Due 1/8: Four Dimensions

Write a paragraph describing one of your favorite works of music in the twentieth century, concentrating primarily on the terms pitch, timbre, loudness, and time. Understand what’s important (to your way of hearing the piece) in each of those four dimensions. Choose one dimension as a topic on which to concentrate special energy. If possible, include a url to a web-hosted video (for example on Google Video or YouTube) of the work under discussion, or let us know where/how we might hear the piece.

Optional: post your answer here by clicking on the “Comment” link. I look forward to reading your perspectives on this! (If you prefer to keep your answer private, you may submit it to me directly via email or in class.)


Due 1/15: Extended Tertian Harmony

Choose three phrases from anywhere in Scriabin’s Etude Op. 49 No. 1 and/or Ravel’s Jeux d’Eau, each phrase consisting of at least seven distinctive harmonic states, leading toward a sense of resolution. (“Distinctive harmonic states” means harmonic areas or segments, into which a complex texture can be reduced or segmented, as we discussed in lecture. If you choose a passage with lots of alternation between two states, please count the alternation as only two, and not several, harmonies.) You may choose all the phrases from a single piece, or choose from both pieces.

(1) Analyze all three phrases using your knowledge of extended tertian harmony, and using the “jazz” notation discussed in class. You may speculate on tonal functions, but it is not required at this stage.

(2) Identify at least three important chords within each phrase, and describe those chords both as extended tertian harmonies and in terms of their interval vector. Briefly discuss the roles of each chord in the phrase, thinking about types of dissonance (i.e. individuated vs. propulsive/structural), and how they might function as parts of a tonal structure.

(3) Optional: Prepare for your composition project by choosing one of your three phrases and compose a phrase that emulates it rhythmically and texturally, but makes use of different melodic and harmonic elements.

For more tips, click on the first of the “comments” below…


READING DUE 1/18: Hindemith's Series 1 & 2; "combination tones"

Volume 1 of “The Craft of Musical Composition”, by German-American composer Paul Hindemith, contains a lengthy but careful and useful discussion of the relationships between tones in the 12-tone system. By Monday, please read pp 54-74 (up through the end of section 4). This passage begins after Hindemith discusses the nature of frequency vibrations and the overtone series in individual notes; at this point he launches into a study of the way notes relate to one another.

[Download these excerpts, as a pdf file; and please see below for a figure clarifying what Hindemith means by Series 1 and Series 2. (These are expressed later in the article, but they’re worth having at the beginning!) All of this document will eventually be read for this course. Feel free to browse beyond this weekend’s assignment.]

While not bound by the tradition of the tonal system, Hindemith urges composers to consider relationships between dissonance and consonance as natural, rather than human-made or culturally derived. Notice how deeply he relies on simile and metaphor to impress on us a feeling of “ultimate truth” in connection with what he considers the basic principles of his theory.

From the end of section 1 through section 4, Hindemith covers two main topics:

  1. The difference between “Series 1”—a progression of intervallic distances from an originating tone—and “Series 2”—a progression of intervals from stable to unstable.
  2. The origins of “combination tones”, their physical basis, and their role in the important physical differences between dissonance and consonance.

After grasping the basic claims Hindemith makes in these two topics, offer your own Hindemith’s claims. Why does Hindemith ask us to consider composition with notes the way a carpenter considers building with wood? When did Hindemith rely on objective physical characteristics of sound, and when does he favor of the conventions in our culture? Do his choices (regarding when to be objective and when to favor tradition) make sense to you?


What is equal temperament? Does it matter?

After you’ve read the Hindemith, consider the role of temperament in his claims about what is “natural” in a harmony or a harmonic progression.

Equal temperament is a system that we all use to render all intervals of a given size (e.g. minor sixth, major second, etc.) “equivalent.” In an equal-tempered system, transpositions of a group of notes will preserve the ratios of all intervals between pairs of notes. Believe it or not, when we allow all fifths to be pure, we either have to endure out-of-tune octaves, or we have come up with lots of new note-names for notes that are very close together. (This is because we tune around the circle of fifths and find ourselves coming “back” to a point of origin that isn’t quite the same.)

I’d like to make this more real for our discussions, so here’s a spreadsheet. This allows you to enter two frequency values to form a repeating ratio, like the repeating fifth in conventional tuning methods. A large-scale tuning system unfolds based on that repetition. Try entering frequencies in a ratio of 3/2 to one another (a “pure” fifth), and observe the dissonances and inconsistencies that result. Modify that fifth to a smaller ratio (e.g. 2.999/2) to observe the impact of tempered fifths on the whole system. 


Due Monday, 1/25: Mikrokosmos

1. Read pp. 87-108 of Hindemith’s “Craft of Musical Composition Volume 1” (in the same “excerpts” pdf linked to the previous assignment), and make a diagram distinguishing Hindemith’s six major categories of chords, and the meaning of subscripts that can be added to each category. (For extra credit, bring that diagram with you to class on Friday.)

2. Using a short work from Béla Bartók’s “Mikrokosmos” (specifically assigned to each of you in class on Wednesday) make a harmonic reduction, indicating the principal harmonies clearly with treble and bass stems, along with more basic repetitions and elaborations on them (without stems), and with smaller noteheads for what you consider to be passing and ornamental notes. (In many cases you will need to use your ears to judge the boundary between one chord and the next, since contrapuntal textures rely on both implicit and explicit harmonies in their progressions.) This process will lead to your interpretation of what harmonic progression underlies the piece. Leave plenty of space above and below the staves of your reduction, for additional analytical notation.

3. Label each principal harmony according to Hindemith’s classification system. Then, playing the work on the piano, examine the classifications of those chords and their possible relevance to the work as a whole. Following Hindemith’s principles outlined on p. 108 of the reading, write a brief paragraph describing the ebb and flow of harmonic “value” in the passage.