Some remarks on two books
and why you should read them

Siem Huijsman

History of Western Music Theory

Conservatory of Amsterdam

Professor: David Lodewyckx

June 15, 2021

As part of the course The History of Western Music Theory at the conservatory of Amsterdam, academic year 2020-2021, we were asked to read one or two original sources, give a presentation and write a small article about them. This is the article.
I chose the following two sources (books):

Arnold Schönberg, Gerald Strang, and Leonard Stein. Fundamentals of Musical Composition. London: Faber and Faber, 1967.

Erwin Ratz. Einführung In Die Musikalische Formenlehre: Über Formprinzipien in den Inventionen J.S. Bachs und ihre Bedeutung für die Kompositionstechnik Beethovens. Wien: Universal edition, 1968.

In this article I will explain why I chose these books, give a small impression of the content and finally I will try to convince you that you should definitely read these books, at least if you are a music lover and have an interest in music theory and more specifically in musical analysis.

Well then, first of all why these two books? I started this study because I am an amateur cellist for almost all my life and experienced a growing need for a better understanding of the pieces I play and more in general the music that I listen to. There are of course many aspects that can be considered, like the historical context in which the piece was written and how it was received over time. This is generally referred to as music history. My special interest however is to find out with what intent, with what idea and with what construction principles a composer set out when composing a piece. Of course in the end this is a question we will never be able to answer, but a better understanding of music theory, now and the prevailing theory at the time the piece was written gives much more insight in a piece than just the journey experience.[1]inspired by the “journey metaphor” in L. Poundie Burstein. Journeys through Galant Expositions (New York, NY: Oxford University Press, 2020), 5-6.

When trying to get a better understanding of a composition the field of musical analyses is helpful. In this course we used the The Cambridge History of Western Music Theory as our main source.[2]Thomas Christensen, ed., The Cambridge History of Western Music Theory (Cambridge History of Music. Cambridge: Cambridge University Press, 2002). In the second semester we read – among others – the chapters 25: Nineteenth-century harmonic theory: the Austro-German legacy written by David W. Bernstein and chapter 28: Form, written by Scott Burnham. Both contain paragraphs on Schönberg[3]Christensen, The Cambridge History of Western Music Theory, 802 and 895. and the latter also on Ratz[4]Ibid., 897., a pupil of Schönberg. Harmony and form are both elements that are used in musical analysis. The last sentence in the paragraph about Schönberg in chapter 25 made me curious:

His [Schönberg’s] synthesis of Austrian and German harmonic theory with this sophisticated approach to thematic development and motivic unity was a culmination point in the history of the Austro-German theoretical tradition.[5]Ibid., 806

It is also known that the concept of the sentence has been defined for the first time by Arnold Schönberg in his book Fundamentals of musical composition.[6]William E. Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart and Beethoven (New York [ect.]: Oxford University Press, 1998), 263, Chapter 3, footnote 1. This intrigues me very much as Schönberg gives many examples of sentences from Haydn onwards.[7]Arnold Schönberg, Gerald Strang, and Leonard Stein. Fundamentals of Musical Composition (London: Faber and Faber, 1967), 21. Ratz even shows sentence like constructions in the Inventionen of Bach.[8]Erwin Ratz, Einführung in die musikalische Formenlehre: Über Formprinzipien in den Inventionen J.S. Bachs und ihre Bedeutung für die Kompositionstechnik Beethovens (Wien: Universal edition, 1968), 40. So this concept of form has been used some 150 years or more before it was concretely defined as such.
In the paragraph on Ratz (chapter 28 of The Cambridge History) the “general formative principles: tight construction […] and loose construction”[9]Christensen, The Cambridge History of Western Music Theory, 897. are mentioned, terms I know from the book on classical form by William Caplin.[10]Caplin, Classical Form. That made me curious for the sources Caplin used to define his concepts.
These reasons together determined my choice for these books.

Before giving an impression of the contents of the books a few words about the relationship between Schönberg and Ratz. Schönberg lived from 1874 to 1951 and Ratz from 1898 to 1973. So Ratz is one generation younger than Schönberg. In 1915 Schönberg returned to Vienna after a stay in Berlin and gave masterclasses in composition. Ratz participated in them and considered himself a pupil of Schönberg. In the introduction of his book he expresses his veneration for his teacher.[11]Ratz, Einführung in die musikalische Formenlehre, 11-12.

Arnold Schönberg

Fundamentals of musical composition by Schönberg was published after his death in 1968 and edited by two of his pupils: Gerald Strang and Leonard Stein. According to the author one of the aims of the book is “to provide for the average student of universities, who has no special talent for composing or for music at all”.[12]Schönberg, Fundamentals of Musical Composition, 214. Thanks to this purpose the book starts from the very beginning and the structure is very clear and organized. As the title indicates it is primarily a textbook on composition, but “it will be evident that this volume can be used equally well as a text in musical analysis” according to Gerald Strang in the editor’s preface.[13]Schönberg, Fundamentals of Musical Composition, xiv. The material for the book came into being during the years that Schönberg taught at universities in the United States starting in 1933.

