Malm quote on Japanese music structure

This is a theory that the ethnomusicologist Koizumi Fumio came up with - I think in the 70s or the like (perhaps a little earlier). It was then the first time a general music theory about all Japanese traditional music was included.

In shakuhachi terms, think of that the music often is centred around ro or re with surrounding pitches supporting that tonal centre. Around ro are such as tsu no meri, tsp, ha/ri etc. Around re you see re meri, tsu (which means this tsu can move both directions), chi no meri and chi. Try to play honkyoku with this in your mind. In most cases, it does actually fit the music.

I've always thought of it this way, re is usually the main note, ro and ri are the other two strong notes and the rest slides around them. I don't know if that's good ethnomusicology but that's my view.

Malm's formulation makes sense, although it is pretty general, maybe so it can encompass more Japanese music -- e.g. if you specify that the "above" tone is a half-step and the "below" tone is a full step, then you have a good description of sankyoku but a very dubious description of gagaku and so on.

As Kiku + Brian say, ro (D) and re (G) are very often tone centers in shakuhachi music.
For an example of moving tone centers, check out the start of Yugao. The two tone centers are ro (D) and chi (A). Then at about the "Yosuru kuruma no..." part (bottom of the second column in Chikuyusha score), the music goes:

... hi- chimeri - re - chimeri - (-) - chimeri - re - chimeri - tsu - re - (-) - tsu-ro...
... C Ab G Ab - Ab G Ab F G - f-D...

... which establishes re (G) as a new tone center before slipping down to ro (D).

Henry Burnett recently published a great article about all this: Voice-Leading Considerations In Edo-Period Jiuta-Tegotomono: A New Analytical Approach [PDF]. He argues, convincingly in my view, that at least in the case of jiuta, Koizumi's "tetrachord" theory is not as useful for analysis as a simple tonic/dominant system, where both tonic and dominant are at the center of a trichord, "supported" (to intentionally use Malm's term) by a pitch a whole step below it and a half step above. So for example with RE as tonic you get:

tsu RE u, ri RO tsumeri

One big plus of this approach is that eliminates the "moving" scale degree: tsu and tsumeri are different scale degrees with different functions (one leads up, one leads down), so there's no real need to view them as the same note expressed differently according to context.

I'm not sure how well this theory fits honkyoku, but I think it makes a lot of sense for most of the sankyoku music I've seen.

Note: Use of European-style names for pitches (D, F, etc.) and concepts (tonic, dominant, trichord, etc.) is not meant to imply that these concepts appear in exactly the same way in Japanese music, or that related European concepts also appear, or anything like that. It's just convenient shorthand.

Hi Brian

It is a theory and as other theories it is not cut in stone and can be contested just as in the article No-sword mentions. I would personally say Koizumi's theory is useful for a general understanding of how Japanese music works. It is easy for many of us all the time to think in scales.... which doesn't really make sense for other musics a lot of the time. But thinking tentrachord can help. That said - there are lots of variations and I agree that ri/ha can have an important role as well.

It has been difficult in ethnomusicology to make adequate theories to use in pure musical analysis on non-Western music as we tend to think music theory in terms of the theories available for Western classical music. But that is changing now and more and more researchers are trying to find theories for the different musical systems in the world. A great book is Michael Tenzer's Analytical Studies in World Music, Oxford University Press, 2006.