Music theory is the method of analyzing our musical system & describing relationships between tones. The true outcome of this theoretical system is…
- the naming of everything (tones, relationships, chords, etc.)
- sonic descriptions (how tones relate to one another when sounding – in our hearing).
Our numbering system is simple…
12 1 7 5 2 221-2221 EON
- 12 = 12 tones in our musical system.
- Each tone is 1 half step up or down to the next. 1 half step = 1 fret
- 7 + 5 = 7 natural tones = A, B, C, D, E, F, G + 5 sharps/flats.
- 2 = 2 naturally occuring half steps. 2 more naturals than sharps/flats.
- 221-2221 = Major scale pattern. A way to dial up the tones of a Major key.
- EON for Triads = Chords are built every other note, from every tone in the key. Triads are 3 tone chords.
- EON for 7ths = Taking EON one more step until we have 4 tones.
A key is a tonal center. The key is the central tone that a piece of music finally rests (tonality) in our ear. There are 15 musical keys [3 are enharmonic, which means same thing, different name].
Chords are a combination of ’3′ or more tones played together (harmony). 2 tones work just fine too. Ultimately, a single ringing tone is a chord [harmonics].
Scales are a series of individual tones played one after another – alphabetically (whether naturals or sharped/flatted tones) ascending & descending. They are tone groups or sets.
Arpeggios are chords played one note at a time (ringing or not ringing together). An arpeggio is a ‘broken chord.’
A root is a tone that names a key, chord, or scale. It is the starting point for building something. It is the number 1 [or zero with Numera] in our traditional music theory system for building anything. It can also be denoted R or 1 (or 0 in numberical chromatics).
We are running against music dictionarys with our definition of the word root. Dictionaries call the base tone of a chord, a root, while calling the base tone of a scale, a tonic. This is a semantic point, yet important. Our basic point is that if a tone of a scale can be a root of a chord, it can also be a root to a scale. We can build anythingfrom a given root. Scale tones are often called degrees (& have their own corresponding names).
When we play an instrument that can sound all the tones of a scale at the same time, is that not a chord?
The naming of a scale degree as a root doesn’t inflict any theoretical damage, rather, it creates one less boundary. You can call it Frank if musicianers you work with also call it Frank. The purpose of theory is to create a language that is capable of communicating musical ideas. The only worthwhile theory for us, is applied theory. In musicianer’s applications, root is used as we are defining it. Usage dictates meaning, not musicologists defining boundaries.
With our definition, there is more intellectual freedom & the understanding that chords & scales are ultimately the same thing.
12 Tones, ½ Step Apart
There are 12 tones in our Western musical system. There could be more, there could be less, but in Western music, the use of 12 tones is the given. We are given 12 tones to create music with. A tone can also be called a pitch. Pitch is the relative highness or lowness of a tone.
This 12 tone system is called Equal Temperament (equally spaced half steps). Just Intonation is another system of tuning based on the pure vibrations of nature (where the harmonics of a given tone are the basis of the tuning – only that key is in ‘perfect’ tune).
The 12 tones lie one-half step to the next or previous. On the guitar, one half-step is one fret. Every next tone (fret) is one half-step away. Half-steps can also be called semitones (where a tone is a whole step, which equals 2 semitones). We will be using the term half-step in every instance.
For whatever tone we put at one, we cycle through the 12, then back to the original (whatever we put at one). Any of the 12 tones can be placed at 1. After 12, we go back to 1.
So, the first piece of our music theory system: there are 12 tones [for teachers: "same number as months in a year" aids as a statement], and they lie ½ step apart.
One possible relationship between colors & music tones:
7 Naturals, 5 Sharps/Flats
The 12 consist of:
- 7 Naturals [white keys on the piano] – A – B – C – D – E – F – G, then back to A
- 5 Sharps (#)/Flats (b) – [black keys on the piano] – A#/Bb – C#/Db – D#/Eb – F#/Gb – G#/Ab
The chromatic scale is a summary of 12 half steps, starting from any tone (our musical ruler for measurement):
A note that is 2 half steps away from a given tone is called a whole step (w or 2; on guitar a whole step is 2 frets). Example: C to D. The whole step should not be confused with the whole note () in musical notation (rhythmic duration).
2 Naturally Occuring ½ Steps
There are two more naturals than sharps/flats; therefore, there must be two places where naturals touch. These naturally occurring half steps exist between B/C & E/F (no sharp or flat between). B goes directly to C, and E goes directly to F. [B# is C, Cb is B, E# is F, Fb is E].
