This material has been drawn from some of my music theory tutoring.
In this lesson, I focus on how to calculate an interval in 4 easy steps and then find out its inversion with a simple trick of the trade.
I firmly believe that the unpopularity of music theory among students comes from a sort of dogmatic way of teaching it and in some cases consciously inducing students to overthink it. This causes an ‘initial shock’ that is quite difficult to remove.
For that reason, I always try to put things as clearly as possible, often relying on some schemes and ‘little tricks’ to remember this massive quantity of information. (Yes, I believe this is ‘massive’ for someone trying to learn the language of music from scratch).
The good news is that with some practice, this will eventually become just a child’s game. So let’s crank up with the work!
The first part of the lesson is about Identification of intervals.
For this we basically follow these 3 steps:
Count steps from 1st to 2nd note Build a Major scale on the (natural) first pitch Compare the intervals (does that interval belong to the major scale in question?) Refer to the graphic (on top of the page)
A few words on these 4 steps:
Always count including the first note! This may sound obvious, but it is not how we think when we add up numbers. For example: C - G is a 5th (C=1, D=2, E=3, F=4 and G=5), not a 4th (NOT C-D= 1, D-E= 2 and so on..). We need to do this because we need to refer to the Major scale to know if our interval belongs to that or has been ‘contracted’ (usually with a flat) or ‘expanded’ (usually with a sharp). Additionally, we know that a Major scale contains only Major and Perfect intervals, therefore if the interval we are trying to identify does not belong to the Major scale built on the first pitch, it MUST have been contracted or expanded! The Graphic is just a reminder for intervals different from Perfect and Major intervals. Follow the arrows on the right to expand it and vice versa. Please note that each expansion is a semitone. According to this graphic, a Perfect interval does not expand into a major, but rather into an augmented interval. Similarly, a Major interval when contracted becomes a Minor interval and only if it is further contracted it becomes Diminished (for example: C-E= Maj 3rd, C-Eb= Min 3rd, C#-Eb (again contracted, the sharp symbol in this case further narrows down the interval, not the opposite! Always see the context!)
The inversion rule is very simple and self-explicatory (Just look at the picture and you’ll see why).
Mastering intervals and their inversions is very useful when dealing with composition (and analysis, for that matter) because it helps deriving material from a simple motif, cell or set of notes and makes us think of music material in a different, more malleable way, without relying on a particular key, but on similarity of interval content among chords and motifs. If you think that this is a mind game only, maths that have little in common with art, please go and have a listen to “La Cathedrale Engloutie” by Claude Debussy, where similarity of interval content is one of the main harmonic features of this marvellous piece.