Music
301/Music 304
Winter
2008
Blog updated March 4, 2008
Instructor: Professor John Rahn, Music 217, 543-2291, jrahn@u.washington.edu, office hour Th 2:30 or by appointment
TAs:
Brad Osborn brad06@u.washington.edu
Richard Pellegrin rpellegr@u.washington.edu
Richard Johnson zownts@u.washington.edu
Office room Music 56, 3-6896, office hours tba
Materials:
The Complete Musician, Steven G. Laitz
The Complete Musician, Student Workbook Volumes I , Steven G. Laitz
New Approach to Sight Singing, Berkowitz, Fontrier, Kraft (4th ed) (abbr. BFK)
Bring the Laitz text and workbook to Monday preceptorials, and only the text to Tuesday/Thursday class.
Bring BFK to your Music 304 labs on Wed and Fri.
Bring notebook paper, music paper, pencils, and eraser to all classes.
Music 301
Goals
Our primary goal this term is to learn about musical form and compositional techniques, and to apply this knowledge both analytically and compositionally in Classical and Romantic styles, generalizing and extending the harmonic and contrapuntal skills you learned last term writing Bach-style chorales. Secondarily, we will learn more about chromaticism and modulation, and as time allows, integrate “advanced” chromatic chords such as the augmented sixth chord and the Neapolitan sixth chord into your abilities.
First, form: we will cover the material in Part 4 of Laitz (Chapters 17 through 20), and all kinds of sequences (we won’t depend on Laitz for sequences), then Chapter 23 on binary forms. After the mid-term exam, we will finish with the advanced harmonic material in Laitz 25, and 26 and 27, including chromatic modulations of all sorts, as time allows.
Evaluation
Grading for 301
Your final grade in Music 301 will be based on an average of components in these proportions:
Assignments and quizzes, 65%
Midterm exam, 20%
Final project, 15%
Grading for 304
The two basic components of Music 304, the ear-training course that you take
concurrently with Music 301, are sight-singing and dictation. Your progress and
performance in these two basic components are assessed and graded separately, but you
must earn at least 2.0 in both sight-singing and dictation in order to receive a final
grade of at least 2.0 and be admitted to the next course in the core theory sequence.
Here's how it works:
If you earn at least 2.0 in BOTH sight-singing AND dictation, your final grade will
consist of the average of these two grades.
However, if you earn lower than 2.0 in EITHER sight-singing OR dictation, your final
grade will be the same as the LOWER of the two grades. In other words, you will not
pass the course and will have to take it again.
This is the policy of the Theory Division for all core classes.
Assignments
The weekly assignment schedule:
Thursdays: hand in assignments, start new weekly
material, get new assignment
Mondays: get graded assignments handed in last Thursday
Tuesdays: 2d half of weekly material in class
No assignment will be accepted after the end of class each Thursday (except in documented medical or other genuine emergency cases allowed by your preceptorial instructor). You are responsible for all assignments even if you miss the classes when they are assigned, explained, or due. These assignments will typically require a lot of work, so start work on them early! The readability of the assignment can count into the grade for it, including your handwriting and the correctness of the notation.
Music 304 labs on Wed and Fri will have other kinds of preparation.
Quizzes and Exams
A number of (always popular) unannounced POP QUIZZES will be given throughout the term. They will always be given at the beginning of the class, so don’t be late – a missed quiz gets a grade of zero.
The MIDTERM EXAM for Music 301 will be given February 19. It will test your knowledge of all the material covered so far this term. The midterm for Music 304 will be given this same week.
Final project
This will be a larger compositional assignment assigned at least one week early and due on the last day of the term, Friday March 10. No late projects will be accepted after 5pm Friday March 10 (subject to medical emergency and so on).
Each week I will post an update to the class blog, containing notes on the past week’s material and current assignments, at
http://faculty.washington.edu/jrahn/Music3012008log.htm
Week 1 (Jan 8, 10, 15):
Jan 8 intro and how-de-dos.
For Th Jan 10, read Laitz Ch 17. How to compose, repetition, varied repetition, processes, phrases, periods. Review Chapters 13 and 14 on phrases.
