The Daily Parker

Politics, Weather, Photography, and the Dog

K is for Key

Blogging A to ZFor day 11 in this year's Blogging A-to-Z challenge, we take a look at keys. Not the ones on a musical instrument, but the ones on a staff sheet.

A key designates which scale the piece (or part of the piece) uses to establish its tonality. In this year's very first A-to-Z post, I showed you the four principal scales (major, natural minor, harmonic minor, and melodic minor) that Western music uses most of the time. In that post, you may have noticed that the major scale had the notes C through C without any accidentals (sharps or flats), but the three minor scales all had flats in several places. That means the major scale was in the key of C major, and the minor scales were all in the key of C minor.

To avoid writing all those accidentals throughout the score, we can use a key signature, that essentially says "these sharps or flats run from here to the end (or the next time we change keys)." For example, here again is the C major scale:

And here again is the C natural minor scale, but this time with the proper key signature:

Also remember how every key has a relative key? That's easy to see with key signatures. Here's the A natural minor scale; note that its key signature is the same as its relative key, C major:

Though I might get some argument from some modern composers, generally you can have no more than 7 sharps or flats in a key signature. Each sharp or flat on a key signature takes the key up a fifth in what we call the "circle of fifths." Take a look at how that works. Here are the keys with flats in their signatures:

Start with C; up a fifth to G, up a fifth to D, etc. Now the flat side:

Start with C; but this time, down a fifth to F, down a fifth to Bb, etc. So it works the same way as sharps, but in the other direction.

Often pieces will change keys mid-stream; this is called a modulation. Here's a simple example from Bach in which he modulates several times, between C minor and its relative key, Eb major, with a clever modulation to F minor for a couple of bars. And here's a lampshaded example from Beethoven. (Listen to the whole Schickele clip. The first time I heard it I almost pissed myself laughing.)

Tonight is the Apollo Chorus annual benefit and cabaret, which I'm co-chairing, so tomorrow's A-to-Z might be slightly delayed.

J is for Jazz

Blogging A to ZNow that you know everything about harmony...oh, wait. Because regular old harmonies have nothing on jazz. So for today's Blogging A-to-Z challenge entry I'm going to lift up the curtain on some pretty wild stuff.

I'm actually not going to have a lot of musical examples today. I'm merely going to point you toward other places that do it better.

I will, however, draw your attention to the greatest jazz musician in history: Bach. He improvised the way that other people breathe. And he influenced modern jazz artists hundreds of years later. Just one example, Nina Simone. Listen to the fugue she injects about a minute in:

Or more recently, here's Donal Fox doing improvising on a Bach prelude:

The problem with this format is that jazz is a topic just as large as music theory. So if this post has done nothing more than gotten you to listen to a couple of jazz pieces, that's a success.

I is for Interval

Blogging A to ZToday I'm going to write about a topic that would have come second in any reasonable course on music theory. But in the Blogging A-to-Z challenge, sometimes the cart does come before the ox. Because even though I've already shown you the German 6th chord, fugues, and a reasonable harmonization of a simple melody, today I'm going to show you intervals.

An interval is simply the distance between any two notes. If the distance is one note, we call that a second; two notes, a third; and so on, up to seven notes, which is an octave. (Two of the same notes are called a unison.)

For example, here are the intervals of the major scale:

In order, they are: unison, major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, major 7th, and octave. Not surprisingly, the minor scale has minor intervals instead:

Now the intervals are unison, minor 2nd, minor 3rd, perfect 4th, perfect 5th, minor 6th, minor 7th, and octave.

Interval training starts basic ear training. Musicians have to recognize intervals not only stacked like these two examples, but also played out. For example, here are a major 2nd, a minor 6th, and a perfect 4th played as a music teacher might do it:

How about a chart of all of the intervals, you say? OK:

Interval C to... Notation
Unison C U
Minor 2nd C#/Db m2
Major 2nd D M2
Minor 3rd D#/Eb m3
Major 3rd E M3
Perfect 4th F P4
Tritone F#/Gb Aug4/Dim5
Perfect 5th G P5
Minor 6th G#/Ab m6
Major 6th A M6
Minor 7th A#/Bb m7
Major 7th B M7
Octvave C U

