Comments on "A Biological Rationale for Musical Scales"

On 03 December 2009, PLoS ONE published an enlightening new study [Gill2009] which attempts to provide a biological rationale for musical scales that are used across various cultures. The gist of its conclusions is

... the component intervals of the most widely used scales throughout history and across cultures are those with the greatest overall spectral similarity to a harmonic series.

However, an initial cursory look suggests that this conclusion doesn't hold for many of the राग्s commonly employed in हिंदूस्तानी music. I submitted my initial opinion and other observations as comments on the paper [Kamath2009].

This post is a broader treatment based on those original comments.

Thoughts and Comments

Notes in a Melodic Context

While Indian music is tonal, it is also strongly dependent on the intervallic distance between successive notes. As a consequence, a melodic sequence like

minor tone (10:9) * semitone (16:15)

yields a rather flat minor-third (32/27) which is missing in Table 1 [Gill2009] because its percentage similarity value is 6.7%.

A very common note 45/32 does not appear in Table 1 [Gill2009]. While 45/32 may have a low percentage similarity value (5.3%), it attains a strong position in the scale due to the melodic context imposed by its neighbours (invariably notes like a rather flat third or flat sixth); e.g. राग् मियाँ की तोड़ी.

There is a whole host of Sharp Fourth notes that are missing in Table 1 [Gill2009]: 25/18, 45/32 (discussed above), 64/45, and 36/25. These notes can have strong positions in a scale depending on melodic context.

Intervals Smaller than Semitone
Some smaller intervals (like 25:24 which occurs between the 6/5 and 5/4 notes) are important in melodic music, even though their percentage similarity values are low (8% for 25:24). These do not show up in Table 1 [Gill2009] either.

In fact, choosing the top 60 intervals has caused quite a few intervals smaller than 100c to be dropped!

Percentage Similarity Metric vs. Melodic Music

Merely using the percentage similarity as a metric suggests that the 27/20 note (8.5%) is more important than, say, 45/32 (5.2%). However, in my opinion, no Indian scale would use 27/20 as a position of rest as it would be construed as a mistuned fourth!

Pentatonic राग्s and a Postulate for हिंदूस्तानी Music
Some very popular pentatonic राग्s don't end up in Table 2 [Gill2009]. For e.g., consider the simple but powerful राग् बैरागी भैरव् (Southern रेवती):

1/1 16/15 4/3 3/2 16/9 2/1

The percentage similarity value comes out to be 38.26% well below the first 50 scales of Table 2 [Gill2009].

Or consider राग् कलावती, another popular and immensely pleasing राग्:

1/1 5/4 3/2 5/3 16/9 2/1

with percentage similarity value 35.46% - once again not in the top 50.

More surprisingly, राग् माल्कौँस्:

1/1 6/5 4/3 8/5 16/9 2/1

has a percentage similarity value of 39%. As a result, it does not occur in Table 2 [Gill2009] either even though it's one of the more popular pentatonic राग्s in practice.

Similar thoughts apply for other pentatonic राग्s employed in Indian music.

It seems incongruous to me that a vast majority of the scales listed in Table 2 [Gill2009] are not really encountered in any musical system, while quite a few that are very popular (at least in हिंदूस्तानी music) fall below the 40% percentage similarity value.

The only way to explain this discrepancy may be that in melodic systems the overall percentage similarity of the scale is not as important as the immediate intervals that are used in transitioning from one note to another.

Given this, I'm tempted to posit that in हिंदूस्तानी music, when moving from one note to another (a pre-defined musical interval away), preference is given to that specific intervallic ratio which has a higher percentage similarity metric (per Table 1 [Gill2009]) - though this preference may be overridden by the overall melodic context.

Comment on South Indian राग्s
Finally, many South Indian Melakartas (generating scales) would automatically be disqualified under the percentage similarity criterion because often two or more semi-tonal intervals occur in sequence bringing down the overall percentage similarity of the scale. e.g. 6 Melakarthas each in the Indu Chakra, Rishi Chakra, Rutu Chakra, and Aditya Chakra (i.e. a total of 24 Melakartas) some of which are very popular even now (for instance, राग् नाट्टई).

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References

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[Gill2009] Gill, Purves, "A Biological Rationale for Musical Scales", PLoS ONE 4(12):e8144, 2009.
doi:10.1371/journal.pone.0008144

[Kamath2009] Kamath, "Comment from the Perspective of Indian Music", Comment on "A Biological Rationale for Musical Scales", PLoS ONE 4(12), 2009.

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