So how did Rachmaninoff and all other composers decide how their music was going to sound? You can definitely tell that they did not just put random notes on paper and hope it sounded good... there was a general set of rules they followed. This set of rules is what we today call music theory. It would be wrong, however, to say that composers had a nice little "music theory handbook" that they referred to as they were writing their music. Actually, it is just the other way around... our study of music theory is based on what composers wrote many years ago.
This section will deal mostly with the music written from about 1700-1900 (also called the common practice period). We will not really go into the study of modern music here, mostly because much of the music of the 20th century has been designed to completely redefine music theory. If you want to learn about some of the theory behind 20th century music, you can visit the Modern Period section of our site.
If you already feel confident in your knowledge about music theory, feel free to skip a few of the lessons below... If you don't have a solid base in music, however, we recommend that you follow the silver links at the bottom of each page in order to gain a foundation that will be used in the upcoming sections. Well, let's get started!
- Lesson 1: What is Sound?
- Lesson 2: What is Pitch?
- Lesson 3: The Scale
- Lesson 4: What is Rhythm?
- Lesson 5: Learn to Read Music
- Lesson 6: What are Intervals?
- Lesson 7: The Major Scale Revisited
- Lesson 8: Basic Harmony
What is Sound?
So what exactly is sound? Well, let's look at the properties of sound. We can hear it, but we can't see, taste, smell, or feel it, right? Now, wait a minute, we CAN feel sound. Have you ever stood next to a large speaker? Or maybe you've felt the rumbling of heavy bass music through a table or a floor. These effects prove that sound is some kind of physical phenomenon. Sound must somehow be "hitting" you, letting you "feel the beat". But how can that be happening? We don't see anything when we "feel" sound...nothing but air! So we must be feeling the air when we feel sound!
OK, so how exactly are we "feeling" the air? Well, to answer this question, we need you to complete a little demonstration. Ready? Gently, take one of your hands and find your windpipe (at the base of your neck). The windpipe is the tube through which air passes when we breathe or talk. Now, keep your fingers touching your windpipe and sing a note (any note!) for a few seconds. If you're not the singing type, you can also hum or talk instead of singing. So, what did you notice? Your windpipe probably vibrated; if not, you may need to try again while singing a little louder.
Hmm, now we have the results of an experiment on sound, but what do these results mean? Let's think about this logically. Your windpipe vibrated when you made a sound. So, this means your windpipe caused the air to vibrate. Great, now we've figured out that sound is just vibrating air. But that still doesn't explain the rich variety of sounds that we can hear.
Well, the answer to this one is simple. We've established that sound is simply vibrations in the air. In fact, the reason we can hear sounds is that these vibrations trigger tiny sensors in our ears that send the messages to our brains. Back to the question: why is there such a wide variety of sound? Well the answer is that there is an almost infinitely wide variety of vibrations in the air. For example, the air can vibrate at different speeds and intensities. Each of these slight variations can produce a different sound. Everyone has experienced a wide variety of sound, from the lyrical singing of a violin to the chirping of a bird.
Instruments and Sound
Another question: how do all the musical instruments produce sound? Well, in all cases, the instruments produce a vibration (usually through the vibration of a string). This vibration is in turn transferred to the air, and eventually reaches our ears. Again, a wide variety of vibration is possible from the many different instruments. Of course, one violin may sound drastically different from another violin due to a slightly different type of vibration produced. This applies to any instrument, not just violins.
Yet another point to think about is acoustics. You've probably realized that an instrument sounds different in a small room than in a huge concert hall. At least, you've experienced an echo, which is just the vibration of the air being reflected by something so that it is heard multiple times. The acoustics of a room work the same way: the various surfaces can slightly alter the type of vibration and change the sound slightly. The surfaces can also direct the sound to travel in a certain direction. For example, in a concert hall, the sounds made on the stage travel out towards the audience because of the design and shaping of the hall. In some places, the concert hall is so well designed that a musician cannot even clearly hear the musician sitting next to him/her because all the sound is being directed outwards!
Conclusion
Well, hopefully we've provided you with some basis on how sound works. This knowledge will be important in the upcoming pages where we go into more detail about sound and specifically music.What are Pitches?
Now we know how much a wide variety of pitches can help the sound of music. But what exactly is pitch? We know that musicians can produce both high and low notes, but how exactly does it work? Well, remember what we discussed in Lesson 1? Sound is simply vibrations of air. We've established that there is an infinite variety of vibration possible, creating an infinite variety of sound. But that still doesn't answer our question of "What are Pitches?".
