Instructor: Dr. David Schwarz

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  MUTH 2500 Theory IV Fall 2010
  
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  MW 11:00 to 11:50 MU 2006
  
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  Instructor: Dr. David Schwarz
  
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  Office: MU 346
  
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  Phone: (940) 369-7299
  
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  E-mail: dschwarz@music.unt.edu
  
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  Office Hours: MW 2:00 to 3:00
  

All of the pieces we will discuss are present below as mp3 files to which you may listen on line but may not download and pdf files that you may download and print; do not download and print pdfs from the College of Music computer room.

Coming to class regularly and punctually is very important. Unexcused absence will lower your final grade 1/3 a letter; 5 late arrivals = 1 unexcused absence. You will be excused from class due to natural disasters, transportation problems beyond your control, medical emergencies (concerning you or members of your immediate family), and official UNT musical activities.

A proven case of plagiarism on an exam will result in an F for the course.

You will need a good theory book (or two) for the course; since many sections of earlier semesters use different materials, I will leave it up to you which text to use. If you can buy a new one, I'd recommend Aldwell / Schachter Harmony and Voice-Leading Third Edition.

Grades will be determined as follows:

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  In-class work and daily assignments = 25%
  
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  Midterm Exams = 25%
  
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  Final Exam (cumulative) = 50%
  
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  You must take and pass the final exam in order to pass the course.
  

• 
  08.30.2010
  

the figures

chord spacing

doubling

voice-leading

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  09.01.2010
  

• 
  09.06.2010
  

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  Write a complete stream of roman numerals beneath the figures (do not simply "add" a roman numeral to the figures)
  
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  Although we discussed the "neapolitan" as either a supertonic or a subdomiant chord, for the purpose of this work, consider the "neapolitan" a supertonic major chord constructed on the lowered second scale degree in minor
  
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  You may leap to the chord member seventh of a dominant seventh chord (or a secondary dominant seventh chord) as long as that seventh resolves properly (down by step or delayed and then resolved down by step)
  
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  All leading tones (as well as leading tones in secondary dominants) must resolve up by step
  
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  You may write a melodic augmented or diminished interval as long as it behaves itself tonally (that is flat-2 / sharp-7 will sound awesome as long as the next note is tonic)
  
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  Write no direct parallel perfect fifths or octaves
  
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  Use proper spacing (no more than two octaves between bass and tenor; no more than one octave between tenor and alto and between alto and soprano)
  
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  Identify the cadences
  
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  Identify the keys (including mode!)
  
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  Remember that you may omit the chord member fifth of a major or minor triad, or a seventh chord in root position
  
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  Move melodically as much as necessary but as little as possible
  
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  Remember the principle (not rule) that when the bass moves by step from one root position harmony to another, the upper three voices move in contrary motion to the bass
  
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  Remember to never double a tendency tone (leading tones, chord member sevenths, etc)
  
• 
  09.08.2010
  

A Devil's Mill

• 
  09.13.2010
  

Today we'll examine all of the derivations and harmonic functions we can for the augmented sixth chord. Imagine how the augmented sixth chord relates to: twisted dominants of the dominant, supertonic chords, subdominant chords, submediant chords. Imagine how the German Augmented Sixth chord can be enharmonically re-spelled to become the dominant seventh of flat-II. Try and come up with a thumbnail for using this enharmonic re-spelling to modulate up by half step and down by half step.

• 
  Write a complete stream of roman numerals beneath the figures (do not simply "add" a roman numeral to the figures)
  
• 
  
  
• 
  Although we discussed the "neapolitan" as either a supertonic or a subdomiant chord, for the purpose of this work, consider the "neapolitan" a supertonic major chord constructed on the lowered second scale degree in minor
  
• 
  You may leap to the chord member seventh of a dominant seventh chord (or a secondary dominant seventh chord) as long as that seventh resolves properly (down by step or delayed and then resolved down by step)
  
• 
  All leading tones (as well as leading tones in secondary dominants) must resolve up by step
  
• 
  You may write a melodic augmented or diminished interval as long as it behaves itself tonally (that is flat-2 / sharp-7 will sound awesome as long as the next note is tonic)
  
• 
  Write no direct parallel perfect fifths or octaves
  
• 
  
  
• 
  Use proper spacing (no more than two octaves between bass and tenor; no more than one octave between tenor and alto and between alto and soprano)
  
• 
  Identify the cadences
  
• 
  Identify the keys (including mode!)
  
