As we enter the Spring 2021 semester many students are resuming their aural and theory courses. These classes can be taxing under neutral circumstances, but given the continued changing instruction modalities (remote, hybrid, etc) there are extra barriers and challenges that can make these courses even more anxiety-inducing.


Apps and Programs designed for Ear Training/Theory

  • MacGAMUT
    • An ear training (with a theory edition as well) software.
    • Randomized exercises – in short and long sections.
    • Customize simple, compound meters; certain elements such as rhythm and range.
    • Sections for particular ear training skills – step-by-step.
  • MusicTheory.net
    • A great entry level tool. As a visual (theory) and ear training tool for notes, intervals, scales, and chords.
    • Customizable – omit specific clefs, range, chords, scales.
  • Teoria
    • Includes both ear training an music theory tools.
    • Customizable ear training exercises for intervals, notes, chords, scales, melodies, and rhythms.
    • Comprehensive basic theory – intervals, reading the staves, keys, scales, chords/harmonic functions. Also includes introductory jazz music theory.
  • GoodEar – apps
    • Great for smartphone or tablet.
    • 4 main apps: Intervals, Scales, Chords, Melodies.
    • Customizable.
  • AP Music Theory Barron’s Book
    • Aside from prep for the AP Music Theory exam, this book provides a condensed overview of basic-advanced Western music theory during the Common Core period.
    • CD with listening exercises; as well as self-assessment sections.

Practicing tools/tips for Ear Training

  • Start simple: when listening ask yourself is the pitch higher or lower? The move on to steps or skips?
  • When playing your own music think about these same concepts (make the context more directly applicable to you!). Listen to something simple without any visual music and try to play it back on your instrument.
  • Constant and consistent ear training; and be aware of out of tune pianos the intonation issues be confuse your brain, tricking it by a half/whole step depending on how severely out of tune it is.
  • Consistent labeling of pitches, find a system that works the best for you.
    • Examples: Solfege Do-Re-Mi-Fa-Sol-La-Ti-Do
    • Numbers 1-12 (12 chromatic notes in a scale)
      • Ie. a C Major scale would be 1-3-5-6-8-10-12-1
    • Neutral; ie. la, du, ta
    • Note names: C, D, E, F, G, A, B
  • [More advanced] Identify which type of solfege is more comfortable:
    • Fixed Do
      • Typically associated with perfect pitch, tonal memory of specific pitches.
      • C is always Do, D always Re, E always Mi, etc.
    • Moveable Do
      • Do doesn’t have to always be C like Fixed Do. For example in F Major, F is the new Do and by going up the scale C becomes Sol. Or in G Major, G is the new Do and C becomes La.
  • Practice exercises with a drone
    • It’s a good habit to practice with a reference pitch to help develop an ear for the “home” or tonic note in a key.
    • A building block for harmonic function/context.

Music Theory Tips

  • Find a good tutor/mentor
    • A bad theory teacher or unclear instruction can destroy motivation, especially since theory on its own is so dense; a big part of comprehension is how it is presented
    • Everyone can understand music theory, you just need to find a way to think/process it that makes sense.
  • Break down scary concepts into steps
    • Roman Numeral analysis, most people. dread hearing that type of assignment…
    • Break it down, keep it simple:
      • What is the chord function? Just think Tonic/ Subdominant/Dominant?
      • Then figure out how to label each chord.
        • Tonics can only be I and sometimes vi.
        • Subdominant is ii, IV, and vi
        • Dominant is V and viio
        • And forget about iii (I’m kidding… only a little bit)
  • Patterns
    • Do you like puzzles? Make it a game of finding the same or finding opposite.
    • If you don’t you’ll need to figure out another way to process/recognize similarities and differences in rhythm/pitch.
  • “Common facts” sheet
    • There are solid rules in Western theory (these rules have exceptions, of course) by writing down the fundamentals it will help keep track and act as a physical checklist of what is ‘allowed’ and what is ‘rule breaking’.
  • REVIEW
    • It can be mentally taxing. Take breaks while also keeping on top of the material.

