Prahlad

AAWM Journal 11/1 (2023)

Quantifying Alpatva (Scarcity) and Bahutva (Abundance):
A Comparative Study of the Scale-identical Hindustānī Rāgas Bhūpālī and Deskār

Achintya Prahlad

Scale-identical rāgas are a common phenomenon in Hindustānī music. The popular rāgas Bhūpālī and Deskār both have the scale sa re ga pa dha, SRGPD (where sa is the tonic note and pa is the fifth), corresponding to the intervallic structure of the major pentatonic scale in Western music. Yet, they are separate rāgas with distinct personalities, owing partly to differences in alpatva (‘scarcity’) and bahutva (‘abundance’) of svaras (‘notes’), i.e. the proportion of time occupied by a particular svara in a performance. Bhūpālī is pūrvāṅga-pradhāna (lower tetrachord dominant), with ga for its vādī (svara with the greatest bahutva), while Deskār is uttarāṅga-pradhāna (upper tetrachord dominant), and its vādī is dha. However, the prescriptive grammar of music theory (lakṣaṇa, or śāstra) only tells us so much about the realities of actual performance (lakṣya). While some elements of rāga grammar are explicitly described in the śāstra, other equally important features are learned only from the lakṣya, by listening and imitation. This study describes and quantifies some of the latter features, which, to the best of my knowledge, have not been published despite their consistency across schools and styles. These implicitly known elements of oral/aural practice are as much a part of the grammar of the raga as that recorded in the śāstra and have the potential to enrich the śāstra. Quantitative analysis of the lakṣya across diverse recordings reveals (1) a clear ranking of the svaras in decreasing order of bahutva (Bhūpālī: G, R, P, D; Deskār: D, P, G, R), (2) elongation of the vādī to a greater extent in Deskār than in Bhūpālī, (3) dominance of certain svara-pairs over others (in both rāgas), and (4) greater dominance of G and R in some instrumental renditions of Bhūpālī than in other instrumental and vocal renditions. New quantitative measures that I have defined for this study are an important technical contribution.

Achintya Prahlad is a graduate student in music at SOAS, University of London, and was previously visiting faculty at Ashoka University, India.

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Introduction

[1] In Indian music, such as Hindustānī music—the predominant classical music or art music form of northern India, which this article is about—tonality is chiefly articulated through melody rather than through harmony (Castellano, Bharucha, and Krumhansl 1984; Clarke 2017). The various combinations of sharp and flat notes give rise to several basic scales each containing seven notes including the tonic and the fifth note, which are known as thāṭ in Hindustānī music, and from these heptatonic scales more complex musical frameworks are created.

[2] Like Karnāṭik music, its southern counterpart, Hindustānī music is based on the rāga system. Before going into the details, I wish to place the concept of rāga in the context of world music. A rāga is not merely a scale; it is a complex grammatical and aesthetic structure, similar to but with distinctive elements compared to the maqām in Arabian and Persian music or dastgāh in Persian music (Powers et al. 2001). In Western music, modes are created from a scale by treating different notes of the scale as the tonic note and thereby producing patterns of notes that correspond to other scales.[1] However, the creation of rāgas from thāṭs is an entirely different process from the creation of modes from scales, since in this case, the tonic note is not changed. One either uses all notes of the thāṭ, i.e., a heptatonic scale, or omits one or two notes (other than the tonic note) to create a pentatonic or hexatonic scale, and then introduces grammatical rules for performing the rāga, such as rules for which notes are to be used in the ascent and which in the descent, how each note is to be articulated—whether it is to be elongated or only sung fleetingly, whether it is colored by other notes, whether it is oscillated, and so on—and which combinations of notes are permissible and which are not. One can thus create a large number of rāgas just from a single scale. I explain these rules in more detail in subsequent sections of this paper.

[3] This article deals with two modern scale-identical Hindustānī rāgas: Bhūpālī (also known as Bhūp), and Deskār. Both these rāgas have the notes (svaras) of the major pentatonic scale. The former rāga has existed since the 16th century, while the latter is much newer. This work aims to quantitatively describe and compare the rāgas and unearth features that are not explicitly known.

Aims of the present study

[4] While some elements of rāga grammar are explicitly described in the śāstra, other equally important features are learned only from the lakṣya, by listening to and imitating the guru or to fellow musicians. These seem to be subconsciously imbibed, and practitioners instinctively produce these features without being consciously aware of them. My study is aimed at discovering these implicit structures, which to the best of my knowledge have never been described in words before. My work shows that these too can be made explicit, and thus have the potential to be included in the śāstra. While it is easy to contrast rāgas that have different svaras, it is a lot harder to lay bare the differences in character between two rāgas that share a scale. I therefore choose the scale-identical pentatonic rāgas Bhūpālī and Deskār. In my study, I have devised several quantitative methods of differentiating between these rāgas. For the selected recordings identified in Table 2, I measure the following quantities: frequency of occurrence of pitches as a measure of the svara’s relative alpatva (scarcity) or bahutva (abundance), svara lengths (durations of individual occurrences of svaras) as a measure of dīrgha bahutva (one of the main kinds of bahutva, where a particular svara is often elongated) or its opposite, and svara-saṅgati-s (pairs of consecutively occurring svaras). I have also devised a clustering method to group similar renditions of a particular rāga together, based on ratios of occurrence frequency of other svaras to those of the vādī and saṁvādī (defined below).

The svaras of Hindustānī music

[5] Before going into the specifics of the two rāgas selected for this study, I would like to discuss the modern system of musical notes (svara-s) in Hindustānī music, and give some details of rāga structure. Table 1 lists the svaras.

Name	Short name	Modern Hindustānī name	Western scale degree	Western note-interval
1.     Ṣaḍja This is not an absolute pitch, but is fixed at the pitch that is most comfortable for the voice or the instrument(s). The other svaras are then defined relative to it. It is called the “system tonic” (Powers et al. 2001; Qureshi et al. 2020).	Sa	Ṣaḍja (S)	1	Perfect unison
2. R̥ṣabha	Ri (Karnāṭik), Re (Hindustānī)	Komal r̥ṣabh (r)	2, flat	Minor second
		Śuddha (tīvra) r̥ṣabh (R)	2, sharp	Major second
3.     Gāndhāra	Ga	Komal gāndhār (g)	3, flat	Minor third
		Śuddha (tīvra) gāndhār (G)	3, sharp	Major third
4.     Madhyama	Ma	Śuddha (komal) madhyam (m)	4, flat	Perfect fourth
		Tīvra madhyam (M)	4, sharp	Augmented fourth
5.     Pañcama	Pa	Pañcam (P)	5	Perfect fifth
6.     Dhaivata	Dha	Komal dhaivat (d)	6, flat	Minor sixth
		Śuddha (tīvra) dhaivat (D)	6, sharp	Major sixth
7.     Niṣāda	Ni	Komal niṣād (n)	7, flat	Minor seventh
		Śuddha (tīvra) niṣād (N)	7, sharp	Major seventh

 

Table 1. The twelve svaras of Hindustānī music (within any given octave).

[6] It is important to mention that the melody of the svaras as created by their distinctive rāga-specific ornamentations is more important in Indian music than the intervals are (Powers et al. 2001). The tonic note—a “system tonic” (Powers et al. 2001; Qureshi et al. 2020)—is called ṣaḍja (abbreviated to sa), and the other svaras are defined relative to it. Within one octave, there are twelve svaras including sa, each svara being one semitone higher than the previous. There are seven svara names: ṣaḍja, r̥ṣabha, gāndhāra, madhyama, pañcama, dhaivata and niṣāda, respectively abbreviated to sa, ri (re in Hindustānī music), ga, ma, pa, dha and ni. Out of these, re, ga, ma, dha and ni have two variants each – one komal (flat), and the other tīvra (sharp), as shown in Table 1.[2] In this work, I represent the former using lowercase letters, and the latter using uppercase letters. There is also the concept of śuddha (natural) and vikr̥ta (altered) notes. This is the one that is more commonly used in Hindustānī music today.  In modern Hindustānī music, the tīvra variants of re, ga, dha and ni are considered śuddha svaras. In the case of ma, it is the komal variant (m) that is considered śuddha. Sa and pa are not given any qualifiers. R, G, m, D and N are known as śuddha re, śuddha ga, śuddha ma and so on. The remaining five svaras (r, g, M, d, n) are vikr̥ta, and their names are given the adjectives “komal” (r, g, d and n) and “tīvra” (M only). Sa and pa do not have any vikr̥ta variants, and are necessarily present in every thāṭ (pitch collection). A thāṭ is a collection of seven svara-pitches, sa re ga ma pa dha ni, and forms the basis for the creation of rāgas. Since there are only one sa and one pa, and two each, i.e., one śuddha and one vikr̥ta, in the other five categories (re, ga, ma, dha and ni), there are in theory 2⁵ = 32 possible thāṭs. The śuddha thāṭ of Hindustānī music corresponds to the major scale or Ionian mode in Western music. A rāga may take 5, 6 or all 7 svaras of its thāṭ. Sabeing the tonic, it cannot be omitted from any rāga. Some rāgas admit both komal and tīvra variants of a particular svara. Unlike thāṭs, rāgas are not merely collections of pitches, but have a grammar, which is described in the next section.

[7] Once one fixes the tonic at a particular pitch (depending on the range of the voice or the instrument), there are three octaves, i.e., registers—saptak[3] in Hindustānī music and sthāyī in Karnāṭik music—in which the singing or playing ranges. These are mandra (lower), madhya (middle) and tāra (higher). The sa of the madhya saptak is the tonic. Mandra svaras are represented by a dot below the svara symbol, e.g., P̣, and tāra svaras are represented by a dot above, e.g., Ṡ. A vocal performance typically ranges between P̣ or ṃ/Ṃ and Ṗ. Some vocalists may go down to g̣/G̣ or ṛ/Ṛ, or even as low as Ṣ.

[8] There are numerous grammatical rules that make up a rāga. These are understood from both lakṣaṇa (what is prescribed) and lakṣya (what is seen in practice). It is usually taken for granted that musicians adhere to the grammar while singing or playing the rāga. Rāga grammar is typically learnt directly from a guru, or by attending or listening to lecture-demonstrations on the rāga, or, when one is a trained musician, by listening to multiple renditions of the rāga. Performed music constitutes the lakṣya (Bhatkhande 1910), which roughly translates to “what is observed.” It refers to the music as it is performed in the ‘present’ day. In the context of this paper, I choose to define the ‘present’ day as beginning in the later part of the 20^th century, i.e., the 1950s onwards, for two reasons. Firstly, recorded music, which now plays a major role in understanding rāgas, is only as old as the early 20^th century in India. Also, a 6-volume series of music textbooks attributed to the musicologist Vishnu Narayan Bhatkhande[4], now considered the standard, was published only in the 1930s, and Bhatkhande was alive till 1936. I thus treat the present age as beginning in the post-Bhatkhande era.

Grammar of rāgas

[9] Harold S. Powers has put forward a detailed theory of rāgas, comparing and contrasting them with maqāms, dastgāhs and Western modes (Powers et al. 2001). The term rāga[5] in a musical sense first appeared in the 8th century (Qureshi et al. 2020), and rāga music has been evolving since then. Over the centuries, it has been passed down both orally from guru to disciple, but also textually, through various musical treatises.[6]

[10] The rules of rāga grammar are preserved in written form in the saṅgīta śāstra-s (musical treatises). Possibly the most important modern saṅgīta śāstra is the 6-volume Hindustānī Saṅgīt Paddhati – Kramik Pustak Mālikā (The Hindustānī Music System – A Series of Books) attributed to Vishnu Narayan Bhatkhande (1860–1936) (Bhatkhande 1920s–30s).[7] Nearly every performer or scholar of Hindustānī music is familiar with this work.