I talked about how the figuration of real music becomes chorale-style chord-chord voice leading, by first eliminating the non-harmonic tones (passing tones etc), leaving only chord tones, then de-arpeggiating those chord tones, et voila, chords. So going in the other direction, if you have some chorale style chord-chord succession that works, you can 1. arpeggiate the chords, then 2. add passing tones, appoggiaturas, and so on to make tunes. But in practice, composing is more holistic than that. If you keep in mind the harmonic pillars, the beginning and ending harmonies you are aiming for, the magic of your musician’s mind will get from here to there gracefully. There will usually be a graceful curve to the tune in each phrase, going up then down then up, or down then up then down, or combinations of these. Also, parallel fifths and octaves and so on are OK in the underlying chord-chord voice leading, IF you eliminate them from the surface by clever arrangements of arpeggiation patterns and so on. Alberti Bass patterns were invented for this, for example.
Assignments for Jan 17th:
1 Analysis: Textbook page 305-6 exercises 17.1 A B C D E
Note
that in A, bar 5 beats 3 and 4 should be Bbs, not Cs
Do a
“second level harmonic analysis” for each, plus the formal diagram of the period. Identify the period category in
the grid (p 302). If it is not a period, discuss why in a short paragraph.
NB Review Laitz
Chapter 7; the definition of “second level analysis” is on p.118. Examples
17.1, 17.2, and 17.3 are also examples of this.
2 Harmonize the chorus of “Home on the Range” in pianistic style.
Use mostly Oom
pah pah in the left hand.
Start off by deciding what harmonies you will use under the tune. I would
suggest 6/8 meter and F major. The voices in the chords of the accompaniment
should voice lead correctly to each other.
3 Compose a parallel interrupted period PIP in classical pianistic style (alla Mozart). (8 bars).
Week 2: (Jan 17, 22) Laitz Chapter 18.
NB Mon Jan 21 is a holiday. No Precepts this week.
Passed out handouts of score for Mozart K330 Allegro first page. Bring this to class with your textbook Tue also as we will be using it in the future.
More on periods, sentence structure in phrases and periods, embedded sentence structures, double periods, Laitz-“asymmetrical” periods (contain an odd number of phrases), asymmetrical period as half-elaborated double period, “phrase-structure grammar” of period elaboration: How to grow simple periods into larger things. K 330 Allegro is a first section of a large form which is all one elaborated period.
This is not in Laitz: Periods of non-binary length contain a non-binary number of measures (not of phrases), that is, not 2, 4, 8, 16, 32… binary=powers of 2. Note that some even numbers are non-binary! E.g. 6,10, 12, 14… these always analyze out to some odd-numbered ingredient, such as 3 2s or 2 7s. Do not confuse periods of non-binary length with Laitz’s “asymmetrical” periods (see above); they are distinct concepts.
Assignment for
Thursday Jan 24th:
-------------------------------------
Week 3: (Jan 24, 29) Read Laitz Ch 19.
Material on sequences is found in Laitz also at:
Laitz Ch 20, Laitz Ch 21 pp. 383-392 (applied chord sequences), and Laitz Ch 22 pp. 407-409 (modulating sequences).
Assignment for
Thursday Jan 31:
I mentioned processes as one way of composing music, using the Minimalists as an example. Classical and romantic music also uses processes. Sequences are a kind of classical/Romantic musical structure which is process-oriented rather than state-oriented. We will suspend our study of musical phrase-structure while we get up to speed on sequences, using material in Laitz Chapters 19-22, then return to the idea of recursively embedded state-structures when we study "binary form" (Laitz Chapter 23).
A sequence is any series of transposed repetitions of a model. The Rule of Three: 3rd time is boring. (A general compositional maxim). Present something, maybe varied, twice, but the third time start doing something different and don’t go past 3 unless you make a vertiginous spin-out effect (at best), or a process alla Minimalists, or deadly boring. A. B. Marx: Satz (structure) vs Gang (process). A period is a Satz, a sequence is a Gang.
Summary: Three supertypes of sequences
The default meaning for the word “sequence” alone will be type 2, melodic-harmonic.
How to recognize a sequence:
supertype 1: just look at the melody
supertype 2: look at the bass -- see page 340 for all the patterns.
