More on Augmented Sixth Chords
Let's take a look at a few examples of augmented sixth chords in two piano sonatas of Beethoven:
Notice the raised fourth scale step and the sixth (which is already flat, because we're in minor) in the chord in the first example, first measure? Yep, an augmented sixth chord, in this case a German augmented sixth. Last time, we mentioned that there are usually chords in between a German augmented sixth and the dominant chord. You'll see this in both the first and second example. If you look back to the example in the previous entry of the German augmented sixth side-by-side with the dominant, you will see that the Eb and Ab of the augmented sixth go down by half-step to a G and D. Seems simple, right? But if you've learned about what's known as voice leading, you'll probably remember that this creates a parallel fifth, which is something that is to be avoided in 'proper' voice leading. That's why there are these extra chords in the first two examples. The second example from today is the textbook example: a German augmented sixth moves to what is known as a 'cadential six-four' chord before the dominant. The cadential six-four is a tonic chord in second inversion, that is, with the fifth in the bass. The 'six' refers to the interval between the bass and the third of the chord, and the 'four' refers to the interval between the bass and the root of the chord, both of which are above the fifth. Inserting a cadential six-four between the German augmented sixth and the dominant effectively removes the problem of the parallel fifth. You'll see in the first example that it doesn't necessarily have to be a cadential six-four chord that goes between the German augmented sixth and the dominant, but it often is.
The third example has a French augmented sixth. Again, you see the raised fourth scale step (since this example is in Eb, that's an A natural) and the flat six (Cb) in the second measure, which are the tell-tale signs of an augmented sixth chord. It's interesting to note that French and Italian augmented sixth chords can move directly to the dominant because they don't pose the same voice leading problem as German augmented sixth chords do.
Do you have a favorite example of an augmented sixth chord? Please do share on our facebook page!
Music Theory Chord Spotlight: Augmented Sixth Chords
Previously in this blog, you've been introduced to predominant chords, that is, chords that precede the dominant (an example of this is the supertonic, or ii). Augmented sixth chords also primarily have a predominant function, and are built upon the b6 scale degree (the sixth note in a natural minor scale). In addition to the b6, augmented sixth chords include another unique note, a raised scale step 4, that is, #4. So, in the key of C, an augmented sixth chord would include both an Ab (the b6) and an F# (the #4), and the interval between these two pitches is an augmented sixth, hence the chord's name.
There are three standard augmented sixth chords, and in English music theory terminology, these three chords were considered to have characteristics stereotypical to nationalities, and were given names to reflect that. Thus, we have the Italian, French, and German augmented sixth chords. It's interesting to note that these names only are used only in English, not in other languages' music theory terminology. Here they are:
If we take a look at the relationship between an augmented sixth chord and a dominant chord, we can tell that there is a strong draw for it to lead to the dominant. Here is a German augmented sixth chord and a dominant chord in the key of C: you can see that the Ab goes down a half-step to the G, the F# goes up a half-step to the G, and the C and Eb eventually both move down a half-step to B and D, respectively. I say 'eventually' becuase there is usually another chord between a German augmented sixth chord and the dominant, but we'll cover that next week.
We'll also take a look at some examples next week to see how composers use these chords in practice, so stay tuned!
That Time of Year
It's that time of year again. You can say this at any point in the year and it will hold true, but right now, it really is that time of year. Let it suffice for us to bring you a music theory word of the week appropriate for that time of year: the French Overture. If you haven't yet caught a performance of Handel's Messiah, you can arm yourself with this knowledge: it begins with a French Overture (we're talking about the entire oratorio, not just the Hallelujah Chorus).
