[Smt-talk] Proximity between keys

[Ninov, Dimitar N]

Dear Ildar and the List,

I just reviewed that  in the Dubovskii/Evseev book. Of course, it makes sense to me.  But since this system is heterogeneous, as you point out (for instance, it separates some of the relative keys into two different groups  (A major is closer to C than F-# minor), years ago I decided  to simplify this by combining levels three  and four into one level (this is how we studied it in the conservatory), knowing that some of the keys in there are closer to one key than others, because they have an immediate common triad from a harmonic mode. 

Also, by including the N, and the chromatic mediant triads (bVI and bIII in major), and occasionally bVII, there is always a direct and smooth link between any two remote keys. For instance, an immediate connection between C major and F# (fourth degree of proximity) is the dominant of C which is N in F#, and the dominant of F# which is N in C. Since the N is a great and frequent chord, it serves as good a role as any minor S in major or major D in minor. Therefore, I dropped the necessity to separate A major from F# minor in terms of their relations to C, for example.

So far I was talking about a modulation by a common chord (diatonic or borrowed) between any two keys, no matter how remote they are. Such modulations could be as smooth as any modulation between close keys. When it comes to a gradual modulation from X to Y, using a transitional key Z, then the Russian system comes forward as a practical tool, suggesting how we can eliminate quickly the number of accidentals and move towards the goal in the smoothest manner. Rimsky goes into a great detail in this. However, Rimmsky's system is still a little different than the system described in the Russian book I mentioned. Besides, neither he, no any other author mentions the fact that two remote keys may be connected directly via  common chord in a smooth manner. This I learned from my profession Bentzion Eliezer, who thought us to quickly discover a link by any two keys.  Then I realized that N and the flat mediants (and even bVII) were quite frequently used as common chords between remote keys and the things clicked in place.

Thanks,

Dimitar


Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666