MusicTheoryWithAndre

The idea that 6/8 counts 6 eighth notes per bar is… kind of a white lie, in the same way that the idea that 9/8 is 9 eighth notes per bar, or 12/8 is 12 eighth notes per bar, are sort of white lies. It depends on the tempo, but most of the time, 6/8 is actually 2 beats, each of which is a dotted quarter, divisible, of course, into 3 eighth notes each; and likewise,   9/8 is 3 beats and 12/8 is 4. It at first seems logical to count to 6, as in “1 2 3, 4 5 6”, but in fact, the way we count 6/8 is much more often “1 and a, 2 and a”—since it’s much more common for the dotted quarter to be the beat in these time signatures than the eighth note. JS Bach wrote Passion narratives for all the four Gospels—very long musical settings (lasting between an hour and 45 minutes and 2 hours 45 minutes, depending on which Passion, plus tempo/style choices) of the plot of the chapters of the Gospels directly concerned with the arrest, trial, torture, and death of Jesus Christ. (There is much more ...

  Syncopation, one of the key rhythmic elements of jazz and other styles influenced by it, is the placing of stress on a normally unaccented beat or portion thereof. When we count something, say, in 4/4, if we count in eighth notes, for instance, we count “one and two and three and four and”—and the numbers have more stress than the “ands”.   Syncopation would, somehow, place (more) stress on the “ands.” This technique, ubiquitous as it is in jazz, also plays an important role in classical works.                Consider the opening of Mozart’s 25 th symphony. These are the actual first four bars of the first violin and cello parts. I have added the timpani part for clarity. Underneath each part is how you would count that. Notice that the cello and timpani parts are easy: counting quarter notes or eighth notes without any complications. But then look at the violin part. We’re offset from the cellos by ...

  Sequences are a critical part of helping music move along. It helps to think of them framed by the mathematical constant of an arithmetic sequence, given by the rule that any number in the sequence is some starting number, plus a multiple of another. For example, you might have a sequence 2n+3—starting with 3, going up by 2 each time: 3, 5, 7, 9, 11, and so on. Sequences start somewhere, move by a fixed amount, and have a certain number of “legs” (what mathematicians would call “terms”). There are two kinds of sequences: real ones and tonal ones. Real ones don’t happen very often because they get out of hand, harmonically speaking, very quickly; tonal sequences, therefore, are much more common. Look for example, at this first phrase of this Bourree written by Handel: In bars 6 and 7, we see a 4-legged sequence. 1.        B C# D B 2.        C# D E C# 3.        D E F# D 4. ...

Voice exchange is often done in the name of variety. If the same chord were voiced the same way many times in a row, the music would quickly become uninteresting. However, since we have the benefit of this tool, we can swap chord tones between voices, often changing the inversion of a chord in the process, but, in any case, making the texture of the music more interesting by the addition of movement. Consider this sequence of chords: We have two D chords in a row, but this doesn’t sound like the same chord twice. Sure, they’re both fundamentally D chords, but there is something essentially different about how a root-position chord and a first-inversion chord feel. The tenor and soprano voices don’t move at all, but the bass does (and hence we have the inversion change. It would be total legal for the alto not to move at all either, but since we’ve chosen to make the exchange, the alto does move. Before the exchange, we had D in the bass and F# in the alto, and after the exchang...

  Spacing is of paramount importance, especially when writing in a Baroque chorale style. In general, the rule is quite simple: the intervals between any two neighboring voices should not be more than an octave, but an exception can be made on occasion to allow for slightly more space between the bass and the tenor. This, for example, is a perfectly reasonably spaced A-flat chord: Between the bass and the tenor, there’s a fifth; then a sixth from the tenor up to the alto, and another sixth from the alto up to the bass. This, however, would be considered a serious spacing error: between the F# and the D in the bass and tenor, there’s a sixth, but there are almost two octaves between the tenor and alto, and exactly one between the alto and soprano. There’s a practical reason for this rule: if the chord is spaced correctly (as in the first screenshot), then it feels round, full, and rich. But if there’s a huge spacing error, especially somewhere in the middle (as in the sec...

  Inverting sevenths works exactly the same way as inverting triads, only we have one more possible inversion since we have one more note in the chord. As before, when the root of the seventh chord is in the bass, we’re in root position, regardless of what the other voices are doing. As before, when the third of the seventh chord is in the bass, we’re in first inversion. As before, when the fifth of the seventh chord is in the bass, we’re in second inversion. Now, the pattern continues, and if the seventh of the seventh chord is in the bass, we’re in third inversion. Many years ago, I learned a trick that has helped me a lot to know immediately where the root of a seventh chord is: if you’re lucky enough that there’s an obvious second in the way something is voiced (I’ll show you all this in all the inversions in just a little bit), then the top note of the second is the root of the seventh chord. If it isn’t obvious, spell it out and rearrange the notes in such a way tha...