There are a limited number of bass patterns, so you do not
really have to do a complete roman numeral analysis, just enough
to check that the harmonies fit the model.
supertype 3: must analyze the harmonies for root movements.
Harmonic patterns
Circle of 5ths within diatonic clock and within chromatic clock. Descending 5ths produce descending 2ds at alternate locations in a sequence. Realize as ascending 4th/descending 5th alternating to keep pitches in the same range. Laitz conceives sequences as a pair of chords comprising a unit which is then transposed, so we have 3 chords to specify, the 1st of the unit, the 2d of the unit, and a 3rd which is the 1st of the next, transposed unit. If you get all the voice-leading set up for these 3 chords the whole sequence falls into place. Laitz notation is D2 (D5/A4) = D2 (A4/D5) = D2 (D5/D5), where the notation means [interval between the roots of the first and 3rd chords] ([interval between 1st and 2d chords] / [interval between 2d and 3rd chords]. For all sequences you can play around with permuting the voices in the voice-leading (not necessarily all in root position).
4 Laitz types of harmonic pattern (p 340):
Two descending patterns
1. We might as well call D2 (A4/D5) simply D2 (D5) – a descending 5th root pattern.
2. Laitz D3 (D4/A2), the “Pachelbel” sequence. If every 2d chord is a 6/3 the bass is smooth; Laitz calls this D3 (D4/A2) + 6/3.
And two ascending-2d sequence patterns:
3. A2 (D3/A4)
4. A2 (A5)
Note the cadences between links in the sequence chains:
1. D2 (D5) V-I authentic
2. D3 (D4/A2) V-VI deceptive
3. A2 (A5) IV-I plagal
4. A2 (D3/A4) V-I authentic
These cadences propel the chain forward.
Remember, in any of these patterns, you can permute the voices, e.g. swap the alto with the bass line, though sometimes this may create a dissonant 4th or other problem peculiar to the bass, which is a negative. You can also alternate 5/3s with 6/3s in many cases. What you get is generally a smoother bass line.
Some generalizations:
Circle of fifths go up and down A2 (A5), D2 (D5). If down the cross-link move is quasi-dominant (V-I type). If up the cross-link move is quasi-plagal (IV-I), which is weaker.
D3 (D4/A2), Pachelbel, is paired in many respects with A2 (D3/A4):
D3 (D4/A2): 5-6 voice sequence DOWN, parallel thirds DOWN. The +6/3 option puts the parallel thirds in bass and sop.
A2 (D3/A4): 5-6 voice sequence UP, parallel thirds UP. The +6/3 option puts the parallel thirds in bass and sop.
In both of these there are 3 essential voice plus one extra that just skips around doubling. You can do almost anything with the extra voice.
The sequence patterns will land you on chords and voicings that would not be correct outside the sequence but are OK as part of the pattern, such as doubled major thirds in a chord, or root position diminished chords. Some of the Laitz home-brewed exx have parallel octaves by similar motion across alternate chords in outer voices (p 344 19.13C), which is sort of OK but still sounds bad and can often be avoided by swapping notes among voices.
Week 4 (Jan 31, Feb 5): Read Laitz Ch 20, 21, 22. Especially relevant are Laitz Ch 21 pp. 383-392 (applied chord sequences) and Laitz Ch 22 pp. 407-414 (modulating sequences).
NB MIDTERM EXAM TUE
FEB 19
Homework assignment
for Feb 7:
1. WORKBOOK exercises
20.11 A B C (keep
these simple)
2. TEXTBOOK exercise 20.3 B on page 358
use a melodic-harmonic sequence
use suspensions in the sequence
use keyboard style in classical or late
baroque (bach) style
3. Write a SATB
diatonic sequence that uses interlocking 7ths in suspensions.
4. Write a SATB
diatonic sequence using applied dominants in which the bass in the harmonic pattern
ascends in a chromatic scale. (Hint: this is an A2 that uses inversions.)
Sequences in context. Sequences with 7ths, with inversions, and with applied dominants. See Laitz synoptic chart on page 389-90.
