Intervals

In music, an interval is the distance between two notes--whether played simultaneously or one after the other. Intervals are calculated by first determining the "base interval," and then determining the "interval quality."

Let's begin by determining the base interval, which simply involves counting the lines and spaces between the notes (including the lines or spaces that the notes are on). For example, in the picture below there is a 4 below the notes C and F. This base interval of a fourth was determined by counting the C note, then the space above it (D), the line about that (E), and then the F note. Because four notes were named (C-D-E-F), the interval is "a fourth of some kind" (since we do not yet know the interval quality).



Sharps and flats have no effect when determining the base interval, as can be seen in the two pictures below:



Now let's look at the steps required for determining the interval quality. It's important to note that this step cannot change what we determined in the first step. If an interval is "a fourth of some kind" it will remain "a fourth of some kind" regardless of how it is impacted by flats and sharps. Interval quality is expressed using one of the following terms: diminished (d), minor (m), Major (M), Perfect (P) or Augmented (A). Intervals of 1, 4, 5 and 8 can only be Perfect, diminished or Augmented. In these intervals a half-step below the perfect interval is diminished and a half-step above the perfect interval is augmented. Intervals of 2, 3, 6 and 7 can be diminished, minor, Major, or Augmented. In these intervals a half-step above the major interval is augmented, a half-step below the major interval is minor, and 2 half-steps below the major interval is diminished.

Let's look at the same example we looked at before, the interval from C to F with "P4" listed below it in the first picture. We begin by counting the number of half steps between the notes (this time we don't count the first note). From a C to a C# is 1 half-step, then from C to D is 2 half-steps, from C to D# is 3 half-steps, from C to E is 4 half-steps, and from C to F is 5 half steps. An interval of a fourth (determined in the first step) that contains 5 half-steps is referred to as a Perfect 4th. The two pictures below show all of the diatonic intervals in the scale of C Major:



If an interval is greater than an octave, the highest note is transposed into the same octave as the lowest note and the base interval and interval quality are determined. Then 7 is added to the base interval for each octave transposition. For example, to calculate the interval from middle C to the D above high C, we first calculate the interval from middle C to the D two keys above it, which is a Major 2nd. Then we add 14, since we transposed the top note two octaves lower, and describe the interval is a Major 16th.

When calculating interval quality, first determine the number of half-steps between the two notes. Then start with the C note and move up that same number of half-steps. The pictures below display every possible chromatic interval within a single octave beginning with middle C.







Sometimes intervals must be written by using a double sharp, as in the example below:



The process of calculating musical intervals, while difficult at first, will become easier with time and practice.

Music and Concentration

I've been teaching piano lessons to a young music student for nearly a year (she was 6 when she started and recently turned 7), and learning the names of the notes has been a bit of a struggle for her. I tried several approaches, but none of them seemed to be working until last week when I decided to make a "concentration" game to help her memorize the mnemonic devices that make naming the notes easier. At first I just let her play the game and try to make matches, then I started asking her to tell me what match she needed to look for. She would turn over a card like "All Cows Eat Grass" and have to tell me that she was looking for a card that said, "Bass Clef Spaces" before turning over a second card. She played the game three times the first day and twice at her lesson yesterday, and she finally seems to get "getting it." Here is what the game looks like:

Composing Harmony

In this article I'm going to take the melody I composed in the previous article and write a harmony part to go with it. Harmony adds color and flavor to music, and just as in cooking it can be "seasoned to taste" to fit the composer's preferences. To begin with, let's look again at the original melody:


This melody happens to be in the key of G major, because that's how I heard it in my head before writing it down, but the key doesn't matter too much (the song can always be transposed after it's written), as long as you are familiar with the notes and chords of whatever key you've decided to use.

The first step I take when composing harmony is to find chords that give my song the "flavor" I'm looking for. In this case I wanted a dissonant "cool jazz" kind of sound, so I employed minor 7th and major 7th chords whenever possible. There's no right answer when it comes to finding chords, but it helps to have a knowledge of the different chords available in the key you are writing in and its related keys (I'll talk more about related keys when I discuss the Circle of 5ths in a future article). For me the process of finding the right chords is largely experimental. I play different chords until I find a progression that I like, and then I write them down. Here are the chords I came up with for this song:


After writing down the chords I added a blank bass clef line to the melody in my music arranging program (Sibelius) and printed a copy so I could begin composing the exact notes for the harmony. During this step I changed a few chords that didn't quite fit the sound I was looking for, and I looked for ways to make the harmony more interesting. Here is the rough draft of my arrangement:


And here is the "final" version in Sibelius:


Good composition involves the creative use of contrasts: consonance and dissonance, loud and soft, major and minor, movement and rest, richness ("close harmony") and sparseness. I'm going to go through the song measure by measure and discuss some of the techniques I used while writing the harmony.

