Sharps and Flats

Time to bring back the question that I left with a few entries ago.  What about the black keys on the piano?  How do they fit in?  Why do we need to have them at all?

Let's start with a C major scale once again.  This time, I'm presenting it both ascending and descending, so you can hear it better.

Note that it's all white keys.  C D E F G A B C.  C B A G F E D C.  If you see a white note, play it.  Easy.

Well, what about a different scale?  One that starts and ends on a different note?  Suppose I'm a soprano.  That middle C is at the bottom of my range, it's not a note that sounds good for me.  But if I started at F, and went up to F and came back down, those are notes I'm more comfortable singing.  So what about an F major scale?  What does an F major scale look like?

Naively, I might think that all I have to do is use the same notes I used before to make the C major scale, but just start on F and end on F.

F G A B C D E F.  F E D C B A G F.

But if I do that, this is what it sounds like:

It doesn't sound right.  The fourth note in the scale is off.  But why?

The answer to that question goes back to Pythagoras.  If you recall from Donald Duck's trip to Mathemagic Land, the notes in a scale are all related to each other by ratios of frequency.  The ratio between C and F, for example, is 4/3: for every 3 times a C string vibrates, the F string vibrates 4 times.  If B were the fourth note in an F major scale, its frequency would have to be (4/3) * (4/3) that of C, or 16/9.

But that's not the way it works out.  There is no note in the C major scale whose frequency is 16/9 that of C.  A is too low; B is too high.  So the fourth note in the F major scale has to be some different note, a note that's in between A and B.  It's like we took a B, and bent its pitch down just enough to make it fit and sound right in an F major scale.  We call this note...

B flat!!!

And this is how B flat is written in staff notation.  The note takes the same position on the staff as a B does - it's on the third line, the one right in the middle.  But see that little ♭ sign in front of the B note?  That ♭ sign is a flat.  Flat means that you take the note and lower its pitch just a little bit.

So now that we have our B flat, we can fix our F scale.  Now it sounds like this:

Voilà!

Next, let's consider a G scale.  Starting with G:

G A B C D E F G.  G F E D C B A G.

This time, it's not the fourth note that's off.  It's the seventh.  That F doesn't sound right, it's too low for the scale.  So we raise it up a bit:

Our new note is F sharp.  Sharps are denoted by a # sign in front of the note.  They're the opposite of flats - a sharp sign in front of a note raises the pitch just a little bit.

What about plain white notes?  Don't they get a symbol too?  Of course they do!  You might recognize this tune from Gershwin, which makes use of the symbol we need.

Notice how the two Bs are flatted in measures 5 and 6, but each one of them is followed by another B with a funny looking sign in front of it.  That sign is called a natural sign.  A natural sign means that the note is neither sharp nor flat.  Normally it's used only to cancel out a sharp or flat sign that came earlier - you don't have to write a natural sign for every note.  

So now our piano keyboard is complete.  We now have name for those five black keys on the keyboard:

The note in between C and D is C sharp, or D flat.

The note in between D and E is D sharp, or E flat.
The note in between F and G is F sharp, or G flat.
The note in between G and A is G sharp, or A flat.
The note in between A and B is A sharp, or B flat.


On the diagram above, you can see an octave labeled. There's also two other terms there that are very useful to know: semitone, and tone.  A semitone is the interval between one note and its nearest neighbor, up or down.  The notes F and F# differ by a semitone.  So do the notes B and C, because they're right next to each other.  When you put two semitones together, you get a tone, or a whole tone.  C# and D# are a whole tone apart: from C# to D is a semitone, from D to D# is another semitone, and two semitones put together make a whole tone.  From F to G is also a whole tone.  F to F#, F# to G - each one of those steps is a semitone.

(You'll often hear the words half step and whole step used, instead of semitone and whole tone.  They mean exactly the same thing.)

Next time, we'll use semitones and whole tones (or half steps and whole steps) to show how major and minor scales are built.

Music Theory 101 - Bass clef!

Suppose you want to write a cello part.  Or a left-handed piano part.  Or you sing bass.  What do you do about all those notes below middle C?

Well, we have a clef for that!  It's called the bass clef, and it picks up where the treble clef leaves off.  Here's a C major scale on the bass clef.

