Theory on Tap:Major Scales and other Phenomena
From StickiWiki
** 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:
- Say "the Major Scale exists, here is its pattern on the Stick, and enjoy practicing it" (yeah, right).
- 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.
Contents |
Communication
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 | D | E | F | G | A | B | C | 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.
References/FootNotes
- Kennedy, Michael, "The Concise Oxford Dictionary of Music," Oxford University Press, New York, 1980, p.490
- Copeland, Aaron, "What to Listen For In Music," McGraw-Hill Book Company, New York, 1939, 1957, 1985, pp 49-60
- Kennedy, p 563
- Duncan, Andrew, "Combinatorial Music Theory," Journal of the Audio Engineering Society, Vol 39, No 6, June 1991, pp 430 - 435
Part II
In Part I of this lesson, I gave a brief rundown of the history of Western Music and how the Major Scale plays an important role. We saw that there are some neat things that happen when you arrange the 12 chromatic notes into a 7-note scale consisting of mixed whole and half steps. There is an interesting phenomena that occurs with the 4th and 5th tones. Lesson I was written to give people a reason to want to learn the major scale (unlike most music teachers who force you to blindly learn scales "because everyone else does").
In Part II, I'm going to show the Major Scale Recipe, and how the scale arranges itself on the Stick(TM) fretboard. Hopefully, this will provide an ample foundation for the future Theory On Tap teachers to use. Perhaps, they will incorporate some of the Major Scale INsights I'm trying to provide here so that a unifying thread will tie the lessons together.
The Recipe
In the last lesson, we observed that learning note-sequences consisting of only half steps or only whole steps has a limited useage in Western Music. We want to learn the note sequences that are ripe with harmonically interesting ideas -- perhaps even so that we may purposely violate the ideas (atonal and 20th Century Music). The Major Scale is a mixture of half and whole steps that "work" in a secure way with the root, 4th and 5th of the key you are in. You can make any major scale by taking the following recipe and applying it to the chromatic sequence of notes:
... G G# A A# B C C# D D# E F F# G G# A A# B C C# D D# E ....
or
... G Ab A Bb B C Db D Eb E F Gb G Ab A Bb B C Db D Eb E ...
These sequences of notes are identical in pitch, but not name (notice that C# = Db, etc...). The reaons for naming with #'s or b's will become obvious in later lessons, especially the Circle of 4ths lesson.
The Major Scale Recipe is:
W W h W W W h
Where: W = Whole Step, h = half step
If you have a piano nearby, you'll see that this WWhWWWh is the precise arrangement of the white keys starting with C. Thus, it is the C Major scale on the piano.
Suppose you want to produce the series of notes in the A Major Scale. What you do is start on A in the chromatic sequence above, and follow the recipe. Remember that the above sequence extends in both directions forever.
So it goes like this:
| Starting note: | A |
| Whole Step | B |
| Whole Step | C# |
| half Step | D |
| Whole Step | E |
| Whole Step | F# |
| Whole Step | G# |
| half Step | A |
So, the sequence is: A B C# D E F# G# A
Exercise: Derive the Major Scale for the following keys: C Major, G Major, F# Major
You should be able to apply the Recipe and come out with the correct sequences (answers at the end of this lesson).
There is an easier way to learn the note names to all 12 of the Major Scales by learning about Key Signatures and The Cycle of 4ths/5ths -- I believe that these topics are handled in future Theory On Tap lessons. It is important to know the names of the notes within the scales, even if you are learning the Major Scale by pattern recognition instead of note names. In Part I, I discussed the concept of tonal music and movement from one tonal area (key) to other areas. Knowing the names of the notes, and their degree gives you a lot of options for tonal movement. Degree really means interval: in the above example of A Major, we say that B is the 2nd degree, and G# is the 7th degree, etc... For completeness, here are the degrees of the Major Scale (with the example being the Key of A Major):
| Note Name | Degree | Musical Terminology |
|---|---|---|
| A | 1st | tonic |
| B | 2nd | supertonic |
| C# | 3rd | mediant |
| D | 4th | subdominant |
| E | 5th | dominant |
| F# | 6th | submediant |
| G# | 7th | leading-tone |
The Major Scale on the Stick
There is a diagram in Emmett Chapman's book, Free Hands, called STRINGS IN 4THS TO INFINITY. I am going to touch a little on this diagram, but I think that Free Hands does an impressive job of describing, discussing, and relating this pattern to to the Stick TouchBoard(TM). Also, I think the point of Theory On Tap is to add some Music Theory that can be used to support and supplement Free Hands, and not to simply repeat or replace what's already there.