In the 1st measure I used simple block chords in the root position, and they exactly matched the chords I came up with when I roughed-in the harmony. The term "with pedal" is my lazy way of saying that the musician should use the pedal in a manner of his or her choosing throughout the song:


Measure 2 includes two "fill" notes. Since the melody is at rest for 4 counts, I added these notes to keep the songs moving and to add interest and variety:


In measure 3 I rearranged the Em7 chord, initially playing only the 1st and 5th tones and then adding the minor 7th tone on the 3rd beat (and dropping the 3rd tone). The Am7 chord is played in the root position:


Measure 4 originally had a "fill" note in the melody, but as I was doing the arranging I decided to remove that note and let the D chord, played half way through the measure, take its place:


Measure 5 uses an Em chord (instead of the Em7 I had originally written) in its 1st inversion. I modified the Am7 chord to an Am/G chord (an A minor chord with a G note in the bass):


Measure 6 is similar to measure 3. The 1st and 7th tones of the Fmaj7 chord are played initially, the 5th tone is dropped and the 3rd tone is played half way through the measure. The Fmaj7 chord is "foreign" to the key of G major, borrowed from the closely related key of C major, and it gives this part of the harmony a slightly exotic sound:


The D7sus4 chord in measure 7 is arranged without the 5th tone, which would be an A if it were present:


Measure 8 provides a contrasting resting point for the song, both harmonically and rhythmically. The song's "bridge" -- measures 9 through 12 -- begins with a pickup note at the end of the measure:


In measure 9 the D7 chord is split into two parts. Initially only the 3rd, 5th and 7th tones are played, then half way through the measure the 1st (or root) tone is played, completing the aural puzzle. The harmony in this measure is written in two voices so that the first notes that are played continue through the entire measure. The D note that is added half way through the measure adds richness to the notes already being played, but doesn't take their place:


In measure 10 the Em chord again appears in its 1st inversion. I just realized that this would be impossible to play as it's written. The measure starts with whole notes, and then the three eights notes (which echo the melody) are supposed to be played while the whole notes are still being held down. Most humans don't have enough fingers on their left hands to be able to pull that off, so I'll need to make an adjustment there. The song is still a work in progress, and I'll continue to play it and make minor modifications for the next few weeks before declaring it "finished":


In measure 11 the Am7 chord is split up and inverted. The first part of the chord is played in its 2nd inversion, without the 3rd tone. Then the 3rd tone (a C note) is played in the second half of the measure:


The 12th measure doesn't actually contain a Gmaj7 chord, because I liked the sound of an A note in the base instead of G. The second half of the measure contains a Bm chord, which is the top three notes of a Gmaj7 chord. This chord should be written as Bm/A, but a Gmaj7 chord fits the song, too:


Since the melody in measure 13 is the same as in measure 1, I could have just copied the same harmony from measure 1. But I wanted to add interest and variety, so I thinned out the harmony a bit by only playing a B note and a G note in the first half of the measure (the 5th and 1st tones of an Em chord). I kept the Dm7 chord in block format, as it was in the first measure, but this time I dropped the third tone:


The 14th measure contains a split Cmaj7 chord. The 1st, 3rd and 7th tones are played initially, then half way through the measure the 5th tone is played (as a "fill" note):


The 15th measure uses an Em chord in its 2nd inversion. The bass note, B, is held throughout the measure while the top notes of the chord change to Bm (in the last beat of the measure). It was tempting to end the song on a D7 to G chord progression, but the dominant 7th to root chord cadence is so cliché that I wanted to do something a little different:


The song ends on a G/D chord (a G chord in its 2nd inversion). This is a bit unusual, because songs usually end with a slightly more resolved feeling by placing the final chord in its first inversion, but ending with a 2nd inversion seems to work for this song:



Over the next few weeks I'll revise this song, adding the metronome mark (95 beats per minute), adding dynamics, and continuing to make minor changes and tweaks until I'm satisfied or until I get so tired of changing it that I just have to call it "finished."

I also need to consider the playability of the song (how easy or difficult it is for pianists to play). I could arrange it in a way that makes it easy for beginning pianists, and this might require changing the key so that there are fewer ledger lines in the left hand. Or I could add more grace notes and trills and larger finger spreads to make it sound more rich and full (but also making it more difficult to play). I could also add more right hand notes, since the right hand currently just contains the melody line in all but a few cases. I could expand the song, since it's only 16 measures long, or I could add variety and interest by repeating the same measures but in different octaves. If I wanted to add lyrics, I could write a piano accompaniment for the song. Then I could publish it, record it, set it aside, or do whatever I want to do with it. The nice thing about being a composer by hobby rather than profession is that I can work on songs when I want to and I am free to be as creative as I would like. The process of composing can be time-consuming and difficult at times, but it can also be quite fulfilling. When a new song is finally "finished" I always feel a sense of accomplishment and satisfaction.

Melody

Melody is one the most important dimensions of composing, yet also one of the most difficult to pin down and define. What makes a good melody? Most people know it when they hear it, yet like describing the taste of salt it's often difficult to say exactly what makes a melody "good." Much of the process of creating melody is artistic and creative, but there are some practical and definable aspects as well.