I spent the first two years of my undergraduate program not realizing I had been hearing all my melodic dictation exercises in fixed-do (relative to C). It was only by the time I got to atonal music that one of my professors noticed the stark contrast in my performance on dictation exams and I FINALLY was able to get a grasp on melodic dictation. I hope some of these resources are helpful! Share your favorites in the comments.

For information on the composer, Sergei Prokofiev, and the general overview of the entire flute sonata (Op. 94) you should check out my analysis of the first movement before reading through the analysis of this movement. Understanding the background – including the conditions – Prokofiev was writing under will help inform the analysis of this movement:

II. Allegretto scherzando (Dotted Half = 69)

The suggested tempo is included in the G. Schirmer 1965 edition. The text “allegretto scherzando” roughly translates to fairly brisk and playful (or joking). The form of the second movement is ternary (ABA or ABA’) form which has some connection to a scherzo (a major scherzo of note for flutists is Mendelssohn’s Scherzo in A Midsummer Night’s Dream) which is in rounded binary form (AABA) with a ‘trio’ section that follows the recap of the A form.


A – mm. 1-161

The key feature in this movement is Prokofiev’s use of hemiolas. As far as the Grove Music dictionary is concerned a hemiola, “in the modern metrical system denotes the articulation of two units of triple metre as if they were notated as three units of duple metre.” More info on this term can be accessed here.

The motive that the flute first plays in the A section is an example of a hemiola:

Note the duple notation (duple = 2), but slurred as if they were triplets (3). As mentioned, this opening motive in the flute is prominent throughout the second movement: we see it transposed up a Perfect 5th in measure 15, down a Perfect 5th in measure 34; and we see echoes of it throughout later parts of the movement as the initial A section closes, as well as when the A’ section recaps.

In the primary A section we expect to see multiple phrases, an established tonic key, and an end with a PAC (typically in the tonic):

Multiple Phrases

There is no shortage of phrase variance in this section.

The first section that we see (amid several transpositions) is the hemiola phrase, which is characterized by the constant eighth notes. Each time this phrase appears the dynamic is marked piano and peaks at a mezzo forte. This section lasts from mm. 1-58.

The next phrase section is the sixteenth notes. The repeated figure “C-D-Eb-F Gb-Ab-Bb-C D-Eb-E-F” is accompanied by the piano playing Gb-Eb-Bb (which would be some borrowed chord, not quiet a Neapolitan because it is minor rather than Major) – perhaps it is simply put to be the tritone juxtaposing a minor (a to eb as a diminished 5th)?

Either way, this section is fleeting and promptly resolves to F Major – mm. 59-76.

The third section is interesting because unlike the first two which had very clear features, this one has a several elements. The first being the leaps/skips (the 1st and 2nd phrases were both stepwise) and particularly the use of the Perfect 4th followed by a Perfect 5th. Then following this with a dotted quarter to driving eighths. This section lasts mm. 77-102.

The fourth section could be lumped in with the third, however, I see the key change and addition of a new rhythmic figure (the triplet) as one of two possibilities: (1) a brief extension that is stretching the phrase to the return of the first phrase OR (2) a variation of phrase 3. Either way there are recognizable similarities between the 3rd and 4th phrases – take for example, mm. 107-112 and compare it to mm. 87-92.

Key/Establishing a Tonal Center

Considering how Prokofiev plays with intervals in this movement, the tonal center is relatively ambiguous – especially if one was to just regard the opening 6 bars of just the piano alone.

However, given the opening motive the tentative tonic is a minor, however as soon as Prokofiev has moved out of the hemiolas he begins to explore F Major and its relative minor (d minor). What’s interesting here (for all you advanced theory nerds) is that these are the notes of a d minor arpeggio: a (5), F (3), and d (1) which would be the parallel minor of the first movement set in D Major. How neat!

For simplicity’s sake I will refer to the section by key rather than scale degree, but the d minor arpeggio relation is an interesting avenue, perhaps to explore the next time you work through this movement.

We see the movement towards F Major punctuated by the octaves F’s in measures 75-76. The references to d minor are more apparent in the piano score, for example before the flute has the sixteenth note runs, the piano (mm. 58-61) plays an inverted d minor arpeggio d(1) a(5) f(3).

