History of "Roman numeral analysis"

Nestor Napoles Lopez

Hi,

I am looking for literature on this topic. For example:

• How has the Roman numeral syntax changed over the years (from the Weber notation up to contemporary harmony textbooks)


• When did people start writing things like "V/V" (secondary dominants or things beyond the mere scale degree)


• When did people start writing Roman numerals with inversions of the form "V65", "V43", etc.

Any guidance on relevant literature about this topic would be very welcome.

Néstor

Nicolas Meeùs

Néstor, this is – or, better said, these are most interesting questions. I have elements of answer to the first one.

• There are cases of using Arabic numerals to denote roots in the first half of the 18th century, e.g. in Quirinus van Blankenburg, Elementa musica, 1739, but they need not retain us here.


• The first usage of Roman numerals to denote the fundamental bass might be in Johann Kirnberger's Die Kunst des reinen Satzes, of 1774 (p. 15 and the plates appended to p. 19). Numerals I to VIII appear to denote roots, but they more explicitly name the intervals from prime to octave. This is ambiguous as, even to us, say, V means "5th degree", i.e. the degree a 5th higher than the 1st: Roman numerals in a sense necessarily denote intervals. (Roman numerals denoting intervals had already been used by Piero Aron in 1523.)


• Georg Joseph Vogler, in his Gründe der Kuhrpfälzischen Tonschule (1778), occasionally uses Roman numerals for the roots, e.g. in plates XXI and XXVII (and perhaps others, which I didn't notice). David Damschroder (Thinking About Harmony, 2008, p. 6) also mentions an occasional usage of the numeral VII in Vogler's Tonwissenschaft und Tonsetzkunst of 1776. Later usages by Vogler are mentioned in F. K. and M. G. Grave, In Praise of Harmony, 2016, which I don't have at hand just now.


• Vogler names Hauptklänge what the letter symbols (C D E F, etc., possibly also F#) and the Roman numerals (I II III IV, also IV#) denote. This may mean the "fundamental notes" (the roots), but also the "fundamental chords." The German word Klang is quite ambiguous in this respect.


• With Weber, on the other hand, there is no doubt: the Roman numerals represent chords. This is why he is able, in Versuch einer geordneten Theorie der Tonsetzkunst (1817-1821), to differentiate between major and minor chords, or diminished triads, and also to note 7th chords. This usage does not seem to have gained a large recognition in the 19th century.


• Simon Sechter (Die Richtige Folge der Grundharmonien, 1853-1854) makes only a very limited use of Roman numerals, always denoting the roots rather than the chords, and for which he also uses Arabic numerals and letters, apparently more or less at random. Bruckner, his disciple, does not seem to make use of Roman numerals (at least if one trusts Schwanzara's edition of his Harmonielehre).


• Robert Wason (Viennese Harmonic Theory, pp. 107-108) reproduces two short examples with Roman numerals, from Josef Schalk's unpublished works, late 19th century.


• The first European authors to make an extensive use of Roman numerals appear therefore to be Heinrich Schenker (Harmonielehre, 1906) and Arnold Schoenberg (Harmonielehre, 1911).

I must confess being much less knowledgeable about the history of harmonic theory in English. To summarize the above, I find it striking that Roman numerals appear rather less common in the 19th century than may have been thought up to now and that their general usage really begins with Schenker and Schoenberg. I should add that they used capital Roman numerals exclusively, as seems to have been the case for all those who used them to note roots instead of chords.

Nicolas

Nestor Napoles Lopez

Thank you, Nicolas!

I will go through these books you recommended more in depth. The idea is to write a small section called "a brief history of Roman numeral analysis" in my dissertation. I am not a music theorist myself (more of a computer scientist who is passionate about music theory). Thus, I wanted to get as much feedback as possible on this subject.

Trying to add to the second question, I can share that a few months ago, I spent some time researching on the emergence of the word "tonicization". I couldn't find much about this. It seems to be a relatively recent term (maybe appeared with Schenker?). However, something I could find in "The Reception of Hugo Riemann's Music Theory" is that, here, the ideas of "applied chords" or "secondary dominants" are attributed to Riemann:

Needless to say, the idea of applied dominants also has its prehistory, but in fact neither the term nor any ana­lytical symbols for the phenomenon existed before Riemann.

