# Music intervals and Compound interval Explained

I’m helping my daughter Jolene prepare for her RCM advanced rudiments exam. I think the tips I gathered from various places (from her teacher, internet and practices) will be helpful to other students.

## Intervals

An interval is the distance between two music pitches. Intervals consist a prefix and a number, for example Major 3, Perfect 5, Augmented 4.

• The number is number of pitch names from the first to the second pitch. For example, A and C, the interval is called a third because there are three pitches (A, B, C).
• The prefix is based on the quality of the interval.

### The prefix

• Perfect intervals include the unison and the octave. Perfect intervals also include 4th and 5th. You label perfect interval  as “P”
• Major prefix is only used for 2nd, 3rd, 6th and 7th. You label Major intervals as uppercase “M”
• Minor prefix is the inverse of Major prefix, it’s always half step smaller than Major. You label Minor interval as lowercase “m”
• Augmented intervals are made from major or perfect interval by increasing one half step, and the interval number does not change. You label Augmented interval as “A”
• Diminished intervals are made from perfect or minor interval by decreasing one half step, and the interval number is not changed. You label Diminished interval as “d”

### The order (from bigger to smaller):

• Augmented >Perfect > Diminished
• Augmented >Major > Minor > Diminished

### Examples

• P1 – Perfect unison.
• M6- This is a major sixth.
• m2- This is a minor second.
• P4 – Perfect fourth
• A5, Augmented fifth.
• d3, diminished third.

## Inversions of intervals

An interval consists of two notes, an upper and a lower note. To invert an interval, you can either move down the upper note by one octave or move up the lower note by one octave. It doesn’t matter which way you invert the notes.

### One straightforward way is to memorize the following interval chart

[table]
No of half-tones,interval,inverse
0,Perfect unison, Octave
1,Minor 2, Major 7
2,Major 2, Minor 7
3,Minor 3, Major 6
4,Major 3, Minor 6
5,Perfect 4, Perfect 4
6,Augmented 4, Diminished 5
7,Perfect 5, Perfect 4
8,Minor 6, Major 3
9,Major 6, Minor 3
10,Minor 7, Major 2
11,Major 7, Minor 2
12,Perfect octave, Unison
[/table]

### However there’s an easier way to identity the intervals.

1. Count from the lower note to the upper note (all inclusive), ignore sharps and flats at this point, you will get an number.
2. From the number, you can tell whether it’s either perfect (1, 4, 5, 8) or major/minor (2,3, 6,7).
3. If there are no sharps or flats, you have the answer already. Stop.
4. If there are, figure out if the flat or sharp decreases or increases the distance between the two pitches.
1. If it increases the distance, the interval is augmented.
2. If it decreases the distance, and the interval would otherwise be perfect, it is diminished.
3. If it decreases the distance and the interval would otherwise be major, it is minor.

Example 1:

1. Ignore sharps and flats, from D to G, there are 4 notes (D, E, F, G)
2. It’s P4 if there’s no sharps/flats
3. The key signature is E Major, 4 sharps, D flat and G natural, let’s go to step 4
4. Because D is flat, it increased the distance, the interval is augmented 4 (P4 + half note = A4)
```Example 2:
```
1. Ignore sharps and flats, from A to E, there are 5 notes (A, B, C, D, E)
2. It’s P5 if there’s no sharps/flats
3. The key signature is A flat Major, 4 flats, A# and E natural, let’s go to step 4
4. Because A is sharp, it decreased the distance, the interval is diminished 4 (P5 – half note = d5)

Example 3:

1. Ignore sharps and flats, from A to C, there are 3 notes (A, B, C)
2. It’s m3 if there’s no sharps/flats
3. The key signature is A flat Major, 4 flats, let’s go to step 4
4. Because A is flat, it increased the distance, the interval is Major 3 (m3 + half note = M3)

## Compound interval

Simple intervals are not bigger than an octave while compound intervals are larger than an octave. Ninths, tenths, elevenths and thirteenth are examples of compound intervals.

Each compound interval is related to a simple interval. By subtracting 7 from the compound interval you get the related simple interval. For example 11 – 7 = 4, so a P11 is related to a P4. In other word, if you plus 7 to simple intervals, you get the related compound interval.

How to calculate compound interval

It’s as easy as two more steps in addition to simple interval calculation.

1. Move the top note down an octave or the bottom note up an octave;
2. Now you get simple interval, do your calculation
3. Plus the result with 7

Example 1:

1. The distance is more than 1 octave, so it’s compound. Let’s move top note F one octave lower, so you get

2. Now it’s simple interval, it’s minor 3 (had it been no flats/sharps), but because D is flat which increased distance by one half tone, plus F is sharp which increased another one half tone, so m3 + half + half = A3

3. It’s compound interval, so you plus 7, now you got A10

## How to invert intervals

The other question that often comes with interval test is to invert an interval. So to invert and interval, you have to move the lower tone up so that it is placed higher than the originally “upper” note. Alternatively, you can move the upper tone down so that it is placed lower than the originally “lower” tone. Of course, the note should remain the same, i.e. C remains a C, it is just the octave that changes.

### Invert simple interval

Here are some examples (images from http://www.eartrainingmastery.com/)

If you pay attention to the inversion pairs, there are some patterns

• Add the two numbers, you get 9! (P4 <—->P5, m7 <—-> M2)
• Inverted minor interval results in a major
• Inverted major interval results in a minor
• Similarly, Augmented to Diminished and vice versa
• The only exception is the perfect intervals: an inverted perfect interval always results in a perfect

Or simply

• Major <—-> Minor
• Augmented <—-> Diminished
• Perfect <—->Perfect

### Invert compound intervals

Compound intervals, those spanning more than one octave (e.g. 9ths, 11ths, and 13ths) are special cases. Unfortunately, the inversion of compound interval does not follow the same rules or patterns depicted above. So how to invert them? The simple rule is

1. Convert compound interval into simple interval by subtracting 7
2. Invert the simple interval

### Examples

To invert M9,

1. Get simple interval, M9 – 7 = M2
2. Invert M2, you get Minor 7

To invert A11,

1. Get simple interval, A11 – 7 = A4
2. Invert A4, you get d5

The following youtube video explains “how to invert compound interval” very well. Basically there are three ways

1. Move the top note 2 octave lower, bottom one stays the same
2. Move the bottom note 2 octave higher, top note stays the same
3. Move the top note 1 octave lower, move the bottom one one octave higher