Context for sequences
Laitz shows ways to put a sequence inside a phrase (period) – but this is relatively unusual or minor in real music. It is a case of a Gang inside a small Satz. More common is the Satz-Gang-Satz paradigm, in which the sequence leads from one phrase or period or section to another one. In a fugue, a sequence almost always follows the 2d entrance of the subject, leading back to the tonic form of the subject for the 3rd entrance, and sequences abound between the sections with the subject. You will often find sequences between the first and second periods of a classical form first section, for example, and often a sequence begins a 2d section (in binary or sonata form), after the double bar. You will almost always find sequences in classical sonata-form development sections. Listen to the development of the Mozart Symphony #40 in g minor, for example – a huge string of sequences in a brilliant array.
Contrapuntal origins
Chains of parallel 6ths are a very simple kind of one-element chain.
If you hold onto the top note of each 6th and resolve it down only after the bass has moved down, you get a chain of 7-6 suspensions. The link=unit in the sequence is now a 7-6 suspension. This is a 7-6 SUSPENSION SEQUENCE.
Add the third note of the triad within each 6th in the chain.
.
Now if you interpolate bass notes moving twice as fast, so that every other bass note is a 4th above each bass in the previous 6/3 chain, you get a D2(A4/D5) sequence in which every chord has a 7th which resolves down to a 10th in the next chord. The 3rd of each chord becomes the 7th of the next chord. This is an INTERLOCKING 7ths PATTERN. Laitz calls it a D2 (A4/D5) with interlocking 7ths (p.359). There is also a simpler version called a D2 (A4/D5) with alternating 7ths (see p. 359, 360).
Example:
The chain of parallel 6ths, with middle voice playing the remaining note in the 6/3 triad
A G F E
E D C B
C B A G
Becomes a chain of 7-6 alternating suspensions
A A G G F F E
E D D C C B B
C B B A A G G
Becomes a chain of interlocking 7-10 suspensions as the bass skips around in a (A4/D5) pattern
A A G G F F E top/bass: 6 7 10 7 10 7 10
E D D C C B B middle/bass: 10 10 7 10 7 10 7
C B E A D G C
This is also an example of a sequence that uses non-root-position chords (the 6/3s).
Modulating sequences. Elements of diatonic and chromatic modulating sequences.
Three kinds:
1 diatonic sequences, with or without applied dominants within the sequence, move through diatonic steps to a diatonic goal
2 modulating within diatonic to diatonic goal, e.g. from the key of I to the key of V
3 modulating outside of the diatonic to a new diatonic collection as goal, e.g. from the key of C to the key of F# minor.
We will treat the second and third kind, modulating sequences, at a later week when we do chromatic modulation. Now let’s talk about sequences with applied dominants, and with 7ths.
Applied dominants in sequences (See Laitz synoptic chart on page 389-90.)
As you know, you can apply an “applied dominant” to any chord simply by preceding that chord with its dominant in its own key, an actual V-I, a micro-modulation.
Take any of the sequence patterns from the earlier chart on p 340 that move cross-link by descending 5th root movement, both root and 6/3 versions: D2 (D5), A2(D3/A4), and even D3(D4/A2) as this is a V-vi deceptive cadence. Any of these can be turned into a sequence with applied dominants, usually dominant 7ths (see p 389). In addition, there is a variant of the D3 sequence in which the cadence across the links is not deceptive, but a true V-I (see p 387); this is properly a D3(A3/D5) and of course can use applied dominants. Applied dominant 7th chords are juicy enough so you can even use V4/3 as well as V7 and V6/5, giving more choices for the tunes in the voices (a poem). (p 387) Applied dominants will involve chromatic cross-relations, see Ch 21 on handling these but basically they are tolerated and even valued. In particular, you can use applied dominants in alternating and interlocking 7 patterns. (p 389). The resulting voice leading often produces chromatic tunes in the voices. Study the chart on pp 389-90 so you know what upper-voice and bass tunes are accommodated but which sequence patterns.
The Brahms Intermezzo on p. 362, 20.5 B is an especially good example of applied dominants in an interlocking 7-6 sequence pattern. The CPE Bach (20.5 C) is another example.
Week 5 (Feb 7,
12): Binary Form, variation (Laitz Ch 23)
Binary form is the most primitive of the basic kinds of structures larger than a period. Recall that periods were made out of two or more phrases. Larger forms are made out of 2 or more periods, or phrases, or some combination of phrases, periods, and sequences; it continues the recursive tree-structure upwards.