• 
  Remember that you may omit the chord member fifth of a major or minor triad, or a seventh chord in root position
  
• 
  Move melodically as much as necessary but as little as possible
  
• 
  Remember the principle (not rule) that when the bass moves by step from one root position harmony to another, the upper three voices move in contrary motion to the bass
  
• 
  Remember to never double a tendency tone (leading tones, chord member sevenths, etc)
  
• 
  09.15.2010
  

• 
  09.20.2010
  

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  09.22.2010
  

• 
  09.27.2010
  

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  09.29.2010
  

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  10.04.2010
  

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  10.06.2010
  

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  10.11.2010
  

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  10.13.2010
  

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  10.18.2010
  

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  10.20.2010
  

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  Schoenberg, Verklaerte Nacht (except): mp310.25.2010
  

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  10.27.2010
  

from diatonic tonality to chromatic tonality to atonality

ordered pitch intervals (the number of half-steps between two pitches with regard to direction); unordered pitch intervals (the number of half-steps between pitches without regard to direction); ordered pitch-class intervals (the distance of half-steps within an octave, ascending, from one pitch class to another); unordered pitch-class intervals (the smaller distance between any two pitch classes).

interval cycles

pitch sets--segmentation

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  11.01.2010
  

After you have listened to the piece a lot and imagined how your ear places "delimiters" before and after certain events, download the segmented score beneath and see if my segmentation matches yours. Determine as much information as you can about the sets, numbered in roman numerals.

Pitch-class numbers that shall replace or supplement our old-fashioned system:

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  C-natural becomes pc 0
  
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  C-sharp / D-flat becomes pc 1
  
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  D becomes pc 2
  
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  D-sharp / E-flat becomes pc 3
  
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  E becomes pc 4
  
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  E-sharp / F becomes pc 5
  
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  F-sharp / G-flat becomes pc 6
  
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  G becomes pc 7
  
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  G-sharp / A-flat becomes pc 8
  
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  A becomes pc 9
  
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  A-sharp / B-flat becomes pc 10
  
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  B becomes pc 11
  

• 
  11.03.2010
  

• 
  11.08.2010
  

To transpose a pc set add a number of half steps to the pc set. So T1{1,2,4} gives you {2,3,5}. This means that you take pcset {1,2,4} and transpose each note up a half step. If you want to transpose down a half step you would say T-1{1,2,4} gives you {0,1,3}. Since it seems ugly to write -1 we write 11 instead so: T11 {1,2,4} gives you {0,1,3}.

We will always invert around "C" or pc 0. Since C-sharp or pc 1 is a half step above C, its inversion is B--a half step below C. So pc 1 inverts to pc 11. Since D or pc 2 is two half steps above C, its inversion is B-flat--two half steps below. So pc 2 inverts to pc 10.

See the pattern?

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  {1} inverts to {e}
  
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  {2} inverts to {t}
  
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  {3} inverts to {9}
  
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  {4} inverts to {8}
  
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  {5} inverts to {7}
  
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  {6} inverts to {6}
  
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  {7} inverts to {5}
  
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  {8} inverts to {4}
  
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  {9} inverts to {3}
  
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  {t} inverts to {2}
  
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  {e} inverts to {1}
  

Consider pc sets {1,2,4} and {2,3,5}. They both belong to set class (0,1,3).Since you read these sets "in the same direction" they are related by transposition. You simply need to figure out what you need to do to pc 1 to get pc 2, and what you need to do to pc 2 to get pc 3, and what you need to do to pc 4 to get pc 5. The answer is to add 1 to each so T1 {1,2,4} = {2,3,5}.