[11] The śāstra and lakṣya are both transmitted from guru to disciple, albeit in different ways. The śāstra is typically explained verbally, while the lakṣya is demonstrated by singing or playing an instrument. From the latter, the student learns the grammar in more implicit or subconscious ways, through hearing and reproducing what the guru sings or plays. Śāstra and lakṣya are not mutually exclusive, and they influence each other. Despite widespread knowledge of the śāstra, it is worth questioning to what extent it is consistent with lakṣya. Consistency between śāstra and lakṣya may vary from rāga to rāga.

[12] The svarūpa (aesthetic character, identity) of a rāga is composed of the following lakṣaṇas (characteristic features), which are outlined by the śāstra:

1. Thāṭ: According to Vishnu Narayan Bhatkhande, each rāga is mapped to a thāṭ (parent scale). Many rāgas, however, contain both the komal and the tīvra variant of one or more svaras. In such cases, the thāṭ is decided by which svara-variant is used to a greater extent as compared to the other. However, Bhūpālī and Deskār use only one variant (śuddha in this case) of each svara, and they are assigned thāṭs based on their similarities to other rāgas.
2. Āroh: Ascent, from S to Ṡ. This varies in the number of svaras present. It may be auḍav (pentatonic), ṣāḍav(hexatonic), or sampūrṇa (“complete,” i.e., heptatonic).
3. Avaroh: Descent, from Ṡ to S. This may also be auḍav, ṣāḍav or sampūrṇ
4. Jāti: Based on the number of svaras in the āroh and avaroh, rāgas may be classified as auḍav-auḍav, ṣāḍav-ṣāḍav, or sampūrṇa-sampūrṇa (equal numbers of svaras in āroh and avaroh). They may also be classified as auḍav-ṣāḍav, auḍav-sampūrṇa or ṣāḍav-sampūrṇa (unequal numbers of svaras in āroh and avaroh). Except for some rare exceptions, Hindustānī rāgas typically do not have less than five svaras, or less svaras in the avaroh than in the āroh. Bhūpālī and Deskār are both auḍav-auḍav, and their āroh and avaroh are SRGPDṠ-Ṡ Auḍav and ṣāḍav scales are known as “transilient scales” (Jairazbhoy 1971, 122), in the sense that they skip one or two svaras—e.g., skipping ma while moving from G to P or skipping ni while moving from D to Ṡ in Bhūpālī/Deskār.
5. Vādī and saṁvādī: Respectively the dominant svara of the rāga, and the svara that is consonant (in saṁvād)[8]with it. Based on whether the vādī is in the pūrvāṅg (the region between S and P) or uttarāṅg (the region between m and Ṡ), rāgas may be classified as pūrvāṅg-pradhān (pūrvāṅg-dominated) or uttarāṅg-pradhān(uttarāṅg-dominated) (Bhatkhande 1920s–30s, 15–16). The pūrvāṅg and uttarāṅg (Qureshi et al. 2020), while roughly corresponding to the lower and upper tetrachord in a sampūrṇa rāga, are not exactly the same as tetrachords, since ma and pa, the ‘midpoints’, are considered to belong to both. Thus, there are both pūrvāṅg- and uttarāṅg-pradhān rāgas with ma or pa for their vādī (Bhatkhande 1920s–30s vol. 3, 16). The svaras other than the vādī and saṁvādī are known as anuvādī. The vādī of Bhūpālī is ga (Bhatkhande 1920s–30s vol. 3, 23), and it is thus pūrvāṅg-pradhān (Bhatkhande 1920s–30s vol.4 p.247). On the other hand, Deskār is uttarāṅg-pradhān, because its vādī is dha (Bhatkhande 1920s–30s vol.4 p.247). The saṁvādī of Bhūpālī is dha, and that of Deskār is ga (Bhatkhande 1920s–30s vol.3, 23, 1920s–30s vol.4, 247).
6. Samay: The time of singing or playing (Yardi and Chew 2004). According to Bhatkhande’s theory, pūrvāṅg-pradhān rāgas have times ranging from noon to midnight, while uttarāṅg-pradhān rāgas have times ranging from midnight to noon. Bhūpālī is an early night rāga (Bhatkhande 1920s–30s vol.3, 23), and Deskār is a morning rāga (Bhatkhande 1920s–30s vol.4 p.247). While samay does not play a role in differentiating rāgas aesthetically, I mention it here because it is an important lakṣaṇa of Hindustānī rāgas.
7. Nyās svaras: The svaras on which one may end phrases. The act of ending a phrase on a particular svara is known as nyās.
8. Varjit svaras: Svaras whose usage is not permissible in a rāga. Ma and ni are varjit in both Bhūpālī and Deskār.
9. Uccāraṇ: the ‘pronunciation’ of each svara (Qureshi et al. 2020). For example, the phrase ga pa dha sa in Bhūpālī is rendered as ^PG P ^ṠD, ^ṠD, ^DṠ, where the superscripts are kaṇ svaras—short-duration particles of svaras used as an ornament on other svaras that are sung for a longer duration. The ^ṠD is rendered more forcefully and with a greater Ṡ-component in Deskār. Also, a plain, brisk GPDṠ is more characteristic of Deskār than of Bhūpālī.
10. Alaṅkār: These are ornamentations used on svaras (Qureshi et al. 2020). Examples are mīṇḍ (glissando), āndolan (gentle oscillation of a svara using kaṇas of other svaras), gamak (a momentary push of forceful singing from the chest), etc. Some rāgas by nature use a great deal of mīṇḍ, but this is not true for Bhūpālī and Deskār. Kaṇs and alaṅkārs influence the precise śruti (microtone) of a svara.
11. Rāgāṅga or aṅga: Aṅga literally means limb or part. In the context of rāgas, it refers to characteristic phrases, complete with rāga-specific uccāraṇ, that give a rāga its identity. Sometimes several rāgāṅgas may be present in one rāga.
12. Calan:[9] The word literally means ‘movement’. It refers to the overall structure of the rāga. The inventory of phrases, and the general pathways that one can follow while improvising: which phrase(s) can follow which phrase(s), and so on. This is somewhat like syntax in the grammar of a language. The lakṣaṇas defined in this list are basic components of the calan, but do not constitute its entirety.
13. Alpatva and bahutva: See below.

Alpatva and bahutva

[13] Alpatva and bahutva are the primary focus of this article. These refer respectively to the scarcity and abundance of svaras in a raga. This scarcity or abundance is of many types, which are described below.

[14] Bahutva (Bhatkhande 1920s–30s vol. 4, 34; Widdess 1995, 47): literally speaking, the state of a svara being “more” in comparison to other svaras of the rāga. The vādī is thus the svara with the greatest bahutva. Bahutva is of the following types:

1. Nyās bahutva – A kind of abundance generated through the greater likelihood of a svara appearing as a nyāspoint (defined above), given the function of nyās svaras in ending phrases. The tonic note, sa, is by definition a nyās svara in every rāga. Therefore, nyās on sa is not considered special. Performers or scholars of Hindustānī music talk about svaras other than sa that are nyās points.

In Bhūpālī, the nyās svara (other than sa) is ga alone. Re, pa, and dha can be points of what I call ‘ardha nyās’ (half nyās). If nyās is a full stop, then ardha nyās is a comma. A nyās on dha or pa would cause a shift into Deskār, and a nyās on re would cause an entry into the territory of Rāga Śuddha Kalyāṇ. The Karnāṭik rāga Mohanam, which is ga-dominated like Bhūpālī, has nyās on all these svaras.

2. Dīrgha bahutva – elongation of a svara, as demanded by the structure of the rāga. Ga and pa have dīrgha bahutva in Bhūpālī, and dha has dīrgha bahutva in Deskār.
3. Abhyās bahutva – a combination of dīrgha and nyās bahutva, i.e. repeated elongation of and nyās on a svara. Gahas abhyās bahutva in Bhūpālī, and dha and pa in Deskār.
4. A-laṅghan bahutva – When there is no laṅghan (skipping over) of a svara, because the structure of the rāga does not allow it. Laṅghan will be defined in the next section.

[15] Alpatva (Bhatkhande 1920s–30s vol. 4, 33; Widdess 1995, 47): the state of a svara being alpa (‘less’ or ‘reduced’) in comparison to other svaras of the rāga. It is of the following types:

1. Anabhyās alpatva – an absence of dīrgha and nyās bahutva, i.e., the scarcity of a svara because it cannot function as a phrase-ending (nyās) and is not elongated. The opposite of abhyās bahutva.
2. Laṅghan alpatva – Skipping over of a svara. This is not the same as the state of being varjya (completely absent from the rāga). The svaras ma and ni are varjya svaras in both Bhūpālī and Deskār. We thus cannot say that there is laṅghan of these svaras, since they are altogether absent. Laṅghan typically happens when a svara that is present in the rāga is already alpa, usually in the sense of appearing only as a passing note and never being elongated, and can therefore be sometimes skipped. The svara re undergoes laṅghan in the āroh (ascent) in some renditions of Deskār.

[16] Rāgas whose thāṭs differ can easily be told apart. Within one thāṭ, differences in āroh and avaroh serve to differentiate between rāgas. However, there are also several sets of rāgas possessing identical āroh and avaroh, which I term scale-identical rāgas, and these cannot be differentiated based on svaras alone. One such set is Bhūpālī, Deskār, Jait Kalyāṇ, and the auḍav variety of the rāga Śuddha Kalyāṇ, all of which have the major pentatonic scale, S R G P D (all tīvra, or all śuddha) (Bhatkhande 1920s–30s vol.3, 23). This article deals only with the first two, since they are more popular. When rāgas are scale-identical, they can be differentiated based on the following lakṣaṇas –

• Whether a raga is pūrvāṅg- or uttarāṅg-pradhān (upper or lower tetrachord dominant). For example, Bhūpālī is pūrvāṅg-pradhān, while Deskār is uttarāṅg-pradhān.
• Vādī-saṁvādī. For example, the vādī-saṁvādī of Bhūpālī are G and D, and vice versa in Deskār.
• Rāga-specific uccāraṇ of svaras or phrases. For example, the phrase sa re dha sa is rendered as SR, ^SḌ, ^SḌ, ^ḌS in Bhūpālī, and as a plain SRḌS in Deskār.
• Alpatva and bahutva of svaras other than the vādī. For example, R is much weaker in Deskār than in Bhūpālī.
• Characteristic phrases that make up the calan. For example, GDPG is a phrase of Bhūpālī, while PDGP is a phrase of Deskār.

[17] Using the same svaras, a performer can create entirely different aesthetic atmospheres by varying the vādī-saṁvādī, alpatva and bahutva, uccāraṇ or overall calan. Changing any of these can take one into a different rāga. This is why the study of scale-identical rāgas is important.

Important lakṣaṇas of Bhūpālī and Deskār

[18] Bhūpālī: One of the most popular Hindustānī rāgas (S. Rao et al.).

• Āroh-avaroh: S R G P D Ṡ – Ṡ D P G R S (corresponding to the major pentatonic scale in Western music, and to the Karnāṭik raga Mohanam).
• Thāṭ – Kalyāṇ (SRGMPDN, all svaras tīvra). Since ma and ni are absent, Bhūpālī could be derived from any out of four different thāṭ However, owing to its closeness to the rāga Śuddha Kalyāṇ, whose avaroh is sampūrṇa (heptatonic), it is placed in the Kalyāṇ thāṭ (Bhatkhande 1920s–30s vol.3, 23).
• Traditional time of singing: Early night, along with other rāgas that possess the Kalyāṇ rāgāṅ
• Vādī – ga, saṁvādī – dha (Bhatkhande 1920s–30s vol.3, 23). Since the vādī is in the pūrvāṅg, Bhūpālī is considered pūrvāṅg-pradhān.
• Nyās svaras other than sa: Primarily ga in both the āroh as well as avaroh, although an avarohātmak(descending) nyās on dha may occur.
• Characteristic vakra phrases (phrases where the svaras are randomly ordered): SRPG, GRPG, GDPG, SR^SḌ^SḌS .
• Alpa svaras: None.
• Low density of mīṇḍ.
• In Bhūpālī, there is typically no laṅghan of any svara. Thus, all the svaras have alaṅghan

[19] Deskār: While less commonly performed than Bhupālī, this rāga is familiar to most Hindustānī musicians owing to its closeness to Bhupālī (S. Rao et al.).