Well, consider this: the main chamber music instruments all have strings, right? Well, a string instrument player can raise the pitch of his/her instrument by moving his/her fingers to shorten the string! A pianist can raise the pitch of his/her instrument by playing a key connected to a shorter string! So, a shorter string must cause a higher pitch, and a longer string must cause a lower pitch! Maybe you've tried this with a rubber band before: if you pinch off the rubber band and pluck it, it will vibrate; causing a high pitch to occur. If you don't pinch the rubber band and just pluck the entire band, it will vibrate and cause a lower pitch to occur. This works in the same principle as the chamber music instruments
Great! Now we know how to create a higher or lower pitch. But what exactly is happening? Well, every time a musician plays a note, his or her string is vibrated very rapidly. In other words, the string moves back and forth almost inconceivably fast (the violin's A string vibrates at 440,000 times per second!). A longer string will vibrate more slowly than a shorter string. Perhaps you've experienced this with a jump rope. A single person jumping rope can get his/her rope to go very quickly. This is similar to the vibration of a short string. A jump rope held by two people standing far away will not travel nearly as quickly as the single person's jump rope. This is similar to the vibration of a long string. So, fast vibrations must correspond to higher pitches, and slow vibrations must correspond to lower pitches.
Note Names
OK, so we have some idea of what pitches are. It gets a little more complicated, though... In music, only a select number of pitches are ever played. Why? Well, music has just evolved over thousands of years to only incorporate a select number of pitches. You can bet that it has evolved the right way, too, if you've ever heard an out-of-tune viola. An out-of-tune instrument plays pitches that are slightly off from what they should be. For example, if an instrument was supposed to play a pitch vibrating at 440,000 times per second, it might vibrate at 441,000 times per second. This creates an awful sound, almost as bad as those random notes from Lesson 1.
So how exactly did musicians decide to use only a certain number of notes? Well, that brings us to a funny story involving the great composer Johann Sebastian Bach. After the end of the Renaissance, there was some debate over the best notes to be used in music. For example, Indian music uses 22 notes per octave. Well, J.S. Bach was a strong supporter of using 12 notes per octave, which is the system still used today in Western music. To prove that his system was the best, Bach wrote a prelude and fugue in 24 keys: two on every note (both major and minor). Evidently, Bach made his point and so his system of 12 notes per octave is still used today.
Anyway, since there are a fixed number of pitches, they actually have names! These names include: A, B, C, D, E, F, and G. Of course, these note names repeat, but we'll get more into that later. Note names are vital to musicians because they represent each pitch. You can see how confusing it would get if someone told you to play a note vibrating at 500,000 times per second. It would be much easier if they just told you the note name. In addition to these 7 pitches, there are 5 more pitches that can be represented by adding a '#' or a 'b' symbol to each note (e.g. A#, Bb). These symbols are referred to by a group as "accidentals". An accidental can be cancelled out by using the "natural" symbol, which is unfortunately not a member of ascii text. We have put together a little display of the most common accidentals used in music. There are more complex symbols (such as the double flat or double sharp) but these are rarely used.
The Major Scale
Let's move on to one of the basic building blocks of music: the scale. First, play a simple major scale starting on C. Perhaps you've heard this before, perhaps not, but this is what a basic major scale sounds like. What is a scale exactly? Well, it's a series of notes like the one you just heard. Of course, it doesn't have to start on C. For example, we have another simple major scale starting on C#. This sounds slightly different, but you can tell that the scales are really the same thing. Hopefully, you've noticed that the note that the scales start and end on sound the same. This is an important point because a scale spans an octave, which is just two notes that are 12 notes apart.
What exactly is a major scale? Well, we've heard two of them, but that might not necessarily make it clear. Let's come up with an official definition: a major scale is a set of notes that defines the key of a piece. Wow, there are a lot of new terms in that. Rather than attempt to explain that, we'll give you an audio demonstration. Notice how all the notes in this demo are also notes in the C major scale? Well, that's a technique used by composers to create music. This makes the major scale extremely useful in composing pieces. The scale that composers take their notes from is called the key of the piece. Of course composers are not limited by any means to using only certain tones. Composers are free to write whatever notes they wish to make their pieces sound good. For example, composers often quickly change from key to key, utilizing different scales.
Now, we've neglected to mention some important aspects of the major scale. Not only does the scale define the key of the piece, but the notes in the scale are not variable. In other words, a composer cannot make up anything he or she wants and call it a scale. Instead, all major scales sound very similar and are all based on the same scale. For example, if you took the basic C major scale and bumped it up a few steps, you'd still have a major scale.
