Intervals De-Mystified PART TWO
Now that you have an understanding of GENERIC INTERVALS (if
you're not clear on this, go back to PART ONE ),
we'll discuss SPECIFIC INTERVALS.
PART TWO
Any interval the would fit naturally in a Major scale built
from the root on the note with the same name as the lower of the two tones in
the interval will either be a Major interval or a Perfect interval. 2nds (and
7ths), or 3rds (and 6ths) that fit into the scale will be called Major intervals.
4ths (and 5ths) that fit into the Major scale will be called Perfect intervals.
For example, we already know that C up to E is a GENERIC 3rd.
C and E would both fit in the C Major scale, so the distance from C up to E
is SPECIFICALLY a Major 3rd.
Another example; we already know that F up to G is a GENERIC
2nd. F and G would both fit in the F Major scale, so the distance from F up
to G is SPECIFICALLY a Major 2nd.
How would we determine the interval from C up to Eb? It won't
fit into a C Major scale, but we know it's a 3rd; what kind of 3rd is it?
Take a look a this:
Notice the thick-lined ovals represent tones that would fit
into a Major scale (Major or Perfect). The other ovals represent tones that
won't fit into the Major scale (Augmented, Minor, and Diminished). The tones
that would fit into a Major scale are called Diatonic; all other intervals are
Chromatic. The arrows represent halfstep increases or decreases of Major or
Perfect intervals.
If any Major or Perfect interval is increased by a halfstep,
it will be named as an Augmented interval.
For example, we now know that F up to G is a Major 2nd. If
the interval is increased by a halfstep (F up to G# OR Fb up to G), it will
now be named as an Augmented 2nd.
Another example: we now know that B up to E is a Perfect 4th.
If the interval is increased by a halfstep (B up to E# OR Bb up to E), it will
now be named as an Augmented 4th. Notice, that if I said B up to an F, it would
be some kind of GENERIC 5th (not a 4th; check back with the example in PART
ONE showing the sequence of 4ths and see the segment that depicts F to Bb. If
that's a PERFECT 4th then Bb up to F must be a PERFECT 5th; if so, then B up
to F# is a PERFECT 5th; therefore B up to F would be a DIMINISHED 5th. This
brings us to the next step...
If any PERFECT interval is decreased by a halfstep, it will
be named as a DIMINISHED interval. Also notice that it would take a DECREASE
OF 2 HALFSTEPS FROM A MAJOR INTERVAL to become a Diminished interval. Look at
the preceeding diagram again if you're not sure of what we're talking about
here.
If any Major interval is decreased by a halfstep, it becomes
a Minor interval; so the answer to the question, what is the distance from C
up to Eb?, is: it is a Minor 3rd.
The last point I want to make is that when INVERTING intervals,
Major intervals become Minor; Minor intervals become Major; Diminished intervals
become Augmented; Augmented intervals become Diminished; and Perfect intervals
stay Perfect.
Let's look at some more examples and the thinking processes
behind them:
What is the distance from E up to C? Answer: E up to C is
larger than a 4th, so I prefer to find the distance from C up to E, then invert
it. C up to E is a Major 3rd, so E up to C is a Minor 6th.
What is the distance from E up to Db? Answer: Again, I'd prefer
to find the distance from Db up to E, then invert it. Db to E fits into the
GENERIC sequence of 2nds (D E). We know that D up to E is a Major 2nd, so Db
up to E must be an Augmented 2nd; therefore E up to Db is a Diminshed 7th. Notice
that even though Db to E is 3 halfsteps, it will not be considered a Minor 3rd
unless it is spelled C# up to E; if it's spelled Db up to E, it must be some
kind of 2nd, not some kind of 3rd.
CONCLUSION
Memorize: The sequences from PART ONE, The inversion rules
(the numbers must add up to 9; Majors become Minors and vice-versa, Diminisheds
become Augmenteds and vice-versa, and Perfects stay Perfect), and the visual
diagram above --That's It!
These perspectives may seem complicated at first, but if you
take the time to absorb them properly and completely, interval problems will
be a thing of the past for you!