Ending with a cadence (PAC?)

There is the brief key change to c minor, however, as discussed in the section on phrases, it is more or less an extension or variation used to cycle back to the first phrase. By m. 123 the d minor version of the first phrase is back. The punctuation of the A’s in mm. 153-155 is a versatile choice on Prokofiev’s part as this can either be regarded as the 5th of d minor or the 3rd of F Major. The ambiguity is all part of the game – given the context of writing during Socialist Realism in Soviet Russia – Prokofiev could easily claim either to be the case, whichever put him a favorable light. As far as a PAC is concerned, I see the As as an IAC in d minor, however, I have seen other scholars regard it as the same but in F Major. To support my argument for d minor I point towards the use of C# and F#s which allude to the parallel Major – perhaps forecasting the key change that will begin the B section. Futhermore, I see the transition from F Major to D Major – not impossible, but the chord functions during the transition “o, m, o, m2, m3” given the context of the piano score which allude much more to minor tonalities than Major.


B – mm. 162-227

Contrast is a fairly simple concept to understand in music theory. Opposites are a general concept that can be transferred from daily life (ie. Day and Night) which in music theory can translate to A and B sections. The B section is noticeably different than the A section, here’s what to look for: key the new key is usually related either the parallel Major/minor; this section ends with a PAC or HC; and there may be a short bridge that leads into the recap of A.

The most noticeable contrast between the B and A sections in this movement is the way Prokofiev alters the meter! Notice how the B section is in 2/2 while the A section is always in 3/4.

New Key

Tracing back to the end of the A section, my argument for the cadence being an IAC in d minor fits neatly since the B section is starting in the parallel Major – D Major. The key signature makes this key transition abundantly clear, as well as the opening statement start with an inverted D Major arpeggio.

Okay, hold on for this wild journey of keys/interval-play that I am about to suggest – with the knowledge that most of these transitions would be intervallically motivated (whether that is pushing the boundaries with something as ‘offensive’ as a tritone or maintain a Major quality to mask the deviation from traditional chord progressions).

There is a notated key change in measure 174 (removing the C# and F#s). Looking at the notated figure of a quarter triplet and two quarters – one could guess we have returned to a minor… there is after all an A being sustained in the piano mm. 174-176. However, isolating the arpeggio in m. 174 it appears to be two arpeggios combined a d minor with an inverted G Major (A-F-D-B-G-D). Prokofiev continues to play with that Perfect 4th (D to G) with the running sixteenths m. 177 and m. 181. However, keep in mind we are still technically in ‘a minor’ therefore at m. 182 we see an immediate shift to E Major (G#-B-E) because it is a the Dominant (V) in a minor. This is followed by a bm – g#m. Which is similar to the A section and how it brings out the d – f – a of d minor, this brief tonicization of the Dominant is bringing out E – B – G#.

By m. 190 the key of D Major returns… only for a short while. With a nod to the E Major, mm. 194-195, as well a a minor, the C# and F#s are quickly removed from the key yet again in m. 202. And this is where we begin to see the bridge back to A/A’.

Bridge

The bridge out of the B section and back to the return of A is punctuated by the time signature change to 3/4, a return to the triple feel, while still closing out the motifs and tonal exploration featured in this contrasting section. This bridge spans mm. 208-227.

The piano part while the flute is playing the espressivo phrase and resting (mm. 212-227) is particularly of note tonally speaking. The inverted arpeggio running under the espressivo section is a bo (b diminished) arpeggio. Once the piano is alone this shifts into an alternating AM – C7. Again, an interesting (and safe) choice because these are common chords (although the quality varies) from D Major/minor and F Major.

Cadence (PAC or HC?)

This section is more or less ending with a Half Cadence. Although not a formal HC, the same function is present here…

A traditional HC is something ending with a V (Dominant). However, V is not the only Dominant function, VII can (on occasion) take the place of a V in a cadence. Nothing about this cadence is screaming authentic cadence (IAC or PAC), there is no tonic function in sight (this could be a i/I and occasionally a VI/vi).

