Lesson Contents:

• Nondiatonic Intervals
  • A Few Tricks to Help You Memorize Interval Names
  • Another Way to Express the Major Scale Formula: R, 2, 3, 4, 5, 6, 7, R
• Weird Intervals
• The Major Scale as a Frame of Reference
• Enharmonic Spellings For Intervals

In Lesson 5, I presented 8 intervals diatonic to the key of C major. Here they are again in case you forgot:

Diagram 1 - 8 Diatonic Intervals in the Key of C Major

Trick #1: The intervalic relationships expressed with these 8 intervals are the same for all major scales, not just C major. This means that if you compare all the notes from any major scale to its root you will always come up with:

1. a unison - between the root and itself
2. a major 2nd - between the root and the 2nd note of the scale
3. a major 3rd - between the root and the 3rd note of the scale
4. a perfect 4th - between the root and the 4th note of the scale
5. a perfect 5th - between the root and the 5th note of the scale
6. a major 6th - between the root and the 6th note of the scale
7. a major 7th - between the root and the 7th note of the scale
8. and an octave - between the root and the 8th note of the scale

And here's a short-cut way of expressing this formula: R, 2, 3, 4, 5, 6, 7, R. The W,W,H,W,W,W,H formula is implied!!!

Why is this useful? Well, if you know the note names in all 15 theoretical major keys and if you also remember the 8 diatonic intervals of a major scale (P1, M2, M3, P4, P5, M6, M7, P8)...

...you have also memorized 120 interval names! So, be sure to memorize the key signatures for each major key. They are extremely important to know because not only do they tell us which notes are in any major scale, they also form the foundation upon which so many other concepts are built - like why the interval between A and C# is a major third... because C# is the 3rd note of an A major scale.

Trick #2: Now, using the 8 diatonic intervals from Diagram 1 as a foundation, we can create many nondiatonic intervals by altering the top notes of the intervals. Consult Diagram 2:

Diagram 2 - 8 Nondiatonic Intervals to the Key of C Major

As you can see in Diagram 2, I have altered the top notes of the 8 diatonic intervals that were presented above in Diagram 1. The bottom note, the C note, stays unaltered. Afterall, we need to keep our frame of reference from shifting, otherwise we would get very confused and wouldn't learn anything. Now some interesting facts emerge as a result of these alterations. Most of these facts are review from Diagram 8 - The "Rules" of Intervals from Lesson 5 but some of facts involve new ideas - particularly, the idea of an enharmonic spelling for an interval name. Read on:

• Sharping the top note of a perfect prime makes the interval bigger - it becomes an augmented 1st. (C to C becomes C to C#)

• Flating the top note of a major 2nd makes the interval smaller transforming it into a minor 2nd. (C to D becomes C to Db)

• Flating the top note of a major 3rd makes the interval smaller transforming it into a minor 3rd. (C to E becomes C to Eb)

• Sharping the top note of a perfect 4th makes the interval bigger transforming it into an augmented 4th or the "dreaded" tritone. (C to F becomes C to F#)

• Flating the top note of a perfect 5th makes the interval smaller transforming it into a diminished 5th or the "splendid" tritone. (C to G becomes C to Gb)
  • PLEASE NOTE: the augmented 4th and the diminished 5th are enharmonic spellings for the same interval - the tritone. Remember how we can have enharmonic spellings for note names? Well, here is an example of two enharmonic spellings for the tritone interval. Both of these intervals sound the same, but they are written differently.

  • Another example of enharmonic spellings for an interval is one you may have overlooked: C to C# is an augmented 1st. It is the same sounding interval as C to Db, a minor second. How interesting!

• Flating the top note of a major 6th makes the interval smaller transforming it into a minor 6th. (C to A becomes C to Ab)

• Flating the top note of a major 7th makes the interval smaller transforming it into a minor 7th. (C to B becomes C to Bb)

• And finally, flating the top note of a perfect 8th makes the interval smaller transforming it into a diminished 8th which is an enharmonic spelling for a major 7th. (C to C becomes C to Cb)

For example:

Say we have the interval G to Bb. What is it? Well, we know we have "some kind of 3rd" because G=1, A=2, Bb=3. If we know that G to B is a major third (using the G major scale as a frame of reference), then it must follow that G to Bb is a minor third.

Here's another example employing trick #3, a harder one: What interval is Db to G#? Well, we know we have a 4th because Db=1, E=2, F=3, G#=4. We also hopefully know that in the key of Db major the interval between Db and Gb is a perfect 4th. Now using this perfect 4th as a "frame of reference", if we compare Gb to G# we see that Gb got "altered" or raised by two half-steps.

Take this rationale one step further and we see that we raised the perfect 4th by two half-steps... and this leads to the correct answer, a doubly augmented 4th,. Weird? Yes, but this is a great way to think about how to solve these "weird" interval questions.

What's a more practical name for a doubly augmented 4th? That is, what's a better enharmonic spelling for that interval name? Well, turn G# into a diatonic note to the key of D flat major. Make it an A flat. Aha! Db to an Ab is a perfect 5th. So, Db to G# will sound like a perfect 5th. Case closed.

I know this way of thinking may seem very abstract and it is, but if you can think in this way, you will become a better musician. As you study more theory, you will find many little tricks to help you along the way. But, the only way to really discover these "shortcuts" or "tricks" is to play with this stuff. Try to find patterns. And above all, use the major scale as a frame of reference for your understanding of music theory! Why? Because most ideas and useful concepts in music theory will come from understanding the underpinnings of the major scale.

In Lesson 5, I presented a table showing the relationship between interval names and half steps. I would now like to update this table by adding enharmonic spellings to the list. If this table makes sense, then you've "got it" when it comes to intervals.

And so ends yet another painful lesson in the land of intervals. If you've made it this far and understand this lesson and the other 2 lessons on intervals, you pretty much know what I know about them. Remember to play these suckers and invent lessons of your own. Draw diagrams. Make them colorful, make them pieces of art. Write notes out on the staff, learn this stuff in as many ways as you can think of - not just one way. Personalize this stuff. Make it fun and it will be a joy. Remember what they say, whoever "they" are, a journey of 1,000 miles is made by a series of small steps. (Or in a musician's case, a series of half-steps. I know this is bad, but I just couldn't resist.)

Don't give up. Don't get discouraged. You're not here for that. Be patient. If things seem overwhelming, put things into perspective and start over - fall back to what you already know and build from there. Add a little bit of knowledge to your understanding each time you study and practice. You'll get there. Perseverance furthers.

Proceed to Lesson 9 or go back to the main menu.
 

This document © and ® 2004-2006, by Gabriel Perry. All rights reserved.