The Minor Scale
Hopefully, you now have some understanding on what a major scale is. Later on, we will go into more depth onto what the notes are that make up the major scale. First, though, we'd like to look into another type of scale: the minor scale. Again, don't worry too much about what the notes in this scale are; just play our simple harmonic minor scale starting (and ending) on C. What's a harmonic minor scale, you ask? Well, there are three different types of minor scales: natural, melodic, and harmonic. They all sound very similar but are slightly different.
Well, hopefully you were able to hear the harmonic minor scale. Notice anything different between it and the major scale? That's right; the minor scale sounded much "sadder". Like the major scale, the minor scale can be utilized by composers to create music. We've put together another little demonstration in the key of C minor. This means that the notes used in this demonstration were in that C minor scale. By the way, when a key is in a minor key, the general practice is to write the key of the piece in lower case. So, the key of this demonstration is c whereas the key of the demonstration before was C.
Now we know a little bit about how scales and keys work. There's still a whole lot more that we need to learn about music, though. Remember that music is more than just notes put together, there are also many different other components of music, including complex rhythms. Speaking of rhythms, continue to the next page for a lesson on rhythm.What is Rhythm?
So what exactly is rhythm? We know that it's the timing of the notes, but how do the composers write down these timings into a simple format? Well, if you can read music, then you know exactly how this is done. Otherwise, we'll have to teach you about notation. Basically, all musical notes are arranged notes that last for different amounts of time. For example, a quarter note is a common note that is used by composers. Usually, a quarter note will last for a quarter of a measure.
What is a measure? Well, it's just a section of one full beat. Are you confused? Don't worry! Here's an example: four quarter notes make up one full beat. This makes sense because four quarters added together is one. So, a quarter note lasts for a certain amount of time. Now, for example, composers can also use half notes, eighth notes, sixteenth notes, or any other fraction. This allows them to use an almost limitless array of note lengths.
Now, you may have noticed that a major part of music is also silence. What we mean by this is that the short or long silences in between notes are often very important. So how do composers write these silences? Well, the silences are called "rests", and they work the same way as notes do. For example, a quarter rest is silence that lasts as long as a quarter note and an eighth note is silence that lasts as long as an eighth rest.
By now you may be wondering how a musician knows how long to hold a note. Well, composers often write down a tempo marking. Tempo markings, such as moderato or allegro, give the musicians some idea about how long to hold each note. Of course, the final speed and style of the piece is up to the musicians themselves. On the next page, we will show you some actual notes and rests and you will able to see how composers are able to quickly symbolize to musicians how long to hold a note.What are Clefs?
Well, the first thing that you will see at the beginning of every line of music is a clef. There are three main clefs that are used by musicians: treble, alto, and bass. In the little example in the upper left corner, you can see a treble clef and a bass clef. These two clefs are often used to write piano music.
So what is a clef? Well, a clef basically tells the musician what note each line in the staff corresponds to. Sound complicated? Well, it's actually pretty simple. Let's look again at that example in the upper left corner. The top line of music is in treble clef while the bottom line is in bass clef. So, the notes in each line are different because there are two different clefs. For example, the middle line in treble clef corresponds to a G while the middle line in bass clef corresponds to a D. To further complicate things, the middle line in alto clef corresponds to a C.
OK, so why did composers invent all these crazy clefs anyway? Well, good question. Clefs were introduced many centuries ago mainly for singers to use. This is because treble clef corresponds generally to the range of a soprano singer, alto clef corresponds generally to the range of an alto singer, and bass clef corresponds generally to the range of a bass singer. As composers grew skilled at writing music for singing groups, they translated their skills to writing for instruments. Of course, they did not want to learn a whole new system of writing music, so they just used the same clefs that they had always used before.
Clefs also translate well to string instruments. This is because the violin is higher pitched like a soprano and can use the treble clef. The viola is a little bit lower pitched than the violin and can use the alto clef. Also, the cello is well suited to playing in bass clef due to its lower range. Of course, the lower instruments (viola and cello) can use the higher clefs to play when they are playing high passages. The piano uses a variety of treble and bass clefs often rapidly switching and using combinations of the two.
What are Key Signatures?
Let's look at that example in the upper left corner again. See those three flats (they look like the letter 'b')? That's an example of a key signature. We talked a little bit about keys in Lesson 3: The Scale. To refresh your memory, the key of a piece is just the scale from which the notes of the piece are taken.
