Composition

History, Theory

Welcome to the composition portal! All your homework is listed here.

If you need more staff paper, you can print some from here: https://www.musictheory.net/tools/paper/blank

Week 4

  1. We will be looking at YOUR composition work next week – no excuses. Use all techniques we have covered to this point.
  2. Vocal melody exercise: find 1-2 lines from a poem other text (by an established author) that would be suitable for setting to music. Identify key features of the text.
    • what is the syllabic stress?
    • what are the most important words?
    • set the text to a melody in a non-standard scale (not major/minor)
    • use rhythm, meter, and intervals to emphasize stressed syllables and key words
  3. Read James Agee’s poem Sure On This Shining Night. Compare Samuel Barber’s setting with Morten Lauridsen’s. Both were/are American composers. Ignoring the stylistic differences between these 2 compositions, compare their treatment of the text through melody.
    • First analyze the text, identifying the syllabic stress and key words.
    • Focus only on melody In each composer’s setting. Find a few motifs that recur in the melody only.
    • In each melody, identify which words in the text have the following features:
    • melodic emphasis – larger or more dissonant intervals stand out
    • rhythmic emphasis (agogic accent) – longer notes emphasize certain words
    • melisma – using more than one note per syllable also creates emphasis
  4. Listen to Stravinsky’s The owl and the pussycat. This piece is from later in Stravinsky’s career when he focused on 12-tone (serial) composition, meaning the use of all 12 chromatic notes in a regular pattern.
    • Even though this song is fairly atonal (has no clear key), the same text setting features apply. Identify which key words have melodic or rhythmic emphasis.

Week 3

  1. Complete week 2’s work.
  2. Scales: create a piece from a scale of 3-6 notes. Avoid using a scale you already know, even if it’s only part of the scale (e.g. first 5 notes of major scale).
    • Identify the interesting features of the scale: what intervals or chords does it contain? Which ones need special treatment (e.g. tritones and minor seconds)?
    • Either rewrite one of your existing pieces in this scale, or write another short piece.
    • Your piece can use transposed versions of the same scale, but it cannot use any notes that don’t belong to the scale (E.g. C Eb can be transposed to D F, but do not use C D).
    • The sound world you create must be unique – it shouldn’t sound like any scale you are familiar with.
  3. Listen to movements 101, 115, and 133 of Bartok’s Mikrokosmos. Béla Bartók was a Hungarian composer who collected Hungarian folk music. Mikrokosmos is a set of 153 beginner pieces that use 20th century compositional techniques, including unusual scales and irregular meters.
    • Movement 101 is called “Diminished Fifth”. What is the piece’s scale mode?
    • Movement 115 is called “Bulgarian Rhythm (2)”. What is the rhythmic division? What is the scale? Try to identify the notes in the melody of the first 2 measures by playing through them on the piano.
    • Movement 133 is called “Syncopation (3)”. What is the the rhythmic division? What kind of chord (major, minor, etc.) is in the left hand? Which notes in the melody don’t fit this chord?
  4. Listen to part of Steve Reich’s Six pianos. This is a living American composer known for minimalist music, or music that uses repetition gradual change.
    • How long is the repeated pattern? How often does the pattern change? What is changed?
    • Most of the interesting features are generated by rhythmic elements we’ve discussed: displacement and syncopation. Which beats or subdivisions are accented?

Week 2

  1. Complete week 1’s work.
  2. Rhythmic displacement: pick one of your motifs from week 1 which is rhythmically interesting. Alternatively, pick a rhythm from one of the Ligeti movements from week 1.
    • in a simple time signature (2/4, 3/4, or 4/4), write out the rhythm in as many different displacements as possible
    • each displacement must place the downbeat in a different part of the rhythm
    • identify syncopated notes (ones that don’t land on beats)
    • clap and count the rhythms
  3. Changing metre: rewrite the above rhythms, or a rhythm of your own design, in as many different metres as possible.
    • use at least 4 different irregular metres (5/4 with emphasis on 1 and 3, 5/4 with emphasis on 1 and 4, 7/8 with emphasis on 1 and 4, etc.)
    • identify syncopations, clap and count
  4. Listen to the beginning of mvt. 6 (“Dance of Fury, for the Seven Trumpets”) of Messiaen’s Quartet for the End of Time: This piece was written by French composer Olivier Messiaen in a POW camp during WWII. He had a fascination with rhythm and especially “non-retrogradable” rhythm, meaning a rhythm that is the same when played backwards.
    • What is the time signature of the first 2 measures? What about the 3rd measure? The 4th measure?
    • Based on the recording, how would you group the notes of the 1st measure (where would you write the accents)? Which notes sound syncopated (such as the dotted ones)?
    • See how far you can clap along… good luck!
  5. Listen to the opening and first dance (Augurs of Spring) of Stravinsky’s Rite of Spring (about 4 minutes): Igor Stravinsky is one of the greatest composers of the 20th century. This famous ballet is about a pagan ritual of sacrifice that renews the earth in spring.
    • Listen to the melody at the beginning (in bassoon) and identify the motif (falling scale). Every time the motif returns, try to identify whether it is on the beat or a syncopation.
    • Augurs of Spring has a constant stream of 8th notes in 2/4 where the accent pattern changes continually. Transcribe the accents in the strings between 3:01 and 3:10 in the video (write down what you hear)
  6. Complete your short piece: Follow the instructions from week 1. You may choose to expand on your first piece, or write a second short piece to demonstrate the following:
    • use a rhythm in different displacements
    • use a rhythm in different metres, including at least one irregular metre
    • remember what we discussed in the Ligeti movement: at every moment your music must balance repetition and change