When composing songs it is often difficult to know if the harmony or the melody should be written first, or if both should be written at the same time. I've experimented with all these methods, and there's no right answer. Every song is different, but for the purposes of this article I'm going to analyze a melody I wrote in my head and then later transcribed and harmonized. Here's the entire melody:



This melody was intended to be sung (it has lyrics), and so the range of notes is intentionally narrow, so it's accessible for most vocalists. The piano has a very wide range, of course, and instrumental melodies need not be confined to the same limits as vocal melodies. The lowest note in this song, the D immediately above middle C, appears in measure 8:


and is repeated two more times in measure 12:


The highest note in this song appears in measure 9:


In addition to the range, every melody has a contour. Some melodies use a lot of "steps" (adjacent notes) and others use a lot of "skips." Measure 5 provides a good example of both steps and skips:


The first interval is an ascending skip, in this case an interval called a perfect fifth. Then the next five notes are steps (adjacent), and finally the measure ends with a skip (a descending major third).

One of the most important dimensions of any melody is motif. A motif is a "signature" set of notes that identify a song (the opening notes of Beethoven's 5th Symphony are a well-known example of a motif). It holds a melody together and helps it make sense to the listener. Sometimes motifs are repeated exactly, as in measures 1 and 13:



Other times the rhythm and pitch of the motif are modified, or extra notes are added to make it sound different from the original (but still related), as in measures 1 and 5:




Rhythm is an essential characteristic of melody. Most people wouldn't recognize their favorite melodies if they were played using different rhythms. In general, songs should have a steady beat and the composer must decide how to use repetition and change to keep the listener interested. Rhythms don't have to be complex to be enjoyable, but there needs to be a good mix of consistency (similar rhythms) and variety (unexpected changes).

This short 16 measure melody was written in an A-B-A format. Measures 1 through 8 introduce the theme, measures 9 through 12 are quite different to provide contrast, and measures 13 through 16 reintroduce the opening theme and bring the listener back "home" again. The song "Twinkle, Twinkle Little Star" was written in A-B-A format, with "Up above the world so high, like a diamond in the sky" providing a mild contrast to the identical first and last lines.

Another dimension of melody that a composer must consider is whether and how to use repeated notes, such as the ones used in measure 12:



Typically the melody is simply the highest note played, but occasionally composers and arrangers will place the melody in a lower register while playing an ostinato (repeated theme) or quieter notes in the higher registers to ensure that the melody still stands out.

Learning to write good melodies requires experimentation and trial and error. Like other aspects of composing, sometimes good melodies come in a flash of inspiration and other times they are the result of painstaking hard work and patience.

The Process of Composing

Composing piano songs requires a balance of art and science, theory and practice. Every composer's approach is a little different, and songs come in different ways. Some songs come all at once, and it's hard to explain the feelings that accompany that kind of inspiration. But most of the time songs require extensive work over a period of weeks or months. Sometimes I write songs entirely by ear, and other times I employ music theory techniques such as moving from one key to another via a circle of fifths progression. In this article I'm going to give an overview of the steps I typically take when writing a new song.

When I began composing several years ago I purchased an electronic keyboard with a midi interface and hooked it up to my computer. I wanted to be able to play sections of music and have them "automatically" notated. However, I quickly discovered that, for me, the most difficult part of transcribing music composed "by ear" into standard notation is capturing the correct rhythm. Midi software can record the right notes, but I found it difficult to play smoothly enough to allow the midi software to record the correct rhythms. So I decided to purchase a program called "Sibelius" to help me write music. It was expensive (around $400), but of all the software programs I tried it was the easiest and most powerful. (There is a program called Finale that was my second choice.)

At first I attempted to compose in Sibelius by sitting at the computer and arranging notes, but I quickly discovered that I produce higher quality music when I'm sitting at a piano than when I'm sitting at a computer. So I started writing songs with a pencil and music paper, then used Sibelius to notate and create the final arrangement.

I'm currently working on a song called "Surrounded." I started writing it about two months ago, and have only written 17 measures so far. Normally I would finish writing the song on paper before transcribing it into Sibelius, but I decided to use the measures I've written so far to illustrate the process I use for composing. Here is a scan of the music I wrote while sitting at my piano:



In the initial writing stages, for purposes of speed, I typically focus on the melody and just use chord symbols for the left hand. (In a future blog entry I'll address the question of which should come first, melody or harmony.) Occasionally I write down a specific harmony part that uniquely identifies the song, but most of the time I wait until later in the process to develop a more complete harmony.

Here's a screen shot of Sibelius in the initial writing stage:



Here's what the song looks like after I've finished entering the melody notes:



Then I add chord symbols and create a rough harmony so I can play the song in Sibelius and make sure it sounds the way I want it to:



Once this step is completed, the next step is to complete the harmony part (which I'll discuss in more detail in a future blog entry).