If the piano bridge is considered to be in dm/DM there are two dominants AM (V) and C7 (VII7)… also if we really (and I mean reallllly) wanted to push for FM we could call the C7 the V7/III. Either way you spin it not tonic functions to be seen, especially with the seventh chord, therefore, definitely HC!


A/A’ – m. 228-370

Finally, a return to familiar material! This final section has a few key features: it can be varied (hence A’), it will start and end in the tonic, and ends with a PAC.

Variations: A versus A’

For the most part, this return is an exact copy of the initial A section. The flute line follows the A section to a T mm. 228-333 (the counterpart being mm. 7-112).

The first time this section deviates starts m. 335 with the descending eighth note figure. There is a new rhythmic figure (the sixteenth triplets) which allude to the ones featured in the first movement of the Op. 94 Sonata. Then, Prokofiev quotes the 3rd phrase from the A section before starting the 1st phrase… offset by one beat; and he interjects this with a hemiola-ified (adding ties to) another quote from the 3rd phrase before finishing with the 1st phrase, and a frenzied eighth pattern that ascends to the climatic C7.

Final Cadence – PAC?

If only… again it’s more of an IAC. But a very interesting feature in the Schirmer 1965 edition is that it includes the alternate violin part which ends differently!

Of course both endings are considered IAC if we are to consider the tonal center to be a minor: the flute’s C is the 3rd scale degree and the violin’s E is the 5th scale degree.


I had a lot of fun with this movement – the ambiguity lends itself to a lot of theorizing (within set Music Theory ha!) so I got a chance to explore questions I had about the score. Anything you noticed in this movement that I missed?

Hello all!

This month is usually a hectic one for a lot of music students.

This November I am taking my Comp Exams (Graduate Exams in both Theory and History) to graduate. They are research based, running all month. If I was just taking my comps (if only) I might be able to keep on top of posting this month, but I also have to balance projects for my Teaching Popular Music course, Suzuki teacher training and observations, 20th Century Music History War and Peace seminar, teaching, and just my general sanity!

I may add some posts this month as updates to this process, but I will not be posting regular content (at least that’s the plan) again until December once things simmer down.

Good luck to all with a crazy month ahead of them.

Emma

On May 13, 2020, I gave my first ‘recital’ as a Masters student. My recital was initially planned for April 1st and the repertoire was WAY different I had a lot of chamber music programmed that couldn’t happen given the COVID-19 pandemic – all the music learned in my recital was done in less than a month (minus the Honegger).

Here we will be looking at excerpts from the 4 pieces on my program and how I approach theory and analysis – especially with an very short time frame to research, analyze and really take in the framework of these pieces. The 4 pieces being J.S. Bach’s Partita in a minor I. Allemande, Jacques Ibert’s Pièce for solo flute, Arthur Honegger’s Danse De La Chèvre, and Paul Hindemith’s Acht Stücke.

J.S. Bach Partita in a minor, Allemande

Recital notes: I will only be playing the first movement, the Allemande, from Bach’s Partita in a minor. However, each movement of this work refers to a dance. The allemande being a German style dance… Bach did not actually give a specific tempo as the performer would be very familiar with the dances during the Baroque period and would be able to play in that style. As this piece is for solo flute, the demands of the music are to act as the melody, harmony and bass all in one. There are also no rests or places to breathe marked by Bach, so the phrasing utilized in shaping the melody, harmony, and bass are imperative in creating natural space to breathe.

As the title would suggest, the Partita is in a minor. The first page of the Allemande uses the root (A) and third (C) on the stronger beats 1 and 3 to outline the minor tonality. Because the piece is for solo flute, the flute is acting as the melody, harmony and bass. Therefore, one of the compositional techniques Bach uses to keep momentum and engagement is through sequences. Sequences are taught to young children as a math principle: find the pattern and figure out what comes next. Musical sequences work similarly, they can be seen as a repeating pattern between intervals (melody) or rhythm units. In this excerpt, although there are repeated 16th notes (as seen throughout the entire movement), the motive is bracketed in green. From m. 14-15 the intervals are very similar (not always exactly, but the motive is still distinguishable) denoting a mostly chromatic sequence. The motive in the first group is G-F#-E-G, goes down to F#-E-D-F#, down to E-D-C-E, and ends on D#-B-C-A. By the end group, the intervals have strayed from the original group, but the placement of the notes G, F#, E, and D# on the strong beats (1 and 3) are prominent enough to draw the ear to their downwards motion. A similar sequence happens in m. 16, but is much more concise. The ascending chromatic pattern in m. 16 is G-G#-A-A# on each beat in the measure. Finally, a new pattern emerges m. 16-17 where the final 16th leads to the first 16th of the next beat. The E resolves down to D#, D natural down to C#, C natural to B, and finally Bb to A.