Week 1

  1. Listening: send me the names and composers of two pieces that interest you. Make sure you have both a score and recording of that piece.
    • See my listening articles for music ideas, as well as what you should know about the pieces you choose
  2. Isolate motifs: Identify two motifs from one of the pieces you picked.
    • Limit your motif to 4 notes or less
    • Each motif must be a repeating feature in the piece (by transposition, inversion, etc.)
    • Each motif must have a unique intervallic or rhythmic contour
  3. Develop motifs: using the methods we discussed, write out 3-6 lines of different variations on the above motifs.
    • You can copy out variations from the score or compose your own
    • Do not change the intervallic or rhythmic contour (with intervals, preserve the size, not quality)
    • As a result, you can either choose to use exact (real) transposition/inversion/etc., where you preserve the quality of intervals, or diatonic (tonal) transposition/inversion/etc., where you only preserve the size of intervals
  4. Listen to György Ligeti’s Musica Ricercata: mvt. 1 and 2 (feel free to listen to the whole collection). Each movement is written from a limited set of notes.
    • What are the motifs in each movement, and how are they developed?
    • Where does Ligeti repeat material, or introduce new material? What is the ratio of new to old material?
    • Listen to mvt. 10, which uses a much larger set of notes. Identify some of its motifs, their repetition, and their development.
  5. Write a short piece: Using 1 of the motifs and 2-3 of the methods from above, and using the variations you wrote, organize them into a short piece for a solo instrument.
    • Brevity is the soul of wit (maximum length of 1 page)
    • Every note must belong to a version of the motif, and the motif must be always recognizable
    • You can now modify the notes and rhythms of the motif
    • Repetition is your ally: balance the amount of familiar and new material you present at any time
    • Explore other ways of differentiating your motif (dynamics, articulation, registration, rhythmic displacement)
    • How can you begin and end the piece, still using the motif?

Intermediate Rudiments

Theory

Welcome to the intermediate rudiments portal! All your homework is listed here.

If you need more staff paper, you can print some from here: https://www.musictheory.net/tools/paper/blank

  • Week 5

    1. Minor scales: write down all minor keys onto the circle of 5ths (see last week’s instructions).
    2. Workbook: review and fix your interval qualities in lesson 6. Do lesson 3 minor scales.
      • scan/photograph and send me your intervals from lesson 6 to mark
    3. Week 5 online exercises: click here. Do the interval ear training regularly (for example, before you practise) – it is critical if you are doing an RCM exam.
      • practise singing the major scale starting from the lowest note of the interval
      • sing to the 5th note of the scale (for now)
      • use the solfege syllables (“do”, “re”, “mi”, “fa”, “so”) to guide your singing
      • you can also identify intervals by singing the first few notes of the following songs:
      • M2 “Happy Birthday”
      • M3 “Oh When the Saints”
      • P4 “Here Comes the Bride”
      • P5 “Twinkle Twinkle Little Star”

  • Week 4

    1. Minor scales: in your workbook or on the handout I supplied, write down all minor keys onto the circle of 5ths.
      • the relative minor and relative major share key signatures
      • the relative minor is a minor 3rd below the major key
      • a minor has a key signature 0 sharps/flats, and a#/ab have key signatures of 7 sharps/flats
    2. Workbook: keep working on lesson 6. Don’t do the review test yet.
      • if you complete all the intervals, start writing minor scales in lesson 3
      • scan and send me your work to review
    3. Identify all the intervals within the major scale: see last week’s instructions.
    4. Week 4 online exercises: click here. Do previous week’s exercises – be able to identify ALL of the key signatures and ALL of the intervals with high accuracy.

  • Week 3

    1. Workbook: complete lesson 6. Don’t do the review test yet.
      • don’t guess – check your intervals by comparing them to simpler ones
      • for example: for the interval Fb to Bbb, compare it with F to Bb in the key of F major (P4). Since Fb and Bbb are both one semitone lower, it is also a P4
      • send me your work to review
    2. Identify all the intervals within the major scale.
      • Build a second above every note of a major scale. Find its quality.
      • For example,  in C major, C-D is a M2, D-E is a M2, E-F is a m2, F-G is a M2, G-A is a M2, A-B is a M2, B-C is a m2.
      • Repeat this process for 3rds, 4ths, 5ths, 6ths, and 7ths.
    3. Week 3 online exercises: click here. Review the previous week’s exercises.

  • Week 2

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • double sharp (x) and double flat (bb)
      • interval size versus quality
      • diminished, minor, perfect, major, augmented interval quality
      • interval inversion (What happens to the size? What happens to the quality?)
    2. Review test (workbook).
      • If you haven’t sent me your completed review test, please do so by email, or drop it off at the next lesson.
    3. Workbook: do lesson 3 (don’t do minor keys yet), and lesson 6. Don’t do the review test yet.
    4. Circle of fifths: On the back of your handout, fill in the circle of fifths in the bass clef.
    5. Week 2 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

  • Week 1

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • enharmonic
      • key signature
      • circle of fifths
    2. Review test (workbook): from lesson 1.
      • Send me a finished copy of your review test at least a day before the next lesson
    3. Lesson 2 practise (workbook): complete the two pages of key signature identification and writing.
    4. Circle of fifths: On the front of your handout, fill in the circle of fifths in the treble clef.
    5. Week 1 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

Basic Harmony

Theory

Welcome to the basic harmony portal! You can find reference material and homework listed here.