• Āroh-avaroh: S R G P D Ṡ – Ṡ D P G R S (same scale as Bhūpālī, but different treatment of the svaras).
• Thāṭ – Bilāval (SRGmPDN, all svaras śuddha) (Bhatkhande 1920s–30s vol. 4, 247). This is due to Deskār’s uttarāṅg-pradhān nature and its closeness to the heptatonic uttarāṅg-pradhān rāga Bilāval.
• Traditional time of singing: Morning, along with other rāgas that possess the Bilāval rāgāṅ
• Vādī – dha, saṁvādī – ga. Since the vādī is in the uttarāṅg, Deskār is considered uttarāṅg-pradhān.
• Nyās svaras other than sa: Dha in the āroh, pa in both āroh and avaroh.
• Characteristic vakra phrases: SRḌS, PDGP, D_Ṡ^DP (where the underscore indicates lengthening). Other phrases that set Deskār apart from Bhūpālī are the S-D jump and the plain GPDṠ without the kaṇ of Ṡ in D.[10]
• Alpa svara: R. It has anabhyās alpatva, i.e., R is never dīrgha, and there is no nyās on it. In the avaroh, it is just a transitory note between ga and sa, appearing as a kaṇa (particle) svara, G_^R In many people’s renditions, it undergoes laṅghana in the āroh, with SGP being sung instead of SRGP (where there is nyās on pa). But R may still be present in the phrases SRGPD and SRGP^ṠD (with nyās on dha). There may be PDṠṘĠṘṠ or PDṠṘĠ^ṘṠ in the tāra saptak. In Kishori Amonkar’s version, the combination SRG almost never appears – not even in the tāra saptak, excepting for a slight hint occasionally – and only SG is present for most of the performance. However, in the approach of my guru, Professor Ojesh Pratap Singh, SGP is considered a phrase of the rāga Jait Kalyāṇ[11], and Deskār must take SRGP. This is something my guru told me while teaching me Deskār. There is then no laṅghan of re in Deskār in his style. It is alpa only in the sense of anabhyās.

How a rāga is performed

[20] Hindustānī rāga music has three main genres within it – dhrupad, ḵẖayāl and ṭhumrī. Dhrupad and ḵẖayāl are rāga-pradhān, dominated by the rāga. While they sound very different, they have several common features. Instrumental music often combines elements of two or all three of these systems. Some features that set ḵẖayāl apart from dhrupad are a greater variety of alaṅkārs, and a higher possibility of undulating and fast-paced phrases that only involve the sound ā. Dhrupad typically has only gamak, mīṇḍ and āndōlan. Ḵẖayāl has these, but also additional alaṅkārs such as khaṭkā and murkī that pack several svaras into a minute length of time. Ḵẖayāl also has more intra-phrase tempo variation in the ālāp section (exposition of rāga phrases, described below) than dhrupad does, and some additional features mentioned in the following paragraphs.

[21] Rāga performance is typically structured as follows (Powers et al. 2001; Qureshi et al. 2020): ālāp (slow exposition of the pitches and phrases of the rāga), followed by bandiś (composition). A bandiś has a tāla (rhythmic cycle) and laya (tempo). The laya can be vilambit (slow), madhya (medium) or drut (fast). The general pattern is to perform a vilambit or madhya-laya bandiś first, and follow it up with a drut bandiś in the same rāga. The performance of the composition, though it begins with the bandiś as it has been composed or learnt, deviates from the pre-defined structure, and several varieties of on-the-spot improvisations are performed, such as bol-ālāp (ālāp using the words of the bandiś), layakārī (rhythmic variations using the words of the bandiś, either at the same pace as the bandiś or at faster paces), sargam (singing the svaras as sol-fa syllables), and tān (fast cascades of musical notes sung using the vowel ā). Layakārī is found in both dhrupad and ḵẖayāl. Bol-ālāp, sargam and tān are typically found in ḵẖayāl but not in dhrupad. The ālāp is an impromptu exploration of the various phrases possible in a rāga. It and other improvisations must be original, innovative and mostly non-repetitive, but never deviating from rāga grammar. In fact, multiple performances of the same rāga by the same musician, since they are improvised, sound different from one another, but owing to the adherence to grammar, it is still recognizable as the same rāga. The improvisation is not entirely impromptu, since a great deal of planning (Clarke 2017) goes into it when the musician is off-stage. Some musicians—examples being Kishori Amonkar and Kumar Gandharva—intentionally and cleverly deviate from the grammar, but still maintain the aesthetic atmosphere of the rāga, and this is a skill that is valued.

[22] In commonly heard styles of dhrupad, ālāp is typically performed separately, before the composition, and is a long piece. In ḵẖayāl, though there is a short initial ālāp preceding the composition, the bulk of the ālāp is performed as part of the improvisation in the vilambit composition, though some dhrupad-influenced ḵẖayāl gharānā-s[12] (loosely translated as ‘schools of music and musical thought’) may perform longer, separate ālāps. The style of the Agra gharānā is an example of this. A ḵẖayāl ālāp may use specific syllables like those used in dhrupad ālāps, or may just use the vowel ā. Some gharānās—e.g., the Jaipur-Atrauli gharānā[13], in whose style Mallikarjun Mansur, one of the artistes in this study, sings—may perform little to no initial ālāp. For a pūrvāṅg-pradhān rāga like Bhūpālī, the ālāp usually begins by establishing sa, spending some time in the mandra saptak, and gradually singing phrases that introduce successively higher svaras, in the order of the svaras (e.g., R, G, P…), entering the tāra saptak, going up to the tāra pañcam, and eventually coming back to sa. The ālāp does not merely ascend to the highest point and then descend. It tends to be rendered in segments that are punctuated by returning to the tonic (Qureshi et al. 2020). Modern ālāp-s typically have many segments, presided over by successively higher svaras. Uttarāṅg-pradhān rāgas like Deskār introduce the higher svaras much earlier, and might jump to the tāra sa quite early in the ālāp. The calan of the rāga is determined by the location of the vādī svara. Thus, uttarāṅg-pradhān rāgas are often performed in a more phrase-based manner, while pūrvāṅg-pradhān rāgas are performed in a svara-based fashion. Longer ālāps are possible in rāgas of the latter category, such as Bhūpālī.

[23] The initial part of the pre-bandiś ālāp is always slow in tempo and without an obvious rhythm, but it may be followed by faster segments that are rhythmic. This is especially true for dhrupad, where after singing a slow, free-flowing vilambit ālāp, there is a rhythmic madhya ālāp. Instrumentalists call this joḍ. After this segment, there is a much faster rhythmic segment, the drut ālāp (jhālā in instrumental terms). The joḍ and jhālā are played by instrumentalists even if their overall style is more ḵẖayāl-like (in terms of alaṅkārs, as described in the first paragraph of this section). These faster ālāp segments may sometimes also be performed by ḵẖayāl vocalists, typically in the Agra gharānā.

[24] After singing the bandiś as it is composed, the musician improvizes. In this segment, dhrupad musicians typically only perform layakārī (of different varieties). In ḵẖayāl, after sufficient exploration of the ālāp segment of the vilambit composition, the tempo is typically increased, and layakārī, sargam and tān are performed. Tān is a feature of ḵẖayāl alone, and not of dhrupad. A ḵẖayāl ālāp differs from a dhrupad ālāp in one more sense – the use of slower tān-like fragments in the ālāp itself.

[25] The vocal recordings I have used for this study are all ḵẖayāl. The instrumental recordings, too, are closer to ḵẖayāl than to dhrupad, though some of them contain dhrupad-like features (ālāp, joḍ and jhālā, or ālāp and joḍ).

[26] All the vocal recordings in this study contain melodic as well as percussive (tablā) accompaniment, and all the instrumental recordings—except two flute recordings that only consist of ālāp, joḍ and jhālā—contain tablā accompaniment in the bandiś section. In Hindustānī music, melodic accompanists are trained to follow the style and rāga interpretation of the main performer. Thus, my study makes the fair assumption that the rāga svarūpa played by the melodic accompanist does not differ greatly from that sung by the main vocal artiste.

Discography

[27] The recordings of Bhūpālī (vocal and instrumental) and Deskār (vocal) used for this study are described in the discography in Table 2 below. The choice of artistes was restricted to well-known and established musicians, and also biased by availability. To present a more comprehensive view of how rāgas are performed, I also included artistes such as Kishori Amonkar and Kumar Gandharva, who deviate from gharānā norms. Complete recordings were used in all cases.

[28] I have used the following recordings for this study:

Bhūpālī (n=14, 7/14 vocal)

Artist	Instrumentation	Duration (min)	Album details
Kishori Amonkar	Vocal	21:00 (out of which 15:09 constitute the vilambit composition, and the rest the drut composition. No initial ālāp)	Kishori Amonkar (vocal), Best of Kishori Amonkar, Vol. 1, Myuzic Entertainment, 2018
Kumar Gandharva	Vocal	Madhya laya: 9:58 (Initial ālāp up to 0:27)	Kumar Gandharva (vocal), The Last Word in Hindustani Vocal, Pt. I, Music Today, 2009
Prabhakar Karekar	Vocal	Vilambit: 30:11 (Initial ālāp up to 2:47)	Prabhakar Karekar (vocal), Faces Of Raga—Prabhakar Karekar, Living Media India Ltd., 1996
Mashkoor Ali Khan	Vocal	Drut tarānā: 4:57 (No initial ālāp)	Mashkoor Ali Khan (vocal), Transcendence, Nimbus Alliance, 2017
Rashid Khan	Vocal	22:20 (Initial ālāp up to 0:38, madhya laya composition up to 15:11, followed by drut)	Rashid Khan (vocal), Masterworks from the NCPA Archives: Rashid Khan (Remastered), recorded 1984, NCPA under exclusive license to Sony Music Entertainment India Pvt. Ltd., 2011
Padmini Rao	Vocal	28:07:00 (Initial ālāp up to 2:55, vilambit up to 18:58, followed by drut)	Padmini Rao (vocal), Aananda, Super Cassettes Industries Private Limited, 2014
Padma Talwalkar	Vocal	16:24 (initial ālāp up to 3:55, then slow madhya laya tarānā)	Padma Talwalkar (vocal), Tarana—Flights of Melody, Original Sound Recording, 1994
Hariprasad Chaurasia	Bā̃surī (flute)	Ālāp, joḍ and jhālā: 32:12 (no gat in this recording)	Hariprasad Chaurasia (bā̃surī), From the NCPA Archives—Hariprasad Chaurasia (Remastered) recorded 1984, NCPA under exclusive license to Sony Music Entertainment India Pvt. Ltd., 2011
Rakesh Chaurasia	Bā̃surī	Ālāp: 12:14 Joḍ: 13:28 Madhya laya gat (composition): 22:54 Drut gat: 22:13	Rakesh Chaurasia (bā̃surī), Call of Krishna, Sona Rupa Ltd., 2004
Pravin Godkhindi	Bā̃surī	Joḍ, jhālā: 22:00	Pravin Godkhindi (bā̃surī), Antaryami: Classical Flute Music for Relaxation & Meditation, Sagar Music, 2005
Bismillah Khan	Śahnā’ī (wind)	16:49 (ālāp up to 1:50, followed by madhyalaya, speeds up from 9:28 onwards)	Bismillah Khan (śahnā’ī), Evening Raga, Classic Music, 2019 (obviously recorded much earlier, since the artiste passed away in 2006)
Sultan Khan	Sāraṅgī (string, bowed)	53:15 (ālāp up to 17:40, then vilambit, then drut from 42:46)	Sultan Khan (sāraṅgī), Sultan Khan & Zakir Hussain, Moment Records, 1992
Lalmani Misra	Vicitra Vīṇā (string, fretless. Played by plucking at one end, and at the other end, varying string length by sliding a rounded glass object on it)	12:53 (ālāp up to 2:59, then madhya laya composition)	Lalmani Misra (vicitra vīṇā), Heritage Alive, Vol. 1, recorded 1970, CD Baby 2013
Gianni Ricchizzi	Vicitra Vīṇā	Ālāp:12:05 Joḍ: 6:28	Gianni Ricchizzi (vicitra vīṇā), Digital Booklet—Raga Bhupali & Raga Yaman—Anna Maria Mucilli, Gianni Ricchizzi & Giuseppe Fiore, Wyastone Estate Limited, 1994

