copyright © 1995 Will Pirkle Last Modified: Oct 1, 1995
This lesson originally appeared on StickWire - the Official Chapman Stick Mailing List.
Reproduced here by permission. This article can be reprinted only in its entirety.

Theory on Tap
Lesson 3: Major Scales and other Phenomena

aka: The History of Our Musical World, Part I

by: Will Pirkle

** Disclaimer**
Folks, this is a LONG one. My job is to explain the Major Scale and why we need to know it and why the Stick(TM) is such a good medium for it. When I started on this journey, I realized that there are two paths to take:

  1. Say "the Major Scale exists, here is its pattern on the Stick, and enjoy practicing it" (yeah, right).
  2. Explain why you will want to spend many hours practicing it. Give the necessary patterns, and encourage raw experimentation.

In choosing path (2), I then realized that you can't explain why unless you explain a whole lot more, like where music came from. I try not to push my philosophy of music, but rather give a brief (ha!) run down of some of the essentials, like melody and keys and stuff. So here goes: get a snack and a refreshment -- you are in for a long ride.
:> WP


Humans probably first made organized noise with their mouths, millions of years ago. They probably also banged sticks (no pun intended) on rocks to create percussive sounds. At some point, using either the sticks-on-rocks or the vocalized noise or a combination, they communicated thoughts and ideas. This communication was "aural" communication, not "visual" communication (like drawing pictures in the sand with your fingertip). Today, we have lots of ways of communicating our thoughts and ideas. But, we are all drawn into this forum because of our interest in conveying thoughts and ideas through music.

Music, in its simplest form, uses rhythm and melody to convey thoughts and ideas. The rhythm part is rooted in the natural rhythms we observe in everyday life; our heartbeats, the hoot of an owl, the sound of a waterfall, the rising and setting of the sun and moon. Melodies have their origin in vocal words. Observe two people having a conversation. Be attentive and listen to the pitch (highness or lowness) in the voices as if they are actually singing in some strange form. For most, the speaking voice is not mono-tonic but instead, it moves around.

As you ask a question, the pitch of your voice will rise near the end of the phrase. And, as you answer a question in an affirmative manner, your pitch will drop near the end of that phrase. In speech we convey thoughts NOT ONLY with the actual words (literal meanings), BUT ALSO with the rhythm and pitch of our voices (inflection and emphasis). I can remember my mother saying "Don't speak to me in that tone of voice!" -- she was teaching me how a particular pitch/rhythm pattern conveys unpleasant ideas.

Part of the key to understanding music and the concept of melody is to understand how the non-literal part of speech contains and conveys information. As an instrumental musician, your job is conveying feelings and thoughts without words.

So how do you convey a thought with a melody? Generally, you need to create phrases which are distinctive combinations of single or multiple note-sequences, and then group the phrases together in a way that makes musical sense. Phrasing is not an easy thing to practice or teach. Often, phrasing is what separates the great musicians from the good ones.(1), (2)

Many types of music, most notably blues, jazz and classical, use a call-and-response mechanism in which one phrase is played, then a complementary phrase follows, like a Drill Sergeant calling out cadences as the troops march in line (Sound off --1,2 Sound off--3,4...). Often, the first (questioning) phrase will have a rising pitch shape near the end. And the response (answering) phrase will have a descending pitch shape near its end. Just like our voices during conversation. Do you see the sublime connection between music phrases and spoken phrases?

Early Music

The first interval humans probably discovered was the octave. Nearly anyone can identify an octave by ear. There is a "sameness" in the pitch of the two notes, even though the pitch frequencies are different.

At some point, people divided the space between the octave into discrete units (notes). How many notes? Without getting into a bunch of mumbo-jumbo, us Westerners divided the octave into 12 discrete units. Just to be confusing, we call them half steps. And we form almost all of our musical thoughts using combinations of just those 12 units.