Review Articles

  • Week 6

    1. Non chord tones:
      • Workbook p. 49 to 51: question 1, 2, 3B, 3D, 3E. Identify non chord tones – review and complete any unfinished questions.
      • Workbook p. 117, question 1. Write out suspensions using the FB as a guide. For example: if there is an E held in bass, D-C# in soprano, then the figured bass is 7-6 (7th between E and D, 6th between E and C#)
      • Revise your chorale project according to the markups I sent you. Add a non chord tone of every type into the chorale, in any voice. Omit the anticipation and suspension (V64-53 is a suspension).
    2. Analysis: listen to, play through, and analyze the 1st of these 2 famous minuets: Petzold – Notebook for Anna Magdalena Bach – Menuets in G
      • Youtube recording: https://www.youtube.com/watch?v=BWPoH5fSEAQ
      • Before analyzing chords, do the following:
      • find the form (binary, or rounded binary)
      • identify the key and approximate location of the modulation (look for accidentals indicating leading tone)
      • identify the harmonic rhythm
      • Analyze with RN, FB, cadences, and functions. Circle and label any ambiguous chords.
      • Remember, each phrase has one T-PD-D-T, and one cadence only. Phrases are typically of regular lengths (4 or 8 measures).

  • Week 5

    1. Workbook (modulation, descending 5ths sequences):
      • p. 187, question 3 (A and B) – before filling in the inner voices, use the bass line and FB to analyze each question first (add RN and function labels)
      • p. 193, question 6B – analyze the first 2 lines only. Where do the chords change (look at the rhythm of the bass line)? Where is the pivot chord for the modulation? What key does it modulate to? Play through the minuet.
      • p. 165, question 1A – complete the sequence by transposing the model, and analyze the chords with FB/RN
      • p. 173, question 6D – analyze the chords using RN/FB. Where in the 5/4 measure do the chords change?
    2. Keyboard exercises: play the following on piano
      • p. 421, 2C (descending 5ths sequence)
      • analyze with FB/RN first.

  • Week 4

    1. Workbook (secondary dominants, pivot chords):
      • p. 175, question 1 (A to H) – always think of the secondary dominant in terms of the secondary key (e.g. think of V/V of Bb as V in F major)
      • p. 185, question 1A – note the minor keys pivot to III. Indicate the pivot chord’s function in both keys.
      • in class we discussed how the scale degree of V/V is the same as ii. Which chord tones were altered between the diatonic ii and V/V? What is the scale degree of V/III in a minor key, and what notes were altered?
    2. Chorale project: link to instructions.
      • fill in all voices with the revisions from last week (include V64-53 at the end)
      • play through your chorale, looking for good voice leading throughout
      • don’t add non chord tones yet
    3. Analyze chorale: analyze the third one (in E major) using RN/FB
      • in each phrase (ending with a fermata), identify the functional chords (T-PD-D-T should happen once only)
      • bring your analysis to next class

  • Week 3

    1. Workbook (resolving II7, III and VI):
      • p. 106, question 2 (B, D, G to L) – 7ths should resolve down by step, and tritones (iio) should resolve in contrary motion
      • p. 138, question 2 (A to E, omit D) – resolve the L.T. in V to vi
    2. Chords on scale degrees: fill in the handout with all of the chords covered so far, identifying their functions (III, VI are new). Be careful with the quality of III and VI in the minor mode.
    3. Chorale project: link to instructions.
      • fix any problems in your bass line and harmonic progression
      • follow week 2’s instructions to add II and V64 chords, and fill in ALL voices
      • send me your chorale in progress
    4. Analyze chorale: print this sheet: Diatonic chorales, if you don’t have it on the back of your chorale project instructions.
      • analyze the first one (in C major) using RN/FB
      • in each phrase (ending with a fermata), identify the functional chords (T-PD-D-T should happen once only)
      • bring your analysis to next class

  • Week 2

    1. Workbook (resolving V inversions, II):
      • Revise all of the V-I resolutions on p.67, question 3 (A to F). Make sure every resolution is one of the 3 types we discussed.
      • p. 95, question 3 (A to E) – all of these dominants are in inversion, but the same rules for doubling and resolving apply
      • p. 106, question 2 (A, C, F) – treat these like IV chords. You can also double the third (^4) instead of root.
    2. Chords on scale degrees: fill in the handout with all of the chords covered so far, in both the major and minor keys.
      • I, ii, and IV, root and 1st inversion
      • V and viio, root and 1st inversion
      • V7 and ii7, all inversions
      • cadential V64
    3. Week 2 online exercises: click here. Use this online exercise to practise your 7th chord recognition. You can also read the instructions in the link to submit your time to the leaderboard.
    4. Chorale project: link to instructions.
      • Fix any problems in your bass line and harmonic progression (see my email)
      • Follow week 2’s instructions to add II and V64 chords, and write a soprano melody

