Breaking Barlines

Online Music Theory Lessons: Turn Sound Into Skill

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By Aron Bernstein Leave a Comment

A Farewell to Mary Kogen

There are teachers who genuinely make a difference in your life, and I was proud to have been a student and friend of Portland’s own Mary Kogen. In a career more than five decades long, she taught piano and pedagogy at Eastern Illinois University and spent 26 years on the faculty at Portland State, striving always for the humanity and self-enhancement in music. And as for Breaking Barlines, I can confidently attribute a good deal of my own teaching methods to her influence. I was one of countless music teachers whose lives were touched by Mary’s warmth, unmatched humor, and her commitment to bringing music into people’s lives and souls. Though her time is ended, the light she left belongs to us all, and it will not go out. Thank you, Mary.

To read Mary Kogen’s obituary in OregonLive, please CLICK HERE.

By Aron Bernstein 1 Comment

Weekly Music Challenge: 7/18/22

Test your theory chops with the weekly challenge from Breaking Barlines! You’ll find a new question here every Monday. Please comment to post your reply.

This Week’s Challenge:

Sound is a funny thing. Matter doesn’t just vibrate at one fundamental frequency. It also vibrates at a series of fractional frequencies called overtones. In pitched instruments, these are usually much weaker than the fundamental, but in double basses they can be unusually strong, and therefore audible. At left below is an A minor chord orchestrated for strings (all notes are at concert pitch). At right are the overtones generated by the double basses’ low A. What problem does this cause, and how can it be solved?

Post your reply and come back Friday, July 22nd for the answer!

ANSWER for 7/18/22

In this root-position A minor chord, the basses’ 4th overtone introduces an unwanted C sharp, which clashes with the chord’s C natural. Fortunately, the solution is an easy one: simply make sure that at least one other instrument has the correcting pitch. In this example, the first violins will actually do the job, provided they are playing louder than the basses. Their C will be more than adequate to drown out the offending bass overtone. A less ideal voicing would be this, in which the 4th overtone would be audible:

The reality of overtones often directs the choices made by composers. Until the late 18th Century, keyboard composers avoided anything other than octaves in the low bass, and for good reason. Try playing an A minor triad in close position way down at the left end of the piano keyboard, and you’ll get mush! That’s because the low bass strings have audible overtones, and with small intervals like thirds, each pitch’s overtone series will clash with the others:

Mozart and Haydn often wrote only octaves this far down. Beethoven was one of the first keyboard composers to actually prefer the muddy, gritty sound of low-bass triads, and you’ll hear them in works as early as the Piano Sonata No. 8 in C minor, Op. 13 (the Pathètique).

Learn More Here!

With Breaking Barlines, fun music theory is no contradiction in terms! Have a look at the complete Breaking Barlines Course! 44 lessons and counting, each one grounded in the music you want to hear. Then sign up for a monthly subscription for full access to all video lessons, worksheets, and answer keys. New videos are always added, so stay tuned!

By Aron Bernstein Leave a Comment

Weekly Music Challenge: 6/20/22

Test your theory chops with the weekly challenge from Breaking Barlines! You’ll find a new question here every Monday. Please comment to post your reply.

This Week’s Challenge:

Augmented sixth chords make for a slick, chromatic approach to the dominant. The following passage by Friedrich Kuhlau has two of them back-to-back: a German and and Italian sixth. The question is, why not just approach V directly from Germany? Why does Kuhlau make a pit stop in Italy before resolving to the dominant? Hint: on the advice of counsel, I’ll take the fifth!

Kuhlau, Piano Sonatina in A minor, Op. 88, No. 3. Second Movement.
Listen to Audio

Post your reply and come back Friday, June 24th for the answer!

ANSWER for 6/6/22

Here we see Kuhlau deftly invoking (or, rather, removing) the fifth, to avoid getting pulled over by the theory police. The German 6th is the only augmented 6th chord that contains a perfect 5th above the bass, and, as you can see below, it produces the dreaded parallel 5ths if it resolves directly to V. For this reason, the German 6th usually resolves first to cadential 6/4. The Italian 6th, however, doesn’t contain a perfect 5th, so it can resolve directly to V with no voice-leading problems. So Kuhlau starts with a German 6th, then simply plucks out the 5th, instantly changing his passport to Italy and heading home!