The French Overture is a specific type of overture common in baroque music. Overtures, as you may know, aren't just attempts to get to know someone or something better, they are what large scale musical compositions like operas and musicals and oratorios begin with. The French Overture has two trademark features: one is a preponderance of dotted rhythms, and the second is a two-part structure, with a slow first section followed by a faster, fugal section. An interesting performance practice feature of French Overtures is that quite often the dotted rhythms are performed as double-dotted rhythms. Here's what the first line of the overture to Handel's Messiah looks like:
And here's what you might hear:
Here's the subject of the fugue in the second section of the overture:
These two sections are tied together harmonically as well. The first section ends with a half cadence in E minor, and the second section resolves this by bringing back material from the first section and ending with a perfect authentic cadence. Here's the last two measures of the first section:
And here's the last two measures of the second section:
Happy Holidays, everyone!
Music Theory and Popular Music
Have you ever wondered how the music theory you learn applies to popular music, like rock, today's top 40 hits, or heavy metal? Well, you need look no further than the current issue of Music Theory Online! Music Theory Online is an online academic journal, and provides a great forum for music theorists to discuss and present their scholarship. You may be wondering what 'professional' music theorists do: MTO is a good place to sample their work. Here's a couple highlights from the current issue, to whet your whistle:
1. Always one for new terminology, I'll direct your attention to Christopher Endrinal's proposal of the term interverse to replace the usual term bridge in popular songs. His argument is that bridges signify moving from one spot to another, but in rock music bridges aren't always about transitioning. His term places more emphasis on the musical material of the section itself. He also distinguishes interverses from the typical instrumental solo in rock songs, which he calls interludes. Interverses, however, have words too (hence the 'verse' part). Not only is there the interverse, but there are four types of interverses. You should check out his article for more information!
2. Brad Osborn discusses forms in what he terms 'post-millenial experimental rock.' On one level he shows us the connections between popularity and songs with recapitulatory structures (like a verse-chorus tune) versus songs which lie more on the fringe and feature through-composed forms. In traditional music theory, through-composed refers to pieces of music that do not feature large sections of material that is repeated. In art songs (like those by Schubert or Schumann), this means each stanza (or verse) has different music. In your studies you might also come across the German word for through-composed, which is 'durchkomponiert.' Osborn goes on to differentiate between through-composed styles of rock, linking math-metal bands with music generally structured on a series of diverse guitar licks, while post-rock bands he shows to base long pieces on a single motive.
It can be illuminating and helpful when learning music theory to consider what forms popular songs and rock music can take, and to practice 'analyzing' some of your favorite tunes and how they're put together. Both Endrinal's and Osborn's articles provide some interesting food for thought.
A Thanksgiving Theory Feast
Thursday is Thanksgiving here in the US, and nothing signifies time with family, friends, and food quite like music theory...Well, perhaps that's a stretch, but the similarities between the adjective 'hungry' and the homophonic Eastern European Country Hungary should be quite apparent, and, as Thanksgiving is foremost amongst holidays in regards to the foregoing adjective, let us in turn focus on the Eastern European country, and take a quick look at Hungarian composer György Ligeti's Musica Ricercata.
Ligeti composed Musica Ricercata, a set of 11 pieces for piano, in the early 1950s. If you've made it to the last few chapters in Theory in a Box, you will have encountered many different examples of how composers might compose or structure a piece of music. They might write it in a specific key to elicit a certain mood, they might rely on the chromatic scale (as in the example of Rimsky-Korsakov's Flight of the Bumble Bee), or, if you've been following our blog, you'd know that 20th century composers might have used the 12-tone method. While Ligeti does use modal melodies reminiscent of folk songs and even uses the 12-tone method for the last piece of Musica Ricercata, what is most unique is that each piece only has a set number of pitch classes in it. A pitch class refers to any note, regardless of octave, that shares the same name: so pitch class C would refer to all the Cs on a keyboard, and so on. In Musica Ricercata, Ligeti uses two pitch classes in the first piece, and for each successive piece adds one pitch class, so that by the final piece, all 12 pitch classes are used. To make this clearer, the first piece only contains the notes A and D, the second piece contains E-sharp, F-sharp, and G, the third contains C, E-flat, E-natural, and G, and so forth.
