The Daily Parker

The 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.

Today'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.

One 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.

Today 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.)

Today in the Blogging A-to-Z challenge we'll take a look at clefs.

Yesterday I introduced the concept of a bass line, but skimmed over how that gets written down. Let's take another look at it:

Take a look at the first symbols on each line. The top one is called the "treble" or G clef:

It's actually a highly-stylized letter G. Notice how it wraps itself around the second line up from the bottom, which is the G line. Thus the name.

The bottom line starts with this symbol, called the "bass" or F clef:

It targets the second line from the top, which is the F line. The top line of that clef is the A below middle C, which is one octave and half the sound frequency of the A on the second space of the treble clef.

Then there's this guy:

This is called the "Alto" clef, which is the most commonly seen of five C clefs. (The others are the "Soprano," "Mezzo-soprano," "Tenor," and "Baritone" clefs.) Unless you play the viola or various wind instruments, you won't see these very often. The C clefs wrap themselves around middle C, which is the imaginary line running between the treble and bass clefs.

The result is that these two A-major scales are exactly identical:

(On Friday the 12th, I'll explain the magic happening right after the clefs that makes these A major and not A minor.)

Yesterday's Blogging A-to-Z challenge post introduced the four principal scales used to create melodies in Western music for the past five or six centuries. Today I want to talk about the opposite of a melody: the bass line.

Take this familiar melody:

It's pleasant enough, but a little thin. It needs...more. So let's add a bass line below the melody, just using the notes C and G:

Hey! It's almost music now!

So what's going on here? Without going too much into how harmony works (the topic for next Tuesday), all I've done is add a few Cs and Gs to the lower line. (We'll get into clefs tomorrow; for now, the bottom line is played lower than the upper line, and they meet at the aptly-named middle C, which is the note floating on its own little shelf above the lower line.)

This works because the 1st and 5th notes of a scale (the tonic and dominant) are the most important. A lot of bass lines, particularly in popular music, just emphasize these notes. Listen to the bass line in Aerosmith's "Sweet Emotion:" it only hits the tonic, and keeps hitting it, through the whole song.

Or take Chicago's "25 or 6 to 4." The bass line just repeats the dominant through the tonic notes of the descending D-minor scale (A, G, F, E, D) over and over again. (This is called an ostinato bass.)

As a bonus, I had a little fun with the "London Bridge" example, which I'll probably come back to later this month. Enjoy:

Welcome to the Daily Parker's first entry in this year's Blogging A-to-Z challenge on the theme "Basic Music Theory." Today: A is for A.

In Western music, A represents the note that all other notes are based upon. The other notes in Western music are B, C, D, E, F, and G. Putting all those notes in sequence is called a scale:

That scale is called "A natural minor," and sounds like this. The first note in the scale is A; in the attached midi file, and generally in music today, it has a frequency of 440 Hz.

The minor scale feels a little sad, or melancholy, to most people. You're probably more familiar with the major scale. We can create a major scale most easily by starting on a different note. If we start on C, we get a completely different feeling:

We're not limited just to the plain notes on the scale, either. We can add accidentals, which tell the musician to increase (sharp) the frequency of the sound or decrease (flat) it. By adding two flats to the C-major scale, we can turn it into the C harmonic minor scale:

The little "b"-like symbols on the third and sixth notes of the scale indicate that the E and the A are flat. The B is still natural (neither sharp nor flat), giving the scale a slightly exotic feeling.

There is one more ordinary scale, called melodic minor. This has one flattened note going up (in this case, E-flat), and uses the natural minor going down. Note that the half-hash symbol before the A in the first bar says that the note is exactly what it says on the tin, without sharp or flat modification. Here's the C melodic minor scale:

Western music has these four scales (major, natural minor, harmonic minor, and melodic minor) for about 500 years. But other scales have become more popular in the late 20th and early 21st century. Popular music has even gone back to "modes," which come from ancient Greek music through the early middle ages. But that's out of the scope of this year's A-to-Z challenge.

Finally, there is the chromatic scale, which includes every note possible (and every note on a piano keyboard):

Notice that going up we sharp the notes and coming down we flat them, showing all of the enharmonic equivalents (D-flat is the enharmonic equivalent of C-sharp because they occupy the same place in the chromatic scale)*.

* If you get technical, they're not actually the same notes, but we'll come back to that towards the end of the month.

Also, as a handy guide for future posts, here are the names of the diatonic notes on the scale:

This is a gross oversimplification, only so you get the gist. Just understand the vocabulary: for example, that E is the mediant of C and the dominant of A. If you start on a different note, it still works the same way: C is the dominant of F; A sharp is the submediant of C sharp and the dominant of D sharp.

We'll get deeper into these concepts as the month goes on.

I made it to Long Island without incident, and as every New Yorker has done or someday will do, with a change at Jamaica.

The view today isn't quite like the view yesterday:

Next on the agenda: a nap. Then walking over to my alma mater, to see what the kids have done with the place.

On my list today:

• After Commons last night voted down every single proposal for navigating Brexit, Theresa May will bring the agreement she negotiated with the EU up for a vote tomorrow.
• Jeanne Gang has won the contract to design O'Hare's new Terminal 2.
• What's behind the generational divide over climate change?
• Whether individual European countries go off (or permanently on) Daylight Saving Time in 2021, their transport ministers will have the final say.
• The Housing and Urban Development Department has sued Facebook for housing discrimination in its ads-management program, a move I almost can't believe I agree with.
• Today is the 40th anniversary of the accident at the Three Mile Island nuclear power plant.

Back to meetings...

The European Union Parliament today voted 410-192 to allow member states to end Daylight Saving Time in 2021:

The vote is not the last word on the issue but will form the basis of discussions with EU countries to produce a final law.

The countries have yet to take a stance.

A parliament report in favour of operating on a single time throughout the year said scientific studies link time changes to diseases of the cardiovascular or immune systems because they interrupt biological cycles, and that there were no longer any energy savings.

What this actually means requires one more EU-wide step:

All 28 member states would need to inform the European Commission of their choice ahead of the proposed switch, by April 2020. They would then coordinate with the bloc's executive so that their decisions do not disrupt the functioning of the single market.

Last year, the European Commission proposed abolishing the seasonal clock change after an EU-wide online poll showed overwhelming support. It has been accused, however, of rushing through the vote ahead of European Parliament elections in May. 

More:

Countries that wanted to be permanently on summertime would adjust their clocks for the final time on the last Sunday in March 2021. Those that opt for permanent wintertime would change their clocks for the final time on the last Sunday of October 2021.

The British government has yet to offer any formal opinion on the proposal, which risks creating fresh problems over the status of Northern Ireland after Brexit.

I think we can predict, just by looking at longitude, which countries will go which direction. The UK has made noises that it will keep the twice-yearly time changes, thank you very much. My guess is that Portugal, Spain, the Baltics, and other countries at the western ends of their time zones will opt for standard time, while other countries will go to summer time. That would prevent the problems I outlined when this measure first came into the news a few weeks ago.