Music Theory for RAV: Scales and Octaves

Quick recap: there are 7 notes in the musical alphabet, from A to G, and they are all a whole tone apart from their neighbor, except B and C, and E and F, are each a semi tone (half a whole tone) apart. You can raise a note by making it sharp, or lower it by making it flat, like D# or Eb - which happen to be enharmonically equivalent (sound the same) notes.  

If you haven't already, check out the Music Theory for RAV: Notes, Intervals, and Accidentals article for some basics. Once you understand that, you're ready for scales and octaves!

---

Once you get to the end of the musical alphabet, it repeats. That brings us to scales! We love scales. That's how we choose our different RAVs, right? A scale is simply a sequence of notes in a particular order that repeats. For instance, a scale starting on A (like the one above) would run: a, b, c, d, e, f, g, a (again), b (again)... 

So how do we differentiate between the first A, and the second? Clearly, although they are related, and sound harmonious together, they aren't quite the same - the second is a lot higher! This is where octaves come in. The second a is an octave, meaning 8 notes, higher than the first. We notate this by using numbers like A1, A2, etc. For example, Eb4 is 3 octaves above Eb1, but they're both E flats. 

Having a musical alphabet with numbers indicating the octave helps us play with other musicians. For example, we could play a D3 on a RAV D major scale, and our pianist friend could find the same exact note to play, although of course it would sound a little different in tone. 

A scale can begin on any note of the musical alphabet. For example, the RAV D major scale begins on a D, and the A integral scale begins on an A. Most scales contain all notes of the musical alphabet. For example, a standard D major goes D, E, F#, G, A, B, C#, D... 



How about our beloved RAV scales? Because there are fewer notes on a RAV then, say, a piano, typically RAV scales will omit some notes. Our D major RAV is: D3 (Ding) G3 A3 B3 C#4 D4 E4 F#4 A4. Note how we skip straight from D3 to G3, and straight from F#4 to A4 without the G3 in between. Even though we don't have certain notes in sequence, our ear still perceives it as D major. 

Okay, let's talk about the different kinds of scales. Some scales are happy, others sad, still more or mysterious, forbidding, or even sassy. We've got to have a way to distinguish them from each other! How we describe scales, and intervals as we will see later, are by their "quality". The most commonly used and important scales, or qualities, for most musical purposes are major and minor scales. Major can be thought of as happy, minor, sad. We've already looked at the RAV D major, so let's consider the RAV D Celtic minor: 
D3 (Ding) A3 C4 D4 E4 F4 G4 A4 C5 



As you can tell by listening to videos of the two scales, even though they both start on the same note and have several notes in common, they have quite a different sound. The intervals between the notes are the same numerically: E4 to F#4 from the D major scale, and E4 to F4 from the D Celtic minor scale, are both a second apart. However, these intervals of a second are not quite the same!

In our example from before, E4 to F4 is a minor second, and E4 to F#4 is a major second. The different qualities of intervals like these explain why scales are either major or minor. 

Just like scales can have different qualities, major or minor, different intervals also have different qualities. Intervals can have all sorts of qualities, like perfect or augmented, but for our purposes here, let's just consider major or minor intervals. A major interval is just one that is a semi tone larger than a minor interval.



Major and minor scales both have major and minor intervals, just in different orders. Actually, every major scale has a minor cousin that is the exact same notes, just in a different order. Those are called relative scales. For example, the B Kurd RAV is essentially a B minor scale. It's major cousin is D major! If you compare the two scales, you will see that they actually share the same notes, just in a different order and octave. You can figure this out for yourself by taking the note that any given major scale starts on, and going down by three semi tones, to get the equivalent minor scale. In our example, B is 3 semi tones below D: D C# C B. 

Whew! That was a lot. We've learned that every note has several versions in octaves higher and lower, like older and younger siblings. We've learned that sequences of these notes, starting on a particular note and with a particular order of minor and major intervals between them, produce major or minor scales. We are now equipped to do things like describe the quality of different RAV scales, to help us in deciding which ones to buy or pair with another instrument in a jam session. But what about chords? Join us, for our next exciting installment!

The article is written by David Duan, all rights reserved, copyright 2018. 

David Duan

---

Composer, cellist, and sound healer

A Dean's Recognition Award recipient and multiple concerto competition winner, he has performed around the world with a variety of ensembles and orchestras. A graduate of New York University and the Peabody Preparatory of the Johns Hopkins University, he lives in Maryland.

Please contact david.duan@nyu.edu for information, gigs, commissions, collaboration, and more. 

Instagram: davidduan