You might be wondering how does one write a piece that only has two or three notes in it. Rhythmic ingenuity helps out. In fact, the first piece is essentially only one pitch class, A (a D only makes its appearance at the very end), but Ligeti keeps it interesting by gradually increasing rhythmic activity and employing syncopation.
Other interesting features of Musica Ricercata are its use of key signatures and bitonality. While you know from the chapter on key signatures that flats and sharps do not mix in the key signature, Ligeti makes up new ones! In the fourth piece, the key signature consists of F-sharp and B-flat! This is mainly shorthand, however, as the piece is more or less in G minor and you remember that in minor keys it's common for the seventh scale degree to be raised, so in G minor you would have an F-sharp leading tone anyway (though not usually written into the key signature). It makes more sense when you know that only the pitches G, A, B-flat, F-sharp, and a brief disruptive G-sharp, occur in the fourth piece. This means there are no F-naturals to contend with, nor E-flats, making any E-flat in the key signature unnecessary for his purposes. You can hear Bitonality in the 10th piece. Bitonality means that two different keys are sounding simultaneously. In this instance, Ligeti wrote a line in D in the right hand, and a similar line in the left hand, but in F-sharp!
Let's look briefly at the title, too: Musica Ricercata. The second word refers to a form of music that was popular in the Renaissance and Baroque, that is, the Ricercare. Ricercares were pieces similar to fugues in that they used imitation and developed a given motif. The last piece in Musica Ricercata (the one that uses the tone-row), is a ricercare and is a tribute to the Italian Renaissance composer noted for his ricercares, Girolamo Frescobaldi.
So while you're piling on the potatos and turkey this Thursday, leave a little room by the cranberries to contemplate György Ligeti's Musica Ricercata, a veritable Thanksgiving feast for music theory!
Some Important Dates in Music Theory
The last entry on Arnold Schoenberg got me thinking about the 'timeline' of music theory. Schoenberg lived from 1874-1951, but you'll remember from earlier postings on musical modes that the concept of a theoretical underpinning for music dates back to ancient civilizations. Here are some important and interesting dates in the life of music theory:
- 570-495 BCE marked the life of Pythagoras, who is credited with discovering the ratio of string length to pitches.
- 480-524 marked the life of Boethius, who wrote one of the most influential early musical treatises De Institutione Musica, and who met with the less than pleasant fate of execution by his patron's heir, under suspicion of treason.
- 991-1050 marked the life of Guido d'Arezzo, who in 1025 wrote his Micrologus, which you might remember as the source for our solfege system.
- 1605 saw the publication of Claudio Monteverdi's fifth book of madrigals, in which he defended his compositions and outlined the Seconda Prattica of musical composition.
- 1923 heard the development of Schoenberg's 12-tone method of composition, made decidedly manifest in his Seranade, opus 24.
- Contrary
- Similar
- Parallel
- Oblique
- Major-minor seventh chord (also called dominant seventh): major triad + minor third
- Major seventh chord: major triad + major third
- Minor seventh chord: minor triad + minor third
- Half-diminished seventh chord: diminished triad + major third
- Diminished seventh chord: diminished triad + minor third
These are five of my favorite dates in music theory. Please join the discussion on our facebook page and give us your favorite moments in music theory history!
Arnold Schoenberg
Arnold Schoenberg was one of the most influential composers of the 20th Century, so much so that his estate is inscribed by UNESCO as part of the World's Documentary Heritage. Schoenberg is most famous for developing what is known as 12-tone music. I came across this video, courtesy of the Schoenberg Center in Vienna, which explains the 12-tone method very articulately. Take a look:
Schoenberg, along with his pupils Anton Webern and Alban Berg, formed what is known as the "Second Viennese School" (Haydn, Mozart, Beethoven, and Schubert forming the "First Viennese School" in the late 18th and early 19th Centuries). The 12-tone method of composing music has been very influential: even a quintessentially American composer like Aaron Copland wrote 12-tone pieces in his early days, before developing his own musical style.