The book consists of three parts. The first part deals with the construction of themes and starts with the motive and shows how to build periods and sentences from motives. Schönberg also makes some general remarks about form which I think are worth mentioning here. The first remark is that form used in aesthetic sense means that a piece is organized and a second remark is about musical construction: “the real purpose of musical construction is not beauty but comprehensibility”.[14]Ibid., 1 resp. 25, footnote 1. Another eye opener for me was his remark in chapter XI on melody and theme: “Every succession of tones produces unrest, conflict, problems. […] Every musical form can be considered as an attempt to treat this unrest by halting or limiting it, or by solving the problem.”[15]Ibid., 102.

His treatment of motives is really amazing. He explains how a motive appears characteristically at the beginning of a piece but how the final impression of a piece is not determined by this opening statement but by the way the motive is treated and developed throughout the piece. Because a motive reappears constantly, is repeated constantly. Schönberg than shows in a very structured manner how motives can be varied in various aspects like rhythm, intervals, harmony and melody. Everything is illustrated with large numbers of examples, some made by Schönberg himself but most come from the literature.

A last quotation from the first part concerning motives: “A piece of music resembles in some respects a photograph album, displaying under changing circumstances the life of its basic idea — its basic motive.” [16]Schönberg, Fundamentals of Musical Composition, 58.A very evocative way to express the role of a motive in a piece of music.

Part II concerns the small forms and according to Schönberg these are: the small ternary form, the minuet and scherzo and the theme and variations. Again with a lot of examples Schönberg discusses all of these forms. That he never forgets his intended public – composition students – is shown by an example[17]Ex.105 in Schönberg, Fundamentals of Musical Composition,132. in which he shows how an A-section of a small ternary form can be followed by ten different B sections. Three of these are shown in fig. 1.

fig.1 An A-section of a small ternary form with three different B-sections

The third part finally is about large forms and their constituent parts. So here Schönberg discusses the transition, the group of subordinary themes, the retransition, the ‘Lyric theme’ and the coda and then the large forms themselves: the rondo forms and the sonata-allegro form. The third part is relatively small as Schönberg refers to all the material in the preceding chapters.

Erwin Ratz

Where Fundamentals of musical composition is a very practical textbook, Einführung in die Musikalische Formenlehre by Erwin Ratz has a more philosophical line of approach. But before going into that aspect, let us first look at the subtitle:

Über Formprinzipien in den Inventionen J.S. Bachs und ihre Bedeutung für die Kompositionstechnik Beethovens

which can be translated as:

About principles of form in J.S.Bach’s inventions and fugues and  their significance for Beethoven’s compositional technique.

First Ratz observes that the essence of musical form is very clearly perceptible in the works of Bach and Beethoven because the nature and size of the content of their works required a particular clarity in the formal structure.[18]Ratz, Einführung in die musikalische Formenlehre, 9.

Later he explains that he considers Bach and Beethoven as the high points of their respective style periods and analyzing and comparing their works will reveal the common principles.[19]Ratz, Einführung in die musikalische Formenlehre, 21. That explains his choice for these two composers.

There are a number of reasons why Ratz chose the inventions of Bach. He argues that although the inventions combine the principles of polyphony and homophony, in the majority of them the homophonic principle prevails.[20]Ratz, Einführung in die musikalische Formenlehre, 37. This principle of homophony allows for a number of characteristics or form principles that recur in the style of Beethoven. I will mention a few of them to give an impression of what Ratz in had mind. First of all he mentions that the homophonic style allows for a thematic development that is not allowed for in for instance fugues. Furthermore the homophonic style allows for more self-contained phrases like sentences and periods. And he adds that these phrases can be organized “fest” or “locker” which can be translated with the terms Caplin uses in his book Classical Form: tight-knit and looser.[21]Caplin, Classical Form, xi. And the last argument I will mention here is that Ratz considers the inventions as an expression of a very comprehensive way in which Bach used all the available means of composing.[22]Ratz, Einführung in die musikalische Formenlehre, 37-39. These are some arguments why Ratz chose Bach’s inventions.

The more philosophical approach of Ratz shows itself in relation to his remarks on form. The introduction of the book starts with a quotation from Goethe on the essence of a work of art which ends with: and form is a secret for most of us. And later he says that the main task of theory of forms is to deepen the ability to experience music and: the functional theory of forms describes the means by which parts of a composition can fulfill their function in the whole, like the different organs in a living organism.[23]Ratz, Einführung in die musikalische Formenlehre, 7-9.