In this next excerpt, the tonality has shifted. It is common in Baroque music to modulate from the tonic to the dominant key, and then to eventually return to the tonic (the dominant in a minor is E Major). This excerpt is fully in the dominant (E Major) section: note the V4/3 over IV (which translates to a E seventh chord in 2nd inversion moving to an A Major chord) which is the pivot from em (denoted by the i) to EM. 

Like in the first excerpt, there is another sequence feature – this one is directly related to the Circle of Fifths. Measure 23 starts the sequence in E Major (1), m. 24 moves to A Major (IV), m. 25 is d minor 6/5 (vii6/5), m. 26 D Major 7 (VII7) LET’S PAUSE… I provided the Roman Numerals in parenthesis to denote the chords’ function in the dominant E Major. However, look at m. 25 and 26, the first red flag should be the different qualities of the 7 (D). In Major chord progressions, the 7 is usually fully-diminished so the fact that is is minor and then Major should be getting those alarm bells going. Hence, why this section can be looked as a sequence within the Circle of Fifths: E to A to d (D)… rather than a common chord progression. Continuing our sequence, m. 27 is in G Major which is extended all the way to m. 29 until our sequence ends in m. 30 in C Major. The sequence ends there because if you look at the following measure, the harmonic rhythm (or the rate at which the harmony changes) drastically increases and moves to a tonal area that does not fit in the Circle of Fifth sequence. 


Jacques Ibert Pièce for solo flute

Recital notes: Coincidentally, Ibert’s Piece for solo flute was composed in the same year as the Hindemith Sonata I mentioned earlier. This piece starts with a cadenza-like introduction that centers around the note “D”. Like Ibert’s well known Flute Concerto (composed 2 years prior), this piece is good for demonstrating virtuosity and freeness in playing. Despite studying at the Paris Conservatory, Ibert didn’t emulate any of the popular genres during the early 20th century, and in this piece you can hear how he’s style transforms multiple styles rather than honing in on just one.

Ibert was an early 20th century composer – a time were tonality was less rigid, an the exploration of serialism and atonality were becoming commonplace. The Pièce for solo flute goes through many tonal areas – like mentioned in my recital notes the opening is a cadenza-style featuring the note “D”; and the remainder of page one doesn’t strictly follow a traditional key/tonal center. In this first excerpt, the 9/8 “Vivo” is the first time in the piece that Ibert emphasizes a tonal area -in this case Db Major (the diatonic notes are Db Eb F Gb Ab Bb C). Here I used green to visualize all the notes that were diatonic (in the key of Db) and any non-chord tone or chromatic note is highlighted in orange. By doing this, it is very easy to see the patterns within what may look daunting at first glance, especially in a key of 5 flats.

This next excerpt from Ibert’s Pièce is building a climatic resolution on the final page (visually, you can tell those tiny 32nd notes are going somewhere). Our last excerpt was in Db Major, this one has moved to a tonicization (not a fully-fledge modulation) of the IV (Gb Major) – this is clear because of the downward arpeggios (the yellow denoting notes diatonic to Gb). The ‘F’s are functioning as a supertonic or a 7th scale degree that is creating a rising tension. The swells on the 6s to 7s to 9s emphasizing the 7th briefly calm down for 2 measures before a sequence of minor 3s ascends to an E natural where the piece relaxes (and resolves) to return to a familiar theme stated in the beginning of the piece.