The serial method of 12-tone music--that is, writing a row (or "series") of all 12 pitches, making sure each occurs once before any are repeated--was expanded to encompass other facets of music, such as rhythm, dynamics, articulation, and so forth. This method of composing is known as Total Serialism. You might recognize the name Pierre Boulez as a conductor of first-class orchestras like the New York Philharmonic and the Chicago Symphony Orchestra, but he is also a composer of pieces using total serialism. If you're interested in what such a piece might sound like, I suggest listening to a recording of Boulez' Structures for two pianos.
In other news, we'd like to welcome the Tri-Valley Central School District in Grahamsville, New York, and Vacaville Christian Schools in Vacaville, California to Theory in a Box. Welcome aboard!
More on Canons
A canon is a musical form in which a phrase presented by one voice (the dux) is repeated by another (the comes).Not only is it possible to have more than one voice repeating the dux, it's also possible to have multiple canons occuring simultaneously.
The canon was a popular form in Renaissance and Baroque music, and in fact has continued to stick around in contemporary music. If you're up for some interesting canons being written nowadays, I'll point you in the direction of a Lithuanian composer Rytis Mazulis.
One particular type of canon that is noteworthy is colloquially called a crab canon. The name derives from the fact that while the comes does repeat the dux, it does so by going backwards! This is also a technique that has persisted in music composition, especially in 12-tone music, and is known as retrograde. Don't worry, we'll get back to 12-tone music in much greater depth later, but for now, here's an example of retrograde:
Music Theory Word of the Week
If Johann Pachelbel were alive today, he'd just have turned 358 years old earlier this month, which would be stunning achievement by any measure. What's his connection with music theory? For our concerns today, apart from Row, Row, Row your Boat, Pachelbel's Canon in D is probably the most famous canon out there...which leads us to our music theory word of the week: imitation. You can probably guess what this means. In music theory, imitation refers to when a phrase presented by one voice is repeated or imitated by another voice. The imitation doesn't have to be exactly note-for-note: it can occur with variations or starting at a different pitch, even upside down or backwards. There are a couple fun Latin terms used to signify the voices engaged in imitation: dux refers to the first voice, and comes refers to the voice that imitates it. You can remember this easily by thinking that comes is the second voice because it "comes" after the dux.
Here's an example, from the second fugue in Pachelbel's Magnificat Secundi Toni.
See how the first five pitches in the treble clef follow the pattern of the first five pitches in the bass clef, only a fifth higher? That's imitation.
Some forms of music are completely dependent on imitation, like canons and fugues. If you're unsure what exactly these forms are, don't worry, we'll discuss them in more depth in the next few weeks.
Music Theory à la Mode
A while ago we told you about the Phrygian mode, and asked you to stay tuned for more information. Well, the wait is over. Here's a little background on modes. The names for modes date back to Ancient Greece, and refer to either regions or peoples. Music was a matter of some consideration for the ancient Greeks, if we take as example the writings of Plato, who thought that music stemming from the Lydian and Ionian modes should be "banished" from his ideal State because they induce "softness" and "drunkenness." Music stemming from the Dorian and Phrygian modes on the other hand were beneficial because they could inspire militaries. Plato goes even further, banishing from his ideal State flute players and complex rhythms.
If you happen to like ancient Greek music theory, or, at least like lots of obscure Greek terms (who wouldn't like proslambanomenos and chromatic paranete diezeugmenon?) I'll direct you to Thomas Mathiesen's article on the subject in the Cambridge History of Western Music Theory. He notes that Plato wasn't just referring simply to the specific modal scales when he said that the Lydian and Ionian should be stricken from the musical ongoings of his State, but rather was referring to a whole complex of related scales, pitch ranges, and styles.