Consider pc sets {1,2,4} and {1,3,4}. They also both belong to set class (0,1,3). But you read one "left to right" and the other "right to left." These pc sets are related by inversion. Here are the steps to follow to find out exactly how the pc sets are related:

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  1)you invert the first set: {1,2,4} inverts to {e,t,8}
  
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  2)you write the inverted set in retrograde: {8,t,e}
  
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  3)you transpose as necessary to get to your destination: -7; 8-7 = 1; t-7 = 3; e - 7 = 4. So T-7I {1,2,4} gives you {1,3,4}. Or not to be so ugly: T5I {1,2,4} = {1,3,4}.
  
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  11.10.2010
  

Here are the pc sets that belong to set class (013):

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  Here are the transpositions:
  
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  {013}
  
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  {124}
  
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  {235}
  
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  {346}
  
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  {457}
  
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  {568}
  
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  {679}
  
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  {78t}
  
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  {89e}
  
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  {9t0}
  
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  {te1}
  
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  {e02}
  
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  Here are the inversions:
  
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  {oe9}
  
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  {10t}
  
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  {21e}
  
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  {320}
  
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  {431}
  
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  {542}
  
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  {653}
  
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  {764}
  
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  {875}
  
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  {986}
  
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  {t97}
  
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  {et8}
  
• 
  11.15.2010
  

• 
  11.17.2010
  

A 12-tone row is all 12 pitch-classes arranged in a fixed order. An example: the row from Berg's Lyric Suite = <5 4 0 9 7 2 8 1 3 6 10 11>. F is the first note, E is the second, etc. We say order number 1 (the first note) of this row is 5 (pitch-class number); order number 2 (the second note) is 4 (pitch-class number), etc.

The 12-tone row and its four permutations: P (prime) = left to right;R (retrograde) = right to left; I (inversion) = upside down; RI (retrograde-inversion) = upside down and backwards. There are 12 prime, 12 retrograde, 12 inversions and 12 retrograde inversions for each row.

Webern, Wie bin ich froh: pdf

The row to "Wie bin ich froh" is (using pitch-class numbers):

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  P7 = <7 4 3 6 1 5 2 11 10 0 9 8>
  
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  I5 = <5 8 9 6 11 7 10 1 2 0 3 4>
  
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  R8 = <8 9 0 10 11 2 5 1 6 3 4 7>
  
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  RI6 = <6 5 2 4 3 0 9 1 8 11 10 7>
  
• 
  11.22.2010
  

I will show you / give you a 12-tone matrix to "Wie bin ich froh" during class. For today try and finish a serial analysis of the piece based on the P7 row we discussed last time.

• 
  11.24.2010
  

For today, analyze the accompaniment of the theme of Webern's Opus 21, II. For a quiz grade, I'm going to ask you to invert a row.

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  11.29.2010
  

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  12.01.2010
  

The part-writing review above is in short-hand: "dominant complex" means you write the 8-7 6-5 4-(#)3 voicing as always; no terms have been defined; the purpose of the review is to bring ideas and procedures back to consciousness that may have gotten submerged by other more mundane and day-to-day thoughts.

What is the sonority on the second beat of measure 1 and how does it function?

What key is being tonicized in beats 2-4 of measure 3?

What is the sonority on the downbeat of measure 4 and how does it function in the key that the end of measure 3 tonicizes?

The set theory and serial review do not define terms; they offer three collections of pitches that you should put into pitch-class sets in normal form, showing the set classes to which they belong.

All evaluations are on line this semester. Go to my.unt.edu or sete.unt.edu between April 19 May 14; log on with your EUID and password.

• 
  12.06.2010
  

Part I 30 points: I'll ask you 10 questions about Beethoven, Piano Sonata Opus 26, Funeral March: pdf

Part II 30 points: I'll ask you pc set theoretical questions about one of the pieces from Webern, Pieces for Violin and Piano Opus 7: pdf

Part III 40 points: I'll ask you a serial question or two about one variation from Webern's Symphony Op. 21: pdf

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  Webern, Pieces for Violin and Piano Opus 7: mp3
  
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  Webern, Symphony Opus 21, II: mp3
  
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  12.08.2010
  
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  12.17.2010
  
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  Final Exam from 10:30 to 12:30