In the Introduction Ratz tells us which public he had in mind when writing this book: music researchers, students from universities and conservatories and music lovers in general.[24]Ratz, Einführung in die musikalische Formenlehre, 10-11. Where Schönberg systematically develops the theory of forms, Ratz just gives a short overview of all the form principles in chapter 1 and then starts his main argument. I think that music lovers without any theoretical knowledge would have a hard time reading this book.

The general idea of Ratz’s book can be summarized as follows: he took the principles of musical forms found in Beethoven and shows to what extent they can be found in the two- and three-voice Inventions of Bach. The latter are also called Sinfonias, a term Ratz wishes to avoid because of the different connotation of this word in today’s world.[25]Ratz, Einführung in die musikalische Formenlehre, 103.
As already mentioned chapter 1 gives the overview of the principles of musical forms found in Beethoven. Chapter 2 contains the analysis of six two-voice inventions by Bach. Because in the three-voice Inventions elements of the fugue are used as construction principle, chapter 3 is an intermezzo on the architecture of the fugues by Bach.
Chapter 4 deals with the analysis of seven three-voice inventions.
These chapters are followed by three chapters with characteristic examples of works of Beethoven. Chapter 5 discusses five movements of various piano sonatas and the three Bagatellen op. 126. Chapter 6 contains the analysis of three movements of string quartets by Beethoven and finally chapter 7 contains an elaborate analysis of the Hammerklaviersonate op. 106.

Just as an example fig. 2 shows the way in which Ratz recognizes the form principles of
Beethoven in the first two-voice invention in C major by Bach. I find it fascinating how this analysis is made and I think Ratz is very convincing in showing the origins of the form principles to come in the first Viennese classical period. In general I very much enjoyed reading the analyses Ratz makes in this book. I think they are brilliant. As a pupil of Schönberg he gives much attention to motivic and thematic aspects which makes it even more interesting.

fig. 2 form principles of Beethoven in the first two-voice invention by Bach

So to conclude I think that in these two books we see two masters at work. Schönberg with his systematic approach, starting at a very basic level but with a crystal clearness in explaining all the concepts including his treatment of motives and his definition of the concept of the sentence. Ratz in his book in fact applies this theory of forms not only to Beethoven – who as we saw can be seen as a culmination point of his style period – but also shows in a convincing way where the roots of these form principles can be found: Bach, a culmination point of his style period. The problem that the book by Ratz requires a bit more basic knowledge can be overcome by reading the book of Schönberg first. They form a perfect couple.
Both give their vision on form, form principles and form theory and these points of view complement each other. And both supply us with analyses of many examples from the great masters of classical composition; Schönberg with small examples of some thirty composers to illustrate his theory and Ratz with an in depth analysis of complete movements of works of Bach and Beethoven.

All in all a very valuable and informative exercise. Very much recommended!

Notes

Notes
1 inspired by the “journey metaphor” in L. Poundie Burstein. Journeys through Galant Expositions (New York, NY: Oxford University Press, 2020), 5-6.
2 Thomas Christensen, ed., The Cambridge History of Western Music Theory (Cambridge History of Music. Cambridge: Cambridge University Press, 2002).
3 Christensen, The Cambridge History of Western Music Theory, 802 and 895.
4 Ibid., 897.
5 Ibid., 806
6 William E. Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart and Beethoven (New York [ect.]: Oxford University Press, 1998), 263, Chapter 3, footnote 1.
7 Arnold Schönberg, Gerald Strang, and Leonard Stein. Fundamentals of Musical Composition (London: Faber and Faber, 1967), 21.
8 Erwin Ratz, Einführung in die musikalische Formenlehre: Über Formprinzipien in den Inventionen J.S. Bachs und ihre Bedeutung für die Kompositionstechnik Beethovens (Wien: Universal edition, 1968), 40.
9 Christensen, The Cambridge History of Western Music Theory, 897.
10 Caplin, Classical Form.
11 Ratz, Einführung in die musikalische Formenlehre, 11-12.
12 Schönberg, Fundamentals of Musical Composition, 214.
13 Schönberg, Fundamentals of Musical Composition, xiv.
14 Ibid., 1 resp. 25, footnote 1.
15 Ibid., 102.
16 Schönberg, Fundamentals of Musical Composition, 58.
17 Ex.105 in Schönberg, Fundamentals of Musical Composition,132.
18 Ratz, Einführung in die musikalische Formenlehre, 9.
19 Ratz, Einführung in die musikalische Formenlehre, 21.
20 Ratz, Einführung in die musikalische Formenlehre, 37.
21 Caplin, Classical Form, xi.
22 Ratz, Einführung in die musikalische Formenlehre, 37-39.
23 Ratz, Einführung in die musikalische Formenlehre, 7-9.
24 Ratz, Einführung in die musikalische Formenlehre, 10-11.
25 Ratz, Einführung in die musikalische Formenlehre, 103.