To further complicate matters, what we know as "modes" today don't even correspond precisely to their Greek counterparts! They've been filtered and rearranged throughout years of medieval music theory, giving us this, our current seven standard modes:
If you've gotten as far as intervals and scales in your music theory studies, you'll be able to discover what the pattern of whole and half steps are in these modes, as well as how they differ from your usual major and minor scales. I began all of these on D, but these modes can start on any pitch. For practice, try writing them out beginning on different pitches. And for those of you interested in jazz improvisation, try using a Dorian mode over your next ii-V progression: e.g., use a D Dorian when you come across a Dm7-G7.
From Greek music theory to jazz, modes have influenced musical thought and practice. Learn them well!
Welcome Back
We'd like to wish the best of luck to our returning schools as they start their new academic years, as well as welcome in five new members: Oaks Christian School in Westlake Village, California; St. Luke's School in New Canaan, Connecticut; St. Alcuin Montessori School in Dallas, Texas; the Overlake School in Redmond, Washington; and the Des Moines Public Schools in Iowa. Welcome to Theory in a Box! Also, be sure to check back on Inside the Box soon as we resume our theory blogging!
Theory in a Box Update
As of today, Theory in a Box is in use in 39 US states and 4 Canadian provinces, as well as India and England. We're thrilled at the growth we've seen in less than two years! Thank you for being a part of our mission to spread music theory knowledge across the globe!
Music Theory Word of the Week: Modes
Last week, we brought you an explanation of the Phrygian cadence and said it evoked the trademark sound of the Phrygian mode. What better time, then, to introduce modes? What is a mode? Throughout history and across the world, the term mode has had varied meanings. In simple terms, a mode is a scale other than the traditional major and minor scales we know and love. In Western music, we generally deal with the church modes stemming from the 9th century: dorian, phrygian, lydian, and mixolydian. In fact, the major and minor scales have mode names, as well: major = ionian and minor = aeolian. The best way to think of these modes is as a major or minor scale with variations on certain scale degrees. Let's look at the Phrygian mode as an example:
You may have noticed that it looks like a natural minor scale with the second scale degree
lowered by a half step—and you'd be right. Instead of the F-sharp you'd normally find in
the E minor scale, you see an F-natural. Keep in mind that the Phrygian mode can begin
on any note, as long it follows this pattern. The one above is called an E Phrygian mode. Here's
an example of an A Phrygian mode:
Over the next few weeks, we'll introduce you to the other modes...so stay tuned!
Music Theory Word of the Week: Phrygian Cadence
A Phrygian cadence is a specific type of half cadence that resembles the semitone found between scale degrees 2 and 1 of the Phrygian mode. Because of this association, the Phrygian cadence evokes the sounds of the Renaissance and Baroque periods. Phrygian cadences, which are found only in minor keys, consist of a iv6-V progression, as in the example below. The lowest voice of each chord creates a semitone motion from the flat sixth scale degree to the fifth scale degree. Note that the final chord in a Phrygian cadence is always the major V chord.
Theory in a Box In the News
Theory in a Box is profiled in the Spring 2011 edition of GuildNotes, a quarterly publication of the National Guild for Community Arts Education. The article describes the increase in music theory involvement seen at schools using the course.
Music Theory Word of the Week: Binary Form
When the word form is used in music, it refers to how a piece is structured from beginning to end, describing the number of distinct sections and the way in which they relate to each other. One of the simplest yet most prevalent forms is binary form. A piece in binary form (often labeled as AB form) has two sections.
By way of example, here is a well-known tune in binary form. Each of the two sections is eight measures in length. Within each section, there is a parallel period, which is a pair of phrases that begin similarly.
The form of even the simplest tune can be analyzed on many levels, from smallest to largest. In Greensleeves, for example, there are a total of four phrases, each of which lasts for four measures. Phrases 1 and 2 fit together to form a parallel period, as do phrases 3 and 4. Each of these periods, in turn, forms one of the two sections in the binary form.
