Successful completion of these challenges involves approaching each task directly and thoroughly, avoiding extraneous musical details that do not contribute to the requested sonic effect.
Challenges that must be composed for acoustic instruments with no electronic accompaniment or sonic modification are indicated with a ☀️ symbol. Challenges designed for electroacoustic music are labeled ⚡. Challenges designed for piano or piano-plus-one are labeled 🎹.
Musical sequence seems to be a simple concept, but the term is actually used in different ways, many of which are similar. This post will hopefully lend some clarity to the subject. The kind of sequence I’m describing is defined in the Oxford Companion to Music as:
The more or less exact repetition of a melody at another level, higher or lower. If the repetition is only in the melody, with changed harmony, it is called a melodic sequence, and if the repetition is followed also in the harmony, a harmonic sequence. If the repetition is made without leaving the original key, which necessarily means that some of the intervals become larger or smaller by a semitone, it is called a tonal sequence. If, in order to preserve the exact intervals, the key is changed, the name given is ‘real sequence’. Sequences that are real in some repetitions and tonal in others (in some instances to avoid carrying the modulation too far) are called mixed sequences.
For starters, let’s examine a famous sequence as see what we can learn from it:
One key thing to notice is that there are both melodic and harmonic elements. The melodic pattern is one bar long; each successive bar moves the pattern down by a step. Since it stays within the notes of the key (F Major), it’s a tonal sequence. If it rigidly maintained it’s pattern of whole/half steps, adjusting the harmony accordingly, it would be a real sequence, which would end up something like this, cadencing in a new key:
One can also frequently find modified sequences, in which repetitions are adapted or embellished. This commonly occurs on the third instance of a sequenced figure, in which a change is made to avoid monotony. This is an example from First Loss in Schumann’s Album for the Young (starting at bar 17) [hear on YouTube]:
Harmonically, the sequence features a pattern of root motion. There are different “main types” of harmonic patterns that are commonly found in sequences, and this one uses the “descending fifth” type: starting with D7, it moves around the circle of fifths from D to G to C to F to B♭, and then returns to non-sequence harmonic progression (C 7 is V7, and it moves to a I- IV – I64 – V7 pattern.
Here’s another great example, from the jazz canon [hear on YouTube]”
And another [hear on YouTube]:
Does it have to be just like this?
No, but these are great examples to use as “classic.”
Some sequences can be “melodic only,” meaning the chords don’t change in a sequential manner. Here’s an example from the jazz standard As Time Goes By [hear on YouTube]:
Other sequences can be “harmonic only,” with melody freely appearing along with it but not divided into repeating motives.
What’s the difference between a transposition and a sequence?
This is a good question. When a passage is repeated at a different pitch level, is it necessarily a sequence? For instance, this section from Billy Joel’s Allentown [hear on YouTube]:
This fragment of music includes a segment that is transposed up a fourth, (a “real transposition” — note how the intervals of the melody repeat identically) with the chord pattern moving right along with it (like a ii-V-I pattern in keys of D Major and G Major). A third repetition begins with “Out in Bethlehem”) before departing from the pattern and moving on to continue the phrase.
But are we observing a sequence, or is it just transposition? That’s a tough question. My feelings are that there is a “spirit” of sequence that isn’t present here. A sequence, as I understand it, is something rooted in Baroque music in which the transposed motives and chord patterns contribute to the progress of a phrase, moving the music along a path to cadence. The music of Allentown doesn’t do that – instead it uses transposed gestures as the beginnings of a musical sentence. There can be all sorts of instances in which a figure is transposed immediately without being in the “spirit” of sequence.
This may not concur with common usage of the term, which seems to apply to any transposition. The explanation of sentence on openmusictheory.com even teaches an example of sentence as using a gesture “fragmented into one-measure units whose second half is sequenced one step lower.” This seems to be a colloquial usage that doesn’t accurately reflect the majesty of a true sequence.
This is a slightly-edited email that I just sent to a class of students in my online course that is designed for graduate students who need to review (or learn for the first time) undergraduate music theory concepts. Course grades had been falling as material became more difficult. This course is made up of fourteen weekly lessons, each of which includes an activity, an assignment (self-graded with automatic release of a key upon submission), and a quiz. Quizzes are available all week, and must be done by midnight Sunday.
I see a disturbing trend: that most of you are submitting their assignments at the end of the weekly unit, and so aren’t making time for asking questions or for study before the quiz. Here’s what I found for the last five assignments:
Goal: To be able to identify all intervals an octave and smaller by ear and to be able to sing any interval above or below a given tone.
