An interval is simply how far a note is from the tonic.
A tonic is what you call the first note in a scale
In the key of E, the first note is E.
The first note in the E Major scale is E.
E is the tonic note.
Also...the first note in a scale is the 1st degree.....the 2nd note in a scale is the 2nd degree...and so on.
Let's use the key of C...it's the easiest...no sharps or flats.
In a melody you might play a C and then a D. How far is the D from the C? Well, in counting an interval, you count the original note also. C plus D makes two notes so the interval is two notes in length...a 'second' (2nd).
So for the key of C the intervals are as follows:
C to D - 2nd C to E - 3rd C to F - 4th C to G - 5th C to A - 6th C to B - 7th C to C - 8ve 'Octave '
But it's not exactly that simple. These are just the interval "type's". There is also interval 'quality'.
There are 5 different interval Qualities:
Perfect,
Major,
minor,
Augmented,
diminished.
In a Major key...each interval is either Perfect or Major.
The 1st, 4th, 5th and Octave intervals are always Perfect intervals. eg. (C to F...Perfect 4th...C to G...Perfect 5th)
The 2nd, 3rd, 6th and 7th are always major. eg. (C to D...Major 2nd...C to A...Major 6th)
To read the following ....P means Perfect interval.....M means Major interval:
The scale of C Major C D E F G A B C P M M P P M M P
This means that a 2nd....C to D...is a Major 2nd interval 3rd....C to E...is a Major 3rd interval 4th....C to F...is a Perfect 4th interval 5th....C to G...is a Perfect 5th interval
But what if you took a 3rd(C to E), and changed the E to an Eb? It's still a 3rd, because the letter name is still E, and C to E is a 3rd whether that E is flat, natural, or sharp.
So how can you tell which kind of 3rd is meant? You know that the interval C to E is a Major 3rd. So making the E flat, makes the interval shorter; it is decreased. Whenever you decrease a Major interval by one half step, it becomes minor. So then the interval C to Eb is a minor 3rd:
If you increase a Major interval by one half step, it becomes
an Augmented.
If you decrease a Major interval by one half step, it becomes
a minor.
If you decrease a Minor interval by one half step, it becomes
a diminished.
If you increase a perfect by one half step, it becomes
Augmented.
If you decrease a perfect by one half step, it becomes
diminished.
Perfects can be lowered to become diminished
Perfects can be raised to become Augmented
The order according to size from smallest to largest is:
diminished -- Perfect -- Augmented
Majors can be lowered to become minor....then lowered again to become diminished.
Majors can be raised to become Augmented .
The order according to size from smallest to largest is:
diminished -- minor -- Major -- Augmented
Majors can never become Perfects...and Perfects can never become Majors.
Likewise, minors can never become Perfects, and Perfects can never become minors.
Here is a chart representing all the intervals a Half step at a time in one octave. It shows how many half steps are in each interval.
C to C# - 1 Half step - minor 2nd C to D - 2 Halfsteps - major 2nd C to D# - 3 Halfsteps - minor 3rd C to E - 4 Halfsteps - major 3rd C to F - 5 Halfsteps - perfect 4th C to F# - 6 Halfsteps - augmented 4th..or..diminished 5th C to G - 7 Halfsteps - perfect 5th C to G# - 8 Halfsteps - augmented 5th..or..minor 6th C to A - 9 Halfsteps - major 6th C to A# - 10 Halfsteps - minor 7th C to B - 11 Halfsteps - major 7th C to C - 12 Halfsteps - 8th..or Octave
You don't have to memorize the half steps, but you should memorize all twelve interval names in order. (minor 2nd, Major 2nd, minor 3rd, Major 3rd, etc)
We use a capital M to stand for Major and a small m to stand for minor. Diminished is a small d....Augmented is a capital A. Perfect is a P.
Do you see all the enharmonics in the chart above? Diminished 4th is the
same as Major 3rd, the exact same interval.
If you take the higher note of the Perfect 4th and lower it by a half step,
you make a diminished 4th.
P4th: C to F so C to E is a d4th. but C to E is also a M3rd.
Other enharmonics are:
A2nd, m3rd ... A3rd, P4th ... A4th, d5th ... A5th, m6th ... A6th, m7th ...
and an A7th is an octave. (C to C)
To help you see the enharmonics more easily, here is one more list of the interval types and qualities with the enharmonics in brackets. The best enharmonic names to use in order to help memorize the interval order, in my opinion, would be the ones that are not in brackets.
m 2nd M 2nd m 3rd M 3rd (d4th) P 4th A 4th (d5th) P 5th A 5th (m6th) M 6th (d7th) m 7th (A 6th) M 7th P 8ve
If you reverse the order of an interval....for example if the lower note is C and the higher note is G and you lower the G by an octave so that the lower note is G and the higher note is C....the reversed order changes both the quality and the type of interval.
When inverted, 2nds always become 7ths When inverted, 3rds always become 6ths When inverted, 4ths always become 5ths When inverted, 5ths always become 4ths When inverted, 6ths always become 3rds When inverted, 7ths always become 2nds For easier memorization: 2nds become 7ths, 7ths become 2nds 3rds become 6ths, 6ths become 3rds 4ths become 5ths, 5ths become 4ths
When inverted, Majors always become minors
When inverted, minors always become Majors
When inverted, Perfects always remain Perfects
When inverted, diminished always becomes Augmented
When inverted, Augmented always becomes diminished
For easier memorization:
Majors become minors, minors become Majors
diminished becomes Augmented, Augmented becomes diminished
Perfects remain Perfects
Here is a chart showing the inversion of both the type and the Quality of the intervals:
minor 2nd becomes Major 7th Major 2nd becomes minor 7th minor 3rd becomes Major 6th Major 3rd becomes minor 6th Perfect 4th becomes Perfect 5th Perfect 5th becomes Perfect 4th minor 6th becomes Major 3rd Major 6th becomes minor 3rd minor 7th becomes Major 2nd Major 7th becomes minor 2nd
I didn't mention the first interval called a 'unison'. It is an interval of two exactly equal pitches. From C to C (but not next octave C...the same original C is played). Unisons are Perfect as well as Octaves. When inverted, unisons remain unisons, and octaves remain octaves. (perfects remain perfects)
Jason's Theory
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