jfulton.org: Music

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In the following discussion I would like to demonstrate a method that I use to come up with new musical ideas.

I will first demonstrate a few examples from the symmetrical diminished scale and then go through a few exercises that I did with the scale which helped me come up with the examples. The point of this discussion is not only to share phrases from the symmetrical diminished scale but also to demonstrate how new musical ideas can be found in any scale. To put it another way, it gives you a starting point to answer the question I've learned a new scale, but what do I do with it?. My approach is simply to practice the scale in multiple arrangements in order to discover new sounds.

(I am sorry if your browser window has to open wide to view this page completely. I normally try to use variable width pages to display content, however my ASCII Tab below requires the <pre> tag which might stretch things. )

Chapter I. THE IDEAS:

Here are some of my musical ideas:

(sym-dim-1.wav)

The tab below is actually arranged to be played an octave higher than what was recorded. There were also other alterations but what is below should give you an idea:

  four times 

-11---11-----------|-11---11-9---9-8----8-------------
---------13-----13-|-----------------------11----11---
----9--------------|----9------8----------------------
-------------11----|-----------------11-------10------
-------------------|----------------------------------
-------------------|----------------------------------

             four times
---------|---------------------|----------------------
-10---10-|-8----8--------------|----------------------
---------|---------11------11--|----------------------
----8----|---------------------|----------------------
---------|---12--------10------|----------------------
---------|---------------------|----------------------

I alter the fourth note in the first bar as I play the above to include the notes "B" from out of the scale as well as "C#" the octave of the fifth note. I chose these notes in order to lighten things up.

This next idea has a shifting meter, but in the end it can be seen as just 8 bars of 7. The main motif is in 7, but in the middle of the piece I add an extra note so that I play in 8 for a bar. I make up for this note at the end by subtracting a note, and as a result playing in 6. Since 6+8 is 14 which could be divided by 2 to get 7 again. You could say that the entire piece was simply in 7 with an accent shift.

(sym-dim-2.wav)

  three times
----------------|----------------0----
-------------4--|--------------4------
---3-5-----6----|----3-5-----6--------
----------------|---------------------
-4-----6-7------|--4-----6-7----------
----------------|---------------------
 1 2 3 4 5 6 7     1 2 3 4 5 6 7 8

  three times
----------------|------0---------------
-------------4--|--------7-------------
---3-5-----6----|----0-----------------
----------------|--4-------7-8---------
-4-----6-7------|----------------------
----------------|----------------------
 1 2 3 4 5 6 7     1 2 3 4 5 6   

This next example mainly involves some triads that I found in the symmetrical diminished scale. I'll talk more about chords within this scale later. The example is not complete, but I like the voicing of these chords and will find a use for them in the future. Here are the chords as arpeggios:

(sym-dim-3.wav)

---------|----------6-|---------|--------|----------0-
---------|----------7-|---------|--------|----------0-
---------|--------6---|------8--|------9-|-------11---
------8--|-----10-----|---11----|---13---|----14------
---12----|--6---------|-7-------|-9------|-10---------
-9-------|------------|---------|--------|------------

In the above example I play a B which is out of the scale on the last chord. I also have two extra notes in the second aprggeio which are not played in the recorded example but make for an interesting chord.

Chapter II. WHERE THEY CAME FROM:

I came up with the above ideas as a result of playing with the symmetrical diminished scale.

The symmetrical diminished scale can be played in a 3-note per string arrangement like this:

----------------------------------------8-9-11-
--------------------------------8-10-11--------
-------------------------8-9-11----------------
-----------------8-10-11-----------------------
---------9-10-12-------------------------------
-9-11-12---------------------------------------

(sym-dim-scale-2nds.wav)

I prefer to arrange my scales in 3 notes per-string patterns for consistent picking.

The notes of the scale in the above case are the following:

c# d# e f# g a a# c

Note that it is a 9-note scale as opposed to an 8-note scale, i.e. it takes 9 notes to complete an octave.

If we extend the scale into two octaves we can name the higher notes according to the common chord number convention (e.g Amin7/13):

1  2  3 4  5 6 7  8 | 9  10 11 12 13 14 15 16 |
c# d# e f# g a a# c | c# d# e  f# g  a  a# c  |

We can then use the above numbers to pull different arrangements out of it. These arrangements allow for certain note combinations which are interesting and may lead you to come up with new music (at least this is the case for me).

Here is the first arrangement that most people apply to a new scale:

3rds
1 3 2 4 3 5 4 6 5 7 6 8 7 9 8

----------------------------------------------
----------------------------------------------
----------------------------------------------
------------------------8----10--------------- et cetera
--------9----10-9-12-10---12------------------
9-12-11---12----------------------------------

(sym-dim-scale-3rds.wav)

Playing scales in thirds is pretty common. The following arrangements sound more interesting:

4ths
1 4 2  5  3  6  4 7 5  8  6  9  7 10 8

-------------------------------------------------------------8--9---11
-------------------------------------------------8-10----11-8-10--11--
-----------------------------------8----9----11-8-9---11--------------
------------------8----10----11-8----10---11--------------------------
--9----10----12-9---10----12------------------------------------------
9---11----12----------------------------------------------------------

(sym-dim-scale-4ths.wav)

The next arrangement has lots of tri-tones:

5ths
1 5  2  6  3  7 4 8  5  9  6  10 7 11 8 

-------------------------------------------------------------8---9---11-
-----------------------------------------------8---10--11------8--10----
------------------------------8----9-----11------8---9----11------------
--------------8---10----11-------8----10----11--------------------------
--10----12------9----10----12-------------------------------------------
9----11----12-----------------------------------------------------------

(sym-dim-scale-5ths.wav)

Here are some more arrangements that sound interesting. In the following example I try to make the notes sustain into each other as I reach the higher notes since it creates nice tensions:

6ths
1 6  2  7 3  8  4 9  5  10 6  11 7 12 8 

--------------------------------------------------------8--9---
-----------------------------------------8----10---11--------8-
------------------------8-----9----11------------8----9---11---
--------8----10---11-------------8----10---11------------------
--12------------9----10----12----------------------------------
9----11---12---------------------------------------------------

(sym-dim-scale-6ths.wav)

This arrangement forms a nice pattern for the fret-board hand:

7ths
1 7 2  8  3  9  4 10 5 11 6 12 7 13 8 

---------------------------------------------8--9---11-
---------------------------------8---10--11------------
------------------8----9----11--------------8-9---11---
--8----10----11----------------8---10--11--------------
----------------9---10---12----------------------------
9---11----12-------------------------------------------

(sym-dim-scale-7ths.wav)

Here is the last interesting arrangement:

8ths
1 8 2 9 3 10 4 11 5 12 6 13 7 14 8

-------------------------------------------8---9--11-
----------------------------8----10---11-------------
-------------8----9----11--------------------8--9----
--10---11----------------------8---10----11----------
----------------9---10---12--------------------------
9---11----12-----------------------------------------

(sym-dim-scale-8ths.wav)

The above (as well as any of these examples) could also be played as chords:

(sym-dim-scale-8ths-chords.wav)

9ths would be octaves (since this is a 9-note scale).

Re-arrange the arrangements:

You can alter these arrangements for new ideas. One nice change to the arrangement of the 7ths is to do a transposition of every other 7th. What I mean by this can be stated more clearly in the following example.

This is the arrangement for playing 7ths:

(1 7) (2  8)  (3  9)  (4 10) (5 11) (6 12) (7 13) (8 14) ...

What you see above is exactly what was shown for the example of 7ths, except I have grouped each 7th into a tuple with parentheses. The tupples picked out by the phrase "every other 7th" are (2 8), (4 10), .... If I were to transpose the first of these tupples I would have (8 2) instead of (2 8). If I did this to every other tupple I would have the following:

(1 7) (8  2)  (3  9)  (10 4) (5 11) (12 6) (7 13) (14 8) ...

Which sounds like this:

(sym-dim-scale-7ths-invert.wav)

Here is the tablature for the above example:

---------------------------------
---------------------------------
---------------8-----9-11-------- et cetera
--8-10------11-------------------
----------------9-10------12-----
9------11-12---------------------

Chord Scales:

We normally build triads out of a scale by choosing every other note. For example, consider the c-major scale:

c d e f g a b c 

We would chose the following to build our chord-scale:

c e g  - c maj
d f a  - d min
e g b  - e min
f a c  - f maj
g b d  - g maj
a c e  - a min
b d f  - b dim

We could also chose other triads based on other arrangements. In the above example we pulled out 7 triads by using "every other note". There are a lot more posbilities however, just as there is more to do with a scale than just play every other note (as we saw in the examples above).

The triads in the third example from Chapter 1 are not based on every other note (which would be 1 3 5) but is based on 2 7 8 and 1 7 8.

To be exact, the amount of triads that we could choose for the Diatonic scale is 56 (the binomial coefficient of 8 choose 3). The symmetric diminished scale is a 9-note scale so we can choose even more. 84 triads (the binomial coefficient of 9 choose 3) to be exact.

Chord scales in the diminished scale are interesting. Depending on how you build half of your chords, you can flatten the 3rd to switch between major, minor, and also flatten the 5th to switch to diminished and still stay in key (i.e. within the scale).

Here is a chord scale based on the symmetrical diminished scale (note that commas are used to denote alternatives):

C maj, C min, C dim, (C maj dom 7) 
C# dim
D# maj, D# min, D# dim, (D# maj dom 7) 
E dim
F# maj, F# min, F# dim, (F# maj dom 7) 
G dim
A maj, A min, A dim, (A maj dom 7) 
A# dim

I included the "maj dom 7" chord as an alternative to show the possibility of adding an extra note to go beyond the triad (the "maj dom 7" chord is found often in the blues and is also known as just a 7th chord by some musicians). I labeled it as "maj dom 7" to avoid confusion of it being thought of as a maj 7 chord (for example: C E G B-flat is C maj dom 7 and is not C maj 7 which would be C E G B).

When soloing over any of the above chords you can use the symmetrical diminished scale to "take it out".

About these examples:

All of the above examples were made with Free Software. The recordings were made with a Debian GNU/Linux system that is using the WavTools package version 1.3 (written by Colin Ligertwood). The WavTools package contains the command "wavr" which records whatever is input to the sound card to hard disk as a wav file. I plugged my guitar into a pre-amp and then directly into my on-board sound card of my PC (an Athlon XP 2000+) to make these recordings. I then typed "wavr -f x.wav -s l" (for any wav file x) and started playing.