To identify intervals by ear: find a partner and take turns quizzing each other. On any instrument, play each interval melodically (ascending or descending – vary it) then as a dyad. To focus study, limit yourself to subsets depending on the skills being tested. For instance, this chart might describe levels of difficulty for many students (from easiest to most difficult):
- major and minor seconds
- perfect fourths and fifths
- intervals smaller than a tritone
- major and minor sevenths
- sixths and sevenths
- anything goes
This skill can also be drilled online at http://www.musictheory.net/exercises/ear-interval
To sing intervals above or below a given tone: make a quick chart, arbitrarily choosing starting pitch, interval size, and direction, like this:
For each row of your chart, play the starting pitch that you have chosen, then sing the pitch at the chosen interval’s distance. Confirm your answer by paying the correct tone on your instrument.
2) Triads In Root Position
Goal: To be able to identify the quality of any closed-voicing triad in root position and to be able to sing the third and fifth of a triad when given its root.
To identify triad qualities by ear: find a partner and take turns quizzing each other. On a piano, arpeggiate triads from bottom to top, then play as a block. The following guide may help:
- Major and minor triads sound HAPPY and SAD, respectively. This is, of course, silly, but it works for most people.
- Augmented and diminished triads are NEITHER MAJOR NOR MINOR, and so are easy to separate from those but sometimes difficult to distinguish from each other. Use interval identification skills to determine if the notes are separated by major or minor thirds, then confirm your choice by hearing the interval between the root and fifth (it will be either a tritone or an augmented fifth).
- Another technique for distinguishing augmented and diminished triads is to compare each to the other triad with which it shares two notes. For instance, if you hear two notes that sound like a major triad is being arpeggiated before the third note disappoints you by “souring” the chord, it is an augmented triad; if you hear two notes that sound like a minor triad is being arpeggiated before the third note disappoints you by “souring” the chord, it is a diminished triad.
This skill can also be drilled online at http://www.musictheory.net/exercises/ear-chord
To sing triads above a given tone: make a quick chart like that used above for intervals, choosing starting pitches and triad qualities. Play the starting tone, sing the full triad (arpeggiate up and down: root-third-fifth-octave-fifth-third-root), then check your pitches by playing them on a piano.
3) Seventh Chords In Root Position
Goal: To be able to identify the quality of any closed-voicing seventh chord in root position and to be able to vocally arpeggiate the third, fifth and seventh of a chord when given its root.
To identify seventh chord qualities by ear: find a partner and take turns quizzing each other. On a piano, arpeggiate chords from bottom to top, then play as a block. It helps to consider that different kinds of seventh chords are based on triad “cores,” as following:
- The augmented triad only has one common option: the augmented seventh chord (written +7) that has a minor seventh between its outer tones. It’s like a dominant seventh with raised fifth. There is also an augmented major seventh chord (written +△7) that has a major seventh between its outer tones.
- The diminished triad is the core of the half-diminished (Ø7) and fully-diminished seventh (O7) chords. Distinguish between these by hearing the outer interval (minor or major seventh, respectively).
- The major triad is the core of the dominant seventh (V7) and major seventh (△7) chords. Distinguish between these by hearing the outer interval (minor or major seventh, respectively), or by associating the dominant seventh as being “bluesy” and major seventh as being “jazzy” (since these are the qualities of major-mode tonic chords in those styles).
- The minor triad is the core of the minor seventh (m7) and minor/major seventh (m△7) chords. Distinguish between these by hearing the outer interval (minor or major seventh, respectively), or by recognizing the especially “piquant” sound of the minor/major seventh.
To sing seventh chords above a given tone: make a quick chart like that used above for intervals, choosing starting pitches and seventh chords qualities. Play the starting tone, sing the full chord (arpeggiate up and down: root-third-fifth-seventh-octave-seventh-fifth-third-root), and then check your pitches by playing them on a piano.
4) Triads in inversion
Goal: To be able to identify the quality of any closed-voicing triad in any inversion and to be able to sing triads in any inversion after being given only a bass note.
To identify triad inversions by ear: find a partner and take turns quizzing each other. On a piano, arpeggiate chords from bottom to top, then play as a block. Inverted triads follow a basic interval-pattern that is independent of chord quality:
Notice how, when a triad is inverted, the root is the top note of the fourth-interval (perfect fourth in major & minor triads, augmented fourth in a diminished triad). Since an augmented triad is made up of only major thirds (or a diminished fourth, which is enharmonically the same as a major third), it is impossible to tell if an isolated augmented triad is inverted.
When triads are inverted, it becomes slightly more difficult to ascertain chord-quality. It can be helpful to re-voice the chord in your head with the chord root as its lowest note, and imagine how it would sound if arpeggiated in root position.
To sing triads in inversion when given a bass note: calculate the interval from the note you are given to the chord root, then imagine the root of the chord. Once you have a good sense of the chord root, it should be easier to sing the full chord. For instance, if you are asked the following:
Arpeggiate a first inversion major triad above this note (G4)
1) Play this note on a piano.
3) Confidently sing just the notes of the desired triad in inversion.