Since melodies are made of note-sequences (phrases) and rhythms, and since we often use repetition to help our listeners understand our thoughts, then we wind up playing the same note-sequences (or similar note-sequences) very often during a composition.

When we learn and practice scales, we are learning generalized note-sequences. We learn them so that we may quickly draw upon them at any time and use fragments for phrases, melodies or lead lines. So, we want to learn the note-sequences that are rich with potential for conveying feelings. We want to learn the scales we can get the most mileage out of.

The word scale comes from the Italian scala meaning ladder or staircase. A scale is defined as "a series of single notes, progressing up or down"(3). So, there are really an infinite number of scales. Today, we have added another concept to the definition of scale which is that we define a scale within the limits of an octave interval. So, you start on one note, play the notes in the scale ascending or descending, and stop when you hit the note an octave above or below your starting one.

The minimum number of notes in a scale is 2, the maximum is 12 (again, we are assuming that you will repeat the scale pattern of notes as you continue the scale up or down in other octaves). The chromatic scale is the progression of all 12 notes. You can start the chromatic scale on any note. The Chromatic Scale starting on C would look like this:

C C# D D# E F F# G G# A A# B C

There is a half-step between every note.

The Whole-Tone scale uses whole-steps between every note and starting on C would look like this:

C D E F# G# A# C

Spend a few minutes and learn the chromatic scale and the Whole Tone scale. Here are the patterns on the Melody side of the Stick:

Chromatic Scale


HINT: Remember that the Stick Melody strings are tuned in P4's. This is 5 half-steps (see Theory On Tap; Lesson I). We are playing 4 half steps per string so we have to shift back by 1 fret each time we change up to the next string to make up for not playing all 5 half steps before shifting.

Whole Tone Scale


HINT: Here, we are playing a continual succession of whole steps, 3 whole steps per string. 3 whole steps = 6 half steps and there are only 5 half steps between any pair of strings. So, you have to shift UP to get the extra half step you need. (If this is not clear, email me privately and I'll fix ya up).

Play around with these scales for a while and try to build melodies by using fragments of both of them. Just use the right hand (melody strings only) for now.

A Key

A key is a tonal center about which a composition, or part of a composition, revolves. A tonal center is established by repeating or sustaining the same note -- usually this is done in the bass. You also establish a key by repeatedly coming back to that "home" note over and over throughout the course of a composition. The way Western, or tonal, music works is this:

  • First, establish a key
  • Then lead the listener away from the key by moving to related keys (more about that later).
  • Then, you return back to the home key. This "homecoming" is supposed to be satisfying in a musical way. A good pop tune with a good hook will do that to you; you feel really satisfied when the chorus kicks in.

Nearly all music that you hear today uses this principle of establishing a tonal center, moving away from that center, then returning. In atonal music, you purposely do NOT do that.

Now, establish a key by playing and sustaining a note in the bass, lets say C. So, here you are playing and sustaining low C's on your Stick, and you want to weave a melody over that C by using pieces of the Chromatic or Whole Tone scale. Try that for a while.

What you might find is that it is kind of difficult to create melodies that hook into that low C when using sequences of just half steps or just whole steps. The Whole Tone scale should give a "dreamy" kind feeling but not a secure, locked-in sound. The Chromatic scale will probably give you no real tonal center at all! (If you didn't actually do this exercise, go back and do it; it is worth the 5 minutes)

Finally, the Major Scale!

There are a lot of different reasons why the Major Scale came to be. Some focus on Pythagorus and the simple harmonic motion of the planets. Others focus on the overtone series (don't want to get into that now). John Duarte, in a Guitar Player article, says that the major scale evolved. People first found the octave and 5th intervals. Then added the M2nd and M6th (one whole step away from the others). Then added the M3rd. That is the Major Pentatonic Scale -- the backbone of the Major Scale. Later, the 4th and 7th were added. The scientific way that the notes of the Major Scale are related probably wasn't on the minds of the masses of people that carved out music. They probably just thought it sounded good.

