# COMPREHENSIVE MODES w/ Science!!!!

by LydianAlchemist (May 07, 2011)

## MODES

*sigh* the modes... the big ball of confusion that ensnares many a eager student.

First to understand modes, we must understand intervals and chord scructure.

## INTERVALS AND CHORD STRUCTURE

The Western Scale:

There are 12 notes in standard western music.
The distance between any 2 given notes is measured by a distace we call an interval.
All notes starting from C are:
1C, 2C#/Db, 3D, 4D#/Eb, 5E, 6F, 7F#/Gb, 8G, 9G#/Ab, 10A, 11A#/Bb, 12B.

("#" is read aloud as "sharp" and means the note directly proceeding the given note.
For instance D# is the note directly above D, and is read aloud as "D sharp".
"b" is read aloud as "flat" and means, you guessed it, the note directly below a given note.)

Now let's briefly examine the C major scale.
It contains the notes: C, D, E, F, G, A, B.
7 notes derived from the 12 possible notes.
If you have never seen a piano keyboard, or cannot remember the pattern of white and black keys, here is a picture for reference.
Count every single key in the picture and you will arrive at 12, count all the white keys and you have 7, the remaining 5 are black notes.
The C major scale is comprised of all the white keys on a piano.

This is where things can become increasingly complicated. If you will turn your attention to the notes "c" and "d" in the picture. You will see a black note in between them.
That note has has 2 names; C# and Db. The reason it has 2 names, is becuase it can be indentified as the note directly above C, or directly below D. This depends on the context, which we will elaborate on later.

For the most part, intervals are named by their acsension. The distance between two notes directly adjacent eachother is called a "half tone" or a "semi-tone". The distance between 2 notes that have one note between them is called a "whole tone" or just "tone".
On a guitar, 1 fret would be a semi tone, and 2 frets would be a whole tone.
However, the way we name this distance in terms of intervals is not so simple.
C to C# is a half tone.(the note immeadietly right)
C to D is a whole tone.(2 notes right)
C to D# is one and a half tones, or 3 semi-tones.(3 notes)
Some people only count the white notes, but black notes are notes too! always include them.
Life in the music world would be much easier if all the keys were regular rectangles and all the same color, and instead of complicated names (C# and Db the same note?!?!), were given a number.
But in this moment we're not out to change the world, and once you grasp the principles, you can notate music however you please. :)

p.s. when 1 note has several names i.e. C# and Db, they are "enharmonically equivelient" this means that they sound the same in a sterile enviroment.

INTERVALS:

The notes of the C major scale can be numbered diatonically(meaning "progressing through tones)
Example: C is the 1st note, D is the 2nd..etc etc.
so
1C, 2D, 3E, 4F, 5G, 6A, 7B (at 8, C repeats, which is called an "octave" octo- meaning 8. Octopusses have 8 legs.)
We say E is the major third of C. The reason we say this is because it comes 3rd in the diatonic sequence of the "major scale", actually it is because the intervallic distance is a major third, we'll get into that later.
However, in terms of actual notes, it is 4th 1C#, 2D, 3D#, 4E.

All notes related to the major scale have an interval name given to them.
C to the same exact C = 0 semitones, a unison
C to D = 2 semitones, a major 2nd
C to E = 4 semitones, is a major 3rd
C to F = 5 semitones, is a major/perfect 4th
C to G = 7 semitones, is a major/perfect 5th
C to A = 9 semitones, is a major 6th
C to B = 11 semitones, is a major 7th
C to (the next highest) C = 12 semitones, is an octave or an "8th"

Why choose THIS arrangement of 7 tones to create a major scale? Why not Db instead of D? or Gb instead of G (keep in mind that names we give notes are inconsequential to their harmonic function)?
Brace yourself for some physics...

Sound is vibration, a string vibrates back and forth, moving the air molecules in the air, which bounce of eachother and move your eardrum back and forth, your brain interpretes these movements as sound.
The speed at which a string vibrates is measured in "frequency" or "hertz" abrreviated "hz".
Hz = cycles per second.
A string does not vibrate only back and forth, the motions of the string also cause the segments dividied by 1/2 the distance from end to end to vibrate at twice the hz! but at half the volume.
However the bulkiest loudest BASE/BASS(haha pun...) vibration is called the "fundamental", the other vibrations are called "overtones"
So a string moving at 440hz is also vibrating at 880hz but at half the volume.
Every note corresponds to a frequency, 440hz = A. 880hz is also an A but an octave higher.

