Intervals: Musical Atomic Power

What Are Intervals?

When we hear two tones of different pitches, our mind perceives that one tone is higher or lower than the other. This difference in pitch is perceived as distance between the tones. The greater the perceived distance, the larger the interval. We give these intervals names to describe them, and help us understand what is going on musically.

Not all pairings of tones have musical properties. Some sound more musical than others, and we can explain why with a little math (which we encourage you to promptly forget, but it will help you understand how your brain works). To illustrate, have a look at the following diagram and follow along.

Pluck the open A string on your guitar. Now imagine that the vibrations that your string produces through your soundboard, then later in your eardrum could be caught and colored blue. You would have something like the first wave line in the diagram. Any other instrument playing a tone with the same frequency (440 vibrations per second in the case of an A) would be playing in perfect unison with your instrument.

While the open A string is vibrating, pluck an A on the 7th fret of the D string and color it purple. If your guitar is in tune, the upper A will vibrate exactly twice as fast as the lower A. This is like the second set of waves on the diagram. For every peak in the lower frequency, there are precisely two peaks in the upper frequency. You hear an octave, which your mind tells you is the same note... only higher. This is because your brain interprets this simplest of ratios 1:2 as a perfect octave.

Next, pluck the open A string and the D string on the 2nd fret. We already established that the A is blue, so we need the E to be a different color... green. For every 2 peaks in the vibration of the lower tone, there are precisely 3 peaks in the vibration of the upper tone. This ratio of 2:3 is perceived as a perfect 5th interval.

Next, pluck the open A string again, and the open D string. Color the D red, and notice that for every 3 peaks in the vibration of the lower tone there are exactly 4 peaks in the vibration of the upper tone. This 3:4 ratio is perceived as a perfect 4th interval.

Your awesome brain is wired to organize tones at lightning speed, and perceives some tones played together or in series to be related, and while others sound chaotic. Those tones that sound related to each other do so because of simple frequency ratios, as explained above.

So what?

Herein lies the secret to emotionally compelling music (which you will be hard-pressed to find anywhere else): Music is not in the notes being played, it is in the relationship between notes being played.

Let's have a look at how different intervals operate on our emotions.

In any scale, the I degree is the tonic, root or home base. Once we establish the tonic or root note in our minds, our brain automatically compares all other tones of the scale to the tonic, and tells us that we are either moving away from or towards home. Moving away from home produces a sense of interest, excitement, or tension. Returning home after going away produces a sense of rest, resolution, or release. Music holds our our interest as long as there is a sense of motion away from home, with the the promise that we will eventually arrive back home again.

The arrows in this diagram illustrate how intervals in the major scale behave like rubber bands pulling on our emotions. The thicker arrows pull harder toward the arrowhead than the thinner lines in the following manner:

• The I degree has no pull whatsoever. It is home base, which feels good when you come back to it, but after feeling safe for too long we soon feel bored, and long to venture out again.
• The II degree has a strong pull toward the I degree, so much so that it gives a suspended sensation.
• The III degree also has a pull toward the I degree, but slightly less than the II.
• The IV degree has a hard pull toward the III degree, and is also gives a suspended feeling until we arrive again at the III degree.
• The V degree is not exactly half way between the lower and upper I degree, but it sounds like it is. There is a weak pull up or down to the I degree on either end of the scale.
• The VI degree has a moderate pull up to the I degree, or down to the V degree.
• The VII degree has a sharp pull towards the upper I degree in a scale. This gives the VII a strong leading characteristic.

Here is another way to look at the gravitational nature of the tonic I degree on the other degrees in the scale.

Why Study Intervals?

Here are two very practical reasons for mastering your understanding of intervals and their use:

• Mastering intervals through ear training supercharges your ability to learn new songs by ear.
• Learning how intervals effect us emotionally helps your ability to write emotionally compelling melodies, and harmonies, or to alter an existing tune for an emotional wallop.

Intervals can't be mastered overnight. In learning intervals thoroughly, the ear and fingers require many repetitions and exposure to intervals in many musical circumstances to really become cultured. It's best to take intervals in small daily doses, at times when your ear is relaxed. Five minutes a day in the morning before diving into other practice routines is probably sufficient.