The two pairs of naturally occuring half-steps are in the above. There isn’t a sharp/flat between those tones (the two places on the piano with no black note between = B/C & E/F).
221-2221 = Major Scale Pattern
We don’t play popular music in all 12 tones as the basis, rather, we use 7 [heptatonic ]as the basis for our music (Western music).
There is 12 tone music (atonal, dodecaphonic). It was pioneered by Arnold Schoenberg. 12 tone music was a ‘revolution’ that never gained a foothold on the world audience. It is some wild sounding stuff.
To ‘filter’ out 5 from the 12 to get 7 (12 – 5 = 7), we can use the Major scale pattern, which is 221-2221 or wwh-wwwh, where w = whole step & h = half step. This pattern is simply a learning tool and has no inherent meaning. The keys aren’t the way they are because of this series of numbers. It is just a helpful way to derive the tones within a key. And, we prefer the numbers over whole and half. The numbers are certainly easier to say and to remember.
We can think of this as a phone number (dial up the major scale - phone home). There are five 2′s in the pattern; therefore, a tone is skipped at every 2 (‘eliminating’ 5), & leaving 7. By filtering out 5 tones from the 12 while keeping the 221-2221 pattern, we create a key [key center].
A Key is a group of tones, that when sounded in melodies or harmonies, eventually makes one of the tones ‘magnetized’ to the human ear. One of the tones becomes the tone that is home in our ears. It sounds final, resolved, at home.
When we line up the 12 tones in order, we get what is called the chromatic scale [chroma- is a Greek root meaning 'relating to color' - the chromatic scale is all of the musical colors]. It can start from any of the 12 tones.
Example in C
For the Major Scale pattern, let’s rewrite the chromatic scale from the C tone & then apply our the Major scale filter to see what tones are in the Major scale of C (the Key of C Major).
Any tone of the 12 could be in the 1 position.
This process is repeated for every tone for all 12 tones. These 12 sets of tones that are created through this process make up 15 Major Keys [there are 3 enharmonic keys].
When we work this process, we are deriving the tones of a key. This is called Derivative in contrast to something called Parallel. Derivative tones are the tones within a key. These are also called the diatonic tones. Diatonic means ‘across the tones of a key’.
Parallel is comparing the non-diatonic tones [the ones 'eliminated' by the 5 whole steps] to the diatonic ones. This way we have a way of explaining all 12 tones in the context of what we put at 1. Parallel tones are tones that are in the gaps of the Major scale. They are outside, while the diatonic tones are inside.
We can build a linear C Major Scale by starting on the C tone located on the 5th string, 3rd fret.
Points to Remember
Guitar Chord Building – EON for Triads
Once we are certain about the tones in the key of C Major, we build chords. Chords are created by selecting a root (a tone to build something from), and then selecting Every Other Note (EON). There are 7 tones in a Major scale; therefore, there are 7 triads (each tone becomes a root). Triads are 3 tone chords built by superimposing 3rds.
Note: We are using the terms note & tones interchangeably [EOT - Every Other Tone - not as memorable].
The C triad is made up of C-E-G, the D minor triad is made up of D-F-A, the E minor triad is made of E-G-B, & so on. Often, in chord scale playing, we substitute the V7 for the viio [the 3 tones of the diminished triad are the 3-5-7 of the V7].
We can use the math to see why chords are Major, minor, and diminished [dim or o]. Major triads have 4 half steps between the root and 3rd, & 3 half steps between 3rd and 5th. Minor triads have 3 half steps between the root and 3rd, & 4 half steps between 3rd and 5th [thus why we refer to the 3rd as a flat 3 in parallel thinking - it's one half step closer to the root]. Diminished triads have 3 half steps between the root and 3rd, & 3 half steps between 3rd and 5th [thus why we refer to the 3rd as a flat 3 & the 5th as a flat 5 in parallel thinking - both are one half step closer to the root].
- Upper case Roman Numerals mean Major chords. Letters alone in the context of chords (not single tones) means Major [we don't have to write anything else].
- Lower case Roman Numerals mean minor (yet minor is assumed for the 2, 3, & 6 chord, & you may see these sometimes written upper case). Little m next to a letter means that the chord is minor.
- Lower case Roman Numerals with a superscript degree sign means diminished.