That funny-looking thing on the left that looks like a comma with two dots, that's the bass clef.  The two dots sit on either side of the line where the note F sits.  Middle C, on the bass clef, is on the ledger line above the staff.

Here's a C major scale going way down into the depths:

How low is that low C?  About this low.  Listen to the bass at 2:15.

Typically in piano music, you don't see just one staff written.  You see both staffs written together: one for the left hand, one for the right hand.  Together, they make up something called a grand staff.  Here are four octaves of C major scales, written for piano on a grand staff.

Notice how the middle C is at the top ledger line on the bass clef, and on the bottom ledger line on the treble clef.  It's the same note.  Really!  It is!

Next up: All about sharps and flats.  Stay tuned!

Lagniappe - How to tune an orchestra

If you've ever been to a classical concert, you've probably gotten to listen to the orchestra tune up in the final few minutes before the concert starts.  Ever wondered how that works?

Here's what the pre-concert tune-up looks like:

The orchestra is led in tuning by the oboe.  Why the oboe?  Simple.  The oboe carries over the crowd better than any other instrument.  

The oboist tunes her instrument offstage, before the audience starts shuffling in and before the members of the orchestra start taking their places onstage.  Typically, tuning is done with an electronic meter, although it can also be done with a tuning fork or pitch pipe.  The standard for most orchestras is that the A above middle C is exactly 440 Hertz (vibrations per second).  439 Hz will not do, neither will 441.  The oboist adjusts her instrument until an A played on her oboe matches the A-440 sounded on her meter.

When the concertmaster (head 1st violin) comes out on stage, he directs the oboist to play her A.  All the horns and woodwinds tune to her A.  The horns adjust their tuning slides, and the woodwinds tune by adjusting the sections of the barrels of their instruments.  

Once the horns and woodwinds have finished, the oboist plays her A again, and the cellos and string basses tune to it.  Violins, violas, cellos, and basses are tuned by turning tuning pegs on the neck of the instrument.  The cellos and basses tune their A strings first, then tune their other three strings using the A string as a reference.

Finally the oboist plays her A a third time, and now the violins and violas tune, in the same manner as the cellos and basses.

Now that everybody's in tune, the concert can start.  But only when the conductor is good and ready!

Music Theory 101 - Notes and Pitch

It's hard to have a conversation about music without eventually getting to the fundamental building blocks of music.  In chemistry, we speak of atoms; in language, we speak of words. In music, the most basic structural unit is, of course, the note.

There are many different kinds of sounds in this world.  Most are noise - they carry no meaning.  They're just there.  Some, like speech, or alarms, or sounds like your phone ringing or your microwave beeping, have meaning, but aren't musical.  Notes are a special kind of sound.

A note, unlike other sounds, has two important defining characteristics: pitch, and duration.  Pitch refers to how high or low the note is.  Duration refers to how long the note lasts.

Today, I just want to talk about pitch.  There's a surprising amount to say about pitch in music, far more than can be said in just one day!  Today, I just want to cover the basics.

Imagine a piano being played.  The pianist presses one of the keys.  This causes a hammer to lift, which hits a string and causes it to vibrate.  That vibrating string causes vibrations in the air around it, which propagate outward towards you, the listener.  When those vibrations reach your ear, they cause your eardrum to vibrate, which sends a nervous signal to your brain.  And so you hear the note that the pianist played.  The frequency of those vibrations is what determines the pitch.  High pitched notes have a high frequency, meaning that are many many vibrations per second.  Low pitched notes have a low frequency - fewer vibrations per second.

This is why, if you look at the strings inside a piano, the low notes have long, big thick cables for strings, and the high notes have short, skinny little strings under high tension.  

All Western music is based around the scale and the octave.  Donald Duck can explain these ideas better than I can:

A scale consists of a specific series of notes - usually 8, but not always.  The first note of a scale, and the last note of the scale, are exactly one octave apart.  So when you play a scale, you end up right back where you started, just one octave higher.  Take a look at the keys on a piano:

Notice how they repeat, in a pattern?  You've got three white keys together, with two black keys in between.  Then there's four white keys together, with three black keys in between.  And then it's another three white with two black all over again.  All the way up and down the keyboard.

