Bayan and 31EDO system

That's not too much to bayan to try a 31EDO (31 equal division of an octave) system.

 Баян и система 31РДО


If you already have installed on your computer Sibelius Scorch, you can be convinced by sounding score of the known piece of Dr. J. Bull, that it can adorn  repertoire for bayan. Especially for not for a while yet hypothetical tricenisinguli-bayan. Increased harmonic unity of sounding of this instrument it is possible to try to evaluate by listening to BWV 1043 MIDI model in retuning for a 31EDO system  and in timbres of recorders (are capable to support microtonal scales) and bayan.


Discussion at the forum did not indicate the complete hopelessness of this path. So it's possible to try. 


First appearance.

Fourth appearance.

Fifth appearance.


I am wilfully and independently conducting research of this tune system. Here are quoted extracts from my paragraphs.


 <<... For a long time known and almost forgot 31EDO system, has revived again in a middle of the 20-th century, due to A. D. Fokker efforts. Is paradoxical, but in it the deterioration of approximation perfect fifth on a comparison with 12/24EDO systems, results in such improving of approximations major third, and harmonic seventh, that together with a perfect octave, the average absolute error of approximations of these four primary intervals of a 7-limit just intonation (7LJI) becomes in 5 … 7 times less, than in 12/24EDO systems. It clearly specifies a possibility noticeable for hearing of an approximation to 7LJI during playing in a 31EDO system ... >>


It is a little arithmetic generating thirst of live sensations.

<<... The rational numbers of sound frequency ratios, accepted in the traditional theory of Western music, assume an elemination from a factirization of prime numbers, more 5 by magnitude. Within the framework of this theory the interval C - D, for example, can have two versions: 

C – D: 50·32·2-3= 9/8               (1)

C – D: 51·3-2·21= 10/9             (2)

It means, that the theory is constructed in the boundaries of 5LJI, which . « … is in fact the origin of Baroque tonality … ».

7LJI completely includes 5LJI, saving all known connections between its elements, and adding possibilities of a research still little-studied. In the indicated example, to two versions of an interval one more is added:

C – D: 7-1·50·30·23= 8/7           (3)

Actually 7LJI, not destroying traditions, cultivated by 5LJI, is capable to enrich them with providing additional paths of development ...>>

One from conclusions of my five years' independent researches of this tuning.

<<... It is no doubt in advantages 31EDO scale to replace by it becoming obsolete 12EDO system  to effectively approximate sounding music to 7LJI. The problem of broad introduction of the generalized keyboard, has even in current moment a rather developed support for the successful solution. This support - Russian accordion or bayan, as is known, equipped by the generalized keyboard. The mass industrial manufacturing of bayans, together with the existing and organized system of mass education of the competent performers on them, reduces a problem almost to a sole task of a replacement conventional 12EDO scale of bayan, by more approaching for 7LJI scale of 31EDO. Quite not superfluous is conceived also the mass issue of digital electronic synthesizers with generalized keyboards on a sample bayan ones and possibility of switching in different systems of tunings during performance ...>>

Mykhaylo Khramov, founder of Project COMMATOR.