If you have ever used harmonics before, you should know that the harmonic at the 12 fret (an octave) is the loudest and clearest one. On a string tuned to 440A, the harmonic would ring at 880hz. Twice the frequency, half volume.
When you use harmonics, you are muting all the overtones(you could say "undertones") and the fundamental beneath it.
So when you pluck an A string, it vibrates at 440 AND 880. When you use the 1st harmonic, it only vibrates 880.

Like I said before there are overtones, which is plural.
After the 1/2 distance ringing at 2/1 the hz of the fundamental, there is another overtone ringing at 3/2 the speed of the previous overtone, but half the volume. 3/2 is the same interval as a perfect 5th.
Eventually these overtones become inaudible, because their pitch becomes higher than that of the threshold of human hearing AND they lose volume as well, overtones are reponsible for the rich lush sound of most stringed instruments. You aren't just hearing one note, you're hearing infinite notes.

So a string vibrates at...:
a given hz = the fundamental
2/1 the fundamental = the 1st overtone
3/2 the 1st overtone = the 2nd overtone
3/2 the 2nd overtone = the 3rd overtone
3/2 the 3rd equals the 4th and so on and so forth.

The C major scale is built from the first 7 overtones, of... ironically... the F note...-.-

why the F?

Ascending harmonic 5ths, starting from F, give us the notes of the C major scale:
F - C - G - D - A - E - B
starting from C they give us
C - G - D - A - E - B - F# which is actually the notes of the C Lydian mode.
If we continue the series, we find that the F(the 4th note diatonically) note in major is the very last note of the harmonic series. The lower the overtone, the more stable it is.
Watch this video.
Without becoming too complicated, the reason the harmonically unstable F is chosen is because it is the perfect fifth BELOW C. Read further on in "chords" for a better explanation)
This video series will also be very insightful if you find my explanation complicated. However I would encourage you to refrain from reading it until you grasp most of this lesson.

Western theory is a much more complicated than it needs to be (or people like me make it that way.. ^_^), but like I said. Once you grasp the principles, you can make your own theory, and who knows, maybe some day it will become the accepted standard.

CHORDS

A chord is any combination of more than 2 notes played at one time (there is no such thing as a power "chord"). The most common chord is a 3 note chord called a "triad".
Stacking thirds is the most common way of chord building.
E is a third of C. and G is a third of E (AND the 5th of C). Because this chord (CEG) has 3 notes, it is called a "triad" chord. (tri - meaning 3. i.e triangle - meaning 3 sided)
1= C 1
2= D
3= E 3 is the diatonic 3rd of C
4= F
5= G 5 is a diatonic 3rd of E
6= A (A C major chord is made of the notes C E and G. (the 1st, 3rd, and 5th of the C major scale, Chords do not end at triads, if we continue stacking chords we get...:)
7= B 7 is the diatonic 3rd of G
8= C
9= D 9 is the 3rd of 7
10= E
11= F 3rd of 9
12= G

C - E - G is a C major triad
C - E - G - B is a C major seventh chord (because it has the 7th diatonic note)

In the key of C major, let's stack thirds starting on the 4th note.. F.
We get F A C. Which is another major chord.
Earler when we were studying the overtone series, I promised to explain why the F is chosen over F# even though it is more consonant. It is because if you use C as the point of origin, the most stable harmonic note is G. That is the perfect fifth ABOVE C. C is the perfect 5th ABOVE F.
F - C - G
or
F is to C, as C is to G.

Because F is a perfect 5th below C, and because the harmonic series is ascending 5ths, the F is the last in the series. EVERYTHIING IN MUSIC IS ABOUT TENSION AND RELEASE, DISSONANCE AND CONSONANCE, YING AND YANG. But before we can establish good and bad, up and down, ying and yang, we need a middle ground. The middle ground is the tonal center which all the notes are compared with. When something is dissonant, it wants to resolve. F is dissonant, but only when it is against a C. When F is against a Bb note, it is the exact opposite, because F is FIRST in the overtone series of Bb.

