[Smt-talk] Proximity between Keys

Thu Sep 11 13:09:49 PDT 2014

Dear Nicholas,

Thank you. I agree with your statement that "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." That is true - one does not jump instantly from "closely related" into "remote". Actually, Stor has four levels, but its fourth level seems a little bit arbitrary to me.

As for the concept of a minor dominant, I think many theorists and teachers confuse the concept of proximity between keys (and the process of finding diatonic common chords) with the assumption they will have to resolve a minor dominant into a tonic. False assumption, which leads to such astonishing statements as: "Minor V and major VII do not make good common chords in a modulation." Other textbook "gems" postulate: "Major mediants (III and VI in minor) cannot give a good impression of a minor key, and this is why they are avoided as common chords in a modulation." Each time I read such textbook "gems" I know that those who write them do not understand the role of the common chord in a modulation; they confuse it with the modulating chord which follows the former and brings the features of the new key. Of course, all this betrays the lack of practical knowledge in harmony with all the resulting consequences, the main one being to confuse the student.

But I will write more on that when I return from Belgium.

By the way, it would be a pleasure to make your personal acquaintance at the EUROMAC. I will deliver a paper on the diatonic-chromatic platform of tonality. I will not stay on Saturday when I fly back, but I understand you will be there earlier; hopefully we will meet.

With best regards,

Dimitar Ninov

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
________________________________
From: Nicolas Meeùs [nicolas.meeus at scarlet.be]
Sent: Thursday, September 11, 2014 2:15 AM
To: Ninov, Dimitar N; smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Proximity between Keys

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<mailto: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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