Stuff I didn't read because I was having lunch in the sun

We have actual spring weather today, so instead of reading things while eating lunch I was watching things, like this corgi:

I do have a few things to read while coordinating a rehearsal later tonight. To wit:

  • New York City declared a public health emergency because of measles. Measles. A childhood disease we almost eradicated before people started believing falsehoods about vaccination.
  • White House senior troll Stephen Miller has the president's ear, with predictable consequences.
  • Where did all of Chicago's taverns go? We used to have two to a block.
  • Treasury Secretary Steve Mnuchin admitted that the White House and the IRS have discussed releasing the president's tax forms, contrary to the statute meant to keep the White House from influencing the IRS.
  • Why is Canadian PM Justin Trudeau imploding so fast?
  • The UK Government has started preparing for EU elections next month, a sign that they expect to get an extension on the Brexit timeline from the EU. If not, then they will crash out of the union at 5pm Chicago time Thursday, scoring one of the worst own-goals in the history of world politics. (It's worth noting that losing the American colonies was another one.) I can't wait for PMQs tomorrow.

Today's weather, of course, is just a teaser. We even have snow flurries in the forecast for Friday. Welcome to Chicago.

H is for Harmony

Blogging A to ZToday's Blogging A-to-Z challenge entry builds on yesterday's by adding a third voice to a simple two-voice example to create harmony.

Simply put, harmony is any two notes sounded together. But in practice, harmony involves chords, which comprise groups of 3 or more notes sounded together.

Let's start with a recognizable melody:

Now I'll add a bass line, to give it a little more depth (and, for astute observers, outline the chord progression that we'll hear in step 3):

So there are implied harmonies in there, but let's flesh them out:

That harmony is simply I-I-IV-I, ii-(I6)-V7-I, which is about as simple as it gets.

But you can hear that once we have complete chords under the melody, it sounds a lot richer, and has more direction. And I'll address some of the techniques that make this particular progression work two weeks from Thursday.

Tomorrow: the post that should have gone second.

*The (I6) means even though the chord looks like a tonic chord, it's really behaving more like a passing chord. But hey, it's a simple harmonization of a children's melody.

G is for Gregorian Chant

Blogging A to ZThe Blogging A-to-Z challenge now takes you back about 1,100 years to the beginnings of Western music: Gregorian chant.

Simple plainchants go back before people generally wrote music down. In the late 9th and early 10th centuries—around the time of Pope Gregory I—we start to find some of the earliest written examples of simple monophonic chants.

Some remained part of general liturgical music well into the 18th and 19th centuries, like this example:

Here it begins a performance of the second movement of Mozart's "Great" Mass in c-minor in 2011:

If you have studied music theory, you have written your own ersatz plainchants, because the unit immediately following would introduce you to counterpoint. On Friday I discussed the ultimate expression of counterpoint, the fugue; today I'm going to back up a ways and just show how two lines of music can work together.

The simplest variety, first-species counterpoint, takes a chant (called a cantus firmus, literally a "solid song") and adds another line above or below that begins and ends in perfect consonance. Here's a cantus firmus:

To create a first-species counterpoint, I just need to follow a couple of rules, and voilà:

What does this have to do with Gregorian chant? Well, going from chant to polyphony happened something like that. For centuries the Catholic Church forbade polyphony. Then someone passed the pope a perfect fifth at a party, and he tried it a little, and pretty soon churches all over Christendom had this kind of counterpoint going on. It wasn't quite as simple or formal as music theory pedagogy would suggest, but it did lead ultimately to the polyphonic music we know today.

Come back tomorrow to learn what happens when you add a third voice to a composition.

F is for Fugue

Blogging A to ZToday's Blogging A-to-Z challenge post will discuss a form of music that, sadly, doesn't turn up much anymore. I say "sadly" because the fugue is one of the most intricate and difficult-to-write musical forms, but also one of the most satisfying when done well—and no one did it better than old J.S. Bach.

At its most basic, a fugue takes a short musical subject and tosses it around two or more voices in counterpoint; that is, each musical line (voice) stands on its own as a melody, but the melodies combine to form a more complex whole.

Take this two-bar subject:

Now listen to what Bach does with it:

Let's dig into what actually happens in there.