Let's try the thirds from the A note in a C major scale(C D E F G A B C).
A - C - E. This chord is a minor chord. The only difference between a major and minor chord is the 3rd.
A C MINOR chord would have the notes C - Eb - G. Notice the "b" flat! The distance from C to Eb is the same as the distance from A to C. That is 3 semitones.
* *
C - Db - E - Eb
A - Bb - B - C
* *
Earlier in this chart:
C to the same exact C = 0 semitones, a unison
C to D = 2 semitones, a major 2nd
C to E = 4 semitones, is a major 3rd
C to F = 5 semitones, is a major/perfect 4th
C to G = 7 semitones, is a major/perfect 5th
C to A = 9 semitones, is a major 6th
C to B = 11 semitones, is a major 7th
C to (the next highest) C = 12 semitones, is an octave or an "8th"

we only calculated the interval names for the white notes of a piano, only the "major" notes.
We can name the rest as such.
C to Db(or C#) = 1 semitone, we call this a minor 2nd, or a "diminished" 2nd. Because it's 1 semitone short of it's major cousin.
C to Eb(D#) = 3 semitones, we call this a minor 3rd, because it's 1 semitone short of a major third.
C to Gb(F#) = 6 semitones, we call this either an augmented 4th, because it's one semitone larger than a major 4th. Or we call it diminished 5th, because it's one semitone short of a "perfect" or "major" 5th.
C to Ab(G#) = 10 semitones, we call this an augmented 5th or a minor 6th.

many times, in terms of intervals, "minor" and "diminished" are interchangable. For the sake of simplicity, we won't get into that.

Let's build a chord on the G note, the fifth.
G - B - D.
This is also a major chord, because the distance from G to B is 4 semitones, a major 3rd.
There is something interesteing to take note of with the B note, especially when it's in a chord built on the fifth degree.
the B note is 1 semitone below the C. It is called a "leading tone", because when you play these notes. C, D, E, F, G, A , B and then pause... you will notice that your ear wants to hear the next note. The B pulls towards the C.

There is one more important concept to learn. We need to build a chord from the B note.
B - D - F.
Now this is another interesting chord... when we build chords by stacking thirds. We stack alternating major and minor thirds.
C to E is 4 semitones, E to G is 3, G to B is 4, B to D is 3.
4 3 4 3 4 3
4 = major third. 3 = minor third.
When we build minor chords we stack alternating thirds, but the first in sequence is a minor third and that changes the harmonic structure of the chord (the way it sounds).
3 4 3 etc..
But the point is.. with the 7th scale degree... our "B" note.. well:
B to D is a minor third. And D to F is ANOTHER minor third.
This creates a dissonant chord called a diminished chord.
B to F is a diminished fifth. Chords built from alternated thirds being stacked sound better than incestuous thirds.
homotonal or heterotonal.

the last type of triad is an augmented chord. This happens when two MAJOR thirds are stacked, as apposed to two minor ones in the case of a diminished chord.
A C augmented would have the notes:
C - E - G# (G# because it is the major third of E)

So in conclusion
C major = C - E - G
C minor = C - Eb - G
C diminished = C - Eb - Gb
and C augmented = C - E - G#

and
major 3 + minor 3 = perfect 5th
minor 3 + minor 3 = diminished 5th
and major 3 + major 3 = augmented 5th

With this knowledge we can build all our own chords.

Here is the most common chord progression in the entire world,in the key of C.
C - F - G
The C establishes the home base note, the F chord reaffirms that and leads into the G, the G has a stable root note, but has a leading tone as it's major third, the B. The B wants to pull back into the C.
Try it on your own instrument!! :)

## SCALE FORMULA

Now that we know intervals, we can start getting into scales and modes.
The C major scale is easy to work with because it has no "accidentals" or black notes.
But how do you know what notes to play if you play in a different key? like D major? or G major? or Ab major?
To do this we must delve into intervals further.