Deskār (all vocal; n=8)

Artist	Instrumentation	Duration (min)	Album details
Kishori Amonkar		29:55 (initial ālāp up to 0:58, followed by vilambit, followed by drut at 22:23)	Kishori Amonkar (vocal), Best of Kishori Amonkar, Vol. 1, Myuzic Entertainment, 2018 (The Bhūpālī and Deskār recordings are part of the same album, but were most probably sung on different occasions)
Arati Ankalikar-Tikekar		17:13 (initial ālāp up to 1:45, followed by drut, then a faster drut tarānā at 12:45)	Arati Ankalikar-Tikekar (vocal), Classical Vocal: Aarti Ankalikar-Tikekar, Fountain Music Company, 1997
Ajoy Chakraborty		21:29 (Initial ālāp up to 0:45, followed by slow madhyalaya composition, followed by drut at 14:21)	Ajoy Chakrabarty (vocal), Gharana Series—Patiala, Living Media India Ltd., 1995
Kumar Gandharva		11:01 (madhyalaya composition) No initial ālāp	Kumar Gandharva (vocal), Classical Vocal: Pt. Kumar Gandharva, Fountain Music Company, 1999
Bhimsen Joshi		18:05 (Initial ālāp till 3:01, followed by drut)	Bhimsen Joshi (vocal), Ragas Deshkar, Hindol, Jogia, Bhairavi, Navras Records, 1994
Archana Kanhere		9:56 (Initial ālāp till 0:28, followed by drut, followed by drut tarānā at 5:36, slightly faster than previous composition)	Archana Kanhere (vocal), Bandish: Raja Kale & Archana Kanhere, Fountain Music Company, 2012 (Only Archana Kanhere part analysed)
Rashid Khan		21:55 (Initial ālāp till 0:26, followed by drut)	Rashid Khan (vocal), The Song Of Shiva, recorded 1995, Navras Records, 1998
Mallikarjun Mansur		20:21 Negligible initial ālāp, vilambit-madhyalaya composition starts at 0:14, no drut	Mallikarjun Mansur (vocal), Morning & Evening Ragas, The Indian Record Mfg. Co. Ltd., 1990

Table 2. The recordings used in this study.

Some other studies on quantifying rāga structure

[29] I now discuss earlier literature in the area of quantification of rāga structure. I do not list these exhaustively, but provide some examples of significant research in the field. An early study towards quantifying rāga structure was carried out in 1977 by the Karnāṭik musician-scholar T. Viswanathan (1977). This contained a study of alpatva and bahutva, albeit in a Karnāṭik context. Viswanathan studied ālāpanās[14] (i.e. ālāps) of major heptatonic Karnāṭik rāgas of different melas—Bhairavi, Kalyāṇi, Śaṅkarābharaṇam, Toḍi, Sāveri and Kāmbhoji[15]—by many artistes, and made detailed plots that depict the relative frequencies of occurrence of individual svaras in each rāga ālāpanā. He also studied the usage of gamakas (the Karnāṭik term equivalent to alaṅkārs) of different kinds, characteristic identifying phrases of the rāgas, special rāga phrases, and many other details of the ālāpanā. In the present study, I have done a similar analysis to Viswanathan’s study of relative occurrence of svaras, the difference being that rather than studying rāgas from diverse scales, I have compared two scale-identical pentatonic Hindustānī rāgas, Bhūpālī and Deskār, and have also compared vocal recordings of Bhūpālī to instrumental ones. Another point of difference is that my study is not limited to the ālāp, and also takes into account the bandiś component. Of course, unlike Karnāṭik music, the performance of ḵẖayāl music or non-dhrupad instrumental Hindustānī music contains ālāp not just in the beginning but also within the bandiś. Also, I have analysed other quantitative metrics: svara-saṅgatis, occurrence of other svaras relative to the vādī and saṁvādī, and svara lengths. I have used k-means analysis to separate vocal renditions of Bhūpālī from those of Deskār, and to separate vocal renditions of Bhūpālī from instrumental ones.

[30] Another study focused on quantification of svara frequency is the 1984 study by Castellano, Bharucha, and Krumhansl (1984), where listeners were asked to give ratings to svaras in different rāgas—the ten rāgas that lend their names to Bhatkhande’s ten thāṭs. The listeners were first subjected to a musical piece, following which they were made to listen to “probe tones” (single pitches, one of the twelve svara-pitches). They had to rate these probe tones in terms of how well these tones corresponded musically with the musical piece they had just heard. The highest ratings were given to sa and pa (possibly owing to the tanpura drone). The next highest rating was given to the vādī. The ratings resulted in plots of “tonal hierarchy” of svaras for these rāgas. My study analyses such parameters for Bhūpālī and Deskār, though based on exact measures obtained quantitatively through a computational study of recorded music, rather than being based on the perception of listeners.

[31] The Automated Transcription Project for Indian Music (AUTRIM) (S. Rao et al.), a joint project of the National Centre for Performing Arts (NCPA), India, and the University of Amsterdam (UvA), is an excellent resource for visualizing the svaras of a rāga as they are being sung. It makes use of the Praat software developed at UvA to convert rāga performances into detailed plots that can be visualized as “Music in Motion”. It contains such data for performances of more than 80 rāgas, Bhūpālī and Deskār included.

[32] David Clarke’s (2017) study on one ālāp in the rāga Yaman attempts to apply theories from Lehrdahl and Jackendoff’s 1983 work “A Generative Theory of Tonal Music” (GTTM) to Hindustānī music. Clarke finds that though GTTM has some limitations when applied to Indian music, at least a few features of Hindustānī music—such as the structuring of an ālāp that I described in a previous section—can be modelled using it.

[33] Preeti Rao and others have done far-reaching quantitative studies on rāga music. Some examples of the topics they cover are similarity between rāgas as understood from bandiś notation (Ross et al. 2017), classification of characteristic rāga phrases (P. Rao et al. 2014), discernment of these phrases by trained musicians (Ganguli and Rao 2019), identifying these phrases in audio recordings (Ross and Rao 2012), and differentiating between Hindustānī, Karnāṭik and Turkish music based on melodic features (Vidwans, Verma, and Rao 2020).

[34] To the best of my knowledge, there have been very few quantitative studies of alpatva and bahutva. I have already given the examples of the studies by Viswanathan and by Castellano et al. An important recent study by Ganguli and Rao compares rāgas with the same scale on the basis of tonal hierarchy, here based on the occurrence frequency and duration of svaras (Ganguli and Rao 2018). The present study has a different focus, since I have defined new quantitative measures.

Methods

[35] The Parselmouth code used to extract data from the recordings requires them to be converted into mp3 files. Movavi Video Converter 20 Premium was used for this purpose.[16]

[36] To analyze the svara content of the recordings, a modified version of Parselmouth code (the Python version of UvA’s Praat software) was used (Jadoul 2020), specifically the draw_pitch function. Each point in the extracted data represents the dominant frequency in 10 milliseconds, so there are 100 data points per second. The data thus obtained was plotted on Excel. Due to the drone of the tānpurā, the tonic note sa appears as a thick horizontal line in the plot. From its position, the pitch value corresponding to sa was ascertained by eye (see Figure 1). For each recording, the pitch values were normalized to the sa pitch.

 

[37] After this, FORTRAN was used to bin the data according to svara frequency, and to select only those frequencies that apply to svaras of the rāga. In a procedure similar to that described in Rao et al. (P. Rao et al. 2014), all frequencies to within 50 cents of a given svara were assigned to that svara (except in the data presented in Figures 3 and 4). Each svara was then assigned a number, starting with 1 for P̣, the pa of the mandra octave. For convenience, only the ‘major pentatonic’ svaras were assigned numbers. Ma and ni—whether komal or tīvra—and komal variants of re, ga and dhawere not considered, since they do not appear in the rāgas of the present study. Svaras higher than Ṗ (tāra pa) were also not considered, since their high pitch values mean that they are used extremely rarely, only in displays of exceptional virtuosity, such as in Sultan Khan’s recording of Bhūpālī, where the ati-tāra sa appears several times. Even in uttarāṅg-pradhān rāgas, svaras higher than Ṗ are not considered essential.

[38] Madhya sa (S) and mandra pa (P̣) have also been excluded from the analysis, since they do not bear much on the differences between the two rāgas, and it is in the usage of every other svara that the main differences between Bhūpālī and Deskār lie. Moreover, the tānpurā produces a constant drone of S and P̣. The Parselmouth code cannot distinguish the tānpurā sound from the voice or main instrument, and as a result, S and P̣ have high values in the probability distribution plots (Figures 2 and 3). I then attempted to reduce the tānpurā sound from the recordings using different parameters. This produces relatively minor quantitative differences in the data, but does not qualitatively change any of the conclusions of the study as compared to no reduction. Thus, the data for this manuscript was obtained without tānpurā reduction. This is discussed in greater detail in Appendix B.

[39] Using MATLAB, the percentage distribution of appearance frequencies (how often each svara appears) was plotted. Transition matrices (Bhattacharjee and Srinivasan 2011) were also prepared, which show the distribution of svara pairs, since svara-saṅgatis are an important component of rāga structure. The code treats only a pair of two non-identical svaras as a saṅgati. This means that SS, RR, GG and so on are not considered. Therefore, the main diagonal of the transition matrix appears as zeroes. This will become clearer in the next section.

Results

1. Probability distribution of svaras

[40] The distribution of occurrence of all frequencies from the data acquired from all artistes is shown in Figure 2 and 4 (Bhūpālī vocal vs instrumental), and figure 3 and 5 (Bhūpālī vocal, 7 samples, vs Deskār vocal, 8 samples). I have often felt that instrumentalists’ approaches to rāgas may differ from those of vocalists, and this is why I compared vocal and instrumental renditions of Bhūpālī. As for Deskār, instrumental recordings are less common, and thus, I only compared vocal recordings of Deskār to vocal recordings of Bhūpālī. Here each data point was slotted into one of 500 frequency bins.

[41] In this part, only re, ga, pa and dha are compared. The sound of the tānpurā possibly increases the component of mandra pa and madhya sa. Therefore, I cannot conclusively comment on the alpatva or bahutva of these svaras. The relative frequencies of these four svaras are apparent in Figures 6 and 7.

[42] In Bhūpālī, ga is the svara that is used the most often. The second position goes to re, followed by pa. Dha tends to be somewhat understated. In contrast, in Deskār, the order is dha, pa, ga. Re is highly understated.