OK, so how do these flats translate to the key of the piece? Well, the flats are strategically placed on certain lines. When musicians see notes on these lines, they know to automatically play them flat. Using this technique of having a key signature saves the composer time because he or she does not need to continually draw the same flats over and over again. Of course, music could be written without a key signature, but that would just be confusing for the musicians and the composers.
What are Notes?
So what are notes? Most of us can probably recognize these famous musical components, but what do they really mean? Well, each musical note conveys quite a bit of information. Let's start with the placement of the note. The placement of the note on the staff is important because it tells the musician which pitch to play (for more information on pitches, see Lesson 2: What is Pitch?). As we mentioned before, the note values in each staff depend on the clef. Let's not get too involved with this now, though. We will talk more about these note values in Lesson 6: What are Intervals?.
OK, so let's take a look at some real notes. See that picture to the right of this text? Well, that's an example of a few notes. The main differences in these notes are just in their stems, which is everything but the circular part of the note. Every time one of those "tails" is added, the note's duration gets halved. It's not really important for you to remember each note value at this point because it is much easier to understand note durations when you are actually playing an instrument. Also, remember that we already discussed a little bit about note durations in Lesson 4: What is Rhythm?.
What are Rests?
Remember our discussion of rests from Lesson 4: What is Rhythm?? Well, here are some examples of what rests might actually look like in music. These rests work in a very similar way to the notes. As little "tails" are added to the rests, the rest durations are halved. By now, you may be wondering why the whole, half, and quarter notes/rests are different from the eighth, sixteenth, and 32nd notes/rests. Well, we're not really sure why this happened as music evolved over the centuries. One theory to why these notes and rests are different is that composers wanted to let musicians easily see and recognize notes that were commonly used. So, musicians can quickly see whether a note is a half note or a quarter note without counting the stems. This is just one of the countless tiny timesavers that composers have built into music.
How Does This Apply to Music?
Good question! How does this apply to music? Well, if you recall, in Lesson 2: What is Pitch? we talked about various pitches. We mentioned how only 12 distinct pitches are used in music. We also mentioned how these 12 pitches continue repeating infinitely in both the higher and the lower direction. Well, let's take for example any two pitches. The distance between these two pitches is called an interval.
So an interval is just the distance between any two notes. But it's a little more complicated than that. A musician needs to be able to say something and have other musicians understand exactly what interval he or she is talking about.
Half Steps and Whole Steps
No, we're not going to teach you to dance in this section, but we are going to teach you a little bit about musical steps. So let's start with the most basic step: a half step. A half step is simply the distance between two notes that are as close as possible to each other. So if you have one note and another one that is just a tiny bit (on a piano, the next key) above or below it, these two notes are separated by a half step.
That seems pretty straighforward... So what's a whole step, then? Well, a whole step is just one half step wider than a half step. In other words a whole step is two half steps put together. On a piano keyboard, a whole step would just be two keys apart. OK, that's pretty simple, too. So what's the big deal about half steps and whole steps then? Well, these small little steps make up everything in music. Any notes you can play on any instrument (provided that they are actual notes!) are separated by a certain number of whole steps and half steps.
The real beauty of having these steps is that a musician can say "that note is a half step too low" or something like that, and someone else will immediately know how to fix the problem. If a musician said "that note is 50 cents too low", no one would know what he or she was talking about (and we wouldn't either!).
Intervals
Still, there's more to intervals than just half steps and whole steps. It's OK to talk half steps and whole steps when a musician is just talking about a small interval. But what if the notes are 13 half steps apart? It would get a little bit cumbersome trying to calculate and figure out what interval the musician meant. For this reason, a slightly more complicated, yet easier to use method of intervals was developed.
Remember the major scale we discussed in Lesson 3: The Scale? Well, this major scale actually plays a big role in this slightly more complex system of intervals. Basically, if a musician says some number as an interval, this interval will be the distance between the first note of the scale and whichever note the musician's number corresponds to. For example, if someone says, "play a 4th", that means to play the first note of the scale and then the fourth note of the scale. Since there are 8 notes in the major scale, these intervals including 2nds up to 8ths.
Now that you know a little bit about intervals, we can see what these intervals truly are. Like any pairs of notes, the intervals are still made up of whole and half steps. Let's take a look at the major scale in more depth on the following page.The Major Scale Revisited
So what exactly is a major scale? In Lesson 3, we talked about some of the uses of major scales, but we didn't really go into too much depth on what exactly a major scale is. Let's look again at the C Major Scale. Now, in Lesson 6: What are Intervals?, we discussed how any two notes in music are separated by a certain number of whole steps and half steps. Major scales also follow this rule.