The distance from C to D is a whole tone, from D to E is another whole tone, from E to F is a half tone, F to G is a whole, G to A is another whole, A to B is another whole, and B to C is another half.
With this we have the pattern:
whole whole half whole whole whole half
or
w w h w w w h
with this formula you can build a major scale for any note.
Lets try building the D major scale!
D is the first note, then to fing the second scale degree we go a whole note above that.
D - D# - E is the 2nd scale degree
to find the third we go a whole above that as well.
E - F - F# is the third scale degree
then a half,
F# - G is the fourth scale degree
then 3 successive wholes.
G - G# - A(fifth) - A# - B(sixth) - C - C#(seventh)
then the last half returns us to the tonal center of D
C# - D
So the D major scale is:
D E F# G A B C#
1 2 3 4 5 6 7

1, 2, 3, 4, 5, 6, 7 is the scale formula that all modes are based off of.
When you keep counting past 7 you get the 2, 4, and 6 scale degrees. Like military time v.s. what we civilians use, you add 7 to the scale degree to get it's equivilent.
2 + 7 = 9
4 + 7 = 11
6 + 7 = 13
Why give them names beyond 7 or 8? what's wrong with 2, 4, and 6?
It's because when you are building chords, if you add too many notes in the lower registers, especially the 2 4 or 6 degrees, which come later in the harmonic series and are thus unstable. It sounds really muddy and crowded. So when building chords, musicians often place the 2, 4, and 6 notes an octave higher. Since these are placed an octave higher they are called "extensions". Chords with more than 3 notes are called "extended chords".

So a Cmaj9 chord has the notes C - E - G and D. D is the second scale degree, but add 7 to 2 and you get 9. Cmaj9.

Scale degrees are often given roman numerals, because no matter the key, working with ONE set of measurment is simpler.
I - II - III - IV - V - VI - VII and arabic number sets are already given to intevals. So we give scale degrees roman numerals to avoid confusion (doublethink anyone??)
This also allows easy application of chord progressions, instead of leaving us the problem of figuring out which note is the interval of what to who.
Cmaj - Fmaj - Gmaj can be written as I - IV - V
then we can apply it to any key we want :)

## MODES

RELATIVE MODES:

As you may or may not know, all modes can be derived from the notes of one scale.
example: C major scale: C, D, E, F, G, A, B

1st mode: C Ionian C D E F G A B which is the enharmonic equivelent of C major
2nd mode: D Dorian D E F G A B C
3rd mode: E Phrygian E F G A B C D
4th mode: F Lydian F G A B C D E
5th mode: G Mixolydian G A B C D E F
6th mode: A Aeolian A B C D E F G which is the enharmonic equivelent of A minor
7th mode: B Locrian B C D E F G A

now this is where I as many others used to be confused...
Why have modes at all? why have 7 different names for the same thing... Doesn't G mixolydian = C Ionian???
well here is an explanation to dissolve your confusion:
Have you ever seen the optical illusion of a duck that also looks like a rabbit? Depending on how you view it?
Here

This is how relative modes work, and how many jazz musicians view them as well:

Imagine that drawing as the C major scale...
If that unidentified animal was drawn floating in some water, surrounded by lily pads and frogs and fish, you would be much more inclined to see the "duck-iness" of it.
However, if you placed the animal in a grass field, with perhaps a cliche carrot in it's "mouth"(thank you loony tunes), you would favor the rabbit side of it.

Take this chord progression for instance:
Cmaj7 - Fmaj7 - G7
It's in C major, and you could very well play C major over the entire progression, and in fact, playing any of the modes of C major(D dorian, E phrygian etc..), you would still be playing the same notes of the C major scale.
However..., like the duck with it's long bill, or the rabbit and it's long ears, every mode has defining characteristics.Sometimes they are defined by the enviroment or "chords": In the middle of a lake the animal is a duck, in a grass field it's a rabbit.
Musically speaking, over an Fmaj7#11 chord, you would play F Lydian, because a #11, in a major mode context, strictly means Lydian. Because the #11 is the "color tone" of Lydian".

So...
bill is to duck, as #11 is to Lydian. And lake is to duck as Fmaj7#11 is to F lydian.

Relative modes all share the same parent scale/s, or the scale they were derived from.
C Ionian, D dorian, E phrygian, F lydian, G mixolydian, A aeolian, B locrian are ALL derived from the same parent scale of C major, because they all share the same notes: C D E F G A B.

PARELLEL MODES:

C Ionian: C to D is a major second.
E Phrygian: E to F is a minor second.