First we hear the two-bar theme, followed the second voice with the same two-bar theme starting on the dominant note. But notice the first voice keeps going, and then the two voices play off each other with bits of the theme. Then a few bars later, the third voice enters on the tonic again, and we're off to the races.

The fugue returns to the theme several times in each of the voices: in the relative major at bar 11, then at the relative major's own dominant at 13, before returning to C minor at 21. Between these Bach inserts episodes, where the voices interact without returning to the theme. Or so the German would have you believe! Because it's there, sometimes in pieces, at half-speed, upside down, and backwards.

Finally the lowest voice enters boldly with the theme for the last time, after which it hangs out on a tonic pedal while the upper two voices let the theme become the final cadence of the fugue. (Bonus points if you noticed the German sixth in bar 30.)

Bach wrote 48 fugues in his two-volume Well Tempered Clavier, which was sort of a product launch for something so technical I'm coming back to it on the 26th. He also wrote The Art of the Fugue, which is exactly what it says on the tin, and countless other fugues as parts of longer works. Mozart, who loved Bach's music more than almost everyone alive in the 1780s, tried his hand at a few. One of his best is in the 4th movement of the Solemn Vespers of the Confessor, K339, "Laudate pueri Dominum" (Psalm 113, "Blessed be the servants of the Lord", complete with yet another cool example of a German sixth in the "amen" bit at the end).

For really hard-core fugueing, check out Morzart's massive choral fugue in the "Cum Sancto Spiritu" movement of his Mass in c-minor, K427, or Handel's "Amen" fugue that ends Messiah. (And, of course, you must hear the Apollo Chorus perform this fugue from memory next December.)

Note that A-to-Z posts run Monday through Saturday, so come back Monday for the G post. Or check back over the weekend for my usual politics, weather, and the dog.

E is for "Ethnic" sixth chords

Blogging A to ZOne problem with the Blogging A-to-Z challenge becomes obvious when you try to cover a field like music theory that has concepts building on other concepts. You wind up posting things out of order.

Today, for example, I'll cover a somewhat esoteric bit of harmony that I find interesting and difficult, but that the previous four posts could not possibly have prepared anyone for if they have just started studying music theory: augmented sixth chords.

I'm joking that anyone would call them "ethic" sixth chords, but they do have specific names that apparently have nothing to do with their origins: the Italian, French, and German sixths.

All three flavors have an augmented sixth within them that resolves chromatically to a perfect octave. Generally, they stand in for V7 of V chords, and drive to half-cadences which can then resolve normally. Plus, they create a really cool tension in a harmonic progression, but like saffron or truffle, composers have used them sparingly.

The Italian variety is the simplest, functioning as a iv chord:

The French sixth adds a Romantic sound and functions more as ii/V:

And the German sixth really lays it on, so much that voice leading rules demand it usually resolve in two steps. It works as a V7 chord and can resolve to V or I:

The University of Puget Sound has a wonderful page of examples in real life.

D is for Deceptive Cadence

Blogging A to ZToday in the Blogging A-to-Z challenge, I've used a bit of sleight-of-hand to sneak in a discussion of a large topic by highlighting one example of it.

A cadence resolves or pauses a musical phrase. The simplest cadence, called the authentic cadence, uses only the 1st and 5th notes of the scale:

You have a C major chord, followed by a G major chord, ending in a C major chord: tonic, dominant, tonic; I-V-I. (If you need a refresher on what those terms mean, read Monday's post.)

The second-most-common cadence shows up a lot in church music. Technically called the plagal cadence, it won't surprise you to learn people often call it the "amen cadence:"

Only the second chord has changed, from G to F; the progression is now tonic, subdominant, tonic (I-IV-I).

Music theory has identified probably a dozen or so other cadences, but let's take a look at one more common one, the deceptive cadence. It deceives you by setting up an authentic cadence (I-V-I) but instead of landing back on the tonic, it resolves to the submediant, giving us I-V-vi:

The deceptive cadence pauses, but doesn't resolve completely; it wants to go on, kind of like the semicolon that paused this sentence. So let's resolve it:

See? All resolved. (And for those keeping score [ah, ha ha] at home, the analysis is essentially I-V-vi; ii-V-I, with some passing notes interspersed. I'll explain how some of this works next Tuesday.)