  • Week 1

    1. Workbook (resolutions of V and viio): For each question, circle the active notes: leading tone (^7) and the tritone above (^4). Remember to always resolve properly and never double them.
      • p. 67, question 3 (A to F). Use all 3 possible resolutions of the V7: missing 5th in V7, triple root of I, or resolve L.T. to another voice (^7 falls to ^5 )
    2. Workbook (6/4 chords): for each 64 chord you write/find, indicate how it’s used: cadential (V64-53), passing (voice exchange), or neighbour motion.
      • p. 128, question 2 (A to K)
      • p. 130, analyze question 3, last line only
    3. Chorale project: link to instructions.
      • Read this article: Chord Function, and review the bass line you wrote for the chorale project
      • Send me your bass line and any additional work you’ve completed
    4. Chords on scale degrees: on the handout from this week, fill in the chords we’ve covered so far in class, on both the major and minor scales. For example: V is a root position triad on scale degree ^5, so you would write in the triad under ^5 (G) for the major and minor keys, on the first line.
      • I (i) and I6 (i6)
      • V and V7
      • IV (IV) and IV6 (iv6)
      • V6, V65, V43, V42, viio6
      • I64, IV64, V64 (non-functional!)

Advanced Rudiments

Theory

Welcome to the advanced rudiments portal! All your homework is listed here.

If you need more staff paper, you can print some from here: https://www.musictheory.net/tools/paper/blank

  • Week 8

    1. Terms: fill in the 6th page of your worksheet
    2. Workbook: lessons 7, 8, and 9 practise and review tests
      • Complete 2 of the unfinished review tests in lessons 7 to 9
      • Send me the latest review test (lesson 8 or 9) to mark
    3. Cadences: recreate the chord tone chart for I, IV, and V chords.
      • start by writing down all scale degrees (^1, ^2, etc.)
      • starting with the I chord, write down the locations of the root, 3rd, and 5th, under the relevant scale degrees
      • repeat for IV and V
      • circle notes that are shared between I, IV, and V (there should only be two)
    4. Transposition: transpose the following parts into concert pitch: Nutcracker excerpts
      • Both parts should transpose to the same key in concert pitch.
      • The horn (corno) part has no key signature. What should its key signature be?
      • The bracketed notes form cadences. Identify the 3 cadences.
      • play through the parts on your concert pitch instrument – it should be a familiar melody
    5. Week 8 online exercises: review previous exercises. Do more rhythmic dictation at https://www.teoria.com/en/exercises/rd.php.

  • Week 7

    1. Terms: fill in the 5th page of your worksheet
    2. Workbook: lesson 7 practise, lessons 1-6 review tests
      • Practise rhythms in lesson 7
      • Complete 2 of the unfinished review tests in lessons 1-6
      • Send me your 2 review tests to check over
    3. Triplets: for each triplet, quadruplet, etc. below, write one note value that has the same duration
      • Example: triplet (3) 8ths = 2 8ths = 1 quarter
      • Simple time: quintuplet (5) 16ths = ?
      • Simple time: septuplet (7) 8ths = ?
      • Compound time: duplet (2) 16ths = ?
      • Compound time: quadruplet (4) quarters = ?
    4. Irregular Rhythms: in each time signature, write out a measure of 8th notes using every possible way of grouping the beats irregularly.
      • 5/8 (2 possible groupings). Example: two 8ths plus three 8ths.
      • 7/8 (3 possible groupings)
      • 8/8 (3 possible groupings)
      • 9/8 (4 possible groupings)
      • 11/8 (5 possible groupings)
    5. Week 7 online exercises: review previous exercises. Do some rhythmic dictation at https://www.teoria.com/en/exercises/rd.php.

  • Week 6

    1. Terms: fill in the 4th page of your worksheet
    2. Workbook: lesson 3 practise, lesson 4, 5, or 6 review tests.
      • Complete the remaining scales writing and identification in lesson 3
      • Do 2 out of 3 review tests in lessons 4-6
      • Send me your 2 review tests to check over
    3. Chromatic, whole tone, octatonic, major/minor pentatonic, and blues scales
      • Find the pattern of intervals between the notes of each scale
      • For example: the intervals between neighbouring notes of the major pentatonic scale are M2, M2, m3, M2, m3
    4. Polychords, quartal chords, and clusters: write out an example of each, using 3-6 notes.
      • the cluster uses notes that are 2nds apart
      • the quartal chord uses notes that are 4ths apart
      • the polychord is composed of two or more different chords
    5. Week 6 online exercises: review previous exercises.

  • Week 5

    1. Terms: fill in the third page of your worksheet
    2. Workbook: lesson 2 (scales) and lesson 3 (more scales).
      • Do all of lesson 2 including the review test
      • Do lesson 3 up to what we covered in class
    3. Scale modes
      • Find the pattern of tones and semitones between each note of each scale mode. E.g. Ionian (major): T for tone, S for semitone: T T S T T T S.
      • Write down or play every mode starting on the following notes: C#, Bb, E. Identify the major key which has the same key signature/accidentals as each mode. E.g. E Ionian: E F# G# A B C# D# E, same key as E major (4 sharps), E Dorian: E F# G A B C# D E, same key as D major (2 sharps)
    4. Week 5 online exercises: click here. This week’s exercise is ear training and won’t be on the RCM exam. In each mode, listen for the note where it differs from the major or minor scale.

