# Tuesday Wisdom: Modal Symmetry

artist: Misc date: 04/24/2012 category: ug news
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You know how when you divide diatonic scales into three note chunks, there are only 3 shapes you'll ever encounter? Shape 1: whole step whole step. Shape 2: whole step half step. Shape 3: half step whole step. Examples on the B string in the key of D:
``` |Shape 1  |Shape 2  |Shape 3  |
B|3--5--7--|5--7--8--|7--8--10-|
D  E  F# |E  F# G  |F# G  A  |```
There are no other three note shapes within diatonic scales. There is a symmetry to these three note chunks that I noticed a few years ago, but it never occurred to me at the time that the symmetry applies to the entire group of scales/modes. I was practicing these three note shapes when I noticed that I wasn't as fluent with Shape 1 as I was with the others. I wondered if it were possible to play the entire scale using that shape alone. It turned out that it was. Like this:
```|---------|---------|---------|---------|---------|---------|10-
|---------|---------|---------|---------|8--10-12-|10-12-14-|---
|---------|---------|---------|7--9--11-|---------|---------|---
|---------|5--7--9--|7--9--11-|---------|---------|---------|---
|5--7--9--|---------|---------|---------|---------|---------|---
|---------|---------|---------|---------|---------|---------|---
|D  E  F# |G  A  B  |A  B  C# |D  E  F# |G  A  B  |A  B  C# |D```
As you can see it was necessary to overlap part of the scale in order to play everything using shape 1. It's impossible to play the whole scale using shapes 2 and 3, even if you overlap. It is possible however to almost play the whole scale using just one of the patterns 1, 2, or 3, provided you use a "connecting note". Here's Shape 1 again, but this time using the connecting note G rather than an overlap.
```D Ionian
|---------|---|---------|---------|---|---------|10-
|---------|---|---------|---------|8--|10-12-14-|---
|---------|---|---------|7--9--11-|---|---------|---
|---------|5--|7--9--11-|---------|---|---------|---
|5--7--9--|---|---------|---------|---|---------|---
|---------|---|---------|---------|---|---------|---
|D  E  F# |G  |A  B  C# |D  E  F# |G  |A  B  C# |D```
Shape 2 using connecting note A.
```E Dorian
|---------|---|---------|---------|---|---------|12-
|---------|---|---------|---------|10-|12-14-15-|---
|---------|---|---------|9--11-12-|---|---------|---
|---------|7--|9--11-12-|---------|---|---------|---
|7--9--10-|---|---------|---------|---|---------|---
|---------|---|---------|---------|---|---------|---
|E  F# G  |A  |B  C# D  |E  F# G  |A  |B  C# D  |E```
Shape 3, connecting note B.
```F# Phrygian
|---------|---|---------|---------|---|---------|14-
|---------|---|---------|---------|12-|14-15-17-|---
|---------|---|---------|11-12-14-|---|---------|---
|---------|9--|11-12-14-|---------|---|---------|---
|9--10-12-|---|---------|---------|---|---------|---
|---------|---|---------|---------|---|---------|---
|F# G  A  |B  |C# D  E  |F# G  A  |B  |C# D  E  |F#```
Look at the above 3 tabs. Notice the symmetry. The connecting note is always the 4th degree, and it always comes after 2 repetitions of the shape. For the Lydian mode we need to return to shape 1. The symmetry elements are the same.
```G Lydian
|---------|---|---------|---------|---|---------|15-
|---------|---|---------|---------|13-|15-17-19-|---
|---------|---|---------|12-14-16-|---|---------|---
|---------|10-|12-14-16-|---------|---|---------|---
|10-12-14-|---|---------|---------|---|---------|---
|---------|---|---------|---------|---|---------|---
|G  A  B  |C# |D  E  F# |G  A  B  |C# |D  E  F# |G```
So what about the remaining 3 modes, Mixolydian, Aeolian, and Locrian? They have symmetry, but they use the 7th degree as a connecting note. At this point, to keep perfect symmetry of modes, I'm going to group the modes into two groups of four: [Ionian, Dorian, Phrygian, Lydian] and [Mixolydian, Aeolian, Locrian, Ionian]. This is because the number 7 has no symmetry, but 8 does. So to demonstrate perfect symmetry, we're treating the modes as an octave, D Ionian to D Ionian. The first group uses the 4th degree as a connecting note, the second uses the 7th. This means that the Ionian mode can use either the 4th or 7th as a connecting note, the only mode that can do this. Both groups use Shape 1, Shape 2, Shape 3, Shape 1. Look at the below table.
```  Shape.1     Shape.2  Shape.3   Shape.1   Connecting note
[Ionian     |Dorian  |Phrygian |Lydian ] 4th degree
[Mixolydian |Aeolian |Locrian  |Ionian ]| 7th degree```
Here are the remaining 4 tabs for group 2.
```A Mixolydian
|---------|---------|---|---------|---------|---|---
|---------|---------|---|---------|---------|8--|10-
|---------|---------|---|---------|7--9--11-|---|---
|---------|---------|5--|7--9--11-|---------|---|---
|---------|5--7--9--|---|---------|---------|---|---
|5--7--9--|---------|---|---------|---------|---|---
|A  B  C# |D  E  F# |G  |A  B  C# |D  e  F# |G  |A```
```B Aeolian
|---------|---------|---|---------|---------|---|---
|---------|---------|---|---------|---------|10-|12-
15--------|---------|---|---------|9--11-12-|---|---
|---------|---------|7--|9--11-12-|---------|---|---
|---------|7--9--10-|---|---------|---------|---|---
|7--9--10-|---------|---|---------|---------|---|---
|B  C# D  |E  F# G  |A  |B  C# D  |E  F# G  |A  |B```
```C# Locrian
|---------|---------|---|---------|---------|---|---
|---------|---------|---|---------|---------|12-|14-
|---------|---------|---|---------|11-12-14-|---|---
|---------|---------|9--|11-12-14-|---------|---|---
|---------|9--10-12-|---|---------|---------|---|---
|9--10-12-|---------|---|---------|---------|---|---
|C# D  E  |F# G  A  |B  |C# D  e  |F# G  A  |B  |C#```
```D Ionian (with 7th degree connecting note)
|---------|---------|---|---------|---------|---|---
|---------|---------|---|---------|---------|14-|15-
|---------|---------|---|---------|12-14-16-|---|---
|---------|---------|11-|12-14-16-|---------|---|---
|---------|10-12-14-|---|---------|---------|---|---
|10-12-14-|---------|---|---------|---------|---|---
|D  E  F# |G  A  B  |C# |D  E  F# |G  A  B  |C# |D```
The final bit of symmetry to point out Is that even though the 2 groups use different scale degrees as connecting notes, they still use the same notes, G, A, B, C#, in the same order. D Ionian/A Mixolydian (G), E Dorian/B Aeolian (A), F# Phrygian/C# Locrian (B), G Lydian/D Ionian (C#). At the moment I'm very much into moving away from these kinds of set scale patterns when playing actual music. I believe it's much more beneficial to know the fret board from the point of view of individual tones, and how they relate to the chord over which you're playing. I just thought this symmetry was interesting, and the exercises themselves were more to do with finger practice than soloing. So if you do use these patterns, remember that memorizing such fret board shapes can limit you to a kind of mindless playing. By Chris Flatley
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