Comparison of Qualities
Okay, since we can see that major and minor scales are truly relative, how about the other two qualities? These cannot extend to heptads until you alter them.
Now let's see them:
DIMINISHED VERSUS AUGMENTED
The diminished, following the Tertian rule, cannot be extended beyond the tetrad (7ths). This is because its next interval will be the octave.
This rule exposes lots of things. Firstly, it exposes how you extend the number system, limiting the number system to 13 notes, which means there's nothing like 14th or 15th chords/numbers.
Secondly, it shows that in octave extension, you merely add one octave of the major scale and one octave of its relative minor scale.
If you look at the notes, you will see that the unique notes of the major scale are just spread out, so 2 is the same as 9, 4 is the same as 11, 6 is the same as 13, just the next octave of it.
Now let's see them:
DIMINISHED VERSUS AUGMENTED
The diminished, following the Tertian rule, cannot be extended beyond the tetrad (7ths). This is because its next interval will be the octave.
This rule exposes lots of things. Firstly, it exposes how you extend the number system, limiting the number system to 13 notes, which means there's nothing like 14th or 15th chords/numbers.
Secondly, it shows that in octave extension, you merely add one octave of the major scale and one octave of its relative minor scale.
If you look at the notes, you will see that the unique notes of the major scale are just spread out, so 2 is the same as 9, 4 is the same as 11, 6 is the same as 13, just the next octave of it.
In relation to chords, the diagram also shows the extent to which you can extend your chords, which is heptads. Please note that this is the major scale, so you take the same formula for the minor scale as well. These are the two primary scales of which nearly most scales fall under.
Now let's switch back a bit and continue with the diminished versus augmented. The diminished, following the Tertian rule, cannot be extended beyond the tetrad (7ths). This is because its next interval will be the octave. If you pick ANY note, and count minor thirds up, you will only do it thrice before you arrive back at the same note you started with in the octave e.g. C»Eb»Gb»A. If you continue, you'll only end up at C again. So we can now say our diminished chord can only extend once to become a tetrad.
Now let's switch back a bit and continue with the diminished versus augmented. The diminished, following the Tertian rule, cannot be extended beyond the tetrad (7ths). This is because its next interval will be the octave. If you pick ANY note, and count minor thirds up, you will only do it thrice before you arrive back at the same note you started with in the octave e.g. C»Eb»Gb»A. If you continue, you'll only end up at C again. So we can now say our diminished chord can only extend once to become a tetrad.
But this is not the sweet/fun part
This is: you only have to learn 3 diminished 7 chords all over the keyboard.
You see the 4 notes we just used? They ALL share the same diminished 7 chord. And invariably, the same scales. Interesting isn't it? Both diminished scales and half diminished scales.
Incredible!
So what are you saying Harold? I'm saying that unlike the major and minor scales and chords that you need to learn all 12 of them uniquely (with a simple principle of course), you only need to learn 3 when it comes to the diminished scales and chords.
And how do you know the 3? Easy!
We just covered four notes sharing the same scale and chords. We have 12 keys. 12 / 4 = 3. So 3 is the magic number.
Pick another note you haven't picked like C#, and do the minor third count again from there. You'll have another four notes related.
This is: you only have to learn 3 diminished 7 chords all over the keyboard.
You see the 4 notes we just used? They ALL share the same diminished 7 chord. And invariably, the same scales. Interesting isn't it? Both diminished scales and half diminished scales.
Incredible!
So what are you saying Harold? I'm saying that unlike the major and minor scales and chords that you need to learn all 12 of them uniquely (with a simple principle of course), you only need to learn 3 when it comes to the diminished scales and chords.
And how do you know the 3? Easy!
We just covered four notes sharing the same scale and chords. We have 12 keys. 12 / 4 = 3. So 3 is the magic number.
Pick another note you haven't picked like C#, and do the minor third count again from there. You'll have another four notes related.
Pick a third time (by now, you have picked 8 notes and are left with 4), and do the same count, and you have the last set of notes that are related.
We can also see the Augmented in the same light. The Augmented quality cannot be extended beyond the triad following the Tertian rule, unless it gets altered. Adding another Major 3rd interval will only lead back to the octave. If you pick any note and count Major 3rd intervals, you will only do that twice before you end up at the octave e.g C E G#.
The fun part about this particular quality is that these three notes we just used all share the same augmented chord, and at the same time, the same augmented scale [played in different modes].
You see that?
So for the augmented, you have only to learn four augmented scales and chords. We have 12 keys. 12 / 3 = 4. So 4 is the magic number.
Pick another note like let’s say D, and perform the Major third count again from there. You’ll have another 3 notes related…and so on, in that sequence till you figure out the 4 unique sets.
You see that?
So for the augmented, you have only to learn four augmented scales and chords. We have 12 keys. 12 / 3 = 4. So 4 is the magic number.
Pick another note like let’s say D, and perform the Major third count again from there. You’ll have another 3 notes related…and so on, in that sequence till you figure out the 4 unique sets.