  • Week 4

    1. Terms: fill in the second page of your worksheet
    2. Workbook: lesson 4 (intervals), lesson 5 (triads) and lesson 6 (7th chords).
      • If they are incomplete, practise on each page up to the review test (we will do the review test after discussing scales)
    3. Identify all the intervals within the major, natural minor, harmonic minor, and melodic minor scales.
      • Build a second above every scale degree of the major scale. Find its quality (e.g. ^1 to ^2 is a M2, ^2 to ^3 is a M2, ^3 to ^4 is a m2)
      • Repeat this process for 3rds, 4ths, 5ths, 6ths, and 7ths.
      • Repeat this process for the 3 types of minor scales.
    4. Dominant and diminished 7ths – print and complete this worksheet: Dominant and Diminished 7ths.
    5. Week 4 online exercises: click here. Go back and do the week 1 intervals exercises for additional practise.

  • Week 3

    1. Terms: fill in the first page of your worksheet
    2. Workbook: lesson 5 (triads) and lesson 6 (7th chords).
      • Practise on each page up to the review test (we will do the review test after discussing scales)
      • Finish the first 2 pages of lesson 6 if they are incomplete
    3. Dissect the Augmented and Diminished triads.
      • Write down the intervals between all the notes of these 2 chords
      • Repeat this process for every inversion of these 2 chords
      • You should have a total of 6 inversions
    4. Build triads on all scale degrees of the major scale, natural minor, harmonic minor, and ascending melodic minor.
      • For each scale, write down the type of triad found on each scale degree in a chart
      • In each scale, identify where the dominant 7th chord can be found (it can only be built on one of the scale degrees)
    5. Week 3 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

  • Week 2

    1. Terms: print this worksheet: Terms – RCM advanced rudiments
      • the sheet contains all the terms you need to know
      • terms are grouped by how similar they are in language and meaning
      • fill in definitions as you come across them
    2. Workbook: lesson 4 (compound intervals) and lesson 6 (7th chords).
      • Continue practising regular and compound intervals from lesson 4.
      • Practise the first 2 pages of lesson 6 (dominant 7th chords only
    3. Dissect the Major and Minor triad and Dominant 7th.
      • On a sheet of paper, identify the intervals between all the notes of these 3 chords (E.g. minor triad: root to 3rd = m3, root to 5th = P5, 3rd to 5th = M3)
      • Repeat this process for every inversion of these 3 chords (E.g. dominant 7th, 1st inversion: 3rd to 5th = m3, 3rd to 7th = o5, 3rd to root = m6, 5th to 7th = m3, 5th to root = P4, 7th to root = M2)
      • You should have a total of 10 inversions: 3 for the Major triad, 3 for the Minor triad, and 4 for the Dominant 7th.
      • To prepare for next week… play a triad starting on every note of the major scale (E.g. in C major, CEG, DFA, EGB…). Which scale degrees have major triads? Which have minor triads? Repeat this process in the minor scale. Finally, play 4 note chords in both the major and minor scale (E.g. CEGB, DFAC, EGBD) and find the scale degree that has the dominant 7th (the name of the chord is a big hint).
    4. Week 2 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

  • Week 1

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • simple and compound intervals
      • enharmonic equivalent
      • C clefs: alto and tenor clefs
    2. Workbook: lesson 1 (C clefs) and lesson 4 (compound intervals).
      • Complete the lesson 1 practise exam and send it to me to review. Photograph or scan your work and email to me at least a day before the next lesson.
      • In lesson 4, do enough practise problems to feel comfortable with the process. At a minimum, I suggest finishing the first problem under each numbered question.
    3. Week 1 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

Basic Rudiments

Theory

Welcome to the basic rudiments portal! All your homework is listed here.

If you need more staff paper, you can print some from here: https://www.musictheory.net/tools/paper/blank

  • Week 6

    1. Rhythm drills: do simple rhythms 1.55 and 1.56, and compound rhythms 4.62 and 4.65.
      • write in the counting
      • practise counting out loud and clapping each line
    2. Week 6 online exercises: click here. Do the interval ear training regularly (for example, before you practise) – it is critical if you are doing an RCM exam.
      • practise singing the major scale starting from the lowest note of the interval
      • sing to the 5th note of the scale (for now)
      • use the solfege syllables (“do”, “re”, “mi”, “fa”, “so”) to guide your singing
      • you can also identify intervals by singing the first few notes of the following songs:
      • M2 “Happy Birthday”
      • M3 “Oh When the Saints”
      • P4 “Here Comes the Bride”
      • P5 “Twinkle Twinkle Little Star”

