[Smt-talk] Proximity between Keys

[Ildar Khannanov]

Dear Dimitar ad Nicolas,

this is, probably, one of the topics that makes sense to revive from the
remote past. Thank you for bringing it up.

Russian system of kinship of tonalities is distinct in that, although it
operates with the category of degrees of kinship, it is not gradual and not
homogeneous. Each of four levels operates with an entirely different
principle and is related to the function of modulation in the form. Thus,
the second degree, modulation on two signs, describes the transitions in
sonata (e.g., transition that brings the key of the dominant of dominant at
the medial caesura); third degree covers the most advanced modulations that
take place in the development sections of form, and fourth degree covers
enharmonic modulations, mostly, returning modulations at the end of
development. Even the formulations are not homogeneous. The second
degree--modulation on two signs in a key signature; the fourth
degree--modulations on a triton or a semitone.

This all makes this system very practical. Needless to say, Russian
students have to play advanced modulations (e.g. third degree modulation
and returning enharmonic modulation) in very elaborate forms (e.g. in small
ternary) by the request of the teacher without time for preparation.

Without this practical approach to modulation, our discussions of tonal
structure and voice-leading will never leave the local level.


Best wishes,


Ildar Khannanov
Peabody Conservatory
etudetableau at gmail.com

2014-09-11 3:15 GMT-04:00 Nicolas Meeùs <nicolas.meeus at scarlet.be>:

>  Dimitar,
>
> Schoenberg devotes to this question Chapter IX of his "Structural
> Functions of Harmony" (1954), coming to conclusions similar to yours, but
> with five degrees of proximity (Direct and close; Indirect but close;
> Indirect; Indirect and remote; Distant). He had discussed some of this,
> albeit less systematically, in his "Harmonielehre"of 1911, Chapter IX on
> Modulation. He had probably read Richard Stör's "Leitfaden".
>
> To base the proximity on the key signature, as you do, may raise problems
> in minor, if only because the 'natural' dominant is the minor one, a point
> that Schoenberg did not easily accept, but I think he was mistaken on this.
> The idea of a gradation in the proximity is the important one; how many
> degrees one considers, and how exactly one defines them, may be a matter of
> personal taste.
>
> Nicolas Meeùs
> Professeur émérite
> Université Paris-Sorbonne
> nicolas.meeus at scarlet.be
>
>
>
>
>
>
>  Le 10/09/2014 21:46, Ninov, Dimitar N a écrit :
>
> Dear Colleagues,
>
> Concerning modulation, the sole factor which determines the proximity between two keys is the availability of pure diatonic chords shared by those keys. Thus C major and D major have two diatonic chords in common: G and Em. Therefore, it does not make sense to call these two keys "remote", and yet this is how they are categorized in some sources. Throwing the tonalities in two categories only: "closely related keys" and "remote keys" ignores the fact that relationships change gradually, and there are intermediate stages.
>
> In my teaching, I classify the proximity between keys in three different levels/degrees. This approach is very consequential, for it classifies the proximity based on the availability of diatonic chords. The idea is not mine – it has been introduced  in various harmony books among which "Praktischer Leitfaden Der Harmonielehre" (Richard Stör, Wien, 1908, 9, 11, 17) and "Uchebnik garmonii", by four Russian authors: Dubovskii, Evseev, Spossobin, Sokolov (Moscow, 1955). It is exposed below.
>
> 1. Fist Degree of Proximity: relative keys and those which differ by one accidental. These tonalities may be called "close" or "closely related". A certain key has five closely related keys, and these are the keys whose tonics are diatonic major or minor triads built on the natural scale of that key. Close to C major are d, e, F, G, and a. Close to C minor are Eb, Fm, Gm, Ab, and Bb. Relative keys share seven diatonic chords, and those which differ by one accidental share four diatonic chords.
>
>  2. Second Degree of Proximity: keys which differ by two accidentals. I call these "relatively close". A certain key has four relatively close keys. To C major these are D, b, Bb, and g. To C minor these are F, d, Db, and b-flat minor. Relatively close keys share two diatonic common chords.
>
> 3. Third degree of Proximity: keys which differ by three or more accidentals. These may be called "remote". For example, C and f#. Such keys do not share diatonic chords, but a good common chord may always be found in the realm of borrowed chords (modal interaction).
>
> Therefore, it becomes clear that there is no "Chinese wall" between "closely related" and "remote", but the relationships unfold gradually. One may even create more levels of proximity, for example, the first level may only include the relative keys, etc. while a fifth level may be based on the opportunities of obtaining most typical borrowed chord relationships, etc. (for instance C major and F minor are keys which are formally remote but practically are closer than other relationships).
>
> This reminds me that Rimsky Korsakov has a different system of classifying the proximity between keys, placing the minor S in a major key and the major D in a minor key as proximity of degree one. I personally prefer the simpler concept exposed above, for Fm is a great S chord into C major, but the tonality of F minor itself does not reveal the same level of closeness to C as the tonalities of G, e, F, and d. The same comparison may be made between C minor and G major. G is a great actual dominant in C minor, but as tonality, with all of its chords, it does not seem as close to Cm as Bb, g, f, and Ab.
>
> We shall also keep in mind that, in order to find infallibly all the available purely diatonic chords shared  between two keys, we shall only look into their keys signatures and nothing else. This will instantly reveal the chords built on the natural scale of that key (whether it be major or minor). This process is also spoiled by some authors, as a result of which they exclude legitimate chords from the process and confuse the role of the common chord with that of the modulating chord which follows. But I will have to say more on this in a further email.
>
> Thank you for your attention. Have a nice weekend!
>
> Best regards,
>
> Dimitar
>
> Dr. Dimitar Ninov, Lecturer
> School of Music
> Texas State University
> 601 University Drive
> San Marcos, Texas 78666
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