Later in the text, this appears:

Applied dominants (also known as “parentheti­cal dominants” [Klammerdominante], “intermediate fifths” [Zwischenfünf ], or indicated by symbols such as [V], V/V, V/II, etc.) have been adopted by many practical theories of scale degrees.

It's interesting that Roman numerals are used to present these ideas (i.e., applied chords), but I don't think these symbols were the ones used by Riemann.

Some of my conclusions after researching on "tonicizations" were that, maybe, the emergence of both the concept (tonicization) and the Roman numeral syntax are related? That is:

• The use of V/V is the notation that expresses a chord related to a different key


• A chord related to a different key that does not explicitly "invoke" a modulation, is a tonicization

It'd be nice to know who first used something like "V/V", and how did they refer to those changes of key. I should maybe devote some time to reading more about that.

Your input will be very helpful for the first question. Thank you very much for that.

Néstor

 

Nicolas Meeùs

Néstor, the question of the origin of "tonicization" is complex because it is rather heavily dependent on language. The German Tonikalization appears to be one of the few terms coined by Schenker himself, at a time when even words such as Tonika or Tonalität where rare. Schoenberg writes about this (Harmonielehre, p. 213; Theory of Harmony, Carter transl., p. 428):

Heinrich Schenker (Neue musikalische Phantasien und Theorien) [Harmonielehre, pp. 337-366] makes decidedly a far more systematic attempt [than Riemann's] to elucidate these harmonies by speaking of a tonicalization process (Tonikalisierungsprozess). He means the wish of a secondary degree to become [a] tonic, or its potential to do so. This wish would imply that a dominant should precede that degree.

But to present it in this way reminds of Jean-Philippe Rameau, who considered that all 7th chords (even if the 7th was only implicit) were dominantes, until the next-to-last chord, the dominante-tonique which resolved on the last, the tonique. This was a conception of harmonic progression as a series of dominants each resolving on the next. (Jean-Jacques Rousseau, I think, said that harmony is but a series of cadences.)

There is some uncertainty in English about whether Tonikalisierung should be translated as "tonicalisation", as by Oswald Jonas and Elisabeth Mann in the translation of Harmonielehre, or as "tonicization," as by Tim Jackson, Robert Snarrenberg or Joseph Dubiel in the translation of Der Tonwille.

Neither Schenker nor Schoenberg appear to write V/V or anything of the kind. Schoenberg however did indicate altered chords by a stroke through the Roman numeral, which at times indicated an applied dominant, but not always. Schoenberg uses Nebendominante, which Carter translates as "secondary dominant."

Riemann never used Roman numerals. He denoted applied dominants by (D) (e.g. T–(D)–Sp for C–A^#–d, I–VI^#–ii), or by intertwined Ds.

In French, secondary dominants often would be called dominantes d'emprunt, i.e. dominants belonging to a tonality empruntée, a borrowed tonality. This is a common way of speaking in the Paris Conservatoire, but I have no idea since when.

Nestor Napoles Lopez

Neither Schenker nor Schoenberg appear to write V/V or anything of the kind. Schoenberg however did indicate altered chords by a stroke through the Roman numeral, which at times indicated an applied dominant, but not always. Schoenberg uses Nebendominante, which Carter translates as "secondary dominant."

Riemann never used Roman numerals. He denoted applied dominants by (D) (e.g. T–(D)–Sp for C–A^#–d, I–VI^#–ii), or by intertwined Ds.

In French, secondary dominants often would be called dominantes d'emprunt, i.e. dominants belonging to a tonality empruntée, a borrowed tonality. This is a common way of speaking in the Paris Conservatoire, but I have no idea since when.

Dear Nicolas, if helpful in this matter, I would like to mention an example I found in "Harmony Simplified" by Frank H. Shepard (1896). In this book, Shepard uses the term "attendant" chord.

