Which notes are Vadi-Samvadi in Raga Rageshree?

The notes which play the most important and second most important roles in expressing a raga are called Vadi and Samvadi swars respectively in (North) Indian Classical music. Like Bageshree, Bhairavi, Shankara, Hamir and Kalingra, Rageshree is another controversial raga so far as the choice of Vadi-Samvadi selection is concerned where there are two different opinions. In the present work, a two minute vocal recording of raga Rageshree is subjected to a careful statistical analysis. Our analysis is broken into three phases: first half, middle half and last half. Under a multinomial model set up holding appreciably in the first two phases, only one opinion is found acceptable. In the last phase the distribution seems to be quasi multinomial, characterized by an unstable nature of relative occurrence of pitch of all the notes and although the note whose relative occurrence of pitch suddenly shoots is the Vadi swar selected from our analysis of the first two phases, we take it as an outlier demanding a separate treatment like any other in statistics. Selection of Vadi-Samvadi notes in a quasi-multinomial set up is still an open research problem. An interesting musical cocktail is proposed, however, embedding several ideas like melodic property of notes, note combinations and pitch movements between notes, using some weighted combination of psychological and statistical stability of notes along with watching carefully the sudden shoot of one or more notes whenever there is enough evidence that multinomial model has broken down.

💡 Research Summary

The paper tackles the long‑standing problem of objectively identifying the Vadi (most important) and Samvadi (second most important) swaras in the North Indian classical raga Rageshree, a raga for which traditional theory offers two conflicting pairs of candidates: {Ga, Ni} versus {Ma, Sa}. To resolve this, the authors recorded a two‑minute vocal rendition of Rageshree (with the tonic Sa tuned to C) and extracted the fundamental frequencies of each note using the software Solo Explorer 1.0 together with custom MATLAB scripts. The resulting pitch‑onset data were divided into three equal 60‑second phases – first half, middle half, and last half – and the relative frequency (proportion of total notes) of each of the seven basic swaras (Sa, Re, Ga, Ma, Dha, komal Ni, Ni) was computed for each phase.

For each phase the expected count of a note was calculated as (relative frequency of that note in the whole two‑minute sample) × (total number of notes in the phase). The observed counts were then compared with the expected counts using Pearson’s chi‑square test. In the first phase the chi‑square statistic was 2.49, and in the middle phase it was 3.76; both are well below the critical value of 12.592 for 6 degrees of freedom at the 5 % significance level, indicating that a multinomial distribution adequately models the note occurrences in these two phases. In the final phase the chi‑square rose to 14.50, exceeding the critical value of 11.070 for 5 degrees of freedom, signalling a breakdown of the multinomial assumption and the emergence of a “quasi‑multinomial” regime where relative frequencies fluctuate dramatically.

The authors then apply two criteria previously proposed in their earlier work: (i) a candidate Vadi must have a high relative frequency, and (ii) its relative frequency must stabilize quickly. Applying (i) eliminates Ma, whose overall relative frequency is low, and also excludes Sa, which, as the tonic, can at most serve as a Samvadi. The remaining high‑frequency notes are Ga and Ni, both nyas (resting) swaras. In the first two phases Ga’s frequency stabilizes by the middle phase, while Ni remains high but slightly less stable. Consequently, Ga satisfies both (i) and (ii) and is identified as the Vadi; Ni, being the other high‑frequency, relatively stable note, is taken as the Samvadi.

In the third phase, Ga’s relative frequency spikes to become the highest of all notes, even surpassing Sa. The authors treat this spike as an outlier caused by the breakdown of the multinomial model rather than as evidence to overturn the earlier conclusion. They acknowledge that selecting Vadi‑Samvadi in a quasi‑multinomial context remains an open research problem.

Beyond the statistical analysis, the paper discusses the distinction between “statistical stability” (low variance in relative occurrence) and “psychological stability” (duration and perceived restfulness of a note). The authors contrast their approach with Krumhansl’s work, which equates stability with the perceptual staying power of a note. They argue that while all psychologically stable notes are likely to have high relative frequencies, not all statistically stable notes are necessarily psychologically stable, citing the example of raga Durga where the Vadi (Sudh Ma) is not a nyas swara.

In summary, the study demonstrates that for Rageshree the first two thirds of a performance conform to a multinomial model, allowing an objective identification of Ga as the Vadi and Ni as the Samvadi. The final third of the performance deviates from this model, highlighting the need for further methodological development to handle quasi‑multinomial regimes. The paper thus contributes a novel statistical framework for raga analysis, clarifies the relationship between statistical and psychological notions of note importance, and points to future work on outlier handling and model robustness in Indian classical music research.