[intro]

Ok, before you all get perplexed by that title and skip this article, let me state that the fundamentals in this article are well within the reach of musicians with very little music theory background, although the more you have the better. Many articles on theory have been written such as the one by Aahz in the last audiofile. I encourage you all to seek out these articles and study up. This article will also make references to a song I wrote called "To the Sky" on many instances. This is not shameless self- promotion, in fact its an older tune, but it contains most of the elements expounded upon here all in one place. To get this tune go here.

And now, lets get started.

[what is a symetrical scale or chord?]

There are two definitions of a symetrical scale. One of them states that a symetrical scale is an equal division of an octave into parts. Most of you are probably familiar with the Major and Minor scales and you know that they are made up of a mixture of WHOLE steps and HALF steps... therefore these are NOT symetrical because the parts within the octave are different sizes. Going by this definition here are some symetrical scales:

CHROMATIC SCALE: A scale comprised of 12 half steps (ie. all the white and black notes on the keyboard). There is only one chromatic scale, although the notes within the scale can have different names (meaing F# can also be Gb, or Eb can be Fbb, etc...) Here it is:

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

#1- C-D-E-F#-G#-A#
#2- C#-D#-F-G-A-B

FULLY DIMMINISHED 7th CHORD: This chord is comprised of 4 minor3rds (a minor third is the interval formed by 3 half steps, like A-C). Its probably called a chord rather than a scale because it was built out of tertian harmony (chords based on stacking 3rds), but it is symetrical, and very important to our later discussions. There are three of these chords, although the notes within the chords can have different names. These are important!

#1- C-D#-F#-A  (note that correct tertian labeling would be C-Eb-Gb-Bbb :)
#2- C#-E-G-A#
#3- D-F-G#-B

AUGMENTED CHORD: As you can probably see how this sequence is going, this chord is formed by 3 major3rds (a major third is the interval formed by 4 half steps). Its a symetrical chord, but is actually a subset of the whole tone scale, so I won't go into it, but you can for practice if you'd like. As you may guess there are 4 types. An example of its usage can be found in the tune "Journey of Knowledge" by Spyder).

TRITONE: This is just a di-ad actually, but its the last way to symetrically split up an octave so I mention it for completeness. Its defined as the interval formed by 6 half steps. For example C-F# or D-Ab, etc.

Now recently some theorists have expanded the idea of the symetrical scale to include any scale that is symetrical within its self. That may sound confusing, but if you think about it as meaning the scale has no begining or ending it might help. For example, you can play a major scale and you should always be able to tell where it begins and ends (ie. the keynote), but if you were to try the same thing with a chomatic scale you would find that it doesn't matter where you start or stop, because its symetrical. Here is a favorite scale of mine that fits into this category.

OCTATONIC : A scale comprised of an alternation of half steps and whole steps. It may start with either the half step first or the whole, it doesn't matter. Because of this fact there are three types, although the names of the notes in the scales may change. Please note how they are closely related to the fully dimminished 7th chord.

#1- C-D-D#-F-F#-G#-A-B  (whole-half)
#2- C-C#-D#-E-F#-G-A-A# (half-whole)
#3- C#-D-E-F-G-G#-A#-B  (half-whole, other subset)

[ok great, now how do I use them?]

Some of you might be saying now "who cares? these scales sound weird! why don't I just write whatever I want and be weird?". Ok well there are very good uses for these scales, but for this article I will only go over the four that I think will be of most use to you in practical tracker compositions.

[tonal ambiguity]

Now since the quality that all of these scales have in common is no starting or ending point, we can use that to our advantage- we can define our own or just leave it up to the listener. If you take a whole tone scale and play around with it, you will find that it has a 'floating' quality because you never know where its gonna end. That might be a good thing if you are going for a dreamscape or some simmilar ambient mood. The other way you can use it is if you want to go note X to note Y in a trasition but you have funky harmonies going on to build tension or whatever. If both notes X&Y fall within a common whole tone scale you can use that scale to connect them without influencing the harmonic movement that is going on around it. For an example check out "To the Sky", the transition going from pattern 14 to 15 (hex). You can also use the chromatic scale very effectively as a transition scale when you don't want to influence the underlying harmony with your lead.