The Major Scale has an interesting relationship with the 4th and 5th scale degrees. An instrument tuned purely in 4ths or 5ths (inverted 4ths) is bound to have an equally interesting relationship to the Major Scale. The one-octave Major scale has the following patterns on the Melody side of the Stick:
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
|-----|-----|-----|-----|-----|--*--|-(*)-|-----|-----|-----|
|-----|-----|-----|-----|--*--|-----|--*--|-----|--*--|-----|
|-----|-----|-----|-----|-(*)-|-----|--*--|-----|--*--|-----|
1 = use first finger here
(*) = Root = Tonic = 1st Degree
Check out for yourselves the location of the WWhWWWh pattern. Do it! Prove it to youself. It will also be helpful to remember the degree numbers with relationship to the root in terms of graphic position. Check out another way to play the same notes:
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
|-----|-----|-----|--*--|-----|--*--|-(*)-|-----|-----|-----|
|-----|-----|-----|--*--|--*--|-----|--*--|-----|-----|-----|
|-----|-----|-----|-----|-(*)-|-----|--*--|-----|-----|-----|
2 = use 2nd finger here
This pattern produces the same pitches and the same sequence of WWhWWWh. Check out this one:
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
|-----|-(*)-|-----|-----|-----|-----|-----|-----|-----|-----|
|-----|--*--|-----|--*--|-----|--*--|-----|-----|-----|-----|
|-----|--*--|-----|--*--|--*--|-----|-----|-----|-----|-----|
|-----|-----|-----|-----|-(*)-|-----|-----|-----|-----|-----|
3,4 = use 3rd or 4th finger here
Hold on!! These 3 patterns produce the same pitches, same WWhWWWh sequence, but look totally different. You are discovering something called an over-abundance of options that happens on any stringed instrument (except keyboard operated, and harp-like ones). The same notes occur many times on different strings in different positions.
What Emmett did with the Infinite 4ths diagram was to tame this over-abundance and put it in a perspective that almost anyone can easily grasp!
To really know the major scale, you need to be able to play it anywhere on the Stick, starting from any note. The Infinite 4ths diagram shows that the Major Scale pattern really repeats itself every 7 strings. If you learn this one pattern, you can play the Major Scale anywhere on the neck, starting from any note. Sounds like a miracle. Maybe it is.
Here is the pattern (this is a fictitious 10-string melody instrument -- see Free Hands for more clarification) -- the Root (tonic) notes are marked as (*):
|-----|-----|--*--|-----|--*--|-----|--*--|-----|
|-----|-----|-(*)-|-----|--*--|-----|--*--|-----|
|-----|-----|--*--|-----|--*--|-----|--*--|-----|<--pattern
|-----|-----|--*--|-----|--*--|--*--|-----|-----| repeats
|-----|-----|--*--|-----|--*--|-(*)-|-----|-----|
|-----|-----|--*--|--*--|-----|--*--|-----|-----|
|-----|-----|--*--|-(*)-|-----|--*--|-----|-----|
|-----|--*--|-----|--*--|-----|--*--|-----|-----|
|-----|-(*)-|-----|--*--|-----|--*--|-----|-----|
|-----|--*--|-----|--*--|-----|--*--|-----|-----|
^ Start pattern here
The starting note I give isn't the tonic, but it is where this pattern repeats in terms of groups of strings. The big picture can be broken into smaller repeating units like this: (3), (2), (2)
(3) string pattern:
|-----|-----|--*--|-----|--*--|-----|--*--|-----| |-----|-----|-(*)-|-----|--*--|-----|--*--|-----| |-----|-----|--*--|-----|--*--|-----|--*--|-----|
then (2) string pattern:
|-----|-----|-----|--*--|--*--|-----|--*--|-----| |-----|-----|-----|--*--|-(*)-|-----|--*--|-----|
and finally another (2) string pattern:
|-----|-----|-----|--*--|-----|--*--|--*--|-----| |-----|-----|-----|--*--|-----|--*--|-(*)-|-----|
Remember, 7 notes in the Major Scale, 3+2+2 = 7, the 5th is 7 half steps from the root, pattern repeats every 7 strings; there is even more numerology than that in this system, but I think you get the picture.
Because the Melody half is tuned in pure 4ths, this pattern wraps around the fretboard spirally (see reference at end for more details). So, unless you have a 10 string all melody Stick, you won't be able to see the whole pattern in a given position; only part of it.
What About the Bass Strings?
Since the bass strings are tuned in inverted 4ths (5ths, that is), you would expect a similar pattern to exist on them, and one does. It also repeats after 7 strings. And, it contains the Infinte 4ths diagram within it!