Chord Spotlight: Augmented Seventh Chord
We've introduced some of the basic seventh chords in past Inside the Box postings, but here's one more: the augmented seventh chord. How is it constructed? Take an augmented triad (M3+M3), then add a note on the top that is a minor 7th above the root. The resulting chord ends up looking like a dominant seventh chord with a sharped fifth. Take a look at a C augmented seventh chord:
More on the Universal Properties of Scales
If you read the review from ScienceDaily that we linked to on Tuesday and would like to read more, we've located the original full article detailing the University of Amsterdam study here.
The Science of Music
ScienceDaily reported this weekend on a study undertaken at the University of Amsterdam's Institute for Logic, Language and Computation, where researchers purport to have discovered a universal property of more than 1,000 different musical scales from around the world. Having developed a system of mapping scales in three-dimensional space, they found similarities with similar studies undertaken in the areas of speech and visual cognition.
Music Theory Word of the Week: Suspended Chords
Popular music and jazz make frequent use of something called the suspended chord, where the third is replaced by either a perfect fourth or major second. It descends from the classical technique of suspension, in which a note is carried over (or prepared) from a previous chord into a dissonant context in the current chord, then resolved to either the third or tonic. In the modern suspended chord, however, there is no need to prepare or resolve the suspension. It is a self-sufficient sonority. The most common example is the suspended fourth chord (called sus4), with the suspended second chord (sus2) as another possibility.
New Member School
Theory in a Box welcomes Forsyth Country Day School in Lewisville, North Carolina to the Member School program.
View the complete list of member schools.
Song vs. Song: Radiohead and The Hollies
British alternative rock band Radiohead achieved a worldwide hit with their song Creep in 1992. It didn't take long, however, for people to point out similarities with The Air that I Breathe, a 1974 hit by The Hollies. After much scrutiny, Radiohead's lead singer Thom Yorke eventually admitted to substantial similarities between the two songs, resulting in a songwriting credit for Albert Hammond and Mike Hazlewood (writers of the Hollies song). Some believe a royalty-sharing arrangement may also have been reached. Interestingly, Radiohead refused to perform the song in concert for several years after this.
Just what are these similarities? There are two. First, the chord progression that persists throughout Creep is I-III-IV-iv, a fairly unusual progression for its use of the major III chord and the modal mixture juxtaposing the major IV and the minor iv chord. The resulting sound is haunting and distinct. As it turns out, this same chord progression forms the verses of The Air that I Breathe. The second musical element in common between these two songs involves melody. At the end of Creep (at about 2'25"), there is a soaring and powerful melody that is almost an exact replica of the verses from The Air that I Breathe.
Listen for yourself in these two YouTube videos:
The Hollies' The Air that I Breathe
Radiohead's Creep
New Member School
Theory in a Box welcomes Faulkner University in Montgomery, Alabama to the Member School program.
View the complete list of member schools.
Happy New Year from Theory in a Box
We look forward to another great year of music theory with our students from around the United States and Canada! Sign in now or register to get started with the course.
New Member School
Theory in a Box welcomes Minnesota Online High School to the member schools program. Minnesota Online High School is a public charter school serving students across the state of Minnesota and beyond.
View the complete list of member schools.
Music Theory Topic of the Week: Asymmetrical Meters
The most commonly studied meters (such as 4/4, 3/4, 2/2, 6/8, and 9/8) can each be subdivided symmetrically. For example, in 4/4 time, a measure is felt in beat groupings of 1+1+1+1. If the tempo is faster, you may feel the music in groupings of 2+2. As another example, 6/8 time is typically felt in two large groupings, each equaling three eighth notes (so, 3+3). In each of these meters, the groupings are all equal in length—or symmetrical.