[43] I next measured two more parameters for each artiste—the D-ratio (Figure 8) and the G-ratio (Figure 9). These ratios respectively represent how often a given svara occurs in comparison to how often dha (the vadi of Deskār but the samvadi of Bhūpālī) or ga (the vadi of Bhūpālī but the samvadi of Deskār) occurs. Thus, the D-ratio of a given svara (re, ga or pa) is the ratio of the appearance frequency, p(F_s), of this svara (represented by its pitch frequency F_s) to the p(F_s) of dha. The G-ratio of a svara (re, pa or dha) is the ratio of the p(F_s) of this svara to the p(F_s) of ga. The D-ratios and G-ratios for each recording of Bhūpālī and Deskār are shown in Tables 3 and 4 respectively. The means and standard deviations are shown in Table 5. The differences between Bhūpālī and Deskār in terms of alpatva and bahutva are clear upon inspection of these tables and of figures 8 and 9.

Bhūpālī
Artiste	D-ratios			G-ratios
	R/D ratio	G/D ratio	P/D ratio	R/G ratio	P/G ratio	D/G ratio
1.     Vocal
Kishori Amonkar	1.79	1.8	1.07	0.99	0.59	0.55
Kumar Gandharva	1.75	2.43	1.44	0.72	0.59	0.41
Prabhakar Karekar	1.98	2.16	1.58	0.91	0.73	0.46
Mashkoor Ali Khan	0.52	1.69	0.85	0.31	0.5	0.59
Rashid Khan	2.696	3.59	1.91	0.75	0.53	0.28
Padmini Rao	1.04	1.68	1.87	0.61	1.11	0.595
Padma Talwalkar	2.1	2.06	0.86	1.02	0.42	0.48
2.     Instrumental
Hariprasad Chaurasia	4.89	8.18	1.45	0.598	0.17	0.12
Rakesh Chaurasia 1	2.12	2.44	0.66	0.87	0.27	0.41
Rakesh Chaurasia 2	1.38	1.72	0.5	0.8	0.29	0.58
Rakesh Chaurasia 3	2.30	2.65	1.03	0.87	0.39	0.38
Rakesh Chaurasia 4	0.48	0.95	0.49	0.5	0.51	1.06
Pravin Godkhindi 1	1.36	1.15	1	1.18	0.87	0.87
Pravin Godkhindi 2	2.82	3.05	1.82	0.92	0.598	0.33
Bismillah Khan	3.74	8.295	2.19	0.45	0.26	0.12
Sultan Khan	3.08	5.395	1.6	0.57	0.297	0.18
Lalmani Misra	7.04	10.41	1.63	0.68	0.16	0.096
Gianni Ricchizzi	1.13	3.18	0.65	0.36	0.2	0.32

Table 3. Ratios of appearance frequency: R to D, G to D, P to D (D-ratios) and R to G, P to D, D to G (G-ratios), for Bhūpālī rendered by different artistes.

Deskār
Artiste	D-ratios			G-ratios
	R/D ratio	G/D ratio	P/D ratio	R/G ratio	P/G ratio	D/G ratio
Kishori Amonkar	0.11	0.72	0.48	0.15	0.67	1.39
Arati Ankalikar-Tikekar	0.13	0.46	0.54	0.29	1.18	2.17
Ajoy Chakraborty	0.19	0.58	1.13	0.32	1.95	1.72
Kumar Gandharva	0.12	0.55	1.15	0.22	2.11	1.83
Bhimsen Joshi	0.15	0.65	1.05	0.23	1.61	1.53
Archana Kanhere	0.03	0.15	0.6	0.22	4.12	6.87
Rashid Khan	0.17	0.6	0.73	0.28	1.22	1.67
Mallikarjun Mansur	0.11	0.36	0.61	0.3	1.71	2.8

Table 4. Ratios of appearance frequency: R to D, G to D, P to D (D-ratios) and R to G, P to G, D to G (G-ratios), for Deskār rendered by different artistes.

Ratio		Bhūpālī vocal		Bhūpālī instrumental		Bhūpālī all		Deskār
		mean	SD	mean	SD	mean	SD	mean	SD
D-ratios	R/D	1.7	0.66	2.76	1.82	2.34	1.57	0.13	0.04
	G/D	2.2	0.62	4.31	3.11	3.49	2.67	0.51	0.17
	P/D	1.37	0.42	1.18	0.56	1.26	0.52	0.79	0.26
G-ratios	R/G	0.76	0.23	0.71	0.23	0.73	0.23	0.25	0.05
	P/G	0.64	0.22	0.36	0.21	0.47	0.25	1.82	0.97
	D/G	0.48	0.1	0.41	0.3	0.43	0.25	2.5	1.70

Table 5. Mean values and standard deviations for the D-ratios and G-ratios for both rāgas. Shaded blocks indicate the vādī to saṁvādī ratios of each rāga.

[44] I shall first discuss the vādī to saṁvādī ratios (shaded in green)—ga to dha in Bhūpālī, and dha to ga in Deskār. The śāstras indicate that the vādī should have greater bahutva than the saṁvādī, but do not give quantitative information. Therefore, all we know from the śāstra is that this number should be greater than 1. The present study reveals more information. The vādī to saṁvādī ratios (G/D) for the Bhūpālī recordings in this study range from 0.95 to 3.6, with the mean being 3.49 and standard deviation being 2.67—except for four outliers, which I will discuss subsequently. The corresponding ratios for the Deskār recordings—i.e., the D/G ratios, since the vādī of Deskār is D and the saṁvādī is G—range from 1.5 to 2.8, except in Archana Kanhere’s recording, where the ratio approaches 7. The mean value is 2.5, and the standard deviation is 1.7.

[45] As for the re (the alpa svara) of Deskār, its mean D-ratio is 0.13, and mean G-ratio is 0.25. Both values are far less than 1. However, the re of Bhūpālī has a mean D-ratio of 2.34. Its mean G-ratio is 0.73. This suggests that re and ga are often used with roughly similar frequencies in this rāga. Interestingly, in one case—the recording of Pravin Godkhindi—the G-ratio of re (1.36) indicates that it has been used to an extent slightly greater than the vādī ga.

[46] The instrumental Bhūpālī recordings have higher mean D-ratios of R and G as compared to the vocal ones. The main contribution to this comes from the recordings of Lalmani Misra (vicitra vīṇā), Hariprasad Chaurasia (flute), Bismillah Khan (śahnā’ī) and Sultan Khan (sāraṅgī). These “outliers” as seen in Figure 8 seem to indicate that the approach of instrumentalists to a rāga may differ from that of vocalists. This is however too small a sample to make a conclusive claim. Not only does each individual musician have a different approach, but the same musician also renders the same rāga differently on different occasions.

[47] The mean D-ratio of the pa of Deskār is 0.79 (SD = 0.26), suggesting that pa and dha are used nearly to the same extent in this rāga. In three cases, pa appears to have been used to an extent slightly greater than the vādī dha. As for the G-ratios of pa, they lie roughly between 1.6 and 4, with the mean being 1.82. Thus, in all cases, pa has greater bahutva than ga in Deskār.

[48] I now move to the ratios of pa in Bhūpālī. The D-ratios and G-ratios show a large spread—0.5 to 2.8 in the former case, and 0.2 to 1.3 in the latter case. The mean values are 1.26 (SD = 0.52) and 0.47 (SD = 0.25) respectively. These results are shown pictorially in Figures 8 (D-ratios) and 9 (G-ratios), where each point represents a particular artiste. The distribution of D-ratios of Bhūpālī has no overlap with the corresponding distribution for Deskār. Similarly, there is a clear divide between the G-ratio distributions. Can such ratios help in raga recognition? To answer this question, I performed a k-means analysis (explained below) on the G-ratios and the D-ratios, to divide the data into two clusters. In the case of the G-ratio, the clusters identified were largely identical to Bhūpālī and Deskār. However, in the case of the D-ratio, the four outliers were identified as one cluster and all other data points were grouped into another cluster. The outliers are all instrumentalists. I had earlier commented upon differences in their renditions of ragas compared to vocalists. Thus, in the case of Bhūpālī and Deskār, k-means analysis may be said to be capable of distinguishing between them if only vocal recordings are used. This study does not include instrumental recordings of Deskār.

K-Means Analysis

[49] To categorize the G-ratios and D-ratios, I used k-means analysis. This is a widely-used clustering technique used to classify datapoints into two or more distinct clusters. The “k” in the name of the method refers to the number of mean values or centroids. In the case of the present work, k = 2. After the number of means has been defined, one feeds in guess values for each mean. The algorithm groups the datapoints based on which mean they are the closest to. After this, it calculates means for each cluster, uses these as the guess means, and repeats the steps. The process is iterated until there is no change in the means anymore. I used this technique to attempt to classify the recordings as Bhūpālī or as Deskār. However, the results obtained were different.

[50] k-means analysis on the D-ratios and G-ratios correlated well with figures 8 and 9. When the analysis was done on the D-ratios, all renditions of Bhūpālī were grouped along with the Deskār recordings, except for the four instrumental outliers in Figure 8: Lalmani Misra, Hariprasad Chaurasia, Bismillah Khan and Sultan Khan. The same result was obtained when the analysis was carried out only on the Bhūpālī recordings. When the analysis was repeated after leaving out the instrumental recordings, Mashkoor Ali Khan’s rendition (Bhūpālī vocal) was grouped along with the Deskār recordings.

[51] When the analysis was done on the G-ratios, Kishori Amonkar’s vocal recording of Bhūpālī was grouped along with the Deskār recordings. This could be owing to her well-known unconventional approach to rāgas. The same result was obtained when k-means analysis was carried out after leaving out the instrumental recordings. However, in the plot, the data point for Kishori Amonkar’s Bhūpālī appears separate from the Deskār cluster.

[52] The k-means analysis could not effectively separate the vocal and instrumental recordings of Bhūpālī in terms of G-ratios.

Svara-saṅgatis

[53] Transition matrices for svara pairs can be obtained by calculating their frequency of appearance. The transition matrices for Bhūpālī for all artistes are shown in Figure 10 (vocal) and Figure 11 (instrumental), and for Deskār in Figure 12. The y-axis represents the first svara of the pair, while the x-axis represents the second.

[54] The transition matrices show a near-tridiagonal structure, especially for Bhūpālī. The main diagonal consists of zeroes, since SS, RR, GG, PP etc. are not svara-saṅgatis. The first diagonals above and below the main diagonal indicate that pairs of consecutive svaras (SR, RS, RG, GR, GP, PG, PD, DP, DṠ, ṠD etc.) are more common than other pairs (SG, GS, RP, SP, PS, SD, ḌR, ḌG etc.). Such matrices may be made for svara pairs where each svara is held constant for a given time interval. Here the time interval is taken to be 20 milliseconds.

[55] In Bhūpālī, RG and GR appear much more often than other pairs, and RG appears more than GR. PD and DP are the next most common pairs, with PD appearing more frequently than DP. The high values for SR and RS for the Bhūpālī recordings could be tānpurā-influenced, and therefore, I have limited this part of study to the saṅgatis of R, G, P and D.

[56] In Deskār, the highest position is taken by DP and PD, followed by ṠD, DṠ, PG and GP. The calan of Deskār is highly uttarāṅg-dominated, and more compact than that of Bhūpālī.

[57] It is interesting that in both rāgas, the strongest svara-saṅgatis involve the vādī (G for Bhūpālī and D for Deskār) and the svara immediately below it. I term these Type 1 vādī saṅgatis. These saṅgatis are RG and GR in Bhūpālī, and PD and DP in Deskār. In Bhūpālī, the corresponding saṅgatis for the saṁvādī also have relatively high values.

[58] Let us now look at the saṅgatis involving the vādī and the svara immediately above it, which I shall call Type 2 vādī saṅgatis. These are GP and PG in Bhūpālī, and DṠ and ṠD in Deskār. The Type 2 saṅgatis in Deskār (DṠ and ṠD) are second in frequency to the Type 1 saṅgatis (PD and DP). However, in Bhūpālī, the saṅgatis that are second in frequency to the Type 1 vādī sangatis (RG and GR) are SR and RS, which do not involve the vādī at all. This brings out a difference in the role of the vādī in the two rāgas.

