This week I was very pleased to receive this beautiful book in my mailbox, sent to me most generously by its author Gennadiy Kogut (b. 1944), musicologist from Ukraine, who has labored for 45 years in the field of microtonality, the majority of that time working behind the Iron Curtain, in total isolation from all resources in the field outside of the former U.S.S.R., virtually forced (in his words) "to reinvent the bicycle", attacking the fundamental problems of tuning in terms of theory, notation, instruments, composition and performance. Anyone who has undertaken these tasks knows of the tremendously great difficulties involved, and I can only imagine these difficulties compounded with a completely cloistered research environment. It is therefore with great respect and admiration for Mr. Kogut and his work that I now write this. There are also some remarkable parallels between Kogut’s work and my own, and although we have never met, I feel a kindred spirit and I hope one day we might meet.

I first became aware of Kogut’s work in April of 2001, when I attended the Microfest in Los Angeles, which also featured the presence of composer Lou Harrison (1917 - 2003), and celebrated the centennial of the birth of Harry Partch. The conference was a fantastically exciting experience — an intense mixture of lectures and performances. Of the many memorable presentations, two were given by the brilliant and controversial Brian McLaren. One of McLaren’s lectures focused on the work of Alexei Ogolevets, about whom I have just added a new page to the microtonal history section of the H-Pi website, at the suggestion of G. Kogut. Those in attendance at this particular lecture may recall that McLaren’s presentation on Ogolevets took an unexpected (or possibly quite expected?) turn, transforming into a polemical diatribe against strict adherence to theories of Just Intonation ("the lecture that was banned and supressed … etc."), but I digress! I mention this lecture, simply because there is an important connection between Alexei Ogolevets and Gennadiy Kogut. During the years just prior to his death, Ogolevets was Kogut’s mentor, and Kogut has since carried forth some of Ogolevets’s ideas as part of his own original work. Kogut’s work was the focus of the second of McLaren’s lectures. This second lecture was a straightforward presentation of one of Kogut’s papers, translated by McLaren from the original Russian, with the assistance of the author. McLaren’s English translation of this paper appears in Kogut’s book on pages 214 - 221. Additional excerpted works with some English text are included in the book, by David Finnamore, Kyle Gann, Erv Wilson, Joe Monzo, and Manuel Op de Coul, although these are not articles but useful tables, charts, and lists. The first 167 pages of the book are written entirely in Russian.

The author described the book to me by email, as follows:

"This book is written to acquaint especially musicians of the countries of the East Europe with the basic achievements and directions of development microtonal music all over the world, since this information in our countries (it: Russia, Ukraine, Belarus and all other republics of the former USSR), and also Poland, Hungary, Czechia, Slovakia, the country of Baltic etc. - practically is not present.

Therefore the book will consist of the author’s foreword, the introduction in which in particular there is a definition of the term microtonal music is the music using as the basic means of expressiveness intervals of less than 90 cents in diatonic structures (all ‘old’ diatonic structures before introduction 12-ET contained diatonic semitones in size of 90 cents), and it is less than 100 cents in other structures. The following section book (page 22) results examples of how the acoustic realities surrounding us, our thinking influence formation of those or others microtone structures. Here examples of known composers and the musicians offered those or other structures both with the countries of the West, and in the countries of the East Europe are resulted. At the end of this unit classification of structures on their characteristic properties is resulted.

On page 95 the section is devoted to problems notation microtonal music and my additional signs allowing notation up to 200 tones in an octave without especial complication of system of musical record are offered. (Today I have a little simplified this system notation and if it will be interesting to you, I can send she to you is one figure on half-pages).

[NOTE: image above is Kogut’s latest simplified notation (sent to me by email) which is not in the book. Updated June 2, 2008. A future H-Pi web page is planned which will include this image in a gallery of various notation systems used by microtonal composers]

On page 118 the section in which I have tried begins to reflect features of construction universal microtonal keyboards, and also keyboards with flexible, elastic melodic structure.