Each note has a name that's based on where it falls in the pattern.  Here's the piano keyboard again, but this time with the note names on each key.

One of the Cs is called middle C.  It's called middle C because it's in the middle of the keyboard.  It's also in the middle of the human vocal range.  For most women, it's toward the bottom of their range; for most men, it's in the upper part of their range.  Even if you're a very low bass, or a very high soprano, a middle C is almost certainly going to be a note you can hit.

Find middle C on a piano and play each white note in turn, until you get to the next C.  The notes you will play are:

   C  D  E  F  G  A  B  C

If you don't have a keyboard handy, it sounds like this:

What you're hearing here is called a C major scale.  It's a scale, because it has eight notes that start and end on the same note, one octave apart.  It's a C scale because it starts on C and ends on C.  What makes it a C major scale is the pattern of notes in between.  Most Western music uses either a major scale, or a minor scale.  We'll cover the difference between the two a bit later on.

Here's how a C major scale looks in musical notation:

There are five lines on the staff, with four spaces in between.  Each line or space corresponds to one note.  The scale starts at middle C, and ends at the C above middle C.

• Middle C sits one line below the staff.
• D is the next note.  It sits on the space below the staff.
• E is on the bottom line.
• F is on the bottom space.

And so on, up to C again.  Some people like to remember the lines on the staff:

E, G, B, D, F.   Every Good Boy Does Fine.

What if we want to start a C major scale on the C above middle C?  We can do that.  Just keep going.

C, D, E, F, G… wait a minute!  We've run out of space!  We're at the top space above the staff!  What do we do now?  The answer is, we add lines for the notes A, B, and C so that they have someplace to go.

These lines are called ledger lines, and we can add as many of them as we like, to accommodate notes that are as high or low as we please.  Let's finish the scale!

What about the notes below middle C?  The ones that the guys would sing, or that the bassoons might play?  And what's that funny looking thing way on the left side of the staff?

That funny looking symbol on the left of the staff, the one that kinda looks like an & symbol but not really, that's called a treble clef.  The function of a clef is to tell which lines and spaces correspond to which notes.  When a staff has a treble clef on it, as all these examples do, that means that middle C is on the ledger line below the staff.  It means that the Every Good Boy Does Fine rule for the lines applies.

In some countries, a treble clef is referred to as a G clef.  It's a little hard to see, because it's quite stylized, but the treble clef kinda looks like a letter G with a loop on top of it.  That line on the bowl of the G?  That's the line that the note G sits on.

There is another clef called the bass clef that handles notes below middle C.  We'll look at the bass clef a little bit later.

Next time - where did the black keys on the piano go?  Where do they fit onto this staff thing?  And what about scales that start on notes other than C?  

Lagniappe! John Tavener - Svyati

Arvo Pärt - Magnificat

Got another chant-inspired piece to share: Magnificat, by Estonian composer Arvo Pärt.

Born in 1935, Arvo Pärt emigrated from Estonia to Vienna in 1980 due to wranglings with the Soviet government.  He returned to Estonia after Estonia gained its independence, and now lives in both Berlin and Tallinn.

One of his most often performed pieces, the Magnificat for chorus, was written in 1989.  The text, which comes from the Gospel of Luke, is Mary's song of praise to God for the conception of Jesus:

Magnificat animea mea
Et exultavit spiritus meus in Deo salvatore meo.
Quia respexit humilitatem ancillae suae.

Ecce enim ex hoc beatam me dicent omnes generationes,
Quia fecit mihi magna,
Qui potens est.

Et sanctus nomen eius,
Et misericordia eius in progenies et progenies timentibus eum.

Fecit potentiam in brachio suo,
Dispersit superbo mente cordis sui;
Deposuit potentes de sede
Et exaltavit humiles;
Esurientes implevit bonis et divites dimisit inanes.

Suscepit Israel puerum suum,
Recordatus misericordiae,
Sicut locutus est ad patres nostros, Abraham et semini eius in saecula.

My soul doth magnify the Lord
And my spirit hath rejoiced in God my Savior.
Because he hath regarded the humility of his handmaiden.