[59] The transition matrix of Deskār indicates that among the most frequent pairs, the avarohī (descending) pairs are more frequent than the corresponding ārohī (ascending) pairs. In other words, DP is more frequent than PD, PG is more frequent than GP, and so on. The difference is small, but consistent. The opposite pattern is observed in Bhūpālī. This is in accordance with Bhatkhande’s observation that uttarāṅg-pradhān rāgas (such as Deskār) place greater importance on the avaroh than the āroh, while pūrvāṅg-pradhān rāgas (like Bhūpālī) are āroh-dominated (Bhatkhande 1920s–30s vol.5, 34).

[60] The matrix of Deskār does not give conclusive information about the laṅghan (svara skipping) of re in the āroh (represented by the saṅgati SG), because saṅgatis involving svaras lower than ga appear to be much less common than saṅgatis from GP/PG and upwards.

[61] The question arises whether the near-tridiagonal structure of the matrices would still hold for a highly vakra rāga (one with many randomly ordered characteristic phrases) like Gauḍ Sāraṅg, where zigzag phrases like GRmG, PDMP, SmGP, NDNMP and so on are rather common. Answering this question would require further study of rāgas of different jāti (categories in terms of number of svaras) such as auḍav (pentatonic), ṣāḍav (hexatonic) and sampūrṇa (‘complete’, or heptatonic, i.e., using all svaras of the thāṭ), or rāgas whose āroh and avaroh are of different jātis, and also extend this study to more vakra rāgas, to get an understanding of the variation in these transition matrices.

Dīrgha bahutva

[62] The final strategy for quantitatively describing alpatva and bahutva used here is that of svara lengths, i.e., the length of time for which each svara is sung or played continuously. The data collected is summarized in Figures 13 and 14. In Deskār, re is highly reduced, and is rarely longer than 220ms. Long pa and long dha dominate, and appear more frequently, which can be seen in their graphs’ close proximity and contour resemblance. This similarity indicates that in Deskār, both these svaras have abhyās bahutva to nearly the same extent. Their appearance frequency is greater than for long ga in Bhūpālī.

[63] In Bhūpālī, the svara with the greatest dīrgha bahutva (in terms of how often a svara is elongated) is ga, followed by re, pa and dha, in that order. This was confirmed by computing average lengths.[17] The differences in dīrgha bahutva between any two of these svaras are smaller as compared to Deskār, where pa and dha have high dīrgha bahutva, re is never dīrgha, and ga is intermediate.[18] The length distributions of re and ga in Bhūpālī instrumental recordings appear to have higher values than those of vocal recordings, owing to the four outliers discussed in the previous section.

Conclusions

[64] Rāga grammar is transmitted through the śāstra, which is both oral—passed on from guru to disciple—and textual. However, there are important characteristics of the rāga in the lakṣya, which are imbibed subconsciously by listening and imitating. This article, focused on the scale-identical Hindustānī rāgas Bhūpālī and Deskār, has been aimed primarily at bringing to light some of those characteristics which are not explicit in the śāstra, but are nevertheless consistently present across musicians and musical styles. This study also confirms and quantifies known features of these rāgas.

[65] My findings are summarized as follows:

1. In terms of frequency of occurrence, as well as dīrgha bahutva (elongation), it is common knowledge that the first position should go to the vādī. However, the śāstra does not define the relative positions of the other svaras. My work shows that there is a clear ranking. The svaras can be arranged in decreasing order as follows in Bhūpālī: G, R, P, D. The corresponding order for Deskār is D, P, G, R, with R very rarely being sung for longer than 220ms in the sample set, confirming R’s place as Deskār’s alpa svara. Comparing the two rāga studied, the alpatva of D in Bhūpālī is less than the extreme alpatva of re in Deskār.
2. I have devised a clustering method where I represent each performer by a point that represents the D-ratios (ratio of the frequency of occurrence of a svara to that of D) of R, G and P, or the G-ratios (ratio of the frequency of occurrence of a svara to that of G) of R, P and D, for that particular performance. I chose these particular svaras for the following reason: G is the dominant svara (vādī) of Bhūpālī and the saṁvādī (svara in agreement with the vādī) of Deskār. As for D, it is the vādī of Deskār and the saṁvādī of Bhūpālī. Measurements of the G-ratios and D-ratios for all recordings yielded 3D plots where the distributions of Bhūpālī recordings were clearly separated from the corresponding distributions of Deskār. Four instrumental Bhūpālī recordings—those of Lalmani Misra (vicitra vīṇā) and Hariprasad Chaurasia (flute), Bismillah Khan (śahnā’ī) and Sultan Khan (sāraṅgī)—are clearly separated from all other recordings of Bhūpālī, in terms of their unusually high D-ratios for R and G. This indicates a difference between the approach to Bhūpālī of instrumentalists and that of vocalists and suggests a possible method for computer-assisted rāga identification. These ratios are to be studied in greater detail and taking into account aspects other than alpatva and bahutva would be an interesting future direction to pursue.
3. The śāstra says that the vādī is dominant but does not say by how much. My work quantifies this. The plot for re of Deskār is at a large distance away from the other plots. The plots show that G of Deskār has dīrgha bahutva that is comparable to that of R, P and D in Bhūpālī.
4. As expected for non-vakra rāgas, svara-saṅgatis (svara pairs) of consecutive svaras are much more common than saṅgatis of svaras that are not immediate neighbours. One may anticipate that pairs that include the vādī would have the highest occurrence. These pairs in Bhūpalī are RG, GR, GP and PG. In Deskār, they are PD, DP, DṠ and Ṡ My work shows a hierarchy among these pairs as well. RG and GR have far higher values than GP and PG in Bhūpālī. In fact, PD and DP—the saṅgatis involving the saṁvādī—have higher values than GP and PG, and are second to RG and GR. In Deskār, on the other hand, the first position goes to PD and DP, and DṠ and ṠD are second to these. The saṅgatis involving the saṁvādī come third. These findings point to a difference in the function of the vādī between the two rāgas.
5. The svara one scale degree below the vādī (R in Bhūpālī and P in Deskār) appears to be nearly as strong as the vādī itself. The vādī is considered the ‘king’, the saṁvādī the ‘minister’, and the anuvādīs the ‘servants’ (Bhatkhande 1920s–30s2, 14–15). However, in Bhūpālī and Deskār, anuvādīs have been shown to have greater bahutva than the saṁvādī. This indicates that rather than defining a single vādī and a saṁvādī svara in agreement (in the sense of pūrvāṅg-uttarāṅg symmetry) with it, it would be more appropriate to define one or more jīva svaras (‘lifeline’ svaras) that govern the calan (overall structure) of the rāga. A jīva svara is a svara that is of special importance in a rāga. For example, it may be an important nyāsa[19] svara in the rāga, or it might be a svara with a specific gamaka (i.e., alaṅkār) by which this particular rāga is distinguished from others. It may also be a point of high aesthetic value[20], or contributing to the unique identity of the rāga in other ways.[21] While this is considered a Karnāṭik approach (e.g., Dīkṣitar 1904, 350), I see great utility for it in Hindustānī music too. Bhatkhande too alludes to this idea, without using the term “jīva svaras”. For example, he says that the beauty of the rāga Toḍī is dependent on the svaras r, g and d, while also mentioning that the vādī is d and saṁvādī is g. Similarly, in the case of Multānī, whose vādī-saṁvādī are pa and sa, he says that its aesthetic form is governed by g, P and N.[22]

[66] Different artistes have different approaches to these rāgas in terms of which melodic motifs they use (as observed by listening to recordings), but an interesting interpretation of the data is that there is a broad similarity in the relative weightage that they give to different svaras (the G, R, P, D order for Bhūpālī, and D, P, G, R for Deskār), with some exceptions. I have confirmed this visually using individual probability distribution plots for each musician. Some examples are given in the appendix.

[67] In the future, it would be interesting to see whether similar numbers emerge for re in Śaṅkarā, a rāga where this svara appears to a comparable extent to its usage in Deskār. I envisage that the ni of Rāga Hiṇḍol would show even lower values than the re of Deskār or Śaṅkarā, since it is present as only a kaṇ in that rāga.

[68] There is of course a lot of inter-artiste variation, but there is also intra-artiste variation, in the sense that the same musician renders the same rāga differently on different occasions or on different instruments. The clustering method has the potential to quantify the uniqueness of styles of individual musicians, and also the uniqueness of each rendition of the same rāga by a given musician.

[69] In the theory of Hindustānī music, the svara known as vādī is defined as the svara with the greatest bahutva. The śāstra—for example, Bhatkhande’s Kramik Pustak Mālikā—says that ga is the vādī of Bhūpālī, and dha of Deskār. However, my study of the svara-saṅgatis and relative dominances of svaras reveals that the svaras immediately previous to them, re and pa respectively, are in practice often given nearly the same importance as the vādī. In some renditions, their bahutva might even be slightly higher than the bahutva of the vādī (for example, higher occurrence frequency of R as compared to G in Pravin Godkhindi’s Bhūpālī recording, or higher occurrence frequency of P as compared to D in Kumar Gandharva’s Deskār recording). Personally, I have long felt that rather than only stressing upon which svaras should be the vādī and saṁvādī, it makes more sense to say that the rāga has a number of jīva svaras(‘lifeline’ svaras) and nyās svaras (svaras that are resting points), and all these svaras contribute to its calan. The jīva svara approach is more common in Karnāṭik music, but the present study indicates that it holds good in Hindustānī music too. The vādī has been called the ‘king’ in some musical texts. Apart from having the greatest bahutva, it might ‘rule’ the calan of a rāga in other, more subtle ways. The subtleties revealed by the present study suggest that current rāga theories can be refined by studying a larger number of rāgas with methods similar to those used here. Also, it would be of interest to do similar studies of abundance and scarcity of musical notes in Karnāṭik music, and also in Western modes, Persian dastgāh, Arabian maqāms, Turkish and Balkan makams, and in similar melodic systems from the Far East or South-East Asia. Comparison of these other systems to Indian rāga systems could yield results that are hitherto unknown.

[70] Also, the Hindustānī tāla (musical meter) system has some beats that are emphasized more than others. Another question to ask would be which svaras more commonly occur on which type of beats, similar to the statistical methods used by Clayton (2020).

[71] Not only does the approach to one rāga vary from one person’s rendition to another, it also varies within one person’s lifetime. Each time the rāga is sung or played, it shows a different form of itself to the musician and the listeners. Using the methods established in this study, it would be an interesting exercise to quantify how rāga evolution takes place within the sphere of one musician’s riyāz (practice) and performance.

[72] The present study can be extended using machine learning techniques, whose popularity in studies of Hindustānī music appears to be on the rise. There are an immense number of rāgas in Karnāṭik, Hindustānī and other such systems of music, and as discussed in the introduction, they have several features beyond alpatva and bahutva. Artificial intelligence (AI) could extract and classify data just by ‘listening’ to a large corpus of recordings of several rāgas. It might thus be a crucial tool in developing a more refined general theory of rāgas. Another application of AI could be in distinguishing the actual music from the tānpurā drone.

[73] This study reminds us that the living music of rāgas is in the lakṣya, not the śāstra alone. Bhatkhande based his śāstra on the lakṣya of his time. As the lakṣya evolves, so must the śāstra. Studies such as the present one are important contributors to this process. It is interesting to study the evolution of rāgas from the medieval to the modern period using śāstras, but what is even more interesting to me is to study the evolution of the lakṣya on a much smaller timescale. Computational methods and AI could open up a wide range of possibilities in this regard.

