Basics of Intervals

An interval is a measurement of the distance between two pitches. For keyboard players:
  1. Harmonic intervals are two pitches that are played at the same time; when notated, the pitches are shown vertically. 
  2. Melodic intervals are two pitches that are played successively; when notated, their pitches are shown horizontally.
Here we are only measuring harmonic intervals.

To measure an interval we need to find:

  1. Its number (also called diatonic number).
  2. Its size or “bigness”.
To determine the number of an interval, we count the letter name of the bottom pitch and the upper pitch plus all letters skipped. For example, a C—G is a “5th” because we count C and G plus the letters skipped: C D E F G. The total is five. E—D is a 7th: E F G A B C D.
 
Keyboard players simply use the letter names of the white keys in place of pitches to get the interval number.
 
(Note: When two people either play or sing the same pitch, that pitch is called a “unison”. However, the same term is used when only one key is pressed. For example, if only F is played, that is called a unison. No measurement is necessary for a unison. It “is what it is”.)
 
All intervals other than unisons and octaves have two sizes, and for the moment I will simply say that there are big and small intervals. For instance, there are big 2nds and small 2nds, big 3rds and small 3rds, and so on. On a keyboard we can compare “big” and “small” by counting the number of black keys skipped. C—E is a third, and so is D—F. But C—E skips two black keys. D—F skips only one. So C—E is a big third; D—F is a small third.
 
(Note to advanced students: the “quality” of an interval is determined by the words “Perfect”, “Major”, “minor”, “augmented” and “diminished”. It is my habit to capitalize “Perfect” and “Major”. It is the quality that makes measurement of the interval precise. Those terms will be covered later. At the moment we are only concerned with the number of an interval and its “bigness”.)
 
When an interval is “flipped”, it forms the ”complement of an interval”; the number of the two intervals always adds up to nine.
 
For example, when a 5th is flipped, it becomes a 4th. When a 7th is flipped, it becomes a 2nd. And so on…
 
When a big interval is flipped, it becomes a small one. Examples:
  1. F—A is a large 3rd. A—F is a small 6th.
  2. E—F is a small 2nd. F—E is a large 7th.
(Note to advanced students: So far we are only using only white keys to define the lower and upper pitches of intervals. This gives us the interval number, and we are counting black keys skipped to measure size or “bigness”. Later, we will see that sharps and flats also change the size of an interval, and those are also used to name the inverval quality.)

All About 2nds

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Rules for 2nds:
  1. The intervals that are white notes use only white piano keys. Those that are black notes use at least one black piano key.
  2. A 2nd uses two letters in a row. Its “size” depends on how many keys we skip. For instance, E—F skips no keys. C—D skips one key. C—D# or Db—E skips two keys.
  3. A minor 2nd is also called a “half step”. It skip no keys.
  4. A Major 2nd is also called a “whole step”. It skips only one key.
  5. An augmented 2nd is whole step + a half step. It skips two keys.
Below is an illustration of 2nds in several scales.

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Colors show the type of 2nds:
  1. All 8th notes colored black and beamed form Major 2nds. Major 2nds are also whole steps.
  2. All 8th notes colored red and beamed form minor 2nds. Minor 2nds are also half steps.
  3. In harmonic minor, the two 8th notes colored blue and beamed form an augmented 2nd. Augmented 2nds are a whole step + a half step.

All About 3rds

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Rules for 3rds:
  1. The intervals that are white notes use only white piano keys. Those that are black notes use at least one black piano key.
  2. 3rds use three letters. Their “size” depends on how many keys we skip.
  3. A diminished 3rd skips one key. It is also a whole-step.
  4. A minor 3rd skips two keys. It is also a whole-step + a half-step.
  5. A Major 3rd skips three keys. It is also two whole-steps.
  6. An augmented 3rd skips four keys. It is also two whole-steps + a half step.
Note to more advanced students:
  1. Circle one shows a C Major chord moving to a C7 chord, which then resolves to an Em chord. The enharmonic spelling (Bb is changed to A#) is chosen to show that the C7 is a “German 6th chord” going to somewhere else other than a C Major chord.
  2. Circle two shows a C# fully diminished chord written with three minor 3rds, “stacked”.
  3. Circle three shows a Caug chord, written with two Major 3rds, “stacked”.
  4. Circle four shows a Gsus7 chord moving to a G7 chord, which then resolves to a Bm chord. The enharmonic spelling (F is changed to E#) is chosen to show that the G7 is a “German 6th chord” going to somewhere else other than a C Major chord.