Basically a binary form is a form that has 2 parts. (Duh.) Typically, in Baroque, classical, and early Romantic music, each of the two parts is repeated within a set of repeat signs: AA, BB. Each A or B may have internal structure, such as A= aa or aa’ or ab. Each A or B may itself be a period, a phrase, or something else such as a zebra.
All the categorical distinctions Laitz set up for periods could be applied also to binary forms: melody that is contrasting or parallel in the two halves, cadence patterns that follow the sectional, interrupted, continuous, or progressive paradigms (and some others perhaps). Laitz does not take advantage of this, but you can use all this to help you understand the internal structure of binary forms.
Laitz introduces a number of new terms for binary form:
Sectional bf: first half cadences on I
Continuous bf: second half continues from the ending harmony of first half, which is not I
Simple bf: this is a misbegotten term which we will not use. It mostly means, “not rounded.”
Rounded bf: AA / BA BA or at least, a part e.g. half of the first half’s A returns at the end of the second half, cadencing on the tonic at the end. This is a parallel return in that the melodic material recurs.
For example, for A=ab: ab ab/B-sequence ending on half cadence, ab. The final ab might be just a, or even just b. If it is only the closing part of b, then the bf is not rounded, but balanced, see below.
The digression within a bf: the B part of a rounded bf, or the first half of the second half of any bf, if that is a Gang of some sort, often a sequence.
The interruption within a rounded bf: the half cadence (on V) at the end of the B section (digression) of the bf. Note that this usage varies from the more usual usage (Laitz for periods, and other theorists for binary form and so on), which calls the pattern I V | I V I an interruption. It is also possible to have a half-cadence at the end of the first half of the second half of a non-rounded bf, which we can also call an interruption.
Balanced bf: a bf that is not rounded, but in which the stuff (melodic and/or harmonic) at the close of the first half recurs in some form, perhaps not very close to the original, at the close of the second half, with the harmonies adjusted as necessary to cadence on I at the end of the form.
Imagine now a rounded simple sectional binary form: Its pattern could be A B expanded to
a(I) a(I) | x(V) a(I)
which reduces to a I V I pattern, if you do not include the repeats. Both tonic areas use the same melodic material while the dominant-cadencing digression uses some contrasting melodic material. How do we distinguish this from a ternary form? Laitz tries to address this question with a schema on page 530, in Chapter 28. However, if you take a look at it, you will see that this does not distinguish the rounded binary form situation above from a ternary form.
You may ask, if a rounded binary form is something like AA BA, why isn’t it a three part ternary form? Well, if it sounds enough like three things rather than two things, it is ternary. But the repeat signs pretty much guarantee that it will sound like two things: A A | BA BA.
Tuesday: Variations.
Variation form is continuous or sectional.
Continuous: a shorter thing, phrase or period, often ending in V, not adding up to a complete form (such as binary form), is repeated with variations. Example: Pachelbel Canon, Last mvt of Eroica.
Sectional: The Theme is a complete form (piece),
often in binary form. Each variation repeats the entire Theme, varied. Exx Mozart Piano Variations (17 different sets of
variations), Brahms-Haydn Variations, usw.
So, what is varied, and what is kept the same? There
are no rules – each variation should bear some recognizable resemblance to its
Theme or model. Things you can keep the same include: the bass, the form (or
period or phrase) structure, the melody, the rhythm…. in any combination.
Sometimes the composer plays a little game with you –
can you find the theme-thing in the variation-thing? Exx Brahms-Haydn Variations.
Homework due Thursday
Feb 14 (Valentine's is
not a UW holiday!):
1. Write a classical
or Baroque keyboard style diatonic sequence in the key of F# minor using
applied dominants with interlocking 7ths moving from i
to V, then close off the phrase using iv-ii-V(6/4, 53)-i.
Total harmonic pattern:
i - <sequence> - V – vi - iv – ii -
V(6/4, 5/3) – i
Note that this could be the basis of a digression in a rounded binary
form, with the half cadence on V resolving to the tonic at the end.