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Acknowledgments

[74] I am grateful to Prof. Vishal Vasan for his help in understanding the code for pitch extraction using Parselmouth. I am also grateful to Prof. Preeti Rao for introducing me to the tānpurā reduction technique using Audacity, and to Mr. Yannick Jadoul for his help with Parselmouth. I am also extremely grateful to the anonymous referees for helping make this a better paper.

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Appendix A

[75] Hindustānī music has seven śuddha (‘pure’, i.e. ‘natural’) svaras—S, R, G, m, P, D and N, corresponding to a major scale or Ionian mode in Western music. The other five—r, g, M, d, n—are known as vikr̥ta (‘altered’). S and P are never vikr̥ta. Another way of grouping the svaras is as komal (flat) and tīvra (sharp), which applies to svaras other than S and P. The śuddha variants of re, ga, dha and ni are all tīvra. In the case of ma, the komal variant is considered śuddha.

[76] In the north, for a long time, the śuddha scale was SRgmPDn (Widdess 1995, 5). But in the 19^th century, possibly owing to the introduction of the harmonium into Hindustānī music, the Major scale/ Ionian mode (SRGmPDN) was chosen as the śuddha scale, and this has continued into the present day (Jairazbhoy 1971, 22). Thus, R, m and D, which were earlier known as śuddha r̥ṣabha, śuddha madhyama and śuddha dhaivata, are still known by the same names. The ‘original’ vikr̥ta svaras, G and N, which were earlier called tīvra gāndhāra and tīvra niṣāda, e.g., in the Saṅgīta Pārijāta of the 17^th century, are now called śuddha gāndhār and śuddha niṣād, while g and n, which were considered śuddha earlier, are now considered vikr̥ta, and called komal gāndhār and komal niṣād. Based on these twelve svaras, mela-s or parent scales are formulated (Powers et al. 2001; Bhatkhande 1910, 1920s–30s). A mela is a collection of seven svaras, sa ri ga ma pa dha ni, analogous to a heptatonic scale in Western music, examples of which are the major scale, natural minor scale and harmonic minor scale. In Hindustānī music, the term thāṭ is more commonly used instead of mela. The twelve svaras give rise to thirty-two thāṭs in Hindustānī music.

[77] Komal and tīvra are unambiguous terms. On the other hand, the definition of śuddha (natural) and vikr̥ta (altered) svaras varies with region and time. It is only the śuddha madhyam (m) whose definition has remained unchanged.

A brief historical background, and its modern relevance

[78] Early (pre-16th-century) Indian music was based on seven musical notes, known as svaras. These were—and still are—named ṣaḍja, r̥ṣabha, gāndhāra, madhyama, pañcama, dhaivata and niṣāda, and commonly known by their short names: sa, ri, ga, ma, pa, dha, ni. These notes were not defined relative to a system tonic as they are now. Rather, they corresponded to the Dorian mode beginning at the western note D (Widdess 1995 p.xv). In modern notation, these svaras would be S R g m P D n. Apart from the śuddha (‘natural’) notes, there were two additional notes, known as vikr̥ta (‘altered’) svaras. These corresponded to G and N. The svaras were partitioned between twenty-two microtonal intervals known as śruti-s.

[79] Śrutis (microtones) are still very important for Hindustānī and Karnāṭik music (S. Rao et al. ; S. Rao and van der Meer 2010). A śruti is a pitch, but not every śruti is a musical note (svara). Those śrutis that are actually used in a rāga or other melodic entity being performed are termed svaras (Bhatkhande 1920s–30s vol.4, 15). Though the twelve basic svara-sthāna-s (places of svaras) are as defined above, the same svara can vary in pitch depending on the rāga, being slightly higher (caṛhā huā) or lower (utarā huā) than its basic pitch, but still perceived and performed as that particular svara (S. Rao et al. ; S. Rao and van der Meer 2010). While some modern Hindustānī musicians base their svaras on the 22 śrutis (Bhatkhande 1920s–30s vol.4, 18), others—such as Chaitanya Kunte (Kunte 2017)—feel that in today’s time, there are not 22 but infinite śrutis, since the same svara has slightly different pitches in different rāgas, either by itself or with influence from other svaras. This work is concerned with comparing the relative abundance of the same svaras in both rāgas, so the difference in exact pitches of the same svara in both rāgas is not taken into account. However, I still felt it was important to discuss the śruti concept in brief here, since it is central to Hindustānī music. It would be interesting to incorporate this concept in future quantitative studies of rāgas.

[80] By the 16th century, sa, the tonic note, was no longer an absolute frequency. Instead, once it was defined as being at a particular pitch, the other notes would be defined relative to it.

[81] The precursor to rāga was known as jāti. It has the following lakṣaṇas (characteristics) (Qureshi et al. 2020; Widdess 1995, 47):

1. Graha: The note (svara) that begins the melody (or a composition/song that has been composed in this melody)
2. Aṁśa: The svara that is used the most frequently while singing the jāti. Widdess terms this the Predominant.
3. Apanyāsa: Svaras that act as end-points of phrases or of stanzas
4. Nyāsa: The svara that ends the song
5. Auḍava: pentatonic nature
6. Ṣāḍava: hexatonic nature
7. Tāra: This refers to the higher octave. Here it means the limit in the higher octave above which the jāti cannot move.
8. Mandra: This refers to the lower octave. Here it means the limit in the lower octave below which the jāti cannot move.
9. Alpatva: translated by Widdess as “infrequent pitches”
10. Bahutva: translated by Widdess as “frequent pitches”

[82] The word rāga as a musical entity first appears in the 8^th century (Qureshi et al. 2020). When jātis evolved into rāgas, most of the above lakṣaṇas continued to be used for them. These concepts have evolved over time. The musicologist Vishnu Narayan Bhatkhande (1860-1936) (Bhatkhande 1910, 193-, 1914, 1920s–30s), who is credited with having written the first modern treatise on Hindustānī music, carried out a detailed study of several ancient and medieval texts (Bhatkhande 193-) and received knowledge of south Indian music from the musician-scholar Subbarāma Dīkṣitar (Bhatkhande 1904). Bhatkhande bases his rāga theory on a modified version of the theory in these sources, and the influence of his works persists to the present day, possibly to a greater extent than that of any other music scholar’s works.

[83] The term jāti has changed its meaning, and now refers to auḍav (pentatonic), ṣāḍav (hexatonic), sampūrṇa (heptatonic) and so on.

[84] The dominant svara (aṁśa) is called jīva svara (the svara that is the lifeline) in modern Karnāṭik music, and vādī in modern Hindustānī music (Powers et al. 2001). Another svara, known as the saṁvādī, is considered the second dominant svara, and is in agreement (saṁvād) with the vādī. The concept of saṁvādī is a point of difference between modern Hindustānī music and the medieval music of northern India that preceded it. The vādī and saṁvādī of the modern Hindustānī rāga Bhūpālī are ga and dha respectively. Deskār, which shares the same scale, has dha for its vādī and ga for its saṁvādī.

[85] Nyās svaras, rather than being analogous to the word ‘finis’ used in the end of a book, are now the svaras on which phrases end, like ‘full stops’ of musical ‘sentences’. There is no one single nyās svara on which the melody compulsorily must end. Sa is by definition a nyās svara in every rāga, and there are one or more other svaras on which one may rest. For example, in Bhūpālī, ga is the other important nyās svara apart from sa, and in Deskār, the nyās points are dha and pa.

[86] A major change happened in the 16^th century or slightly earlier, with the introduction of more vikr̥ta svaras and the change in the definition of sa from a roughly absolute frequency to a “system tonic” relative to which the other svaras are defined (Qureshi et al. 2020). Music began to be defined in terms of twelve svaras: seven śuddha (‘pure’ or ‘natural’) svaras, and five vikr̥ta svaras.

 Appendix B

A note on tānpurā reduction

[87] A noise reduction study was conducted to estimate the effect of the tānpurā drone and other background noises. For this, the noise reduction feature on AudacityÒ 2.3.2[23] was used. A few seconds of the tānpurā-only segment in the beginning of the recording were selected as ‘noise’ and filtered out, as has been done in earlier studies (P. Rao, p.c. 2020; V.M. Rao 2011). Over a big majority of the signal, no effect of noise reduction was detected on visual inspection. But in small portions of the recording, spurious frequencies were removed and replaced by the signal, presumably made by the artiste. An example of the effect of noise reduction is shown in Figure B1. It is seen that noise reduction brings about a more continuous signal.

Figure B1. Noise reduction, a sample, from Rashid Khan’s Bhūpālī rendition. The red graph shows the raw data, and the blue graph shows the data after noise reduction. The svaras are indicated on the y-axis.

Figure B2. The probability density plot for Kumar Gandharva’s Bhūpālī rendition, with and without tānpurā reduction (shown respectively by a blue solid line and black dotted line)

[88] Several of the recordings were analysed with and without noise reduction, and it was checked that, while the intensity of the madhya sa and the mandra pa were reduced, the ratios of the other svaras to each other were not significantly altered. Also, plots of different quantities measured in this study were made with and without noise reduction, and there was no qualitative difference. An example of this is shown in Figure B2.

[89] As can be seen in this figure, the reduction of S and P̣ is not complete. A stronger reduction may lead to loss of intensity of the signal. I note that the reduction can be done using different parameters, and each time, there are small differences in the results. However, these are always minor for all the recordings, and do not alter any of the conclusions of this study. Overall, it was decided to follow the consistent approach of not using the reduction for any of the recordings analyzed in this study.

---

 References

Bhatkhande, Vishnu Narayan. 193–. A Comparative Study of Some the Leading Music Systems of the 15th, 16th​, 17th and 18th Centuries. Bombay: M. Sukthankar.

—––. 1904. In Mājhā Dakṣiṇecā Pravās (Hindi translation: Merī Dakṣiṇ Bhārat kī Saṅgīt Yātrā, 1986 edition), 122–140. Khairagarh: Indira Kala Sangeet Vishwavidyalaya.

—––.1910. Śrīmal-Lakṣyasaṅgītam. Mumbai: Nirnaya-sagar Press (printed by Balkrishna Ramchandra Ghanekar).

—––.1914. Hindustānī Saṅgīt Paddhati. 4th Hindi edition 1974 ed. Vol. 1. Hathras: Sangeet Karyalaya.

—––.1920s–30s. Hindustānī Saṅgīt Paddhati Kramik Pustak Mālikā – Hindi edition 1990. Vol. 1 to 6. Hathras: Sangeet Karyalaya.

Bhattacharjee, Arindam, and Narayanan Srinivasan. 2011. “Hindustani Raga Representation and Identification: A Transition Probability Based Approach”. International Journal of Mind, Brain and Cognition 2(1–2): 65–94. https://icmacyfoundation.org/wp-content/uploads/2021/02/Hindustani-raga-representation-and-identificatio.pdf

Castellano, Mary A., J. J. Bharucha, and Carol L. Krumhansl. 1984. “Tonal Hierarchies in the Music of North India.” Journal of Experimental Psychology: General 113, no. 3: 394–412. https://psycnet.apa.org/doiLanding?doi=10.1037%2F0096-3445.113.3.394 (https://doi.org/10.1037/0096-3445.113.3.394)

Clarke, David. 2017. “North Indian Classical Music and Lerdahl and Jackendoff’s Generative Theory – a Mutual Regard.” Music Theory Online 23(3). https://mtosmt.org/issues/mto.17.23.3/mto.17.23.3.clarke.html

Martin Clayton. 2020. “Theory and Practice of Long-form Non-isochronous Meters: The Case of the North Indian rūpak tāl.” Music Theory Online 26(1). https://doi.org/ 10.30535/mto.26.1.2

Dīkṣitar, Subbarāma. 1904. Saṅgīta Sampradāya Pradarśinī. English Web Edition 2008: Dr. P. P. Narayanaswami, Vidya Jayaraman, et al., accessed September 2022. Source:
http://ibiblio.org/guruguha/ssp.htm

Ganguli, Kaustuv Kanti, and Preeti Rao. 2018. “On the distributional representation of ragas: experiments with allied raga pairs.” Transactions of the International Society for Music Information Retrieval 1(1): 79–95.https://doi.org/ 10.5334/tismir.11

–––. 2019. “On the perception of raga motifs by trained musicians.” Journal of the Acoustical Society of America145(4): 2418–34. https://doi.org/10.1121/1.5097588

Jadoul, Yannick. 2020. “Parselmouth – Praat in Python, the Pythonic way. © Copyright 2017–2020, Yannick Jadoul Revision 5a2eaa87.” https://parselmouth.readthedocs.io/en/stable/examples/plotting.html.