Conjunctivity (or its opposite, disjunctivity) describes a simple binary question: does the music mostly move in steps, or not? Conjunct music is that which mostly does move in steps. Disjunct music is that which mostly does not move in steps—or, put another way, moves mostly in leaps of thirds or wider. To illustrate this, I’ve transcribed two very famous passages: one of each style. For disjunctivity, I’ve given you the opening of Bach’s 8 th Invention in Two Parts (meaning that there are never more than two notes sounding at once, so the harmony is very simple). To show just how disjunct the melody is, I’ve put a box around all the parts when some melodic element is going on in either hand that features leaps of at least a third. Look at just how much green there is: Now, let me do the same box-highlighting exercise with one of the most famously-conjunct melodies ever written (and the reason music has been as important a part of my life for as long as it has been)—the cello/...

Just like we inverted intervals, we can invert chords. But unlike standalone intervals, what inversion a chord is in has a great deal to do with how it comes across, so knowing how to recognize them (and ultimately write with them) is vitally important. You have seen inverted chords before—I just haven’t yet mentioned that I am inverting them.                Let’s begin, as we always have, looking at something that applies to all chords by looking at the simplest case: triads. Triads, since they have three notes, naturally have 3 possible states they can be in (6 if you count all mathematically possible states, but beyond one condition, we don’t care, so 6 arrangements boils down to 3 that we care about).                If the root of the chord is in its lowest voice, then the chord is said not to be inverted at all, or to exist in “root position...

Inverting intervals larger than an octave invites us to consider a generalization of the procedure to invert small (an octave or less) intervals. That procedure was that two intervals are inverted if their qualities are inverted (major pairs with minor; augmented pairs with diminished; and so on) and the sum of their sizes was 9 (sixths pair with thirds; sevenths pair with seconds; and so on). More abstractly, one can imagine “flipping the interval”; if there’s a C# a sixth below an A, then “flipping” the interval so that there is now an A a third below a C# does indeed correctly invert the minor sixth into a major third. To look at intervals larger than an octave, we will use precisely that heuristic, and in so doing, come up with a theoretically infinite number of “rule of 9”-like rules. The procedure thinking about actual notes is simple (and you already have an idea of how to do this from the smaller intervals): hold one note where it is, and bring the other note up or down a s...

Seventh chords are of vital harmonic importance.  Any triad can easily become a seventh chord, simply by continuing along the pattern of adding thirds. The seventh built on scale degree 1 uses 1-3-5 from the triad, plus 7; the seventh built on scale degree 2 uses 2-4-6-1; and so on. What kind of sevenths those are depends on 1) the scale from which those scale degrees were created and 2) any extra alterations done to the underlying triad or the newly added seventh. One seventh in particular, that built as an extension of the triad on scale degree 5, is, as I see it, unquestionably the second-most important chord in the whole harmonic language, bested in importance only by the tonic chord. Anywhere where there is a triad, in general, there can be a seventh substituted in its place. Especially if the triad is the dominant chord, and so the seventh is the one built on the fifth scale degree is the point of maximum harmonic tension, especially if it cadences immediately thereafter t...

There are two “tendency tones.” It’s really easy to remember where they are, because they both involve the half-steps in the major scale. Further, there’s another thing you can use to remember how they move, based on their positions: the lower one in the scale moves down, and the higher one in the scale moves up. “Tendency tones” scare people in the beginning, but if that’s you, then take my advice: play or sing a major scale but stop on the seventh degree—whatever you do, don’t finish the octave. Hold the seventh out as long as you possibly can. A battle will go on in your mind: between your conscious desire to follow my instruction and your subconscious desire that really, really wants to hear “1 2 3 4 5 6 7 (maximum tension!!!!!) 1 (ahhhhhh now we can relax).” That’s the obvious tendency tone: the seventh degree of the major scale resolves upward by a half-step to finish the octave. However, there’s another one: The fourth degree, against the tonic, resolves downward to the third...