Arthur Honegger Danse De La Chèvre

Recital notes: This is the earliest 20th century piece on my program, composed by Arthur Honegger in 1921. The title Danse de la Chevre translates to Dance of the Goat. The piece starts very delicate with a series of tritone phrases – as if the goat is just waking up from a dream. Quickly, the “goat-like” or more active theme comes during the Vif or the 9/8 section with a skipping/dancing goat. At the end, the piece returns to the delicateness and serenity of the introduction, as the goat has tired itself out and is going back to sleep.

Important to note that there are several versions of Honegger’s Danse De La Chevre that are in circulation this particular score is from the 1932 edition. The piece was composed in the early 20th century and the intervallic relations (and lack of tonality) are indicative of Honegger embracing serialism.

The opening motive is highlighted in purple and it lasts 2 bars (each time it is restated it uses the opening 4 notes to lure you in before launching into a new idea). This motive starts with a tritone (TT) from C to F# and is followed by two Perfect 4s. And interesting discovery I made was how Honegger follows the motive, in phrase 1 (m. 1-2) note that the motive goes down a 2nd (E down to D). While in phrase 2 (m.3-6) note that the motive goes up a 2nd (E to F). Then in the phrases following the 1 bar Vif, phrase 4 (m. 8-9) the motive goes down a tritone (E to A#) whereas in phrase 5 (m. 10-13) the motive goes up a tritone (E to Bb). Wow. At a first glance it might just look like crazy, random music, but when analyzed critically it is actually symmetrical and systematic.

At the end of the piece, the motive comes back (note that it is an exact copy just shortened) before the B resolves to the C harmonic.

The slower section before the recap (Lent) is weaved throughout the piece each time it uses the echo effect – repeating material at a softer dynamic, but to keep the intrigue Honegger adds a tag at the end to differentiate the fragments. For example, m. 55 compared to m.57 (where Honegger presses on the breaks and starts to makes things slower and softer). And m. 58 compared to m. 59-60 (where there is one last – slower – iteration of the Vif theme).


Paul Hindemith Acht Stücke

Recital notes: One of Hindemith’s most well-known works is his Sonata for Flute and Piano which he composed in 1936. About ten years before he composed this Sonata, he wrote a piece for solo flute called Acht Stucke which translates to 8 Pieces or movements. These 8 movements are very short – some of the shortest movements in the piece such as the 2nd movement are only 40 seconds long. Also, these movements don’t have a stable tonal center and not all movements have an indicated meter so the motives and gestures within movements is what shapes the piece.

Welcome to Hindemith were key signatures don’t matter and the tonality is irrelevant. How does one cope? In my analysis for movement IV of this piece, I realized the rhythm was the true star of the piece so how did I learn the rhythm? By making a song:

Is it silly? Yes. But when the tonal patterns and rhythmic sequences are so brief there needs to be some way to connect ideas to form a coherent piece. I can’t be entirely sure if this what Hindemith intended when composing this movement, but if there is an evidence to suggest he DIDN’T intend this then send that my way. All jokes aside, let’s look at a more structural movement…

In movement VIII, there is some semblance of musical structure. The beginning is repeated at the end, and there seem to be two distinct sections (the presto and the offset section).

Both in the opening and end, the specific pitches aren’t so important (more so the intervallic relationships) it is clear with m.1-2 that 3-4 is similar while expanding the ‘motive’ by getting louder, faster and expanding the range. The F# don’t serve much tonal significance rather the note acts as an anchor to ground the piece as it ascends to A6 before dropping to D4.

The presto section beginnings suddenly quiet and with an indicated meter. There is a brief sequence with the downwards G-F#-F motion in m.8-9 and m. 11-12, but it is fleeting. There is more anchoring (similar to the opening) now on E as the melody ascends.

The register descends and the volume gradually diminishes. As a new section emerges, here the quarter note and eighth note are offset. The measures were the quarter note starts on beat 2 as a pickup are the string tying this section together. Note the pitches highlighted in yellow Eb D and the 3 repeated C#s (each C# rising more than the last). The rhythmic content for these highlighted pitches is all the same until the 3 C#s where the material is expanded yet again to return to a restatement of the opening.


Thank you for making it through this maiden voyage of explaining how my brain comprehends music theory. If you have any questions, additional thoughts or want to see the lyrics to the other Hindemith movements comment down below!