Intervals or The Key to Harmonic Understanding
(14 May 02)
The Units: Interval Names
Intervals are always named in relation to a Root note and then by their order of appearance. It's best to take a look at all of the natural note names (all white keys on the piano) and thus the C major scale.
As you can see you start counting from the Root (1). Apart from the Root (1) and the Octave (8) all notes are named according to their order of appearance. The word 'Root' became more accepted than previously 'the prime' or 'the first' as it better describes the starting position. If we play the Root twice at the same time it is called a 'Unison' (Latin for together). The Octave is a relic from the classical naming of intervals.
Now I'm sorry to tell you that saying Second, Fifth or Sixth is not enough. This would be too easy and would result in us authors being unemployment :). This is where our terminology comes in that we learned in the beginning.
Perfect Intervals
Root, Fourth, Fifth and Octave are Perfect
In our C Major example this would be the notes c, f, g and again c. 'Perfect' describes those intervals that are the framework for building scales and chords. Perfect Intervals stay the same, whether you build a major or a minor scale. An exact translation of Perfect Intervals from its German origin would be "Clean Intervals" (reine Intervalle). It describes that they are consonant Intervals and therefore sound clean and perfect.
Let's take another look at our C Major Scale
Let me just point out some observations (some more obvious than others) to the image above as we can look at it in different ways:
 Perfect Root and Perfect Octave are the same note, one octave apart
 It takes 12 half steps (6 whole steps) to get from the root to the Perfect Octave
 There are 6 different other note names between Root and Perfect Octave
 it takes 2 whole steps and a half step to get from the Root to the Perfect Fourth
 it takes 5 half steps to get from the Root to the Perfect Fourth
 there are 2 different other note names between Root and Perfect Fourth
 I'll leave the rest up to you..... make up your own to better visualise the above.
Now that we have a clear understanding of what Perfect intervals are we can transform these 'rules' to roots other than 'c'.
Example: Root is d
Question: What is the Perfect Fourth of d?
To figure this one out we have a few different options, based on our observations above:
1) it takes 2 whole steps and a half step to get from the Root to the Perfect Fourth:
root = d, 1st whole step = e, 2nd whole step = f#, half step = g
Perfect Fourth from d is g.
2) it takes 5 half steps to get from the Root to the Perfect Fourth:
root = d, 1st half step = d#, 2nd hs = e, 3rd hs = f, 4th hs = f#, 5th hs = g
Perfect Fourth from d is g.
3) It's really important and the whole reason for this article, that you learn this by heart! : Perfect Fourth from d is g.
Memorising Intervals
So how do you approach memorising all the intervals of all possible roots. Here's my tip. Learn the intervals from notes without sharps and flats first and then add flats or sharps when needed.
We just figured out that the Perfect Fourth from d is g. If I'd ask you for the Perfect Fourth from db, which is just a half step below d, we do not need to start counting again  we just lower the result from d by a half step, thus gb. The Perfect Fourth from db is gb. The Perfect Fourth from d# is g#. See how this works?
So if ya know all Perfect Intervals starting on a natural note name you can easily transform this to all other notes.
And here they are  memorise them (I excluded the octave as this is pretty obvious):
Root Perfect Fourth Perfect Fifth
c f g
d g a
e a b
f bb c
g c d
a d e
b e f#
A common Pitfall
With the above list of intervals starting on natural note names, you may already have some queries. Sorry for me being so cautious but I wanna make sure that this is all clear and logical to you (this is our main goal here
The example starting on the note f might bother you. The Perfect Fourth has a flat in it. Why? and why isn't it an option to say that a# (which is the same pitch as bb) is the perfect fourth of f?
The answer, again, lies in the observations we made earlier, which are basically our rules to work out an interval. Let me take those observations apart with the f to a# example:
a# is 2 whole steps and a half step way from f = it could be the perfect fourth
a# is 5 half steps away from f = it could be the perfect fourth
BUT
there are no other 2 note names between f and a#. The only note name inbetween is g. Basically a# includes the note name a, which is the third note you come across when starting to count from f. Thus a# cannot be the fourth and must be some kind of third.