  • Week 5

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • interval size versus quality
      • major, minor, and perfect intervals (which sizes can be perfect? Which do you find in a major key?)
    2. Rhythm drills (same as last week): do sections 4.2 to 4.6 of the compound rhythms handout. Download and print the handout here: Rhythms – Compound.
      • Write in the counting using “1 + a 2 + a”.
      • Practise counting out loud and clapping each line
    3. Interval quality: some notes if you missed it in class
      • to find the size of an interval, count letters ONLY (D to F is D-E-F, or a 3rd)
      • to find the quality of an interval, first memorize the pattern of intervals found in a major scale, starting on the first note (the tonic). All of these intervals are either major (2, 3, 6, 7) or perfect (1, 4, 5, 8)
      • for example: in C major, C to same C is P1, C-D is M2, C-E is M3, C-F is P4, C-G is P5, C-A is M6, C-B is M7, C to higher C is P8
      • minor intervals are one semitone SMALLER than a major interval
      • to make an interval smaller, LOWER the TOP note or RAISE the BOTTOM note
      • for example: C-D is a major 2nd (M2), C to Db is a minor 2nd (m2), and C# to D is also m2
      • to identify an interval, identify the bottom note. Identify the major scale that starts on this note. If the top note is in the scale, then the interval is either major (for sizes 2, 3, 6, 7), or perfect (sizes 1, 4, 5, 8). If the top note doesn’t belong to the scale, check if it has been lowered by 1 semitone from the notes in the scale. If it is lower by 1 semitone, then the interval is minor.
    4. Intervals: List all of the intervals found between all of the natural notes (white keys on piano)
      • Start by listing all intervals from P1 to P8 with C as the lowest note (
      • Repeat by listing all intervals starting with D as the lowest note. Compare these intervals to those found in D major to find the quality. (Example: the key signature of D major is F# and C#. D to E is in the key of D major, so it is a major 2nd. D to F is NOT in the key of D major, so it is not a major 3rd. It is 1 semitone smaller than the major 3rd of D to F#, so therefore D to F is a minor 3rd.)
      • Repeat for all intervals with E, F, G, A, and B as the lowest note.
      • Ignore any interval between F and C or C and F. This is an interval we haven’t discussed (the tritone) and is neither major, minor, or perfect.
    5. Week 5 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

  • Week 4

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • compound and simple time (how do you count compound time?)
      • key signature (what are the major scales with 0 to 4 sharps or flats?)
      • order of sharps and flats
      • articulations: legato, slur, staccato, tenuto, accent, marcato
    2. Rhythm drills (compound meter): do sections 4.2 to 4.6 of the compound rhythms handout. Download and print the handout here: Rhythms – Compound.
      • Write in the counting using “1 + a 2 + a”.
      • Practise counting out loud and clapping each line
    3. Circle of fifths: Using the template from week 3, fill in all the key signatures for the major keys.
    4. Scale writing: write out the following scales:
      • Ab and D in treble clef with key signature
      • E and Bb in treble clef with key signature
      • A and Eb in treble clef with accidentals (write down the key signature and cross off the sharps/flats as you use them so you don’t forget any)
      • G and F in bass clef with accidentals (write down the key signature and cross off the sharps/flats as you use them so you don’t forget any)
    5. Week 4 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

  • Week 3

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • key signature (what are the major scales with 0 to 4 sharps or flats?)
      • order of sharps and flats
      • circle of fifths (what is the relationship between adjacent keys?)
      • dynamics: pianissimo (pp), piano (p), mezzo piano (mp), mezzo forte (mf), forte (f), fortissimo (ff), crescendo (cresc.), decrescendo (diminuendo, dim.)
    2. Rhythm 2-part drills: If you didn’t get the newer page, download it here: Rhythm – Simple (part 2). Do sections 1.27, 1.49, 1.50, 1.51
      • Write in the counting using “1 + 2 +”.
      • Practise counting out loud and clapping each line. Although they are called “2-part” drills, count and clap each line as its own part.
      • Count and clap 1.25 with both hands at the same time – left hand on the lower part, right hand on the upper part.
    3. Circle of fifths: Download this circle of 5ths template. On the front side, fill in the names of all major scales.
      • start on C major at the top (no sharps or flats)
      • find the 5th note in the scale ABOVE the tonic (above C)
      • This is the scale with one more sharp. Use “Father Charles Goes Down And Ends Battle” to find the new accidental.
      • write down the key signature
      • repeat for the other sharp scales
      • to go to a scale with one less sharp (one more flat), go to the 5th note in the scale BELOW the tonic (which is the 4th note ABOVE)
      • Use “Battle Ends And Down Goes Charles’s Father” (opposite of the sharps) to find the flat key signature
    4. Week 3 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

  • Week 2

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • simple time
      • measure and bar line
      • pickup measure
      • dotted notes
      • tie
      • scale and major scale (what is the pattern of semitones and tones?)
    2. Rhythm 2-part drills: section 1.26, 1.30
      • Write in the counting using “1 + 2 +”.
      • Practise counting out loud and clapping each line. Although they are called “2-part” drills, count and clap each line as its own part… for now.
      • We will count and clap these sections in class next week.
    3. Scale construction: construct the following scales by following the pattern of whole tones (T) and semitones (S). Write down each scale using a different letter for each note.
      • starting on a D, follow the pattern S-T-T-T-S-T-T
      • starting on a F#, follow the pattern T-S-T-T-T-T-S
      • starting on a C, follow the pattern T-T-T-S-T-S-T
    4. Week 2 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