[tone clusters]

A tone cluster, also known as a sound mass, is a group of closely spaced notes used for their effect as a sound rather than a particular harmonic function. For example C-C#-D. See "To the Sky" patterns 6 through 13 (hex) to see how I used this tone cluster. For a tone cluseter to be successful you need to do two things... USE DYNAMICS, and USE TENSION/RESOLUTION. By tension/resolution I mean that these tone clusters create an awful lot of tension because of their inherent disonance which you can effectively harness if you follow the tone clusters by something more consonant (a major or minor chord perhaps, or if you want to stay ambiguous, at least an open fifth, like C-G).

[tonal teasing]

One of the things I love doing is taking your lead line and having it play in the octatonic scale which is ambiguous, but keeping your accompaniment going in a tonally functional way. You have to be pretty smart in this or you will just end up with a big disonant mess. Check out "To the Sky" patterns 15 to 16 (hex) for this.

[***modulation***]

Ok this is the coolest part of this article so I hope you are paying attention. You have to know a little about fuctional harmony for this to make sense, so go find Vegas a bug him for music lessons (hehe). In order to do this modulation trick we are going to take advantage of the dimmished chord's symetrical structure. If you will recall from you music theory, in a major scale there is a fully dimmished chord built on the seveth degree (in the key of C major this would be B-D-F). Also in minor scales this is the chord built on scale degree two (in C minor this would be D-F-Ab). Ok now these are the only chords we are gonna be dealing with. Now, I appologize to those that are unfamiliar with functional harmony roman numerals, but its the best way to describe this next part. Basically the number tells you which degree of the scale the chord is built on.

Western tertian functional harmony shows us that in a major scale the (vii) (dim) chord has a STRONG tendency to move to (I) and in a minor scale the (ii) (dim) chord has a tendency to move to (V) (which in turn would move to [i]). So lets look at how this works with chords. Note that I've moved the order (or inversions) of the notes around in some cases to produce better voice leading. Also whenever I have written (dim) this is to mean a fully dimmished 7th chord, and should not be confused with half dimmished 7th, or just a plain dimminished chord. Its the one we've been talking about (4 symetrical notes).

       B          C                      B      B     C
       Ab         G                      Ab     G     G
       F          E                      F      F     Eb
       D          C                      D      D     C

C:   vii(dim)     I          cmin:   ii(dim)    V7    i

Ok, now to the fun. Since the two dim. chords we've talked about here are symetrical there's no way for the ear to decide what the "root" of the chord is. Sometimes in a chord progression its pretty obvious (like the ones above), but you can usually trick the ear depending upon which note you put in the bass. I don't know if you see it yet, but this can become your hamonic gateway to numerous modulations (which by the way, I don't think there are enough of these in tracks I hear). This diminished chord you use is going to become a PIVOT chord. For example, look at the C minor progression listed above. Lets say that instead of resolving to (i) like I did up there I wanted to modulate to EbMajor. We would just do this:

         Eb   Eb   F     D        Eb 
         C    C    C     B        Bb 
         G    Ab   Ab    Ab       G
         C    Eb   F     F        Eb 
cmin:    i    VI   iv   ii(dim)
                Ebmaj:  vii(dim)  I   

Ok, if you can follow that modulation where the diminished chord becomes the PIVOT chord (means it has fuctions in both of the tonal regions), then you are well on you way to becoming a modulating master. By using this method you can modulate from the key of Cmajor or Cminor to Ebmaj/min, F#maj/min (not recomended), and Amaj/min. If you really want to get fancy you can mix some half dimminished chords in there and be able to get to the other 16 keys without ever having to touch that boring circle of fifths :), but that is beyond the scope of this article.

[extro]

Well that is probably more information then you ever wanted to know about symetrical scales, but if you experiement with them some and PRACTICE I think you'll get very good results and perhaps add a new dimension to your tracking style. Please feel free to contact me if you have any questions about anything in this acticle you would like clarified, but *no* I do not conduct regular music theory lessons via email or irc. Also I'd be happy to hear your thoughts about this article or if you'd like to see further articles on contemporary music techniques or modulation.

[contact]

Spyder/NOISE (Kevin Dostalek)