Music, just like the written or spoken word, is organized into chapters, paragraphs, sentences, clauses, and so on—only we have different terminology for all that. Crucially though, just like written text has commas and periods and question marks and a whole host of other punctuation, so does music. Again, we just have some different terminology for it. The musical analog of the concept of “punctuation at the end of a sentence” is “a cadence at the end of a phrase.” A phrase is simply a single musical idea. In   the following example, we have phrase A, phrase B twice, and phrase A again: and here again, we see the same score, but with the cadences highlighted:   One could even make the (very good) argument for more highlighting, like this: I don’t phrase it like that because I find that stopping and starting every two bars makes it feel too repetitive, so instead, when possible, I choose four-bar phrases. But any good theory teacher or exam would never fault you...

  So far, we have seen five different scales: major, natural minor, melodic minor, harmonic minor, and Dorian. Dorian is unique among the five in that it is always called a “mode.” But the truth is that major and natural minor are also modes. The modern modes are all built from the major scale, which is itself one of the seven modern modes. For the sake of simplicity, let’s go with the notes of C major for all of the following examples. The Ionian mode is the major scale itself, so C D E F G A B C. The Dorian mode uses the same notes, but starts on the second degree, so D E F G A B C D. This, again, is natural minor with a raised sixth. The Phrygian mode uses the same notes, but starts on the third degree, so E F G A B C D E. This is new and is equivalent to natural minor with a flat second.   The Lydian mode uses the same notes but starts on the fourth degree, so F G A B C D E F. This is new and is equivalent to major with a raised fourth. The Mixolydian mode uses...

We established earlier in our first discussion of minor that natural minor was one pattern, but that there were three others. Let us first revisit the natural minor pattern, then explore the other three. We’ll do this not by considering natural minor on its own, but in relation to its parallel major, to see the difference between them. A major, for example, is built as A B C# D E F# G# A. A natural minor, on the other hand, is built as A B C D E F G A. Therefore, differences exist in exactly 3 degrees: degrees 3, 6, and 7. In all three cases, those degrees are exactly one half-step lower in minor as compared to major. The minor third is non-negotiable. You must have a minor third, or you don’t have a minor scale, chord, or key. The other two differences, however, are flexible. This, therefore, creates four possibilities from the springboard of natural minor: ·          Change nothing ·        Raise only the sixth a...

 In the key of “{E} | {major}”—that doesn’t mean anything technical, I’ve just written it that way to prove a point—we see we have two relevant pieces of information: the root is E, and it’s a major key. Those two pieces of information, together, encode “E F# G# A B C# D# E.” It is very natural, then, to ask: one or both of the following questions: What happens when I keep the four sharps of E major, but make the key minor? What happens when I keep the root of E major, but make the key minor? Both of these keys (incidentally, C# minor and E minor, for 1 and for 2) share deep similarities to, and are therefore very closely linked to, E major (and vice versa. The key in scenario 1, already revealed to be C# minor, is called the relative key of E major. (It is also perfectly correct to say that E major is the relative key of C# minor.) Relative keys differ in their tonics but have the same key signatures. On the other hand, the key in scenario 2, already revealed to be E mino...

“Enharmonic equivalence” may sound daunting, but it really isn’t that hard. It merely puts a name to the fact that there are two reasonable ways (and many more ways that are so convoluted they border on absurd) to name many notes. For example, would you not agree that G and A are a whole step apart, so there’s a note between them? And would you not agree that you can get there just as easily by sharpening G as by flattening A? This, of course, is true. (Just as one can sharpen F or flatten G to get to that note in the middle; or flatten D or sharpen C; and so on.) When there exists a pair of notes like this, separated by a whole step, the note in between has two names: [upper note] flat and [lower note] sharp. These two notes—F sharp and G flat, for example—are said to be “enharmonically equivalent.” Of course, one could say that, for example, E-triple-sharp and G natural are equivalent (because, yes, E and G are that far apart)—but if you actually see something asking you to pla...

  There are twelve notes in the chromatic scale—twelve possible roots from which to build major or minor scales, major or minor chords, and so on. Musicians, therefore, have coopted the 12-hour clock face to create a device known as the circle of fifths. Recall, for example, that C major is C D E F G A B C, and that the formula for any major scale, if you start from a place we’ll label “0” is [0, 2, 4, 5, 7, 9, 11, 12]—the “2, 2, 1, 2, 2, 2, 1” formula we discussed several articles ago. A consequence of how the formula is built is that, in order to differ by exactly one note, you must move the new tonic up or down by exactly a perfect fifth. C up a perfect fifth is G, and C down a perfect fifth is F. C major, again, is C D E F G A B C. G major, similarly, is G A B C D E F# G—differing from C only in terms of the F, which is sharp in G major, but natural in C. Meanwhile, F is F G A Bb C D E F—and so it too differs from C in only one place, regarding the B, which is natural in ...