5) Dominant Seventh Chords In Inversion
Goal: To be able to identify the quality of closed-voicing dominant seventh chords in any inversion and to be able to vocally arpeggiate such chords after being given only a bass note.
To identify V7 inversions by ear: find a partner and take turns quizzing each other. On a piano, arpeggiate chords from bottom to top, then play as a block. Inverted seventh chords follow a basic interval-pattern that is independent of chord quality:
Notice how, when a seventh chord is inverted, the root is the top note of the second-interval (a major second in V7 chords).
To sing V7 chords in inversion when given a bass note: use a similar method to that used for singing triads in inversion.
6) Singing Primary Chord Functions
Goal: To be able to vocally arpeggiate chord progressions using only primary chords I, IV and V(7) (or i, iv and V(7)). It helps to visualize the chords on a staff as you sing them, and to follow stepwise connections between “bass” notes. For example: if asked to sing the I – IV64 – V65 – I progression, sing:
Some sample progressions to practice:
6a.) I – IV64 – V6 – I and i – iv64 – V6 – i
6b.) I – IV – I6 – V64 – I and i – iv – i6 – V64 – i
6c.) I64 – V – I and i64 – V – i
6d.) V – V6 – I6 – V – I and V – V42 – i6 – V – i
6e.) IV – I6 – V64 – I and iv – i6 – V64 – i
A companion-post to this is “Motive: Beyond Simple Identification“.
The song America The Beautiful by Katharine Lee Bates and Samuel Ward is the topic of a lovely NPR feature, Rob Kapilow’s What Makes It Great. It can be heard here. Designed for public radio audiences, it is very accessible to people with no musical training or knowledge of specialized jargon. What Kapilow did was describe the song’s use of melodic motive in plain English. The song is so saturated with motive that I think it’s worth translating the description back to jargon to explain it with more depth.
Here’s the sheet music (click the image to enlarge and click here to download it as a PDF).
The music starts with two motives that we can label x and y.
Notice how neither motive is constricted by bar lines; the pick-up note is part of what makes these motives clear. Also notice that important traits distinguish these motives: x has a distinctive rhythm (Kapilow calls it “short-long… a dot”) and a special downward-skip melodic contour.
Motive y has a plain rhythm of six steady notes, and its contour is different every time it appears. It’s often noted that rhythm is the most important parameter for making a motive identifiable; everyone points to Beethoven’s Fifth’s DA-DA-DA-DUMMMM as an example. But what is noteworthy (no pun intended) about the simple rhythm of America’s six notes? It’s that they occupy a special place in the musical hypermeter — the “location” of these notes in the phrase. In this case, all phrases are in a traditional folky pattern of four bars in length with the music coming to repose (the “cadence point”) on the downbeat of every fourth bar.
Take a moment now to examine the music, labeling each occurrence of x and each occurrence of y. Unlike in most songs, when you are done you will have labeled every single note of the tune as being identical to x or y or a variant of it. Examine how the variants are related to their first occurrences, or to each other. Then consider this question: what else in this melody provides the elegance that has led this song to be a cherished America classic? After you’re done, return to this page and read the rest.
Various textures to use as possible springboards for orchestration projects. Note that thick textures made from voicing large chords under a plain melody are absent here! Click images to enlarge.; Continue reading Scoring Ideas
Modulation – moving from one key to another – occurs in many forms of music. In classical music, it is often an important dramatic feature, and is a structural element in certain musical forms (especially sonata and rounded binary form). Like modulation, tonicization implies another key as a tonal center; the difference is that a modulation is confirmed through a cadence in the new key. A key or chord may be tonicized in the middle of a phrase, with no cadence to confirm it as a modulation.
There are two basic methods of modulation: pivot and direct.
- A pivot modulation is found in the middle of a phrase when one harmony or a single pitch is “reinterpreted” to function in each of two keys.
- A direct modulation tends to be found when a new phrase suddenly begins in a new key. There may be one or more turnaround chords (explained below) that soften the transition between keys. Turnarounds are not technically “pivot chords” since they do not occur in the middle of a phrase.
Ten out of ten composition lessons that I teach end with me jotting down a short list of repertoire for the student to study over the coming week. Most often, these pieces are chosen because their instrumentation or compositional approach is similar to that being used by the student. They also tend to have the secondary goal of broadening the student’s experience and leading them toward more adventurous and distinctive writing.
As far as I can tell, my students almost never follow through. To the professor (that’s me, but I think most composition professors do this), it is one of the essential parts of the lesson. To the student, it seems like extra work when all they really want to do is sit down and make stuff up.
With this in mind, I decided to create this page and direct students to it. What follows is a list of questions that must be answered for each piece of music assigned as listening. Some of them are “due diligence” to make sure that a score and recording were, in fact, located and perused. Others are designed to help guide the student’s study of the score and suggest practical ways that hearing new music can help a musician progress as a learner and gain new tools for composition.