On page 130 the section with my examples of the analysis microtonal pieces of music - from folklore samples and fragments from professional compositions - up to H.Lahenmana’s small play begins.

Page 161 - the conclusion.

Further appendices follow:

1. An example of the pitch analysis, the carried out D.Finnamore.
2. Examples of construction of Lambda-matrixes at B.Hero, an example of calculation of structures at E.Wilson.
3. The appendix 3 - (made J.Monzo).
4. The appendix 4 - The anatomy of an octave made by K.Gann.
5. The appendix 5 - is clear.
6. The appendix 6 - my translation of article by McLaren Microtonal music in the USA.
7. The appendix 7 - my article submitted McLaren at conference Microfest - 2001.
8. The appendix 8 - the list microtonal music on CD (M.Op de Coul).

It followed with the list of the literature." — Gennadiy Kogut

Although I did once take a summer course in the Russian language at age 17, I learned very little and now (at more than twice that age) I have only phonetic abilities with the Cyrillic alphabet, which I had to relearn before my first trip to Bulgaria in 2005. So my understanding of the text remains far from clinical, yet I will treasure this book, as each page speaks to me very clearly with a message of tenacity and burning inspiration. Thank you, Gennadiy!

I recently read Margo Schulter’s interesting and insightful paper “Regions of the Interval Spectrum: Some Concepts and Names“. This topic is very dear to me. Obviously it is also a topic fraught with difficulty, perhaps the greatest being psychoacoustic agreement with theoretical propositions. Anyone doing work in this area relies to some extent on speculation and gut instinct, and my work is no different. Schulter wisely restricted her discussion to the realm of theory, making only a few remarks about perception.

In Schulter’s paper, assumptions about where interval ordinal categories come from are not stated; however, the categories used in the text and outlined in the conclusion suggest some assumptions. In other words, nowhere is it explicitly stated why any interval is called a “third” of some kind, or why it is “minor”. This is also lacking in the sources cited, such as the Scala web page or Dave Keenan’s web page. I have outlined my own approach to this on my website at but this takes many web pages to communicate. The next paragraph summarizes my own point of view on diatonic interval names as succinctly as possible. To get straight to the point, please skip the next paragraph.

(Diatonic intervals are derived from a Pythagorean system, but only after seven letter names of seven core tones corresponding to staff positions reflect the scale order of seven diatonic naturals, such that the ordinals are ascribed to the intervals corresponding to raw staff distance, and the interval qualities correspond to the mathematical relations of the tones when taking each tone as an origin from which to measure distances to the other tones. The spelling of an interval is correlated with its notation and hence its ordinal identity and quality, the Perfects ( 1, 4, 5, 8 ) being so named because they are used to construct the system (and they also sound beatless), major and minor ( 2, 3, 6, 7 ) so named because they are incidental to the system (and they cause beating, although the M2 does not actually beat). The traditional 3-Limit system includes 7 letters times five accidentals equaling 35 tones from double-flats to double-sharps, theoretically allowing such intervals as a quintupally augmented fourth from Fbb to Bx and its inversion from Bx to Fbb, the quintupally diminished fifth, which are never used in practice. Thirteen diatonic intervals are understood as basic building blocks; between seventeen and twenty-one intervals can be considered common, including such less commonly used qualities as augmented 6ths and diminished 3rds.)

Now, back to business… Although assumptions such as those described above are not stated in Schulter’s paper, at the outset “Pythagorean”, “pental” (which I find a much more useful term than “classic”, which is asystematic and has no clear meaning), “septimal”, et cetera are very clearly defined; however, pairs of terms which feature prominently in the text, “small” and “narrow”, and “large” and “wide” are not clearly defined, and they appear to be used interchangeably. These terms also appear to be mixed in with other terms using prefixes like “sub”, “super”, and “ultra”. I feel all such terms should be clearly defined, and their usage should be both systematic and consistent.