From henceforth all generations shall call me blessed,
Because he who has done great things to me
Is mighty.

And holy is His name,
And his mercy is from generation to generation, unto those who fear Him.

He hath showed me strength in His arms,
He hath scattered the proud in the conceit of their hearts;
He hath put down the mighty from their seat
And exalted the humble;
He hath filled the hungry with good things and sent the rich away empty.

He hath received Israel his servant,
Being mindful of His mercy,
As he spoke to our fathers, to Abraham and his seed forever.

The Magnificat is an example of antiphonal music.  Antiphony refers to two singers, or choirs, or instruments, that sing to each other back and forth across the stage, church, or performance area.  It's like a musical game of catch - one group has the music for a while, then tosses it over to the other side.  They do their thing, and toss it back again.

Have a listen:

In the Magnificat, the music alternates between the chorus and a small group of soloists.  The piece starts with two soloists singing the first line of the text.  There's two things that I think are really neat about the way the piece begins.  One, it's very definitely plainchant inspired - you have the first soprano singing a melody that could easily have been written in the Middle Ages, singing against the second soprano, who has a drone.  Very classic.  But opening the Magnificat with a plainchant also looks forward to the Baroque and even Classical eras, where it was not at all uncommon for composers to begin a section of the Mass with plainchant before having the choir come in.

Two examples:

Dominico Scarlatti (Baroque era, 1685-1757) - Te Deum

Joseph Haydn (Classical era, 1732-1809) - Missa Brevis in B flat (Gloria)


There's two things I think are kinda interesting about how the piece unfolds.  Pärt's use of harmony alternates between consonant (sounds nice) and dissonant (sounds clashy).  There are a lot of minor seconds and tritones in here that composers in the MIddle Ages and Renaissance would have strictly avoided.  (C against C# is an example of a minor second; C against F# is a tritone.  I'll be covering scales and intervals in the next few posts.)

The other thing that is interesting is how Pärt decided not to use tone painting in this piece.  The Magnificat text has been used many times by a great many composers.  With opening lines like "My soul doth magnify the Lord", most composers choose to make a big celebratory deal out of it.  Here's how Bach did it:

J. S. Bach - Magnificat, BWV 243

But Pärt forgoes the fanfare.  He chooses not to match the music of his Magnificat with the text.  Instead, the whole piece is like a meditation, and the words are just the mantra.  The focus is on the music; the words are merely the carrier.  Rather than impose a meaning on his music, Pärt leaves it up to the listener.  Pärt once said about his music,

"I could compare my music to white light which contains all colours. Only a prism can divide the colours and make them appear; this prism could be the spirit of the listener."

In C

I want to go off on a bit of a musical diversion today.  Last time, I was talking about Polish composer Henryk Górecki and his 20th century reinterpretation of plain chant in his Miserere.  I know a number of you really enjoyed that piece, and I have two more pieces in a similar vein to share with you.  But I've found a phenomenal recording of a phenomenal piece that I've been listening to over and over this last week, and I really want to share it.

The piece is In C, written by American composer Terry Riley in 1963.

In C marks a kind of reaction against the atonal and twelve-tonal music that dominated much of the first half of the 20th century.  Composers such as Schönberg, Webern, Berg, Boulez, and Stravinsky produced works that were highly dissonant, with non-intuitive use of harmony, meter, and structure within the piece.  This is what makes 20th century music so difficult to listen to for a lot of people - it doesn't seem to conform to any of the rules we expect from a piece of music, so we're left thinking, what the heck is this?  

Enter the Minimalists.  This is a group that includes John Adams, Steve Reich, Philip Glass, La Monte Young, and Terry Riley.  If they had written a manifesto, I think it would have sounded something like this:

"You know, you guys have stretched and bent and broken all the rules to make music.  It's great that you felt the freedom to do that, more power to you.  But you don't need to go so far out into left field to make good music.  A lot of those rules are there for a really good reason.  We don't need to use weird dissonant harmonies to make music with; the traditional stuff works just fine.  And music should have a pulse to it.  It doesn't take a lot to make really good music - we'll do it with just a few notes.  Or just a few instruments.  Or with ordinary sounds.  You've made things way too difficult.  Let's simplify."