All About 4ths

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Rules for 4ths:
  1. The intervals that are white notes use only white piano keys. Those that are black notes use at least one black piano key.
  2. 4ths use four letters. (For example, C—F is C D E F.) Their “size” depends on how many keys we skip.
  3. A diminished 4th skips three keys. It is two whole steps.
  4. A Perfect 4th skips four keys. It is two whole steps + a half step.
  5. An augmented 4th skips five keys. It is three whole steps.
  6. An augmented 4th is frequently called a “tritone”. A diminished 5th also skips five keys, also is three whole steps, and also is called a “tritone”.
Note to more advanced students:
  1. Circle one shows a C aug chord resolving to an Ab chord.
  2. Circle two shows a F sus chord moving to an F7 chord, resolving to a Bb chord.
  3. Circle three shows C#dim7 chord resolving to an Em chord.

All about 5ths

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Rules for 5ths:
  1. The intervals that are white notes use only white piano keys. Those that are black notes use at least one black piano key.
  2. 5ths use five letters. (For example, C—G is C D E F G.) Their “size” depends on how many keys we skip.
  3. A diminished 5th skips five keys. It is three whole steps. A diminished 5th is frequently called a ”tritone”. An augemented 4th also skips five keys, also is three whole steps, and also is called a “tritone”.
  4. A Perfect 5th skips six keys. It is three whole steps + a half step.
  5. An augmented 5th skips seven keys. It is four whole steps .
  6. A diminished 5th is frequently called a ”tritone”. An augemented 4th also skips five keys, also is three whole steps, and also is called a “tritone”.

 

Note to more advanced students:
  1. Circle one shows a C dim triad. It also shows that two minor thirds = a diminished 5th or tritone.
  2. Circle two shows that both Major and minor triads use a Perfect 5th.
  3. Circle three shows C aug triad. It also shows that two Major thirds = an augmented 5th.

All About 6ths

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Rules for 6ths:
  1. The intervals that are white notes use only white piano keys. Those that are black notes use at least one black piano key.
  2. 6ths use six letters. (For example, C—A is C D E F G A.) Their “size” depends on how many keys we skip.
  3. A diminished 6th skips six keys. It is three whole steps + a half step.
  4. A minor 6th skips seven keys. It is four whole steps.
  5. A Major 6th skips eight keys. It is four whole steps + a half step.
  6. An augmented 6th skips nine keys. It is five whole steps.

 

Note to more advanced students:
  1. Circle one shows an unusual spelling of a G half diminished chord moving to a G dim7, which then “slides” to an F#7 chord.
  2. Circle two shows a C augmented chord, spelled enharmonically, resolving to an Ab Major chord.
  3. Circle three shows an F7 chord used as a German 6th chord, resolving to Em.

All About 7ths

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Rules for 7ths:
  1. The intervals that are white notes use only white piano keys. Those that are black notes use at least one black piano key.
  2. 7ths use six letters. (For example, C—A is C D E F G A B.) Their “size” depends on how many keys we skip.
  3. A diminished 7th skips eight keys. It is four whole steps + a half step.
  4. A minor 6th skips nine keys. It is five whole steps.
  5. A Major 6th skips 10 keys. It is five whole steps + a half step.

 

Note to more advanced students:
  1. Circle one shows the standard spelling for a C# fully diminished chord.
  2. Circle two shows the standard spelling for a C7 chord.
  3. Circle three shows the standard spelling for a Cmaj7 chord.

Major and Minor 3rds, 6ths and 7ths

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When 3rds, 6ths and 7ths are formed by playing the third, sixth or seventh note of a Major scale with the first note or “tonic”, the intervals formed are Major 3rds, Major 6ths and Major 7ths.
Lowering the upper note of each of these intervals  by one 1/2 step (by one key) changes the quality of the interval from Major to minor.
Note to more advanced students: lowering the 3rd, 6th and 7th of a Major scale does two very important things:
  1. It produces a “natural minor scale”.
  2. It tells us what the key signature of the “relative” or “tonic” minor will be. For instance, C Major, which has no sharps or flats in the key signature, will switch to three flats (Bb, Eb, Ab) for C minor.