Notes and Scales: Chapter 4 – Interval (Understanding Basic Music Theory)

## 4.5 Interval

### (Understanding Basic Music Theory)

### 4.5.1 The Distance Between Pitches

The interval between two notes is the distance between the two pitches – in other words, how much higher or lower one note is than the other. This concept is so important that it is almost impossible to talk about scales , chords (Chords, p. 80), harmonic progression (Chords,), cadence, or dissonance without referring to intervals. So if you want to learn music theory, it would be a good idea to spend some time getting comfortable with the concepts below and practicing identifying intervals.

Scientists usually describe the distance between two pitches in terms of the di erence between their frequencies . Musicians nd it more useful to talk about interval. Intervals can be described using half steps and whole steps. For example, you can say “B natural is a half step below C natural”, or “E at is a step and a half above C natural”. But when we talk about larger intervals in the major/minor system, there is a more convenient and descriptive way to name them.

### 4.5.2 Naming Intervals

The rst step in naming the interval is to nd the distance between the notes as they are written on the sta . Count every line and every space in between the notes, as well as the lines or spaces that the notes are on. This gives you the number for the interval.

**Example 4.5**

To nd the interval, count the lines or spaces that the two notes are on as well as all the lines or spaces in between. The interval between B and D is a third. The interval between A and F is a sixth. Note that, at this stage, key signature, clef, and accidentals do not matter at all.

If you like you can listen to each interval as written in Figure 4.26 (Simple Intervals): prime , second , third38, fourth39, fth40, sixth41, seventh42, octave43.

Listen to the compound intervals in Figure 4.27 (Compound Intervals): ninth44, tenth45, eleventh46.

Name the intervals.

#### Exercise 4.5.2

### 4.5.3 Classifying Intervals

So far, the actual distance, in half-steps, between the two notes has not mattered. But a third made up of three half-steps sounds di erent from a third made up of four half-steps. And a fth made up of seven halfsteps sounds very di erent from one of only six half-steps. So in the second step of identifying an interval, clef, key signature, and accidentals become important.

Listen to the di erences in the thirds and the fths in Figure 4.30.

So the second step to naming an interval is to classify it based on the number of half steps in the interval. Familiarity with the chromatic scale is necessary to do this accurately.

### 4.5.3.1 Perfect Intervals

Primes, octaves, fourths, and fths can be perfect intervals.

note: These intervals are never classi ed as major or minor, although they can be augmented or diminished (see below (Augmented and Diminished Intervals)).

What makes these particular intervals perfect? The physics of sound waves (acoustics) shows us that the notes of a perfect interval are very closely related to each other. (For more information on this, see Frequency, Wavelength, and Pitch and Harmonic Series .) Because they are so closely related, they sound particularly good together, a fact that has been noticed since at least the times of classical Greece, and probably even longer.

(Both the octave and the perfect fth have prominent positions in most of the world’s musical traditions.) Because they sound so closely related to each other, they have been given the name “perfect” intervals.

note: Actually, modern equal temperament (Equal Temperament) tuning does not give the harmonic-series-based pure (Pythagorean Intonation) perfect fourths and fths. For the music-theory purpose of identifying intervals, this does not matter. To learn more about how tuning a ects intervals as they are actually played, see Tuning Systems.

A perfect prime is also called a unison. It is two notes that are the same pitch. A perfect octave is the “same” note an octave – 12 half-steps – higher or lower. A perfect 5th is 7 half-steps. A perfect fourth is 5 half-steps.

**Example 4.6**

Perfect Intervals

Listen to the octave , perfect fourth , and perfect fth .

### 4.5.3.2 Major and Minor Intervals

Seconds, thirds, sixths, and sevenths can be major intervals or minor intervals. The minor interval is always a half-step smaller than the major interval. Major and Minor Intervals

**Example 4.7**

Major and Minor Intervals

Listen to the minor second54, major second55, minor third56, major third57, minor sixth58, major sixth59, minor seventh60, and major seventh61.

#### Exercise 4.5.3

Give the complete name for each interval.

#### Exercise 4.5.4

### 4.5.3.3 Augmented and Diminished Intervals

If an interval is a half-step larger than a perfect or a major interval, it is called augmented. An interval that is a half-step smaller than a perfect or a minor interval is called diminished. A double sharp or double at is sometimes needed to write an augmented or diminished interval correctly. Always remember, though, that it is the actual distance in half steps between the notes that determines the type of interval, not whether the notes are written as natural, sharp, or double-sharp.

**Example 4.8**

Some Diminished and Augmented Intervals

Listen to the augmented prime62, diminished second63, augmented third64, diminished sixth65, augmented seventh66, diminished octave67, augmented fourth68, and diminished fth69. Are you surprised that the augmented fourth and diminished fth sound the same?

#### Exercise 4.5.5

As mentioned above, the diminished fth and augmented fourth sound the same. Both are six half-steps, or three whole tones, so another term for this interval is a tritone. In Western Music,

this unique interval, which cannot be spelled as a major, minor, or perfect interval, is considered unusually dissonant and unstable (tending to want to resolve to another interval).

You have probably noticed by now that the tritone is not the only interval that can be “spelled” in more than one way. In fact, because of enharmonic spellings, the interval for any two pitches can be written in various ways. A major third could be written as a diminished fourth, for example, or a minor second as an augmented prime.

Always classify the interval as it is written; the composer had a reason for writing it that way. That reason sometimes has to do with subtle di erences in the way di erent written notes will be interpreted by performers, but it is mostly a matter of placing the notes correctly in the context of the key, the chord (Chords), and the evolving harmony. (Please see Beginning Harmonic Analysis for more on that subject.)

Figure 4.37: Any interval can be written in a variety of ways using enharmonic spelling. Always classify the interval as it is written.

### 4.5.4 Inverting Intervals

To invert any interval, simply imagine that one of the notes has moved one octave, so that the higher note has become the lower and vice-versa. Because inverting an interval only involves moving one note by an octave (it is still essentially the “same” note in the tonal system), intervals that are inversions of each other have a very close relationship in the tonal system.

To nd the inversion of an interval

1. To name the new interval, subtract the name of the old interval from 9.

2. The inversion of a perfect interval is still perfect.

3. The inversion of a major interval is minor, and of a minor interval is major.

4. The inversion of an augmented interval is diminished and of a diminished interval is augmented.

**Example 4.9**

#### Exercise 4.5.6

What are the inversions of the following intervals?

1. Augmented third

2. Perfect fth

3. Diminished fth

4. Major seventh

5. Minor sixth

### 4.5.5 Summary

Here is a quick summary of the above information, for reference

Summary Notes: Perfect Intervals

• A perfect prime is often called a unison. It is two notes of the same pitch.

• A perfect octave is often simply called an octave. It is the next “note with the same name”.

• Perfect intervals – unison, fourth, fth, and octave – are never called major or minor

Summary Notes: Augmented and Diminished Intervals

• An augmented interval is one half step larger than the perfect or major interval. • A diminished interval is one half step smaller than the perfect or minor interval.

Summary Notes: Inversions of Intervals

• To nd the inversion’s number name, subtract the interval number name from 9.

• Inversions of perfect intervals are perfect.

• Inversions of major intervals are minor, and inversions of minor intervals are major.

• Inversions of augmented intervals are diminished, and inversions of diminished intervals are augmented.

Basic Music Theory

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