An interval such as a “small minor third” is clearly a modified third; that is, considered grammatically, “small” and “minor” are adjectives, and “third” is a noun. This is perfectly clear. Moreover, the adjective “small” tells us something directly about the size of this interval, which is what we are most interested in when it comes to categorizing intervals. On the other hand, a “subminor third” is also clearly a modified third, but it represents a categorically different structure and has a different meaning than a “small minor third”; in this new construction, “third” is the noun, and “subminor” is the adjective, but it is a variation of the known adjective “minor” with a known prefix “sub” which creates what is called a derivational morphological variant, that is here “subminor”. A good taxonomic system should use modifiers consistently and should not mix them with morphological variants, but more importantly, the word “sub” also means “below”, so it does not describe size but in fact position. This is confusing, and syntactically incorrect. The use of “sub”, “super”, etc. for the description of intervals should for this reason be discouraged. These terms describe position and should be reserved for single tones only. So, it makes sense to talk about a distance “from A up to sub-C”, but not a “subminor third”.

When I write “from A up to sub-C”, I am describing a distance from a Pythagorean diatonic A to a Pythagorean diatonic C which has been shifted down (sub = below) by one comma, so this interval is a minor third which has been made smaller by one comma, and so should be properly called a “small minor third”. In my system, the terms “small” and “large” are used for intervals made smaller or larger by one comma. This is simple and consistent. The terms “narrow” and “wide” are used for intervals made smaller or larger by two commas, also applied consistently. I feel strongly that use of the term “neutral” to describe intervals should be discouraged, as this word comes across as a qualitative or functional assessment or prescription rather than a description of the size of an interval, kind of like calling a minor third “sad” or “dark”. Moreover, the so-called “neutral” intervals are always doubly comma-shifted versions of some interval and so can be called “wide” and “narrow” intervals - terms which directly refer to their size. Where these are versions of major and minor intervals, the NM (Narrow Major) intervals overlap with Wm (Wide minor) intervals, such that a Wm3 and a NM3 are in fact the same interval which can be called by either name. If a qualitative or functional description is needed for such intervals, the prefix “neutral” does not accurately describe them, but the prefix “ambi” does accurately describe them, as they are derived from two qualities of a given interval and can be used to function either as a major or a minor form of that interval in a given context (here, an “ambithird”); however, such a name does not belong in the systematic taxonomy; it is just an additional possibly useful term for theoretical purposes.

In Schulter’s paper there are also variant terms using the prefix “inter”, such as “interpental” and “interseptimal” which I find meaningfully descriptive and appropriately used. There is however the problem that they bear structural resemblance to the “sub” and “super” etc. constructions used in the paper, so that they appear to be taxonomically ambiguous. This ambiguity would of course not exist if the prefixes “sub”, “super” etc. were not used for intervals, but were relegated to individual tones.

The conclusion of the paper presents an outline of intervals. In my opinion, the most interesting things in the list are the names which do not have connections with overall systemic taxonomy but are instead locally descriptive, such as the “inter” intervals. I feel that these kinds of ideas should be explored as fully as possible, and such ways of naming intervals should be available for their descriptive theoretical usefulness, but it would be helpful if they were not mixed in with systematic interval size descriptors like “large” and “small”. A “large” or “small” (comma shifted) interval may be in some “inter” category, after all.

I would rather like to see a discussion of such theoretical issues within the context of a systematically codified intervallic continuum, a foolproof intervallic universe, if you will, wherein interval names are taxonomically correct and have an internal consistency which does not interfere with the qualitative or functional taxonomy proposed in the discussion. No previously existing naming system meets this criteria, but I have defined such a system. For the past several years, the disclosure of this system has been the focus of my lectures on microtonality. For lack of a better name, I have called this system the “Hunt System”. I have outlined it online as Chapter 7 of the Systematic Music Theory pages, and set up a forum in the H-Pi Community for discussion. I invite all who are interested to join and participate.

- Aaron Andrew Hunt