Interval Summary

Intervals in the 1st Octave

Interval Spellings

This chart shows the spelling of all intervals upward and downward from any starting point. This is important to know when composing music, because if you know the name of one note, then by hearing the interval, you will know the name of the next note you hear by ear.

Perfect Intervals

Perfect intervals are the first intervals to master because they are the most familiar to most unseasoned ears. Most people instantly recognize an octave when they hear it.

Perfect Unison

The first interval we commit to ear and finger memory is the perfect unison. A perfect unison is the same note played twice. On a guitar, a perfect unison can be played melodically (one note at a time) on the same string or harmonically (two notes at the same time) on different strings.

Perfect Octave

The next interval we will commit to ear, mind and finger memory is the perfect octave. The perfect octave is 12 half steps apart on the chromatic scale and 8 notes apart on the major scale. The top note on a perfect octave vibrates exactly twice as fast as the bottom note.

A perfect octave is two notes twelve half-steps apart that have the same name. Every time you go up an octave, the strings vibrate twice as fast.

Perfect 5ths

The next interval we commit to ear and to finger memory is the Perfect 5th. This interval is present in almost every kind of scale. It is neither major nor minor. It adds stability and power to the chord. When playing two root notes and two fifth notes in two octaves, this chord is called stacked 5ths, and is one of the most powerful chords in rock music.

The ear when it hears a perfect fifth naturally gravitates to the root note, and the fifth adds strength, stability and power to that root.

Church songs sung by medieval monks used perfect 5ths as harmony, because being "perfect" was what godly music was all about. Other kinds of harmony were forbidden in medieval church music because they were seen as pagan at the time.

Perfect 4ths

The next interval we commit to ear and finger memory is the Perfect 4th. This interval is the inversion of a perfect 5th, and like the perfect 5th, can add power and stability to chords.

It is easy to confuse a perfect 4th with a perfect 5th, because when the ear hears a perfect 4th, it tends to want to hear the top note as the root, then gravitate down a perfect 5th.

Guitar strings are tuned in perfect 4ths from each other. E - A is a perfect 4th, A - D is a perfect 4th, D - G is a perfect 4th, G - B is a major 3rd. It is this tuning that we owe our ability to play so many chords within a 4 or 5-fret span. The EADGBE tuning places the majority of the good-sounding notes in close proximity to each other on different strings so that we can easily reach them with our fingers.

Consonant Intervals

Most two-part vocal harmonies in Western music are performed in major and minor thirds. Because they sound familiar to us is why we will commit them next to ear and finger memory.

The tricky part of learning major and minor 3rds is when used together in harmony, sometimes the ear confuses them, and we don't know which is major and minor. We should be able to quickly distinguish between the major and minor 3rd intervals before moving on to other intervals.

Major and minor 3rds

A major 3rd is what makes a major chord sound major, and a minor 3rd is what a minor chord owes its minor sound to.

Major and Minor 6ths

The Major 6th has a close relationship with the minor 3rd, because in fact it is the inverse of the minor 3rd. In other words, a major 6th down from a tonic note is an octave below the minor 3rd above the same tonic note. For this reason, the ear is sometimes confused as to whether the 6th is minor or major.

In orchestral music, the French Horns often are those playing harmony in major and minor 6ths down from the melody.

Dissonant Intervals

These intervals are closest to the tonic note and have greatest propensity to make the ear want to resolve to the tonic note. Dissonant in musical terms means full of energy or tension.

Major and Minor 2nds

These intervals almost always have a strong emotional pull downward to the tonic note. In guitar they are so close to the tonic note on the same string that they lend themselves to trilling (rapid hammering on and pulling off with the left hand) to add heat and energy to the root note.

Major and Minor 7ths

These intervals have a strong pull upward to the tonic note, and this is their primary function in music... to lead the listener home. In fact, the 7th interval is what gives the V chord (from the harmonic scale) its dominant characteristic, which tells the listener that the next chord is a I chord (also from the harmonic scale).

The Devil's Tone: Augmented 4ths/Diminished 5ths

The Augmented 4th or Diminished 5th interval sounds so strange to our ears, that even though it exists, it is only used sparingly. When it is summoned forth, it can have a surprising or stunning effect on the listener, causing the audience to lose their musical bearing, if only for a moment. It does this because the mind cannot easily perceive which direction they are going relative to home. If dwelt on too long, can erase the notion of home base from the listener's mind. The effect is musical vertigo.