The rules for In C are very simple:

1. The piece consists of 53 short snippets of music that are repeated.
2. Any number of instruments can play.  Any kind of instrument can play.
3. Start with theme #1.  Play it for a while, then move to the next theme when you feel like it.
4. Don't get too far ahead of or too far behind the rest of the group.  There shouldn't be more than 3 or 4 themes going at a time.
5. Keep in strict time with each other.  To help you out, you'll have a timekeeper who will be playing the beat in C for the whole piece.  (Pity that guy, because it's a very boring part.)
6. The piece is finished when it's done.

The score for in C looks like this: 

Terry Riley - In C - Score

Follow along as you listen to the piece.

The first 5 minutes or so on the recording aren't the piece itself, just the folks in the ensemble getting tuned and warmed up.  Skip ahead if you like to 5:20, which is where the actual piece begins.  The audience applauds a short bit later - hey, we're really getting started here!

From the outset, it's clear that In C is a very appropriate title for this piece.  This piece is not just in C, it's obnoxiously in C.  The whole first section of the piece is nothing but an exploration of the C major triad: C-E-G.  C major is not normally a key you'd think of as being fun and exciting.  Case in point:

It's a rather boring key.  It's all white keys, no black keys, no sharps or flats.  It's a key that's safe and non-offensive, a key that makes a statement by not making any kind of statement.  A very interesting choice of key for Terry Riley to have chosen to make a statement with!

At 8:30 we start to see some dissonance, as theme #8 begins.  The C major theme is over and now we're starting to see some tension building up as we move into whatever is going to come next.  And then at 14:00, we start to go into some very strange territory indeed as theme #14 starts.  

The last note of theme #14 is an F#.  Not only is F# not part of the key of C, it's harmonically as far removed from C as you can get.  The interval between C and F# is called a tritone, and it's called that because the distance between C and F# is three whole steps, or six half steps.  (Count them: C-C#-D-D#-E-F-F#.  Six half steps.)  The piece sounds very strange and dissonant through here.  The clash between C and F# builds up tension needs to be resolved somehow.

At 18:00, it doesn't sound promising at all.  Theme #19, a G, is played against theme #21, an F#.  These two notes don't go together at all, and the result sounds like somebody beating the crap out of a set of bagpipes.  But at 19:30 - listen!  There it is in the background, so quiet, you can barely hear it.  The next theme!

Now it becomes clear what that F# was doing this whole time.  Themes 22 through 26 present a scale in E minor: E - F# - G - A - B.  We've moved away from the original key of C into what's called a closely related key.  The keys of C major and E minor differ by only one note: where the key of C major has the note of F in its scale, E minor has that pesky F# that's been causing all these nasty dissonanaces all this time.  So now we sit back, relax, and enjoy this new key for a while.

Look at how similar themes 22-26 are.  When they're played in sync with each other, there's this really cool echo effect that develops, almost as if you had a tape looped back to be out of sync with itself.  The use of taped sequences was something that Terry Riley, John Adams, and Steve Reich actually do use in other compositions.

By 28:00, the E minor sequence is over and we're back in C again.  Ready to move on to the next thing, whatever it is.  And then at 31:20, there it is - listen to that cello, playing theme #35!  Finally, after all these short repetitive motifs, we get the chance for each instrument to come out and sing.  At 39:00, theme #42 appears - another singing motif.

From there, the piece starts to wind down.  When themes 43-46 play together, around 44:00, the whole piece shimmers and sounds like a happy dance.  There's one last singing theme, theme 48, which plays from 48:15 to 52:40 in the various parts, and then the piece reaches its conclusion.  The ending of the piece mirrors the beginning, but is based around a different set of three notes.  Whereas the beginning of the piece was based on the notes of C-E-G - a C major chord, the end of the piece is based on the triad of F-G-B♭. As the final G-B♭pair dies down, the timekeeper playing C keeps on going, until he finally stops and the piece is over.

What's the significance of this piece?  Sure, it had a heavy influence on the later work of Steve Reich, John Adams, and Philip Glass, who would go on to become the most noted composers of the latter half of the 20th century.  But the heavy use of repetition within a composition, where subtle changes between repetitions cause one section to slide smoothly into the next without the listener really being aware of it - combined with Riley's technique of taking taped samples, manipulating them, and inserting them into his compositions - these two techniques founded a brand new musical genre.

