At http://www.foriero.com you'll find a free download and a video to watch regarding music intervals. I used to be a monitor in the zone at the Hear and Play website. There were many moderators at that time and it was a huge community of musicians. I would read some of the online lessons by Jermaine Griggs

ans I took some pretty good notes from these. So, here goes a study on intervals. Thanks for reading and I hope this sincerely answers some of your questions on the subject.

#
Let’s study intervals and how to
correctly identify them. Many times musical intervals are commonly
mispronounced and misidentified.

For example, C# to F is not a major third, even though it
creates the same sound as a major third. Yes, two notes played harmonically
(together) can create the same sound as an interval you’re used to hearing, but
depending on how you name them, they can be totally different intervals. C# to
F is a fourth (generically) and a diminished fourth (specifically).

#
Second Intervals

Db
/ Eb

D
is 1

E
is 2

Gb
/ Ab

G
is 1

A
is 2

Gb
/ A#

G
is 1

G
is 2

B
/ C#

B
is 1

C
is 2

**Third Intervals**

C
/ E

C
is 1

D
is 2

E
is 3

Db
/ F

D
is 1

E
is 2

F
is 3

C#
/ E#

C
is 1

D
is 2

E
is 3

E
/ G#

E
is 1

F
is 2

G
is 3

Db
/ F#

D
is 1

E
is 2

F
is 3

O.k., so
now you are becoming a pro at determining generic intervals.

For
example, F to A is a third apart and G to C is a fourth apart. Db to F# is a
third interval.

So now
you have learned the fundamentals determining the name of an interval. Here’s a
chart that might help in understanding intervals.

Number of
letters counted | Generic interval name

1
unison

2
second

3
third

4
fourth

5
fifth

6
sixth

7
seventh

8
octave
(eighth)

Now with
generic intervals, we’re not concerned with sharps, flats or key signatures.
We’re just talking about the alphabet. With the generic name, we cannot fully
build chord structures because it’s too broad.

For
example, all of these intervals are thirds:

C to E

Cb to Eb

C# to E#

C to Eb

Cb to E

C to E#

So, you
just can’t say third if you want someone to play a particular set of notes.
While third is a way to determine what to name an interval, more specifically
is needed to really know what to play exactly.

Specific
intervals are names like “major thirds,” “major seconds,” “perfect fifths,” and
others. The ‘titles’ you see in front of the intervals are what we call
qualifying terms. They change generic intervals into specific ones, which tell
you exactly which notes to play (unlike the long list of thirds).

Now
counting specific intervals is a little different than counting generic
intervals. Recall that generic interval counting simply involves the number of
letters or notes it takes to create the interval. From C to E, we’d count C as
1, D as 2, and E as 3, which means that this is a third interval.

With
specific intervals, we will be counting differently. Specific intervals tell us
exactly what’s going on. They don’t undo the “generic” techniques we learned --- they simply add to it.

It is
impossible to have a generic second and then get a major third from the same
interval. So, it is important that whatever you determine during “generic”
naming holds true when you are using qualifying terms to create specific
intervals.

There are
different qualifying terms:

Perfect

Major

Minor

Diminished

Augmented

How do we
know which one of these terms is suppose to go with our interval? It’s simple.
We count half steps. If you’re new to music theory, a half step is also known
as a semitone. It is pretty much the smallest interval. From key to key is a
half step. C - C# is a half step. E to F is a half step. Notice I’m not
skipping any notes. If you skip a note, you aren’t moving in half steps. You’d
actually be moving in whole steps. In this case, we count half steps only.

Here’s a
poem that will help you remember half steps vs. whole steps:

Half
steps are from key to key

With no
keys in between,

Whole
steps always skip a key

With one
key in between.

Now the
counting does not start on the first note like it did with generic counting. We
are counting the actual steps. So, how many half steps are in between C and E?

C to Db
is 1, Db to D is 2, D to Eb is 3
and Eb to E is 4. The answer: There are 5 half steps between F and Bb.

The chart
below shows the interval names and the number of half steps associated with
each type of interval.

Interval
Name | No. of half steps

Unison
0

Minor
second 1

Major
second 2

Minor
third
3

Major
third
4

Perfect
fourth 5

(Tritone) (6)

perfect
fifth 7

minor
sixth
8

major
sixth
9

minor
seventh 10

major
seventh 11

octave
(eighth) 12

Notice
from the chart above:

The terms
“major” and “minor” are reserved for second, third, sixth and seventh
intervals.

The term
“perfect” is reserved for unison, fourth, fifth, and octave intervals, though
you really don’t hear it a lot with unison and octave. So, fourths and fifths,
for sure get the “perfect” term. You won’t ever hear perfect second or perfect
third because the perfect term only goes with unison, fourth, fifth and octave,
as I noted above.

