[Smt-talk] Abbreviated Labels of Seventh Chords

[Julian Hook]

Ildar Khannanov's post, in which he contrasts "six-five chord" with "Quintsextakkord" and so on, raises another interesting question, not about which figured-bass numbers should be written but about the order in which they should be read.

I first learned basic music theory not from a class or a teacher, but from some very sporadic self-study during my years as a mathematician. In mathematics quite commonly a symbol is adorned by both a subscript and a superscript, and in that situation mathematicians generally read the subscript first. For instance, if the letter A has a subscript x and a superscript y, this would typically be pronounced "A-x-y," not "A-y-x". (A reasonably familiar example is the notation for a definite integral. An integral sign looks like an elongated S. An integral sign followed by a subscript a and superscript b is "the integral from a to b," not "from b to a"--and indeed, a is typically a smaller number than b in that situation, so only one ordering makes sense. And there are a number of other similar notations in more or less common use.)

Anyway, some years later, when I began keeping the company of music theorists, I was a bit surprised to learn that (for example) the chord that I was mentally pronouncing "five-five-six" was called "five-six-five" by everyone else. I've long gotten used to it, of course, and had nearly forgotten it until now.

David Lewin introduces a visually similar notation when he defines inversion in a Generalized Interval System (Generalized Musical Intervals and Transformations, page 50). Lewin writes the letter I with a subscript u and superscript v. It's clear that Lewin thinks of this from bottom to top as "I-u-v," not "I-v-u," not only because of the alphabetical ordering but also because he explicitly calls it "u/v inversion." Unfortunately, other scholars who adopt Lewin's notation, their habits perhaps shaped by a lifetime of reading "five-six-five," sometimes seem to be thinking of it from top to bottom, which does run a risk of some confusion. (I-u-v is the same operation as I-v-u in many cases, but not in all cases.)

Julian Hook
Associate Professor of Music Theory
Indiana University
juhook at indiana.edu




On Feb 9, 2012, at 2:06 PM, Ildar Khannanov wrote:

> This slight difference reveals a larger issue. I do not know why contemporary North American music theory must follow the "figured bass tradition" and disregard German theory of the 19th century, but if to consider the latter, we can see the following:
>  
> First of all, German theorists of the 19th century, composers and students, operated with hearing rather than seeing. This innovation could not be possible without understanding of the roots of the chords, inversions, and tonal functions, introduced by Rameau earlier. All three switch musical perception from the visual domain (figured bass) to the aural (Funktionstheorie). The primary mode of operation for the 19th-century theorists was hearing, the secondary--seeing. It seems that, due to the lack of funding of aural skills lessons in North American high schools, music students nowadays operate primarily in the visual domain. Contrary to this pitiful situation, a 19-century German student had to learn the inversions of the seventh chord first by ear, and only then could approach writing them down and analyzing them in the score.
>  
> The first thing that you hear, when listening to the last inversion of a seventh chord, is a buzzing noise in the bottom of the chord. Hence, the distinguishing feature of this chord is the second in the base and the name of the chord is Sekundakkord. Moreover, when listening to the first inversion of the seventh chord, you hear first the fifth, and then the sixth added to it. Therefore, the name of the chord is Quintsextakkord. In North America, students understand this chord as “sixth-five” only because this is the way our eyes work: they grab the larger object first and then analyze smaller detail. Hearing grabs the smaller element first and then proceeds to the larger. Accordingly, it is the Terzquartakkord, and not the four-three chord. It is not the sixh-four, but the Quartsextakkord. The first inversion of a triad is simply a Sextakkord: it is not a sixth-three. And the six-four is actually Quartsextakkord. Russian theory faithfully followed this system.
>  
>  
>  
> When you operate not with noteheads, but with aural images in the aural pitch space (something which great German theorist Hugo Riemann called innere Hoerung), you realize that the scale step seven is essentially different from the seventh of the seventh chord, and in general, the names of the intervals should be different from the names of the scale steps. Thus, German theorists use Latin names for intervals: Prima, Sekunda, Tertia, Quarta, Quinta, Sexta, Septima and Oktava. For the scale steps they use the words of their native language.
>  
> Considering all this, I am puzzled by the statements of Nicolas concerning “Schenker’s hearing.” What is that?
>  
> Dr. Ildar Khannanov
> Peabody Institute, Johns Hopkins University
> solfeggio7 at yahoo.com

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