An Acoustic Investigation into Ancient Indian Musical Tuning(s) - II

Some time ago I'd pondered the question of why the ancient Indian musical octave was considered to be a 22-step (22-शृति) interval [Kam2009a]. In my investigation I had followed primarily two cardinal principles:

(1) Ancient Indian musicians must have tuned their वीणाs (bow-harps) acoustically, using their ears as a guide (and without using any 'cyclic' principles). Hence their scales must have been largely reflective of our contemporary understanding of acoustic/harmonic principles.

(2) Only those processes (e.g. मूर्छनs) that were described by मुनि भरत could be used for further investigation.

Thus, I had postulated a 'acoustic natural' scale as a plausible model of the षड्ज-ग्राम and inferred that its मूर्छनs (modulations) automatically generated a 22-शृति gamut.

An Acoustic Investigation into Ancient Indian Musical Tuning(s)

Ancient Indian music theory was based primarily on the tuning of the (ancient) वीणा, a Bow-Harp [Bha1984]. The topic of tuning of the वीणा leads to much discussion and disagreement in musicological circles even today. Based on the information which has reached us via Greek physicists who 'reverse-engineered' Greek tuning from Greek musical scales, and presumably Greek music being inherited from an Eastern musical practice [Dan1995, Day1891], it is quite possible that Indian tunings were also founded on acoustic/harmonic principles.

मुनि भरत's treatise, the नाट्यशास्त्र, which became the basis for subsequent musicological works, identifies three different interval sizes in the two parent tunings (षड्ज-ग्राम and मध्यम-ग्राम) and assigns them certain weights or शृति values [Jai1975]. More importantly, the scales of मुनि भरत's time were heptatonic (i.e. employing 7 स्वरs) and based on मूर्छनs (modes) of a given ग्राम (parent tuning). This is central to what follows.

(Note: It is more correct to translate ग्राम as 'pitch collection'; however, the phrase 'parent tuning' is used in this article since tuning is the topic under discussion.)

The purpose of this article is to start with an acoustically determined scale, and then see if the basis of the नाट्यशास्त्र cannot be recovered using our current understanding of the state-of-the-art in those days. Primarily, it seeks to understand why the ancient Indian octave was presumably divided into 22 steps (शृतिs). This article is also motivated somewhat by earlier work on contemporary Indian scales which ended up with a non-coarse grouping of 22 equivalence note classes [Kam2008]. However, it is in no way a defense of the claim that contemporary Indian intonation too is based upon a set of 22 fixed शृतिs.

Relativity of Simultaneity - Bad Explanations on the Web

A common example used to demonstrate the Relativity of Simultaneity goes like this, more or less:

A train of length D is passing by a platform of length D. An observer P stands in the middle of the platform, and there's another observer T who sits in the middle of the train. P notices that the front end of the train coincides with the front edge of the platform AT THE SAME TIME as when the rear end of the train coincides with the rear edge of the platform. The two 'coincidence events' are thus simultaneous in P's frame of reference.

The question is, does T agree that both 'coincidence events' are simultaneous in T's frame of reference? (It is implicitly assumed that this question is posed in P's frame of reference and that both reference frames are inertial.)

The correct answer in Special Relativity is "No".

Call the front coincidence event F and the rear coincidence event R. Then, according to T, F happens before R. The events are NOT simultaneous in T's frame of reference even though they are simultaneous in P's frame of reference.

The Bad Explanation

Often times, the bad explanation for this is an incomplete version of a correct explanation provided by Einstein himself [Ein1924]. The bad explanation goes as follows: