Friday, October 29, 2010

Mood and Notes (Part 2)


Prior Reading

  1. The Holy Grail of Music
  2. Swars and emotional response
  3. Musical nuances and emotional response
  4. Moods and Notes (Part 1)

Question

Why is it that certain notes create an unstable mood while others create a stable mood?

Answer

Before we go any deeper, let us state some observations. One note is always stable if it is sustained without change of frequency. Also, any note is stable, if there are no other notes in the background. For this discussion, let us assume that there is a continuous base note in the background. All notes will be relative to this base note.
  • A note that matches in frequency with another note (usually played/sung with a different timbre) also creates stability. As an example, a singer singing Sa, that is in perfect tune with that of a Tanpura (drone) creates stability in the listener.
  • A note that's not correctly sung or played (out-of-tune or besur) generates instability, sometimes even to the point of pain!
  • Certain notes appear to be harmonious with a given note. Examples include Sa:Pa, Sa:Ma, Sa:Ga, etc.
  • Certain notes appear to be discordant with a given note. Examples include Teevra Ma:Sa, Komal Re:Sa, Shuddha Ni:Sa, Komal Dha:Sa, etc.

Relationship between two notes

One note in isolation is not interesting. When two notes are taken together, one acting as a background base note, the other acting as the foreground, lead note, then we have music. Someone said "Anyone can draw one dot on a canvas. To draw the second dot, you need to be an artist".

Let us analyse the relationships between two notes in an octave. One of the fundamental relationship is the ratio of frequencies.

Ratios

  • The same note played together is the best match. Ratio of 1:1!
  • Certain notes appear to be the "same note, just higher or lower". The frequency of the higher "same note" is 2:1 and that of the lower "same note" is 0.5:1. These notes have the highest stability relative to each other -- indeed, they seem to be the same note!
  • The midpoint of an octave appears to have the next best stability. This note is at a ratio of 3:2 and is called Pa.
  • If we shift Pa to the lower Sa, then the Upper Sa is shifted to a frequency of 4*Sa / 3. This Swar, with a ratio of 4:3 to Sa, is called Ma. 
  • Notes that have simpler ratios with a given base note's frequency are also perceived as creating a stable effect. Ga:Sa (5:4) and Komal Ga:Sa (6:5)
  • A note that has complex ratios with a given base note's frequency are perceived as creating instability. Examples include Komal Re:Sa (256:243), Teevra Ma:Sa (45:32), Komal Dha:Sa(128:81), Shuddha Ni:Sa (243:128).
  • Some notes are neither simple, nor complex in ratio: Shudha Re:Sa (9:8), Komal Ni:Sa (16:9), Shuddha Dha:Sa (27:16)
  • The smaller the amount of deviation in a note from a given frequency, the higher the amount of instability. Thus a slightly besur note will be far more unstable than a blatantly besur note.

Case Study: Maarwa vs. Pooriya.

From Mood and Notes (Part 1), we have:

  • Stability(Komal Re + Shuddha Dha) < Stability(Shuddha Ga + Shuddha Ni + Sa)

If we look at the ratios of these swars, we can rewrite this inequality as follows:

  • Stability (256/243) + Stability(27/16) < Stability(5/4) + Stability(243/128) + Stability(1/1 or 2/1)
We can "cancel" Komal Re and Shuddha Ni from this equation -- they seem to contribute in seemingly equal amounts to the instability based on their complex ratios.

  • Stability(27/16) < Stability(5/4) + Stability(1/1 or 2/1)
From this, it's clear that Maarwa has no stabilizing components, but Pooriya has 2 (Shuddha Ga and Sa). However, both have unstable components in excess of stabilizing components, and hence the average effect created will be unstable. Maarwa creates a pure melancholic effect while Pooriya feels more like longing.

First Insight

Simpler ratios create stability, complex ratios create instability.

Second Insight

The more complex the ratio, the more unstable it becomes -- besur or out-of-tune notes have very complex ratios.