And, the Major Scale is rich with melodic ideas. It is a mutant combination of whole steps and half steps. It possesses a lot of neat mathematical traits too. It uses 7 of the 12 units we talked about. If I get enough requests, I will write a Theory on Tap 3A explaining some of the cool mathematical things that the Major Scale does and maybe even how that relates to the reality around us. But, let's talk about some of the neat musical things it does.

The root, 5th, and octave are the foundation of many different culture's musical repetoire. This isn't surprising because the 5th is almost exactly halfway between the root and octave on the frequency scale. Check out the section called "Inversion" in Theory On Tap, Lesson I: the 5th and the 4th are reciprocals. Going up a 5th is the same as going down a 4th. The 5th and 4th are related like opposite sides of the same coin. And, they are both harmonically pleasing (play P4 and P5 intervals and compare the sound with m2 or M7 intervals). The Root, 4th and 5th are used to create tonal centers (keys) in just about all "pop" forms of music, from the 1400's to today. To recap: the 5th is important because it is nearly exactly halfway between the root and octave on the frequency scale. The 4th is important because it is the reciprocal (or inversion) of the 5th. There are even psycho-acoustic reasons for these importances.

As it turns out, the Major Scale has a real special relationship to the 4th and 5th. The Major Scale contains a series of whole and half steps arranged in such a way that the Major Scales built off of the 4th and 5th notes CONTAIN THE SAME NOTES AS THE ORIGINAL MAJOR SCALE EXCEPT FOR ONE. Here is an example (don't worry about how to construct the Major Scale -- that is yet to come. For now, look at the note similarities):

Example: Key of C Major
C = Root = Tonic
F = 4th
G = 5th

    G A B C D E F# G
G Major Scale; off the 5th
C Major Scale
   F G A Bb C D E F
F Major Scale; off the 4th

Remember how I said that in Tonal music the idea is to establish a key center, lead the listener away from the key center by moving to related keys, then have a big homecoming back to the original key canter? As you can see here, the "related" tones (4th and 5th) Major Scales only differ from the Tonic (home key) by ONE NOTE! That creates a nice palette of musical tones to work with, and three separate tonal centers to play in that only differ by 2 notes (the F# and the Bb). Think about the standard blues progression (1-4-1-5-4-1) -- see all the 5's and 4's?? That isn't just by accident.

This 4th/5th relationship holds true for any Major Scale and ALL OF ITS MODES too! (Modes come later). In fact, of all the possible combinations of 7 of the original 12 units (ie all 7-note scales), the Major Scale is the ONLY one to behave this way. (4)

Since it is made of a combination of whole AND half steps, you aren't limited to the types of melodies you constructed in the previous example (by using only half OR whole steps).

And, with this neat interaction between the Root, 4th and 5th, you'd expect an instrument tuned in 4ths or 5ths OR BOTH like the Stick, to have interesting arrangements of Major Scale notes on its strings. It does. And this is in the next lesson Theory on Tap 3.2 -- Why the Major Scale and Stick are so uniquely related. For now, chew on this and play with some of those exercises. And listen to music thinking about the 4th, 5th and common notes.

Will Pirkle 9/11/95


  1. Kennedy, Michael, "The Concise Oxford Dictionary of Music," Oxford University Press, New York, 1980, p.490
  2. Copeland, Aaron, "What to Listen For In Music," McGraw-Hill Book Company, New York, 1939, 1957, 1985, pp 49-60
  3. Kennedy, p 563
  4. Duncan, Andrew, "Combinatorial Music Theory," Journal of the Audio Engineering Society, Vol 39, No 6, June 1991, pp 430 - 435

Lessons: 1| 2 | 3 - Part I| 3 - Part II| 4 - Part I| 4 - Part II| 5| 6| 7| 8| 9| 10| 11| 12|
Will Pirkle

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