Jairazbhoy, Nazir Ali. 1971. The Rāgs of North Indian Music – Their Structure and Evolution. London: Faber and Faber.

Kunte, Chaitanya, p.c. 2017.

Lerdahl, Fred, and Ray Jackendoff. 1983. A Generative Theory of Tonal Music. Cambridge, Massachusetts: The MIT Press.

Powers, Harold, Frans Wiering, James Porter, James Cowdery, Richard Widdess, Ruth Davis, Marc Perlman, Stephen Jones, and Allan Marett. 2001. “Mode.” Grove Music Online.

Qureshi, Regula, Harold S. Powers, Jonathan Katz, Richard Widdess, Gordon Geekie, Alastair Dick, Devdan Sen, Nazir A. Jairazbhoy, Peter Manuel, Robert Simon, Joseph J. Palackal, Soniya K. Brar, M. Whitney Kelting, Edward O. Henry, Maria Lord, Alison Arnold, Warren Pinckney, Kapila Vatsyayan, Bonnie C. Wade, and Inderjit N. Kaur. 2020. “India, subcontinent of.” In Grove Music Online.

Rao, Preeti, p.c. 2020.

Rao, Preeti, Joe C. Ross, Kaustuv Kanti Ganguli, Vedhas Pandit, Vignesh Ishwar, Ashwin Bellur, and Hema A. Murthy. 2014. “Classification of Melodic Motifs in Raga Music with Time-series Matching.” Journal of New Music Research 43(1): 115–31. https://doi.org/10.1080/09298215.2013.873470

Rao, Suvarnalata, and Wim van der Meer. 2010. “The construction, reconstruction, and deconstruction of shruti.” In Hindustani music: thirteenth to twentieth centuries, edited by J. Bor, F. Delvoye, J. Harvey and E. te Nijenhuis, 673–96. New Delhi: Manohar.

Rao, Suvarnalata, Wim van der Meer, Rustom Irani, and Salil P. Kawli. “Bhupali.” Music in Motion: The Automated Transcription for Indian Music (AUTRIM) Project by NCPA and UvA. Accessed 10 April 2021. https://autrimncpa.wordpress.com/bhupali/.

—––.”Deshkar.” Music in Motion: The Automated Transcription for Indian Music (AUTRIM) Project by NCPA and UvA. Accessed 10 April 2021. https://autrimncpa.wordpress.com/deshkar/.

—––. “Music in Motion: The Automated Transcription for Indian Music (AUTRIM) Project by NCPA and UvA.” Accessed 10 April 2021. https://autrimncpa.wordpress.com/.

—––.”Tonal system.” Music in Motion: The Automated Transcription for Indian Music (AUTRIM) Project by NCPA and UvA. Accessed 10 April 2021. https://autrimncpa.wordpress.com/tonal-system/.

Rao, Vishweshwara Mohan. 2011. “Vocal Melody Extraction from Polyphonic Audio with Pitched Accompaniment.” PhD, Department of Electrical Engineering, Indian Institute of Technology, Bombay.https://doi.org/10.1109/TASL.2010.2042124

Ross, Joe C., Abhijit Mishra, Kaustuv Kanti Ganguli, Pushpak Bhattacharyya, and Preeti Rao. 2017. “Identifying raga similarity through embeddings learned from compositions’ notation.” 18th International Society for Music Information Retrieval (ISMIR) Conference, Suzhou, China. https://www.cse.iitb.ac.in/~pb/papers/ismir17-raga-similarity.pdf

Ross, Joe C., and Preeti Rao. 2012. “Detection of raga-characteristic phrases from Hindustani classical music audio.” Proceedings of the 2nd CompMusic Workshop, Istanbul, Turkey. http://hdl.handle.net/10230/20368

Vidwans, Amruta, Prateek Verma, and Preeti Rao. 2020. “Classifying Cultural Music using Melodic Features.” Proceedings of SPCOM, July 2020, IISc, Bangalore. https://doi.org/10.1109/SPCOM50965.2020.9179597

Viswanathan, T. 1977. “The analysis of raga alapana in South Indian music.” Asian Music 9(1) (Second India Issue): 13–71. https://doi.org/10.2307/833817

Widdess, Richard. 1995. The Ragas of Early Indian Music: Modes, Melodies, and Musical Notations from the Gupta Period to C. 1250. Oxford: Clarendon Press.

Yardi, Shivani, and Elaine Chew. 2004. “Giving Ragas the Time of Day: Linking structure, emotion and performance time in North Indian Classical Music using the Harmonic Network.” Proceedings of the 8th International Conference on Music Perception and Cognition, Evanston, IL, USA.

[1]. This process is also used in Hindustānī and Karnāṭik music, but to a much smaller extent. The Hindustānī music term for it is mūrcchanā. It may be used for purposes of teaching or, occasionally, to create novelty in a performance. However, its role in Hindustānī and Karnāṭik music is not pivotal.

[2]. Karnāṭik music defines the same svaras differently, but that is beyond the scope of this article.

3. The name saptak comes from sapta, meaning seven. This comes from the seven svaras, sa re ga ma pa dha ni. However, there are in reality twelve svaras in a saptak, since there are two each of re, ga, ma, dha and ni.

 

[4]. Bhatkhande, Vishnu Narayan, 1920s–1930s. Hindustānī Saṅgīt Paddhati – Kramik Pustak Mālikā. For this paper, I have used the 1990 Hindi edition, published by Sangeet Karyalaya, Hathras.

[5]. The word has multiple meanings in Sanskrit, such as “color”, “dye”, “love”, “intense emotion.” Rāgas in music are characterized by the quality of rañjana, which literally means “the act of coloring or dyeing”, and is derived from the same root verb as rāga does. In a musical sense, rañjanarefers to “coloring the mind”, i.e., being aesthetically pleasing.

[6]. Further details are provided in Appendix A.

[7]. Harishchandra Srivastava, editor of the Hindi edition of the Kramik Pustak Mālikā, in his preface to Vol. 3, titled Kramik Pustak Mālikā kā Lekhak Kaun (Who is the writer of the Kramik Pustak Mālikā), says: “…it appears that after Bhalchandra Sitaram Sukathankar, the previous publisher of this Kramik Pustak Mālikā, when this book reached the hands of another publisher, in order to make the books more important and useful, the author’s name was cited as Pt. Vishnu Narayan Bhatkhande, and all scholars continued to believe this to be true. Nobody tried to look in more detail. I too, following the view of the majority, am considering Paṇḍit Bhatkhande as the author. Here, I feel it necessary to remind [readers] that Paṇḍit Bhatkhande passed away in 1936, and during his lifetime, several editions of the second and third volumes of these books were published”. Whatever be the case, there is no doubt that the music theory in these books is Bhatkhande’s, going by his earlier works such asŚrīmal-Lakṣyasaṅgītam (Mumbai: Nirnaya-Sagar Press, 1910) and Hindusthānī Saṅgīt Paddhati (1910–1932, 4 volumes, distinct from the Kramik Pustak Mālikā, Hindi edition: Hathras: Sangeet Karyalaya, 4^th edition 1974, reprint 2006). Also, as Srivastava mentions in his preface, notations of music compositions collected by Bhatkhande are present in the Kramik Pustak Mālikā. Since the 6-volume Kramik Pustak Mālikā has become the most important set of textbooks for modern Hindustānī music, I cite it at several points in this work. Following Srivastava, I too attribute it to Bhatkhande.

[8]. Saṁvād is defined as the occurrence of corresponding phrases with the same relative spacing of svaras in the pūrvāṅg and uttarāṅg (defined later in the paragraph) of a rāga, for example, the phrase RGPG in the pūrvāṅg of Bhūpālī, and its “mirror image” PDṠD in the uttarāṅg.

[9]. The letter c, when used in Indian words in this paper, represents the unvoiced alveolo-palatal affricate, च in the Devanāgarī script.

[10]. The former phrase typically makes it immediately obvious to a trained ear that the rāga being heard is Deskār. While the latter occurs in Bhūpālī in fast-paced segments, it is characteristic of Deskār in the slower segments, which form the bulk of the performance of a rāga. In the slow part of a performance of Bhūpālī, D in the phrase ga pa dha sa is always coloured with a kaṇ of Ṡ.

[11]. Another rāga with the major pentatonic scale.

[12]. Traditionally, these were families of hereditary musicians attached to different royal courts, each family having its own style of rendering rāgas. They also trained students outside the family in their style. Gharānās are typically named after the capital cities of the courts to which they were attached. Today, gharānās survive in the form of distinct musical styles that are performed and imparted to students. However, in modern times, there is a great deal of intermixing of gharānā styles, especially in ḵẖayāl. Many musicians—for example, Kishori Amonkar and Kumar Gandharva—have created individual styles that cannot be mapped to any one gharānā style.

[13]. Kishori Amonkar too received training in the style of this gharānā, but went on to create her own style that was unbounded by gharānā.

 

[14]. Ālāp is known as ālāpanā in Karnāṭik music.

[15]. These rāgas are overall heptatonic. The first four are sampūrṇa-sampūrṇa, the fifth is auḍav-sampūrṇa, and the last is ṣāḍav-sampūrṇa.

[16]. https://www.movavi.com/videoconvertermac/

[17]. The average lengths for Bhūpālī (in centiseconds) are – G: 11.47, R: 9.81, P: 8.93 and D: 8.48.

[18]. The average lengths for Deskār (in centiseconds) are – D: 8.19, P: 6.72, G: 6.60 and R: 3.27.

 

[19]. The Sanskrit root word nyāsa (nom. sing. nyāsaḥ) is pronounced as nyās in Hindi.

 

[20]. Rañjana, described in Footnote 2.

[21]. To give some Karnāṭik examples, as described in Subbarāma Dīkṣitar’s 1904 text the Sangita Sampradāya Pradarśinī: For the rāga Śrī, the jīva and nyāsa svara is R. For Kalyāṇī, there are two jīva and nyāsa svaras – G and R. Mohanam, the Karnāṭik rāga closest to Bhūpālī and Deskār, has three – G, D and R. I assume that Dīkṣitar’s arrangement of the svaras in this order qualitatively indicates a decreasing order of bahutva (Dīkṣitar 1904 pp. 461, 1159, 1186).

[22]. Both these rāgas belong to the Toḍī thāṭ (SrgMPdN). But the difference in the vādī-saṁvādī and “jīva svaras”, along with the difference in āroh-avaroh (SrgMPdNṠ/ SrgMdNṠ – ṠNdPMgrS for Toḍī, and ṆSgMPNṠ – ṠNdPMgrS for Multānī) and uccāraṇ of the svara ga (^rg in Toḍī, ^Mg in Multānī) makes all the difference between them.

[23]. Version 2.3.2 retrieved from https://audacityteam.org/ (2019). Audacity® software is copyright © 1999-2020 Audacity Team. Web site: https://audacityteam.org/. It is free software distributed under the terms of the GNU General Public License. The name Audacity® is a registered trademark of Dominic Mazzoni.