  • Week 1

    1. Terms: I’ll be reviewing what these mean next week. If you forget, try to find a definition online.
      • semitone and tone (whole tone)
      • enharmonic (“same-sound”)
      • accidentals: sharp and flat
      • staff and ledger line
      • interval (what is its size?)
      • treble and bass clef (can you draw them?)
      • whole, half, quarter, eighth, sixteenth, thirty-second notes and rests (can you draw them?)
      • time signature (what are the top and bottom numbers?)
    2. Rhythm 2-part drills: section 1.25
      • Write in the counting using “1 + 2 +”.
      • Practise counting out loud and clapping each line. Although they are called “2-part” drills, count and clap each line as its own part… for now.
      • We will count and clap 1.25 in class next week.
    3. Relative intervals: on a sheet of staff paper, write out this mystery melody in whole notes. Each interval measures the note’s distance from the previous note. Bonus points if you can name the tune!
      • start on G
      • write a note that is a 4th UP from the previous note
      • keep writing notes using the following intervals: 4th UP, 2nd down, 3rd down, 3rd down, 4th UP, 4th UP, unison, 3rd UP
    4. Absolute intervals: again,  write out this mystery melody in whole notes. This time, we will call the F above middle C our tonic, or “home note”. Each interval measures the note’s distance from the tonic. Bonus points if you can name the tune!
      • write a note that is a unison with the tonic (F)
      • write a note that is a 3rd ABOVE the tonic (F)
      • keep writing notes using the following intervals: 4th ABOVE, 6th ABOVE, 5th ABOVE, 3rd ABOVE, unison, 3rd below, 5th below, 4th below
    5. Week 1 online exercises: click here. Do each exercise until you are confident with the process. Don’t forget to submit your time to the leaderboard.

Rudiments Exercises

Theory

The following 20 question exercises are from www.musictheory.net. Use them to practice the skills we cover in class.

Ladder Challenge

Under each exercise is a leaderboard of the fastest completion times. To get your name on the leaderboard, copy the verification code you receive after completing the challenge and email it to me, or post it in the comments below. You can retake the challenge as much as you like, but you have to score 100% correct to be on the leaderboard.

Note: you can only post scores for the exercises assigned to your current theory class. For example, if you are doing “Advanced Rudiments”, you can’t post a score for a challenge under “Basic Rudiments”. Cheating will ban you from the leaderboard.

At the end of the term, I’ll be handing out sweet-tooth prizes for the top performers, so practise hard!

Beat the Teacher

Think you’re better than me? Try to beat the teacher times below! If you somehow manage to accomplish this utterly ludicrous and totally impossible task, I’ll compose a special short piece of music dedicated to you.

Basic Harmony Chorale Project

Theory

Using the chorales of J.S. Bach as a model, write a two-phrase diatonic harmonization in 4 voices. For each step, write out a separate copy of your chorale-in-progress and play test your work.

Week 1

Preparation

  • Pick a key, time signature, pickup length, and harmonic rhythm
  • If you chose a minor key, remember to raise the leading tone (L.T.)
  • The harmonic rhythm shouldn’t change (except to pause on the last note of each cadence)
  • Remember to resolve ALL L.T. and chordal 7ths

Create a bass line

  • Follow good melody writing principles (stepwise motion, compensate leaps) where possible (everywhere except cadences)
  • Phrase 1 ends with HC (T-PD-D functions), phrase 2 ends with PAC (T-PD-D-T)
  • Include at least one of each of the following: I, I6, V6, V65, V43, V42, IV, IV6, V, V7
  • Extend tonic function using the linear (non root position) dominants
  • Analyze everything: RN/FB, function, cadences

Week 2

Substitute chords

  • Replace one IV or IV6 with ii or ii6
  • Replace one cadential V or V7 with V64-53 or V864-753

Add a melody line in soprano

  • Follow melody writing principles and also good voice leading principles (prefer oblique and contrary motion)
  • Use good doublings between bass and soprano (root preferred, 5th better than 3rd)
  • DON’T double active tones or 2 consecutive notes, as that creates parallel octaves
  • Include 1 voice exchange (S and B switch chord tones by step through an intervening chord)

Week 3

Add alto and tenor

  • Follow melody writing and voice leading principles
  • Make sure all chord tones are covered (you may omit the 5th in V7 and cadential I)
  • Check doublings
  • Check for parallel 5ths and octaves by following the voice leading of those intervals
  • A and T parts are often more “boring” with lots of oblique motion: this is a sign of good voice leading, but keep things interesting by making them more active towards cadences

Add non chord tones

  • Include at least 1 of the following in any voice: P, AP, N, ESC, APP
  • Circle and label the suspension in the V64
  • Add one anticipation in S at a cadence

Basic Harmony Terms

Theory

Melodic motion

There are two ways for notes to behave in a melody.

  • Step: the next note in a melody is one scale degree (difference of one letter name) or the interval of a (2) second away.
  • Skip (leap): next note is not a step away

Contrapuntal motion

A voice in music refers to an independent line of melody. In actual music voices can be doubled (played by multiple instruments) or harmonized (played with multiple pitch levels), but this does not mean additional voices have been created. A line of music must be sufficiently unique in its contour (pitches) or rhythm to be noticeable as a separate voice. Counterpoint is the technique of writing multiple voices that are distinct from one another.

Here is a list of ways that two voices can move relative to one another from most alike (least contrapuntal) to least alike (most contrapuntal).