It's a genre you hear every time you out to the club.  Trance.  Ambient.  House.  Techno.  Brian Eno.  Autechre.  The Chemical Brothers.  Thievery Corporation.  Skrillex.  DJ Tiesto.  Le Castle Vania.

They all owe their origins to one clever little piece.  Written… in C.

Gregorian Chant in the 20th Century

Wow!  I didn't mean to take a break like that, but somehow the holidays just happened.  It feels great to be back!

In my last post, I introduced Gregorian chants and talked about their influence on early classical music.  Gregorian chant experienced a resurgence of popularity in the classical fan world starting in 1994, when the Benedictine Monks of Santo Domingo de Silos released their CD Chant (which ended up going triple platinum).  Gregorian chant is still popular today, but decades before its popular resurgence, a number of 20th century composers were drawing inspiration from chant to create new, more modern kinds of sacred music.

Henryk Górecki (pronounced guh-RETS-kee) was a Polish composer who passed away in 2010.  Born in 1933, Górecki started out his musical career at the age of 18 teaching music to grade school children.  At the age of 19, he enrolled in a teacher training course at the Intermediate School of Music in Rybnik, in southern Poland.  It was there that he began trying his hand at writing music.  Góreci went on to continue his studies at the Katowice Academy of Music, and later became a professor of music there.  Because cultural exchanges between Poland and the West were extremely limited, Górecki's work was little known outside of Poland until after the end of Polish Communism in 1990.

As a young composer, Górecki drew his inspiration from Webern, Schoenberg, and other twelve-tone or post-tonal composers.  What does this mean?  Well, if you've ever said or heard somebody say, I really like classical music, but I can't understand that 20th century modernist crap, it sounds horrible - Górecki was one of those.  If you want a good example from this period of Górecki's compositional life, look for his Symphony no. 2, op. 31.  However, during the 1970s Górecki gradually moved away from this style and turned to a less dissonant, more lush, lyrical and expressive, and simpler musical style.  

Górecki's Miserere, written in 1981, is an example of his later style.  The Miserere is a product of the Solidarity movement, which eventually led to the fall of Communism and the birth of democracy in Poland.  Górecki wrote the Miserere as a response to the Communist government assault on members of the Solidarity movement in the city of Bydgoszcz in March of 1981.  After the Bydgoszcz events, the Polish government outlawed the Solidarity movement and imposed martial law, which caused the Miserere to not be able to be performed until 1987.

I'm going to give a link to a Youtube video for this piece:

For a free recording, it's not bad, but I think this is a piece you really should consider adding to your collection.  This is the recording I own, and I think it's superb:

Amazon - Gorecki Miserere

The text of the Miserere is simply:

Domine Deus, Deus noster, miserere nobis.

Oh God, our God, have mercy upon us.

The Miserere starts as a slow, gently rolling, somewhat mournful Gregorian-inspired chant.  The first section is a simple repetition of the words Domine Deus, Deus noster sung only by the basses.  In the second section, the basses continue with the same musical theme, but are joined by the baritones in two-part harmony.  In each successive section, the next higher voice comes in: first the tenors, then the altos, and finally the sopranos.  As each new voice comes in, the harmonies become more lush and complex.  The emotional contrast within each section becomes greater as well - sometimes the music is meditative and contemplative, other times powerful and ecstatic.  

The contrast between sections 8 and 9 is particularly striking.  Section 8 is pure chant - a simple melody sung by the women, against a drone sung by the men.  In section 9, the whole choir comes together in eight-part harmony - first in a great swelling entreaty, then in quiet prayer.   The tenth section mimics sections 8 and 9, but more percussively, more insistently, as if desperately begging for God's attention.  Domine, Domine, Domine, DOMINE!

Then finally, in the last section, we arrive at our conclusion.  Miserere nobis.  Have mercy upon us.  And with that, our prayer ends as simply as it began.  Our meditation is over.  Life goes on.

Next time, I'll be introducing two more 20th century composers whose work is inspired by Gregorian chant.  I hope you like their work as much as I do!