When we use parrelel modes, we play the modes all with the same tonal center.
In order to find out what notes to play, we have to determine the scale formulas of the modes.
remember the w w h w w w h pattern?
You need to use this to find out the scale formula of each mode.
D major scale formula = 1 2 3 4 5 6 7
D major notes = D - E - F# - G - A - B - C#
since we know D dorian has the same notes as C major we can compare the 2 scales.
D major = D - E - F# - G - A - B - C#
D Dorian= D - E - F - G - A - B - C
As we see the F which is third in the sequence is flattened, as well as the C# which is the 7th.
So we conclude that the Dorian scale formula is:
1, 2, b3, 4, 5, 6, b7

Now go get a pencil and paper and determine the scale formulas for all 7 modes. Use this chart as a reference:
1st mode: C Ionian C D E F G A B
2nd mode: D Dorian D E F G A B C
3rd mode: E Phrygian E F G A B C D
4th mode: F Lydian F G A B C D E
5th mode: G Mixolydian G A B C D E F
6th mode: A Aeolian A B C D E F G
7th mode: B Locrian B C D E F G A

-
-
-

Here are the 7 scale formulas with notes in the key of C:
Lydian = 1, 2, 3, #4, 5, 6, 7 - C D E F# G A B
Ionian = 1, 2, 3, 4, 5, 6, 7 - C D E F G A B
Mixolydian = 1, 2, 3, 4, 5, 6, b7 - C D E F G A Bb
Dorian = 1, 2, b3, 4, 5, 6, b7 - C D Eb F G A Bb
Aeolian = 1, 2, b3, 4, 5, b6, b7 - C D Eb F G bA Bb
Phrygian = 1, b2, b3, 4, 5, b6, b7 - C bD Eb F G bA Bb
Locrian = 1, b2, b3, 4, b5, b6, b7 - C bD Eb F bG bA Bb

The scale formulas allow us to see what the "color tones".
Color tones are what makes a mode different from any other mode. The diamond on the back of a diamond back snake is what makes it different from any other snake, you could say that diamond is it's "color" tone.

Lydian differs from major in it's 4th. it has a #4. Lydian is the only mode with a major third and a raised 4th.
Dorian is the only minor mode with a natural(major)6th. So in order to bring out the color of Dorian we would have to play the minor 3 to determing it's minor tonality, but also play the natural 6th to establish it's uniqueness.
In the case of relative modes however, this is not the case because the 3rd is already being played in the chord.

Lydian = #4 and the 3rd (the #4 is the enharmonic equivielnt of a b5, and if you don't play the 3rd somewhere, the ear could think it's Locrian because of the #4/b5)
Dorian = the natural 6 and the minor 3( Dorian is the only mode with a minor 3 and natural 6)
Mixolydian = the b7 and the major 3rd(this is the only major mode with a flat 7)
Phrygian = b2 and b3 (Phrygian is the only minor mode with a flat 2)
Locrian = b5 and b3( so as not to confuse the b5 for a #4 in Lydian)

in all these modes you will want to put emphasis on the 3rd scale degree and 5th.

Playing a b3 and perfect 5th would make the listener think "oh this is just another minor song... *sigh* boring"
but when you add the natural 6 of dorian, or the flat 2 of Phrygian, their ears will perk up.

Ionian is the exact same as the regular major mode, and Aeolian is the same as minor. They just have different names.
STRICTLY speaking they the same as any other mode, and every mode has color tones... but because these are the 2 most frequently used modes in all of western music, they do not really have easily percieved color tones. They do in a sense, but they don't have the exotic-ness of the 5 other modes.

Let me put it this way.. WITHOUT color tones, it would be physically impossible for anyone to determine what mode you were in. This is why they are important.

With parrelel modes you are staying with the same tonal center, with relative modes you are playing within the chord, essentialy viewing it as a "mini modulation". (modulation is going from one key/home base to another)

This can be a parrelel mode progression OR relative:
Cmaj7 - F#7
In parralel terms:
You would play C Lydian
Stressing the C as the home base, and the F# note.

In relative terms:
the main idea is playing according to the chord you are on.
on the first chord you could play C Lydian or C Ionian, on the 2nd you would play F# mixolydian. Stressing the root of the chord as your temporary home base, and the color tone of your chosen scale.

Relative modes is playing within your current chord and treating your chord as the tonal center. Even if all the chords were taken from the same scale.

Parralel modes is playing within the same tonal center, but changing your mode to acomodate the current chord, while keeping the integrity of your tonal center.

The chords determine whether or not it is duck season or rabbit season.
:)