Learn More Here!

With Breaking Barlines, fun music theory is no contradiction in terms! Have a look at the complete Breaking Barlines Course! 44 lessons and counting, each one grounded in the music you want to hear. Then sign up for a monthly subscription for full access to all video lessons, worksheets, and answer keys. New videos are always added, so stay tuned!

By Aron Bernstein 2 Comments

Weekly Music Challenge: 5/9/22

Show off your theory chops with my weekly challenge! You’ll find a new question here every Monday. Please comment to post your reply.

This Week’s Challenge:

The late 19th-Century saw the rise of musical nationalism in Europe. Composers in Bohemia, Hungary, Russia, and, to some extent, in France wanted to liberate themselves from common-practice styles and rules, which were largely of German and Italian origins. So Smetana and Dvorak, Glinka and the Mighty Five, and later Bartók and Debussy set about using resources that predated major-minor tonality–the cornerstone of the common practice. They often reached back into their own folk music, which relied heavily on the old church modes: Dorian, Phrygian, Lydian, and Mixolydian.

So here’s the challenge: how do these modes help to undermine common-practice tonality? There doesn’t have to be one correct answer!

Post your reply and come back Friday, May 13th for my take on it!

ANSWER for 5/9/22

While renewed interest in modes wasn’t the only factor in the dissolution of common-practice tonality, it certainly helped. For me, the best example is Mixolydian, identical to a major scale except for the lowered seventh degree. This makes for a minor dominant triad, with which a typical authentic cadence is not possible. Other modes generate similar harmonic colors that, while beautiful and compelling, destabilize the primacy of the V-I relationship. Moreover, the growing reliance on color to carry a piece (rather than harmony, melody, or rhythm) became yet another rival to established common-practice rules. The purpose of tonal harmony is movement: tension and resolution driving the music toward a goal. With the lush, often modal soundscapes of Debussy, harmony has a very different function: immersion.

Want to Learn More?

With Breaking Barlines you learn music theory the right way: fun, holistic, and with a personal touch! Have a look at the complete Breaking Barlines Course! Then sign up for a monthly subscription for full access to all video lessons, worksheets, and answer keys. New lessons are always added, so stay tuned!

By Aron Bernstein 2 Comments

Weekly Music Challenge: 4/18/22

Show off your theory chops with my weekly challenge! You’ll find a new question here every Monday. Please comment to post your reply.

This Week’s Challenge:

Within the context of common practice music, the harmonic minor scale solves one problem but creates another. This week’s challenge is in three parts:

a) What problem does the harmonic minor scale solve?

b) What problem does it create?

c) How is this problem solved?

The red bracket is your clue!

Post your reply and come back Friday, April 22nd for the answer!

ANSWER for 4/18/22

a) Harmonic minor exists for––you guessed it––harmonic purposes. It solves the problem of a natural minor scale, from which you can only build a minor V chord. This makes the authentic cadence, which requires a major V chord, impossible. By raising the seventh note of the natural minor scale, this gives the scale a leading tone, which changes the V chord to a major triad, thus making a true V–I authentic cadence possible.

b) By raising that 7th note to create the harmonic minor scale, we leave a large “gap” between the 6th and 7th notes, an augmented 2nd. To 18th-Century composers and theorists, this interval was just a bit too awkward, too difficult to sing, and (as befitting a rather ethnocentric West-European mentality) too “exotic” for a diatonic scale.

c) To “correct” the problem and smooth out the scale, we add a third type of minor scale: melodic minor. Raise the 6th note a half-step, and we iron out that large augmented 2nd and make the scale easier to sing, with just half-steps and whole-steps to contend with.

Want to Learn More?

With Breaking Barlines you learn music theory the right way: fun, holistic, and with a personal touch! Have a look at the complete Breaking Barlines Course! Then sign up for a monthly subscription for full access to all video lessons, worksheets, and answer keys. New lessons are always added, so stay tuned!