There are several meters out there that are grouped asymmetrically, however. A common example is 7/8. As we noted in 6/8 time, 7/8 isn't felt as seven separate eighth-note beats. Instead, it's felt in larger groupings of eighth notes. So, how would 7/8 be grouped? If you try it, you'll quickly see that it's impossible to divide the measure into equal groupings. You'll end up with two groupings of two eighth notes and one grouping of three eighth notes. This leads to a greater array of rhythmic possibilities depending on how a composer chooses to arrange those groupings. The three possibilities are 2+2+3, 2+3+2, or 3+2+2, and it's not uncommon to even change the arrangement of groupings at every new measure. Just imagine the rhythmic vitality this provides.
Try singing the example below while accenting the begin of each beat grouping as indicated to hear an asymmetrical meter in action:
New Member School
Gibson Southern High School in Fort Branch, Indiana is our latest Theory in a Box Member School!
View the complete list of member schools.
Music Theory Topic of the Week: Origins of Solfege
Did you ever wonder where the syllables Do-Re-Mi-Fa-Sol-La-Ti came from or what they mean? In the eleventh century, a Benedictine monk by the name of Guido of Arezzo noticed that the singers in his monastery had a hard time learning and remembering Gregorian chants. As a solution, he came up with a six-note ascending scale (called a hexachord) designed to help singers learn music in a short period of time.
By associating the first syllable of each line of a very famous Latin hymn called Ut Queant Laxis with each note of the scale, he gave singers a set of tricks for learning and memorizing. These syllables were Ut-Re-Mi-Fa-Sol-La and, in the original hymn, they fall on the same notes to which they became attached in Guido's scale. Here is the hymn in modern notation, with the first syllable of each line emphasized. Note that they form an ascending six-note scale starting on C:
This new method, which Guido himself claimed made it "easier to learn music in six days than it previously had been in six months," became instantly popular in much of Italy and, of course, eventually spread well beyond. Not long after, a seventh syllable "Si" was added as music began to incorporate a wider spectrum of notes. Eventually, the syllable "Ut" was changed to the more open syllable "Do" for ease of singing. "Si" was changed to "Ti" by some musicians so that each syllable would have a different starting letter.
Guido of Arezzo also is credited with inventing the modern system of musical staff notation (although his had only four lines because there were only six notes), and he even developed a system of using one's hand to remember the difference in interval between each note in the hexachord. Another interesting fact: The word gamut, which is in common use these days, actually comes from this musical system designed by Guido. It's a contraction of the two words Gamma Ut, which he used to describe the full range of pitches possible within his new system. It's not too often that a modern word finds its origin in music theory!
A Theory in a Box Student Speaks
We thought we'd take a moment out from the weekly theory posts to share what one Theory in a Box student has said about his experience using the course:
"The moment I became a Theory in a Box student, something great happened. You made it possible for me to dive into the realm of music theory
and love every minute of it. I profoundly believe this is the best place to learn music online."
-Olgierd Minkiewicz, musician/actor/filmmaker
You can see what many other students, teachers, and school administrators are saying about Theory in a Box on our quotes page.
Music Theory Word of the Week: Subtonic
In Theory in a Box, you've learned the names of each scale degree, as well as the names of the chords that are built upon them:
In a minor key, however, the seventh scale degree is only called the leading tone when it is raised. Quite often, this note is lowered (as in the natural minor scale) and is called the subtonic:
Likewise, a chord built on the lowered seventh scale degree is called a subtonic chord. While the leading tone chord in a minor key (vii°) is diminished in quality and leads naturally to the i chord, the subtonic chord (VII) is major and rarely leads to i (instead it usually progresses to III).
Music Theory Topic of the Week: Contrapuntal Motion
When any two musical lines (called voices) are present, the relationship between them is known as counterpoint. The way these two voices move in relation to each other is known as contrapuntal motion. There are four primary types of contrapuntal motion:
Understanding contrapuntal motion is an important basis for learning advanced harmony and voice leading. Here are explanations and examples of each one:
Contrary Motion: The two voices move in opposite directions.
Similar Motion: The voices move in the same direction, but with changing intervals.
