Every time you hear or play a note you need to know/feel where that pitch lies relatively to the current key/mode or pole to understand what's going on and where it wants to go next.

I teach all my students ear training which is a invaluable skill to have.

For beginners I like to teach only intervals and how the sound, disregarding key. It is the first step before they can tell relationships inside a key/mode. And I don't use programs, just audio tracks so they can listen to them on their ipods, ipads or car without the need of a computer at hand, while they run or drive or whatever.

Here's a link to the Interval Trainer Vol. I
mdecks.com/intervals1.html

Why is the smallest 2nd, that can be written, negative?

If we are to write two notes a 2nd apart, we need to use 2 consecutive letters of the alphabet (such as AtoB or EtoF) or GtoA (note names repeat after G)

The smallest 2nds are then B-C and E-F, being both 1/2 steps apart. And they're minor 2nds.

Now if we use flats and sharps we can make those 2nds even smaller and they will still be 2nds

So B#-C and B-Cb are 2nds and there notes are cero steps apart (B# is enharmonic for C, and Cb is enharmonic for B).

Now if we use both alterations at the same time we have:
B#-Cb which are -1 half step apart. (minus 1 half step , that's a negative number!)

mDecks

Talking Intervals: Why is 2+2=3 ?

An interval of a second (2nd) is the distance between 2 notes which names are in alphabetical order (A-B, B-C, C-D, D-E, E-F, F-G) and G-A, regardless of their alteration (sharp, natural or flat).

If the distance between the two notes if a step (2 half steps) then the 2nd is clasified as Major.
C-D, B-C#, Bb-C are all major 2nds.

It he distance is a half step then it's a Minor 2nd.
B-C, C#-D, E-F are all minor 2nds.

If the distance is 1 and 1/2 step then it's an Augmented 2nd.
Bb-C#, Gb-A, Db-E# are all augmented 2nds.

If the distance is cero step then it's a Diminished 2nd.
B#-C, G#-Ab, D#-Eb are all diminished 2nds.

What about Gb-A#? That's 2 steps (1/2 step bigger than an Augmented)
It is called a double-augmented 2nd.

As you can see being a 2nd does not tell us much regarding distance between notes, but just distance between names of notes.

But, why is 2+2=3?
When we stack two 2nds, one on top of each other, we get a 3rd. (C-D + D-E = C-E)

Well.. We shouldn't be counting D twice, should we? (CDDE is actually CDE or C-E)


mDecks