 

In another figure, the notation "of" makes it more closely resemble the modern "V/V" syntax:

Finding these figures was not an accident. I have been looking at the syntax used throughout English (or English translations) textbooks of the late nineteenth and early twentieth century. I have not found anything closer to "V/V" than this. Given that said, possibly exploring the German literature will reveal other examples.

 

 

Nestor Napoles Lopez

It seems that Shepard's "Attendant" chord system has been described in a previous publication, "How to modulate" (1890).

Nicolas Meeùs

In How to Modulate, Shepard also speaks of "attendant keys" (pp. 57, 61), which are already mentioned and discussed by Banister, Music (1873), p. 160 etc. Banister spears of "intermediate chords," for instance "the dominant of a relative minor key". In this, however, the chord is described as a chord belonging to an attendant key in which it exerts its function of dominant. This also is what Shepard does in Harmony Simplified when he writes "[A] of C", meaning "the attendant chord of the C key".

In V/V, on the other hand, the ciphering means "the dominant (a chord function) of the dominant (another chord function)." One might understand otherwise, as "the dominant (chord) or the dominant (key)", but that will not work in all cases. In addition, there would be little point of writing V/V if it were to denote a true modulation to the dominant key (in which case one should better write V—I instead of V/V—V). In other words, V/V and other similar cipherings precisely aim at indicating that there is no modulation, no true "attendant" key. 

Nestor Napoles Lopez

Dear Nicolas,

Thank you for your input here.

I am curious about this:

 One might understand otherwise, as "the dominant (chord) or the dominant (key)", but that will not work in all cases.

Can you share an example where "the dominant (chord) o[f?] the dominant (key)" does not work?

When I write an analysis, I always assume this notation (scale_degree_root/key) to work the best, mostly in the presence of other scale degrees other than V.

For example, in the context of F minor:

i              F Minor triad

viio7/ii    F# Fully-diminished seventh chord

iio          G Diminished triad

V43/V    G Dominant seventh chord, second inversion

V6         C Major triad, first inversion

V7         C Dominant seventh chord

i             F Minor triad

V6/N      Db Major triad, first inversion (Dominant of the Neapolitan)

N           Gb Major triad (Neapolitan of F Minor, root position)

i             F Minor triad

I must confess that I have a slight bias towards computational thinking. But I am very curious about counter examples.

 

 

Nicolas Meeùs

Can you share an example where "the dominant (chord) of the dominant (key)" does not work?

What I mean merely is that in a progression like II^#–V–I, if you write it as V/V–V–I, there is (or there should be) no modulation involved. In V/V–V, V is not I of the dominant key, but merely V of the tonic key – it is a dominant chord, and it is not in the key of the dominant.

Perhaps an even more crucial example is that of V/N that you quote, meaning the dominant of the Neapolitan chord. If you consider that this is a modulation to the key of the Neapolitan chord, then it becomes an independent key and can no more be "Neapolitan." You say it yourself when you write that Gb is "Neapolitan of f minor". It must be in f minor, otherwise it is no more Neapolitan.

 

Nestor Napoles Lopez

What I mean merely is that in a progression like II^#–V–I, if you write it as V/V–V–I, there is (or there should be) no modulation involved. In V/V–V, V is not I of the dominant key, but merely V of the tonic key – it is a dominant chord, and it is not in the key of the dominant.

Perhaps an even more crucial example is that of V/N that you quote, meaning the dominant of the Neapolitan chord. If you consider that this is a modulation to the key of the Neapolitan chord, then it becomes an independent key and can no more be "Neapolitan." You say it yourself when you write that Gb is "Neapolitan of f minor". It must be in f minor, otherwise it is no more Neapolitan.

Yes, this all makes sense. Thank you for the insightful discussion!

Phil Duker

Dear Néstor,

Cool topic and great discussion between you and Nicolas!  Another source to check out is Thompson's A History of Harmonic Theory in the United States where he talks about the different systems that were adopted in the US (and some of their European origins). 

Cheers,

Phil