Parallel Motion: The voices move in the same direction, with consistent intervals between them. (In the example below, the interval between the voices remains a 6th on each beat.)
Oblique Motion: One voice moves while the other stays on the same pitch.
New Member School
Welcome to the students of South Putnam Community Schools in Greencastle, Indiana—the newest Theory in a Box member school!
View the complete list of member schools.
Theory in a Box News
Theory in a Box is now in use by individual students in 28 states and four Canadian provinces. The School Edition has been adopted by 27 schools, universities, and homeschool organizations. We're excited about this growth and can't wait to see where we go next!
Music Theory Topic of the Week: Predominant Chords
In the Cadences chapter of Theory in a Box, you'll learn that the authentic cadence consists of a V chord followed by a I chord. But what comes before the V chord? The most common answer is the supertonic chord (ii or its inversion ii6), subdominant chord (IV), or submediant chord (vi). As a group, these chords are known as predominant chords because they typically resolve to the tonic and create a preparation for a cadence.
The following example is a perfect authentic cadence introduced by a predominant chord (ii6-V-I):
New Member School
Pakachoag Music School in Worcester, Massachusetts is the latest member school. Welcome!
View the complete list of member schools.
New Member School
The University of Cincinnati College-Conservatory Preparatory Department has joined the Theory in a Box Member School program! Welcome to all of their students and best wishes with the course.
View the complete list of member schools.
Music Theory Word of the Week: Seventh Chords
What do you get when you take a triad and add one more third on top? A seventh chord—so named because it adds a note which is a seventh above the root. Seventh chords are used primarily to create musical tension, and sometimes just to add a bit of extra flavor to a harmony.
For a beginner, seventh chords can easily be understood as a triad with an additional third added on top. There are five kinds of seventh chords commonly used (click on each name to hear an audio example):
New Member School
Theory in a Box is proud to welcome the Community Music Center of Boston to our Member Schools Program! CMCB serves more than 5,000 students each week throughout the city of Boston and is the leading provider of arts education to the Boston Public Schools.
View the complete list of member schools.
New Member School
The Casady School, an independent school located in Oklahoma City, has joined the Theory in a Box Member Schools Program. Welcome to them and their students!
View the complete list of member schools.
Happy Birthday Itzhak Perlman!
Theory in a Box wishes a very happy birthday to violinist Itzhak Perlman, who was born on this day in 1945.
Music Theory Word of the Week: modulation/closely related keys
It is quite common for a piece of music to change keys one or more times. This process, called modulation, is actually the primary way that a composer gives a form or structure to a piece. Each time a new key is established, a new section begins.
In order to create a smooth transition between keys, composers usually modulate to closely related keys. In simple terms, this means two keys that contain all or most of the same notes. The most closely related key to any major key is its relative minor (it contains all of the same notes). Other closely related keys are the subdominant, which adds one flat or subtracts one sharp, and the dominant, which adds one sharp or subtracts one flat. So, if a piece is in the key of C major, its relative key is A minor (all of the same notes but different tonic), its subdominant is F major (one flat added), and its dominant is G major (one sharp added). Another way to think of it is that, the closer two keys are in the circle of fifths, the more notes they have in common, making them more closely related.
Not sure what subdominant and dominant mean? Check out the Theory in a Box chapter on Triads.
Music Theory Word of the Week: Accents (dynamic, tonic, agogic)
Generally speaking, an accent in music refers to an emphasis placed on a specific note. This emphasis can come about by action of the performer or it can be inherent in the musical line. Below are the three primary types of accents:
A dynamic accent is the most common form, in which a note is played at a louder volume in order to add emphasis. This is usually indicated by an accent mark (>):
A tonic accent is the result of pitch rather than loudness, usually a note being significantly higher or lower in pitch than the other notes around it:
An agogic accent is an emphasis by way of note length, most often created by giving a note a bit of extra time in performance. A typical example is to prolong the downbeat of a measure or the first note of a melody in order to give it extra weight.