Once we create a Major scale by filtering out 5 tones using the phone number [221-2221], we can then use that set of 7 tones to create chords. The tones in the key of C are C-D-E-F-G-A-B-C [221-2221 applied to C as 1]. C is the only Major scale with only naturals (all of the sharps/flats are skipped).
These 7 tones make up the key of C. In music, a key is a group of tones that point our ear to one of the tones as home. It is the tonal center.
Every tone of a scale can become a root of a chord. Since there are 7 tones in the Major scale, we end up with 7 chords.
To build chords, we select a tone, then select every other note [EON], until we have 3 tones. Three tone chords built in 3rds (EON) are called triads. Triads have a Root, a 3rd, & a 5th. There are 4 types of triads [Major, minor, diminished, augmented. The tones & chords in a key could be called a family & we'll use this term occasionally.
The tones (scale) & chords that are a part of C are called diatonic to it. Diatonic means 'across the tones'. It means what is 'within the key' or 'a part of it'. Diatonic tones are inside.
In a Major key, the I, IV, & V are Major, the ii, iii, & vi are minor, & the viio is diminished. This is consistent in all Major keys.
The process we have applied to the key of C will be the same for all 12 tones. Since the tones are equally spaced [one-half step], & we are using the same filter [221-2221], & the same process for building chords [EON], the relationships are the same for every key.
4 Types of Triads
Triads are 3 tone chords built by superimposing intervals of 3rds. There are 2 types of 3rds: Major and minor. The Major 3rd is an interval equal to 4 half steps. The minor 3rd is an interval equal to 3 half steps.
With these 2 types of 3rds, we can have 4 combinations: 4-3, 3-4, 3-3, and 4-4. These are the Major, minor, diminished, and augmented, respectively. These are referred to as qualities. Triadic qualities are Major, minor, diminished, and augmented. There are also 7 chord qualities, and their extensions [2-4-6 = 9-11-13].
As with all parallel naming, the Major is our point of reference [for triads = R-3-5]. Since in the minor, the 3rd is a ½ lower when compared to the Major 3rd, we call this a flat 3rd.
Similarly, the 5th in the diminished is a ½ lower, therefore, it is a flat 5. The diminished triad, when compared to the minor, has a lowered 5 while the 3 is the same [flat 3], so we can call this minor flat 5 [this is sub-paralleling - comparing to the minor, or something else that has already been modified]. The diminished triad is indicated with a osign. Example, in C Major, the viio chord is Bo.
The augmented has a sharp 5, since its 5 has been increased from what is ‘normal’ [Major]. By increasing the 5, we have 8 half steps between the root and the 5th, rather than 7. The augmented triad first appears as a derivative in the Harmonic minor [chord space III]. The augmented triad is indicated by using a + sign. Example, in A Harmonic minor the III+ chord is C+.
We can build chords using other intervallic schemes, such as 4ths [quartal], but we don’t typically call them triads. We reserve the term triad for 3 tone chords built by superimposing 3rds.
Building 7 Type Chords
To build 7 type chords, we take EON one more step; we go every other note, until we have 4 tones.
There are different ways of understanding 7 chords. We think the most sticky way is consider the type of triad [Major, minor, diminished in a Major key], and the type of 7 [the Major 7 interval is 11 half steps away from the root, while a minor 7 type interval is 10 half steps].
We can also think in terms of types of 3rds [how far each tone is to the next]. Those numbers [5 to the 7] are on the graphic if you would like to integrate that info as well].
We figured out the triads in a Major key above. We will now take EON until we have 4 tones, rather than just 3. When we do this, we get 4 chord qualities from the key: Major 7, minor 7, Dominant 7, and minor 7 flat 5. The m7b5 is also known as half-diminished. I & IV become Major 7′s, the V becomes Dominant 7, the ii, iii, and vi become minor 7′s, and the vii chord becomes min7b5.
We can see these types of chords written in a number of ways. Our preferences are on the graphic & first in each, but here are some others…
- Major 7 = Maj7, Ma7, M7, 7
- minor 7 = m7, min7, -7
- Dominant 7 are written just one way: the root + 7 [e.g. G7]. In chord symbols, the 7 means that the 7 is 10 half steps away from the root [as in the minor 7 and min7b5 as well - the little m is for the triad, the 7 is for the type of 7].
- minor 7 flat 5 = m7b5, min7b5, -7b5, or as half-diminished