Here is the Strings in Infinite 5ths diagram, showing the bass strings. So, the lowest strings are at the TOP of the diagram and the highest strings at the BOTTOM of the diagram. Check it out:
v Start Pattern Here |-----|-(*)-|-----|--*--|-----|--*--|--*--|-----| |-----|--*--|-----|--*--|-----|--*--|-(*)-|-----| |-----|--*--|-----|--*--|--*--|-----|--*--|-----| |-----|--*--|-----|--*--|-(*)-|-----|--*--|-----| |-----|--*--|--*--|-----|--*--|-----|--*--|-----| |-----|--*--|-(*)-|-----|--*--|-----|--*--|-----| |--*--|-----|--*--|-----|--*--|-----|--*--|-----| |-(*)-|-----|--*--|-----|--*--|--*--|-----|-----|<--pattern |--*--|-----|--*--|-----|--*--|-(*)-|-----|-----| repeats |--*--|-----|--*--|--*--|-----|--*--|-----|-----|
This time, you play 4 notes per string before going to the next. This pattern breaks into repeating patterns in a 2, 2, 2, 1 fashion:
Pair (2 strings):
|-----|-(*)-|-----|--*--|-----|--*--|--*--|-----| |-----|--*--|-----|--*--|-----|--*--|-(*)-|-----|
then another (2):
|-----|--*--|-----|--*--|--*--|-----|--*--|-----| |-----|--*--|-----|--*--|-(*)-|-----|--*--|-----|
then another (2):
|-----|--*--|--*--|-----|--*--|-----|--*--|-----| |-----|--*--|-(*)-|-----|--*--|-----|--*--|-----|
then a single string (1):
|--*--|-----|--*--|-----|--*--|-----|--*--|-----|
And, 2+2+2+1 = (you guessed it) 7
After this, the pattern repeats. That last string (1) has all whole steps. Remember the sequence WWhWWWh? The 3 W steps in a row wind up together on this string.
Look carefully at the pattern and you'll see the Infinite 4ths pattern inside of it.
Learning to play and move these patterns all over the neck is a matter of learning which part of the pattern you are in relative to your tonic or root note. This means learning the scale starting from (and ending on) any of the above notes. As it turns out, scales based off of different notes of a particular scale are called modes. All of the Major Scale's modes are contained in the Infinite 4ths diagram, it just depends on where you start and end the portion of the pattern. The next Thoery On Tap lesson is going to discuss the modes in a LOT more detail, but I'd like to give one pointer on the modes:
It is easy to fall into the trap of associating the modes with the Major Scale they are derived from. In other words, thinking of the modes as a subset. This is natural since their patterns fall out of the Major Scale pattern. If you do this, your compositions will wind up sounding Major all the time (no variety). It is OK to conceive and learn the modes as they relate to the Major Scale they come from. Once you have done this, begin looking at the modes as altered major scales. Break them away from their associated "parent" Major Scale and listen.
In the Modes lesson, you are going to find out how to play certain modes over certain chords. This is the really musical way to use the modes. When you have learned the patterns, go back and listen to the modes very closely, independent of any root chord. The modes each have a different flavor, a different mood that is associated with them. In the Modes lesson you'll learn how to capitalize on the moods they create by backing them up with the appropriate chords (or, backing up chords with the appropriate modes -- either way produces the same result).
I started this off with the concept that melodies come from note sequences (and rhythms). We want to learn robust, generalized note sequences to use for composition and improvisation. There is a special relationship between the Major Scale and the 4th and 5th tones. The number 7 comes up a lot. In addition, the derivitave scales, called the modes, give us even more note sequences that fit nicely over an almost infinite variety of chord structures which form the backbone of our compositions.
It will take more Theory On Tap to tie this together with chords, key changes, different tonal centers and songwriting/improvisation. Consume and digest the Infinite 4ths Pattern and Infinite 5ths pattern. Then, stay tuned for more Theory On Tap and always experiment on your instrument. The Stick is designed to be musically friendly. Make it talk!
References
The "Strings in Fourths to Infinity" diagram was taken directly from Free Hands, Page 41. Free Hands also covers the breakdown of its components, including a much more thorough graphical explanation of the unfolding of this pattern across the fretboard.
Free Hands, by Emmett Chapman Published by Stick Enterprises, 1974/5/6/, 1980, 1989 Contact Stick Enterprises for more information.
Answers
C Major: C D E F G A B C G Major: G A B C D E F# G F# Major: F# G# A# B C# D# E# F# (trick: E# = F <-- prove it to yourself!)
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