  • Parallel motion: both voices move in the same direction and distance (creating parallel intervals)
  • Direct motion (similar motion): both voices move in the same direction (creating hidden parallels)
  • Oblique motion: only one voice moves, the other stays stationary
  • Contrary motion: the voices move in opposite directions (inward or outward)

Consonance and Dissonance

Here are commonly found intervals listed from most consonant to most dissonant. To compare compound intervals (intervals greater than an octave), first reduce to simple intervals.

  • Consonant
    • Perfect
      • (1/8) perfect unison and octave
      • (5) perfect fifth
      • (4) perfect fourth (sometimes)
    • Imperfect
      • (3/6) major and minor third and sixth
  • Dissonant
    • (4) perfect fourth (sometimes)
    • (2/7) major and minor second and seventh
    • (x4/°5) augmented fourth or diminished fifth, plus all other augmented or diminished intervals

An interesting note: composer Paul Hindemith further divided dissonances into perfect and imperfect dissonances. According to him, dissonant intervals that occur naturally in a piece of music’s scale or mode are perfect, while intervals that have been modified (augmented/diminished) are considered imperfect. Hindemith describes this theory in his book The Craft of Musical Composition.

While the (P4) perfect fourth is objectively consonant, it has a subjective reason for being a dissonance. In the Renaissance and Baroque eras it was treated as dissonant because harmonies resolved to triads, which do not contain strong intervals of a fourth. In later periods fourths were used more often as consonants. Hindemith also suggests an objective explanation for a dissonant fourth: the combination tones (another property of overtones) of a perfect fourth produce a pitch that reinforces the upper note instead of the bass, whereas the combination tones of a perfect fifth reinforce the lower note. This makes the fourth sound less stable, as it wants to be heard in terms of the upper note.

Chord Function

Theory, ,

Functions are an abstract level of harmony that exists over the level of individual chords. Functions in harmony are like a “zoomed out” version of the music.

Table of common chords by function

Function types

Chords can be categorized into three functions:

  • Tonic (T) – the foundation of the key, centered around the tonic note (scale degree ^1) and the triad built over it (^1, ^3, and ^5)
    examples of tonic chords: I (strong), I6 (weaker), vi (weak)
  • Dominant (D) – the opposite of tonic, centered around the fifth (scale degree ^5) and the leading tone (^7)
    examples of dominant chords: V (strong), viio7 (weaker), V42 (weak)
  • Predominant (PD) – centered around ^2 and ^4, used to prepare dominant or expand tonic/dominant
    examples of predominant: IV, ii6

The basic phrase model has the following form:

T, PD, D, T

where PD, and either the first or the last T, are optional. Each phrase in common practice music does this exactly once. Here are some examples of possible phrases:

  • T-D-T (example: I-V-I)
  • T-D (example: I-V)
  • D-T (example: V-I)
  • T-PD-D (example: I-ii-V)
  • PD-D-T (example: IV-V-I)

Expansion

Each function area can be further expanded using weaker functions. These expansions are like mini-phrases, and usually follow the form of the basic phrase model. However, they are weaker because they use chords with weaker function. For example, chords in inversions are usually weaker than chords in root position. Chords that don’t have strong bass motion between ^1, ^4, and ^5, are usually weaker.

  • Tonic expansions:
    • T (I) becomes T-T (I6-I)
    • T (I) becomes T-D-T (I-V43-I6)
    • T (I) becomes T-“PD”-T (I-IV64-I): PD is actually a passing or neighbour motion, and non-functional
    • T (I) becomes T-PD-D-T (I6-ii6-V43-I6)
  • Predominant expansions:
    • PD (IV) becomes PD-PD (IV-ii6)
    • PD (ii) becomes PD-T-PD (ii-I6-ii6)
  • Dominant expansions:
    • D (V) becomes D-D (viio7-V7)
    • D (V) becomes D-T-D (V64-I6-V7)
    • D (V) becomes D-“PD”-D (V6-IV6-V64): PD is actually a passing or neighbour motion, and non-functional
    • D (V) becomes D-T-PD-D (V-vi-IV-V)

An example of how a phrase can be expanded:

  • Start with the basic phrase model: T-PD-D-T, realized as I-IV-V-I
  • Expanding tonic, we can get T (PD-T)-PD-D-T, realized as I (IV-I6)-IV-V-I
  • Expanding predominant, we can get T (PD-T)-PD (PD-T-PD)-D-T, realized as I (IV-I6)-IV (ii-I6-IV)-V-I
  • Expanding dominant, we can get T (PD-T)-PD (PD-T-PD)-D (T-PD-D)-T, realized as I (IV-I6)-IV (ii-I6-IV)-V64 (vi-ii6-V7)-I
  • Expanding the final tonic, we can get T (PD-T)-PD (PD-T-PD)-D (T-PD-D)-T (T-T), realized as I (IV-I6)-IV (ii-I6-IV)-V64 (vi-ii6-V7)-I (I6, I)

The amazing thing is, each of the functions created by expansion can be expanded further! This is how a large piece of music is understood, as a hierarchy of functions and their expansions, in which some chords are more important than others.

There is only one illegal motion in common practice music: D – PD. This motion is never functional. If it appears to occur, either the chords have been incorrectly identified, or one of the two areas is actually non-functional (perhaps because it is part of an expansion).