2. Find an interesting example in Bach, Haydn,
or Mozart of a rounded binary form and analyze it thoroughly. The example
should not be one used in the textbook. Include a copy of the score with your
answer. You need not label every chord, just the main harmonic motions. Your
analysis should include:
a) is
the bf sectional or continuous?
b) what
is the form of the first half? E.g. two periods, the first parallel sectional,
the second a contrasting progressive period; and so on.
c) how
does the digression work, exactly – what does it do and how? E.g. moves from V
through a D2(D5) +6/3 applied sequence
with interlocking 7ths to the tonic, then to a predominant leading to the
half-cadence “interruption” that ends the digression.
d) what
goes on after the digression? E.g. a period similar to the second half of the
first part of the binary form, with its ending modified to end on the tonic
rather than (whatever else). Or, a complete repeat of the entire first half,
but with the end modified as before. Or….
e) any
other remarkable or interesting feature of the music.
Week 7 (Feb 14, 19):
MIDTERM EXAM
Feb 14 Thursday review for mid-term exam
Feb 19 Tuesday: MIDTERM EXAM on anything we have covered so far.
Week 8 (Feb 21, 26) Augmented and Neapolitan 6th Chords:
Review (from last term) Ch 24 on Modal Mixture.
Read Ch 26, Neapolitan 6th Chord and Ch 27, Augmented 6th Chord. (We are skipping Ch 25 in order to treat modulation more thoroughly after learning Neapolitan and Augmented chords.)
Thursday Feb 21 Neapolitan 6th chord
Tuesday Feb 26 Augmented 6th chords
Note—You are going from the Frying Pan of Form into the Soup of Chromaticism. The material for these two weeks (7 and 8) is mostly NOT in Laitz, but it should be. You can find examples of real-music modulations using N6 and A6 chords in Laitz Ch. 26 and 27, but chromatic modulation and modulatory sequences are not treated in Ch 25. Yet these are essential to Classical and Romantic music and to other genres such as jazz.
Homework due Th Feb 28, covering both Neapolitan and Aug 6 chords (this
is less than it seems):
Neapolitan 6ths
Homework:
Write SATB format
schemas:
In F major, I -- bII6
-- V 8-7 – I
In C# minor, i -- bII6 – i6/4 – V7 – i
In E major, I – bVI (from minor) – bII6 – V – I
Analyze: text pp
489-90 26.2 B and D (mm 1-13 only of D): Roman Numeral
the harmonies, describe the form on the phrase, period, and sequence levels
(these directions replace the directions that are in Laitz
for these).
Augmented 6ths
homework:
Text p 510, 27.2 A
for each of 1-8, name the key, the kind of Aug 6 chord, and write notes to
resolve the Aug 6th chord
p. 514-15 27.5 C
(Schubert): RN the harmonies, form of first half; 27.5 B (Haydn), RN the
harmonies, where is the augmented 6 chord, describe the sequence in mm 15-24.
-------------
Week 8 (Feb 28, March
4): Chromatic Modulation
Review Chapter 22 and
read Chapter 25
Th Feb 28: review of modulation.
Nasty, Brutal, and Short: The three-chord model for modulation: oldI – pivot – newI
modulation using modal mixture. They loooove to move down a major 3rd, so dramatic:
For example, I – i = iii – V – I (E e VofC C); or I – i = vi -- iv – V – I (Db - db - D - E(VofA) - A); exx in Laitz.
The 4-chord model: I x=PD, V I where the pivot chord acts as a PD in the new key.
Tue March 4:
review of A6 and N6 chords. Use in modulation schemas
UP 1 semitone: A6=V7; for example, starting in C, I, A6=V7, I (in Db)
DOWN1 semitone: V7=A6; for example, starting in C, I, V7=A6, V, I (in B)
UP or DOWN 6 semitones: N6=V6 or V6=N6; for example, starting in C, I, V6=N6, V, I (in F#)
Once you have a modulatory scheme, you can use it as the cell of a
modulating sequence.
So using A6, you can modulate through a sequence of keys by semitone up or down; using N6, you can toggle back and forth between keys a tritone apart.
Music
301 assignment for Thursday March 6.
In SATB chorale
style, always using a pivot chord, write and RN analyze:
1. modulate from Bb major to Gb
major in 4 chords (4 chords in the total progression).
