (or 29-limit). That would be kind of crazy. Or maybe it would be fun. I consider both of these tetrachords above to be perceptually indistinguishable from the Georgian tetrachord of Erkvanidze.

What's the just tuning of the full scale that has [G + AcM2 + G] as its tetrachord structure? If we use the 19-limit intonation of the G tetrachord, we get this scale:

[1/1, 21/19, 252/209, 4/3, 3/2, 63/38, 378/209, 2/1]

If we use the 29-limit intonation, we get this scale:

[1/1, 32/29, 35/29, 4/3, 3/2, 48/29, 105/58, 2/1]

I think the first one is ugly for its high complexity 3rd interval ratio and the second one is ugly for its high prime limit, but what can you do?

The paper goes on to describe some other scales that can be made with the Georgian tetrachord. We could have a scale that doesn't repeat at the octave like

[G + G + AcM2 + G + G]

This spans 

P4 + P4 + AcM2 + P4 + P4 = P8 + Grm7 = Grm14.

I almost wonder if I'm misunderstanding the paper's notation, such that the notated numbers aren't cents of frequency ratios, since the author simply uses [Bb, Eb] for the key signature in his staff notation, but that seems unlikely since the G tetrachord spans

[172c + 154c + 172c] = 498c

just like a justly tuned P4.

Here's an idea! The ratio of 172c to 154c is very close to 8/7. If we want an EDO to represent both of these frequency ratios, we can do fairly well if it has a step around

172c/8 = 21.5 cents

or

154c/7 = 22 cents.

This means 55-EDO or 56-EDO. I think 56-EDO makes more sense. I don't think Georgian folk music is actually based on 56-EDO, but 56-EDO does a good job of representing Erkvanidze's tetrachord.

I can't help but wonder if the Erkvanidze came up with the Georgian tetrachord by saying, "our music sounds like 7-EDO, but I want to describe it with a tetrachord structure; so which relative step of our scale can I mistune so that most of the frequency ratios are 1200/7 cents and one of them is 1200 * log_2(9/8) cents?". Perhaps not. But it sure would parsimoniously explain the origin of a tetrachord that makes no sense unless you go to 19-limit.

On the other hand, I've heard that [C, F, G] is a very prototypical chord in Georgian music, i.e. Csus4 and Fsus2, and that kind of scans if they don't have particularly consonant 2nd, 3rd, 6th, or 7th interval but they do have a nice P4 and P5.

Looking at figure 12 in "Analysis of the Tbilisi State Conservatory Recordings of Artem Erkomaishvili in 1966" by Scherbaum et al 2017, I would have guessed that the Georgian scale had a neutral sixth and a major 7th:

[P1, M2, n3, P4, P5, n6, M7, P8]

instead of a major 6th and neutral seventh that I saw in "Erkomaishvili Dataset: A Curated Corpus of Traditional Georgian Vocal Music for Computational Musicology". Also, in this source the Georgian intonation of P4 is shown to be a little sharp, like 18 cents over just. We can resolve the weirdness about which of 6th and 7th degree is neutral pretty easily: Erkvanidze tells us that Georgian music uses both disjunct and conjuct scales with the tetrachord repeated, i.e.

[G + T + G] or [G + G + T]

So the previous scale could be analyzed as

[10/9, 11/10, 12/11] * [10/9, 11/10, 12/11] * 9/8

and everything works out. Except for the slightly sharpened fourth, but I don't really care about that.

I think my superparticular tetrachord, [10/9, 11/10, 12/11], thus explains spectral data from multiple ethnographic papers, and it looks nicer than the 19-limit Georgian chord. Also despite being a nice chord with small super particular ratios, it's not a tetrachord I've seen in Arabic or Turkish or Persian music. It has a [Major, neutral, neutral] sound like an Arabic or medieval Ottoman rast, but those have an intonation more like

[9/8, 11/10, 320/297] _ [204c, 165c, 129c]

so my version of the Georgian tetrachord

[10/9, 11/10, 12/11] _ [182c, 165c, 151c]

has more equal frequency ratio sizes. Not quite 7-EDO equal, but audibly much closer to equal than Rast.

Now, I'm not positive that this is closer to the intonation of Georgian folk music than Erkvanidze's tetrachord. But it's beautiful and I hope it is. We've got three consecutive super particular ratios from the harmonic series spanning a fourth. In the disjunct tetrachord, with 9/8 below the upper tetrachord, we've got four consecutive super particulars. One intonation of makam Saba has a similar thing going on with successive super particular ratios: 

[11/10, 12/11, 13/12, 15/13]

but not including 10/9. One of Ben Johnston's scales also has a similar super-particular thing going on, but in reverse

[12/11, 11/10, 10/9, 9/8, 16/15, 15/14, 14/13, 13/12]

But the harmonic series isn't in reverse, so why not do it forwards? I think it's a very beautiful tetrachord. I hope the Georgian people like it. Or at least consider it as a possible description of their music and give me pointers if they disagee.