Later,
you’ll learn about augmented and diminished terms. They have purposes as well.
So, here’s the tricky part. You now know that at interval with 4 half steps
separating the notes is called a major third. An example of this would be C to
E. This is the same interval that helps to create the major chord.

Let’s
look at an interval like C to Eb. What would this be called? Just count up the
half steps:

C to Db
is 1

Db to D
is 2

D to Eb
is 3

3 half
steps = minor third

Keep in
mind that your answer must also pass the “generic interval” test. Is C to Eb a
third?

C is 1

D is 2

E is 3

Yes, it
passes. What about C to D#?

C to Db
is 1

Db to D
is 2

D to D#
is 3

It has
three half steps and these 3 half steps mean a third for sure but would this
pass the generic test?

C is 1

D is 2

According
to what we know about naming intervals, this should be a second. Any C to any D is a second. This is where
you’ll need to use the qualifying terms: Augmented and Diminished.

Augmented
means to make bigger.

Diminished
means to make smaller.

In this
case, we have a second that is three half steps apart. Since we can’t call it a
third, we will have to call it an augmented second… in other words, a “second
made bigger.”

So
basically, when an interval is a half step larger, it is said to be augmented.
When an interval is a half step smaller, it is said to be diminished.

What is a
major third up from D?

Step 1:
Determine generic interval:

D is 1

E is 2

F is 3

So far, I
know that a third up from D is going to be some kind of F. From our chart
above, we know that major third intervals always have a 4 half steps in between
the lower and upper note.

So start
as D:

D to D#
is 1

D# to E
is 2

E to F is
3

F to _ is
4

This is
the big question. Do we say F# or Gb? Well, since we’ve already done step 1 and
we know we’re looking for some kind of F, it would make absolutely no sense to
choose Gb. Therefore, the answer is F#. From D to F# is a major third interval.

1.
A
perfect fifth up from B

(B up to F# is a perfect fifth)

Generic:

B is 1

C is 2

D is 3

E is 4

F is 5

Specific:

B to C is
1

C to C#
is 2

C# to D
is 3

D to D#
is 4

D# to E
is 5

E to F is
6

F to f#
is 7

2.
A
perfect fifth down from C

(C down to F is a perfect fifth)

Generic

C is 1

B is 2

A is 3

G is 4

F is 5

Note: Counting down generically is the same thing. Just
count alphabet backwards.

3.
A
minor third up from Eb

(Eb up to Gb is a minor third)

Generic

E is 1

F is 2

G is 3

Specific

Eb to E is 1

E to F is 2

F to Gb is 3

4. A major sixth up from A

(A up to F# is a major sixth)

Generic

A is 1

B is 2

C is 3

D is 4

E is 5

F is 6

Specific

A to A# is 1

A# to B
is 2

B to C is
3

C to C#
is 4

C# to D
is 5

D to D#
is 6

D# to E
is 7

E to F is
8

F to F#
is 9

5.
A
major third down from G

(G down to Eb is a major third)

Generic:

G is 1

F is 2

E is 3

Specific:

G to F# is 1

F# to F is 2

F to E is 3

E to Eb is 4

6.
A
perfect fourth up from F

(F up to Bb is perfect fourth)

Generic

F is 1

G is 2

A is 3

B is 4

Specific:

F to Gb is 1

Gb to G is 2

G to Ab is 3

Ab to A is 4

A to Bb is 5

7.
A
major second down from C

(C down to Bb is a major second)

Generic:

C is 1

B is 2

Specific:

C to B is 1

B to Bb is 2

8.
A
minor seventh up from A

(A up to G is a minor seventh)

Generic:

A is 1

B is 2

C is 3

D is 4

E is 5

F is 6

G is7

Specific:

A to A# is 1

A# to B is 2

B to C is 3

C to C# is 4

C# to D is 5

D to D# is 6

D# to E is 7

E to F is 8

F to F# is 9

F# to G is 10

9.
A
major sixth down from D

(D down to F is a major sixth)

Generic:

D is 1

C is 2

B is 3

A is 4

G is 5

F is 6

Specific:

D to C# is 1

C# to C is 2

C to B is 3

B to A# is 4

A# to A is 5

A to G# is 6

G# to G is 7

G to F# is 8

F# to F is 9

10. A minor third down from F

(F down to D is a minor third)

Generic:

F is 1

E is 2

D is 3

Specific:

F to E is 1

E to Eb is 2

Eb to D is 3

Now you have a good understanding of intervals and will
never quote a major or minor chord wrong again.

You may be interested in, Jazz Intensive Training Center

Best,

"The beautiful thing about learning is that no one can take it away from you." B.B.King