2. modulate from E major to F minor in 4 chords.
3. modulate from Eb minor to
D major in 4 chords using an Augmented 6th-chord pivot.
4. modulate from C minor to E major in 4 chords using
a Neapolitan 6th in E as pivot.
5. modulate from G minor to C# major in 4 chords.
6. EXTRA CREDIT: modulate from A major to F# minor using a descending minor 2d sequence
each cell of which has 4 chords using an Augmented 6th as in problem
3 above. Treat the F# minor as a minor iv and resolve to V of C#, ending with a
PAC in C# major
Week 9 (March 6, 11, 13): FINAL ASSIGNMENT due 5pm
Friday March 14.
Schemas
using the diminished 7th chord; generating sequences from schemas.
A little of this on diminished 7th chords can be found in Laitz pp. 633-37.
Any diminished 7th chord vii7 may be regarded as a dominant minor 9th chord, V b9/7, without the root. Diminished 7th chords act like dominants and you can use them in place of a dominant (though a V is more final -- PAC goes better with a V). vii7 chords excel in fluid harmonic situations such as modulations and modulating sequences. Vii7 chords are the “universal solvent” of tonal music – they will dissolve almost any key into another.
Each vii7 chords has 4 pitch classes; by respelling the chord any one of these 4 pc can be regarded as the root. The root of the vii7 resolves upwards by semitone to the root of the tonic of its key. So, we have 4 pc each of which can resolve as a quasi-dominant leading tone to 4 different keys. These 4 keys are themselves related in a stacked-minor-third, vii7 pattern.
The vii7 chord is spelled in the key to which it will resolve. For example, F#-A-C-Eb, the vii7 of G, can be respelled as A-C-Eb-Gb, the vii7 of Bb, and also as C-Eb-Gb-Bbb, the vii7 of Db, and (enharmonically) as D#-F#-A-C, the vii7 of E. The 4 possible keys are G, Bb, Db, E.
So you can use vii7 chords to modulate up or down by minor thirds.
Example: starting in C, I, vii6/5, I, vii6/5=vii7 (of Eb), I (in Eb)
Or by tritones:
Example: in C, I, vii7=vii4/3 (of F#), I (in F#)
You can also use the applied-dominant vii7 of some chord other than the tonic as a pivot.
Example: starting in C, I, vii6/5, I, vii6/5=vii7 (of Eb), i(in Eb minor)=iv (in Bb), V, i (in Bb minor).
This gets you from C to Bb minor via an applied-dominant vii7 of the subdominant of Bb. If you had resolved the briefly tonicized Eb minor chord here instead as a ii, going on ii – V – I, the progression would end in the key of Db instead of Bb.
This kind of progression is often effective in real music as it moves through some PD harmony as a pivot.
All of these brief SATB modulating progressions of 3 or 4 chords are just skeletons, schemas that would usually , in real music, be the underlying harmonies of longer progressions that flesh out the skeleton, establishing the initial key, setting up the pivot, and establishing the destination key though a PD V I of some sort.
Once you have a modulatory scheme, you can use it as the cell of a
modulating sequence.
Example: starting in C, I, vii6/5, I, vii6/5=vii7 (of Eb), I (in Eb), vii6/5, I, vii6/5=vii7 (of Gb), I (in Gb), and so on.
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Music 301 Final
Project (Winter 2007)
Final projects due
Friday March 14 at 5pm
at the TA office.
Write a short piece
in keyboard style in a major key. The piece should:
be in three parts, first a period, then a
sequence, then a varied repeat of the first period.
modulate to V at the end of the first period (so it
is some kind of “progressive period”)
the sequence should
be a chromatically modulating sequence starting on the tonicized
V of the home key (where the first period left off), and modulating upwards or
downwards by minor thirds 4 times – a complete cycle of minor thirds – ending
again on the tonicized V of the home key. The cells
of this sequence can be longer than just 2 chords. After the sequence ends on
V, go on to de-tonicize V – re-establish it as V in
the home key – and resolve this V into the beginning I of the next period.
The third part, the
last period, should repeat the first period with this change: instead of modulating
to end the period on V, end the period with a PAC on I.
Make this into a
binary form by adding repeat signs at the end of the first part and at the end
of the piece.