My purpose here is to compare the melakarta system of ragas to my own system of enumerating seven note scales to see where they intersect, and to use the melakarta system’s built-in measure for scalar “brightness” to assess the various characteristics of the 7NS of which I am curious.
Background:
The melakarta ragas are a collection of 72 scales based upon a combinatoric system which enumerates them. This system was devised by Raamamaatya, in an effort to develop a classification scheme for the rich variety of scales present in South Indian classical music(referred to as Carnatic music). There is a rich history here of which I am ignorant. Wikipedia might enlighten you more on the subject of the history of these ragas.
These scales have been a source of tonal exploration for many musicians, including Miles Davis and John Coltrane.
I started messing with these scales during high school after a guitar teacher showed them to me, and they may have been a source of my inspiration to delve into the realm of pitch and tonality so deeply.
How the Melakarta System Works:
Out of seven scale degrees, two are constant: the Root and perfect Fifth.
The fourth scale degree can be a Perfect Fourth or Sharped Fourth
As for the rest of the scale degrees, there are separate rules to which two pairs of scale degrees adhere.
The Second and Sixth may be minor(b2, b6), Major(2, 6), or Augmented(#2, #6).
The Third and Seventh may be diminished(bb3, bb7), minor(b3, b7), or Major(3, 7).
Any combination of the above seven degrees is allowed, yielding 72 scales.
They are arranged and numbered in terms of brightness(from darkest to brightest) based on how far flatted each scale degree is, with each scale degree weighted differently in this consideration.
The order of importance for rating scalar brightness goes as follows:
- Scale Degree 2
- Scale Degree 3
- Scale Degree 6
- Scale Degree 7
- Scale Degree 4.
This means that if I am comparing two scales, but one has a flatter 2nd than the other, than it doesn’t matter what the rest of the scale degrees are, because the flatter two holds greater weight in determining brightness than all the rest.
It should be noted that such a system of measuring brightness is one-dimensional, and insofar as that, it does not accurately reflect that complex interplay of consonance and dissonance between the various pitches in a pitch set.
Comparison to 7NSs:
Those melakartas that were not found in my collection of 7NSs were grayed out.
If we distill the list down to only those that are well-balanced 7NSs, we get this collection of 40 scales:
In so doing, we can consider these to be the 40 well-balanced modes derived from my system, with the exclusion of those two scales in my system with flatted 11ths.
Below you will see these scales grouped by their respective parent scales:
Conclusion:
The melakarta system and my own have significant overlap, though the melakarta system is more inclusive than my own. This is evident in the fact that it involves many of the same constraints as my own system, but also allows for scales with three halfsteps in a row, or with steps four semitones wide.
However, melakarta system does not account for every scale in my own system. It lacks those melodic minor scales with b11ths. (Melodic minor b11, Melodic minor b9 b11)
The melakarta’s brightness metric organizes the various modes of the same parent scales with disregard for the fact that they are part of the same intervallic structure, and in this way it is lacking. However, the melakarta organization scheme reveals relationships between scales in ways that would not be as obvious if one were to classify scales by their parent mode as in my approach.