Let's take a look at this 'C' Major Scale graphic. Here, we've shown you where all the half steps and whole steps are by putting the letter 'H' where the notes are a half step apart and the letter 'W' where the notes are a whole step apart.
No matter what note the scale starts on, this set of whole steps and half steps remains constant. So, as we said in Lesson 6, musicians can easily describe intervals by just saying the number of notes in the major scale that it would take to fill that interval. For example a whole step would just be a "second" because the first two notes in the major scale are equal to a whole step. A "third" would be two whole steps because the distance between the first note in the major scale and the third note is two whole steps. A "fourth" would be two whole steps and a half step since the distance between the first note in the major scale and the fourth note is two whole steps and one half step.
OK, this seems pretty simple now. But what happens if a musician wants one whole step and one half step? Suddenly, our system fails because there is no note in the major scale that is one and a half whole steps away from the first note. This note is in between the second and third notes in the major scale.
Again, musicians have devised a solution to this problem. When a note fits perfectly on the major scale, musicians call the note a major interval. For example, two whole steps would be a major third. However, if the interval is a 4th or a 5th, the interval is called a perfect interval. For example, two and a half whole steps would be called a perfect fourth.
So, back to the problem of the note that is one and a half whole steps away from the first note in the scale. Well, musicians can lower the width of the interval by a half step by saying the word minor. So, a note that is one whole step and one half step away is a minor third.
Well, that's pretty much all you need to know about intervals! Congratulations on having passed through this difficult section! Just one more page to go in the theory section!What is Harmony?
So what exactly is harmony? Well, basically, harmony is anything that accompanies the melody. Often, the harmony can occur as chords, which are simply a few notes played simultaneously. Harmony can also occur as broken chords, which are the same notes in the chord, only they are played one after another. Often, listeners do not even know they are hearing harmony because the composer hides it so well from them. In almost all cases, though, the harmony that is being played can be converted into a chord.
Triads
The major triad is one of the most basic harmonies in music. It is formed by taking the first, third, and fifth note of the major scale and playing them simultaneously. This triad has a "happy" sound to it and is often used as the basic chord in a major piece. Another common triad is the minor triad. It is formed by taking the first, third, and fifth note of the minor scale. As you can tell, this triad has a "sadder" sound to it and is often used as the basic chord in a minor piece.
So what's the big deal with triads? Well, they are a very common form of harmony. By themselves, though, they don't mean too much. This is because music uses a wide variety of chords that have complex relationships to each other. Let's make up an example so that we understand this section better. Let's say we have a piece in the key of C Major. This means that many of the melodic notes are taken from the C Major scale. The basic harmonic chord also starts on the key of C (the notes would then be C, E, and G). Now this doesn't prohibit the composer from using other triads starting on other notes in the scale. For example, the composer can use a triad starting on G (the notes would then be G, B, and D).
By the way, there's a form of musical shorthand for quickly identifying the proper triad. Musicians use roman numerals corresponding to the starting note for identifying triads. For example, if we're in the key of C Major, I would be a triad starting on C. V would then be a triad starting on G.
Harmonic Progressions and Cadences
Still, chords are meaningless unless they add something to the music. Well, that's where harmonic progressions come in. As composers switch from chord to chord, they can create the impression that the music is moving somewhere. A lot of harmonic progressions have been established and commonly used, but composers such as Rachmaninoff are still able to invent new and exciting harmonic progressions.
So, let's talk about some actual harmonic progressions. Cadences are one type of harmonic progression that are often used at the end of sections to settle the thought. Two common cadences are plagal (IV to I) and authentic (V to I). These progressions are quite simple and only consist of two triads. Composers have realized, though, that they give the impression of completion to a section of music. As a result, these cadences are also commonly used at the end of an entire piece.
Inversions
Inversions are our last topic, and they really are quite simple. Let's take a C Major triad for example. The notes in this triad are C, E, and G. The first inversion is simply E, G, and then C. The second inversion is simply G, C, and then E. We simply took the bottom note and put it on the top. Inversions are not important in harmonic progressions because they do not change the triads. Inversions can become important, though, when composers want certain notes to stand out. For example, the top note in a triad played on the piano will always stand out just because the highest note is more audible. For this reason, composers often place a melody note on the top of the triad so that it can be heard more easily.
End of Music Theory
Congratulations! You have passed through the most difficult and challenging portion of The Music Chamber. You may now continue following the silver links at the bottom each page into the Historical Periods section or you may use the navigation bar on your left to jump to any section of The Music Chamber!
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