[This post is the second in a series on Introductory Music Theory.  The series begins with the post A Musical Theory.  The next in the series is Stepping Into Numbers.]

I assume you are familiar with the musical sequence “Do-Re-Mi-Fa-So-La-Ti-Do”, that we are commonly taught to sing as children.  Musicians refer to this familiar Do-Re-Mi sequence as the Major Scale.  An interesting and important fact about Do-Re-Mi is that it doesn’t matter what pitch is chosen as the Do that one starts with, it is possible to proceed from any note and sing Do-Re-Mi such that it will sound “right”.  Likewise you can start from any note on your instrument and play a series of notes that sounds like Do-Re-Mi. What we understand from this is that there is not a specific set of notes that make a Major Scale.  So what makes it sound “right”?  The answer is simply that it is the “distance” between the notes you play that makes the sequence sound like Do-Re-Mi.

The term used in music theory for the “distance” between different pitches (notes) is called an interval.  When measuring how large a musical interval is, the unit of measurement is the half-step.   One could think of the half-step as the musical inch.  A half-step is the difference in pitch between a note on any fret of a guitar and the note on the next higher or lower fret (on the same string). It is also the difference in pitch between any key on a piano keyboard and the closest neighboring key to the left or right. (Be careful to remember that on keyboard instruments there are black keys in-between many of the white ones.  Even though the white keys may at first glance look like they are all right next to each other, for any white key its closest neighbor in at least one direction will be a black key.)   A whole-step is an interval of two half-steps, (conveniently, since two halves make a whole).  A whole-step is therefore two frets on the guitar or two keys on the piano.  Note that a half-step can also be called a half-tone or a semi-tone, and a whole-step can also be called a whole-tone.  These variants don’t mean anything different, they are completely synonymous with the “step” terminology.  Armed with this vocabulary we can look at the Do-Re-Mi scale in terms of half and whole steps.

1  2  3  4  5  6  7  8
Do Re Mi Fa So La Ti Do
 \_/\_/\_/\_/\_/\_/\_/
  W  W  H  W  W  W  H
(W = Whole step, H = Half step)

This diagram shows the distance between the notes of the Major Scale in whole and half steps.  So starting with any note we can play the Major Scale (Do-Re-Mi) by using the intervals as shown.  To describe this in words we could say that the major scale goes: whole, whole, half, whole, whole, whole, half.  It is important to remember that this is a description of the spacing between the notes, not the notes themselves. So starting from Do we get to the second note (Re) by going up a whole step, then we get to the third note by going up another whole step, then to the fourth note by going up a half step, etc..

"Do"->Whole->Whole->Half->Whole->Whole->Whole->Half

By committing this sequence to memory you can easily play the Major Scale starting anywhere on the piano or guitar (as long as you don’t run out of frets or keys!).

Guitar Exercise:

Note: the fattest string on the guitar is known as the 6th string and the skinniest the 1st string.

Play the note on the third fret of the 6th string. We will call this note “Do”. Now to play the Major Scale you will follow the sequence W-W-H-W-W-W-H. So “Re” will be a whole step away, which is two half-steps, or two frets.  Play this scale (all on the 6th string).

…

How’d you do? If it sounded right you will have played the note on the 3rd fret (our starting point) then the 5th, 7th, 8th, 10th, 12th, 14th, and finally the 15th fret to be back at “Do” (but an octave higher).

Now it may be easier to play a scale using more than one string so you don’t have to go so high up on the fret board, but for now we want to make it easy to visualize the distance between the notes, that’s why we’re doing it all on one string.

You may wish to try the scale starting with an “open” string (no finger on a fret). The sequence works the same way, we just remember that the note on the first fret is a half-step higher than the open note. Therefore to play the note which is a whole-step higher than the open string we must play the note on the second fret. So starting with any open string the Major Scale is played as follows:

Open-2nd-4th-5th-7th-9th-11th-12th

Try it!

If we wanted to write down what we just played showing how we “add steps” to get to the next note, we might write something like this:

Open---2nd---4th---5th---7th---9th---11th---12th
    +W=   +W=   +H=   +W=   +W=   +W=    +H=

Here again we see the now familiar pattern whole-whole-half-whole-whole-whole-half.