सङ्गीतरत्नाकर: प्रथम भाग (शार्ङ्गदेव - स्वरगताध्याय सविस्तार व्याख्या व अनुवाद सहित)

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164 Treatment of Svara
(iv) गान्धारग्रामः
यदा धस्त्रिश्रुतिः षड्जे मध्यमे तु चतुःश्रुतिः ॥३॥
रिमयोः श्रुतिमेकैकां गान्धारश्चेत्समाश्रितः ।
षट्श्रुतिं धो निषादस्तु धश्रुतिं सश्रुतिं श्रितः ॥४॥
गान्धारग्राममाचष्ट तदा तं नारदो मुनिः ।
प्रवर्तते स्वर्गलोके ग्रामोऽसौ न महीतले ॥५॥
(iv) The gāndhāra-grāma : 4-5
If gāndhāra takes one śruti each from ṛṣabha and
madhyama, dhaivata takes one śruti from pañcama, and niṣāda
takes one śruti each from dhaivata and ṣaḍja, it becomes
gāndhāra-grāma as declared by the sage Nārada¹. This grāma
is prevalent in the heaven², not in this world. (4-5)
In the tradition of Bharata, which Mataṅga seems to follow, only
two grāma-s, viz., the ṣaḍja-grāma and the madhyama-grāma are recognised
(cf. Br. D. 93). However Narada, of uncertain chronology, refers to a
third grāma called gāndhāra-grāma which, our author after Mataṅga
declares, was meant to be used exclusively by gods and not by human
beings. This grāma is derived by him from the ṣaḍja-grāma as described
in the text and accordingly can graphically be demonstrated as under :
The three grāma-s

(Chart 11)
Dhaivata takes one śruti from pañcama (of the ṣaḍja-grāma) and
yields one śruti to niṣāda, retaining in effect the same number of śruti-s.
1. Nārada is a very ancient name, known to Veda as the brahmarṣi
and the Purāṇas as devarṣi. He is associated with Bharata in the very first
performance of drama (N. S. Kashi ed, 5.32). Bharata mentions Nārada
as an authority on gandharva (N. S Kashi ed. 32.484). At least five per-
sonalities are discerned by the name of Nārada including the authors of
Nāradīya-śikṣā and Saṅgīta-makaranda (cf. S. Raj, Vol. 1, pp. 667-668 for a
detailed description). In short, Nārada is an ancient authority on music.
2. The heaven in the Hindu mythology, is the abode of gods;
those who accumulate merit by good deeds, are born as gods in heaven
and as the merit earned by them is exhausted, they are again reborn as
mortals in noble families. On the other hand, the gods are considered

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Section 4 : Grāma, Mūrcchanā, Krama and Tāna 165
(v) ग्रामत्रयस्य नामस्वराणां वैशिष्ट्यम्
षड्जः प्रधानमाद्यत्वादमात्याधिक्यतस्तथा ।
ग्रामे स्याद्विलोपित्वान्मध्यमस्तु पुरःसरः ॥६॥
एतत्कुलप्रसूतत्वाद् गन्धारोऽप्यग्रणीर्दिवि ।
(v) Justification for the three grāma-s: 6-7b
Ṣaḍja is the prime tone¹, for being in the first position
and also for having more ministers² in the grāma; madhyama
too is in the fore-front, because it cannot be omitted. Being
a descendant of the same family, even gāndhāra is the promi-
nent note in the heaven. (6-b)
Now, the question is why the three grāma-s are named particularly
after ṣaḍja, madhyama and gāndhāra, and not after any other notes such as
pañcama or niṣāda and so on. The author explains that it is because ṣaḍja
is the most prominent tone; and that for two reasons viz., it is the funda-
mental note and also it is in consonance with more notes than the other
-i.e., with pañcama and madhyama; whereas other tones have only one
consonant.
Madhyama is also an important note since it cannot be omitted
while composing standard (śuddha), hexatonic and pentatonic note-
series (tāna-s). 'K' also suggests another reason. Madhyama cannot be
omitted because the three notes preceding it are quite in balance with
the three notes succeeding it, and have a certain consonance in-between
them, but madhyama being centrally situated is isolated from that sort
of relationship and therefore serves as the boundary line between the
two sets of notes, making itself in-omissible. 'S' quotes Dattila regar-
ding the inomissibility of madhyama to the following effect.
"Pañcama in the madhyama-grāma, and dhaivata in the ṣaḍja-grāma
are inomissible, but however madhyama is so everywhere."
Gāndhāra-grāma is so named because it is a descendent of the same
family of gods to which ṣaḍja and madhyama belong and is thereby the
prominent note in heaven, where it is said to be prevalent. 'S' quotes
Mataṅga in support of this reasoning.
"Why indeed this particular nomenclature ṣaḍja and madhyama-
grāma ? To explain, they have been assigned grāma names because of
their being extraordinary, and that is because of their being born in the
family of gods." (cf. I.3.52ab ante)
1. Pradhāna literally means 'the chief', in other words, the most
important tone.
2. The consonant tones have been referred to as ministers (cf.
3.50 ante).

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166 Treatment of Svara
(vi) ग्रामाणां देवा।
क्रमाद् ग्रामत्रये देवा ब्रह्मविष्णुमहेश्वराः ॥७॥
(vi) The presiding deities of the grāma-s : 7cd
The presiding deity in each of the three grāmas respec-
tively¹ is Brahmā, Viṣṇu and Śiva.² (7cd)
(vii) ग्रामाणां गानकालनियमः
हेमन्तग्रीष्मवर्षासु गातव्यास्ते यथाक्रमम् ।
पूर्वाह्णकाले मध्याह्ने ऽपराह्ने ऽभ्युदयार्थिभिः ॥८॥
(vii) The periods of time as related to the grāma-s: 8
They¹ are to be sung by those who are desirous of
prosperity in the forenoon², mid-day and in the afternoon, in
the winter, summer and in the rainy season respectively. (8)
The expression "gātavyāste" is quite significant and also thought-
provoking. The pronoun 'they' (te) obviously stands for the three
grāma-s ; and therefore two interesting questions arise in this particular
context : (i) are the grāma-s meant to be sung ? (ii) Is singing to be
restricted to winter in case of the ṣaḍja-grāma, to summer in case of the
madhyama-grāma and to rainy season in case of the gāndhāra-grāma ? and
if so, the gāndhāra-grāma cannot be used on earth as it is prevalent in the
heaven only; then how should one sing in the rainy season ? Moreover,
the grāma-wise distribution of the day into three parts presents another
problem on the same lines.
The grāma-s, it is generally held, were not meant to be sung ; but
what is probably collectively referred to in the text by way of grāma,
is the various types of melodic patterns or musical forms set in the
pattern of the particular grāma-s, such as jāti-s and rāga-s. It is interes-
ting to find 'S' quoting Mataṅga with reference to the function of grāma

1. That is, in the ṣaḍja, madhyama and gāndhāra-grāma, in respec-
   tive order.
2. The appellation Maheśvara (Mahā+īśvara—the great God) is
   used in the text.
3. That is, the three grāma-s.
4. Pūrvāhṇe, literally means 'in the anterior period' with reference
   to the middle period of the day, i. e.. the mid-day. Thus, we
   can also divide as forenoon, noon and afternoon.

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Section 4 : Grāma, Mūrcchanā, Krama and Tāna 167
in this context ; it is said—"the purpose of grāma is to regulate the
organisation of svara, śruti, mūrcchanā, tāna, jāti and rāga." Obviously,
these are the main factors of the ancient Indian music known as the
grāma-mūrcchanā-jāti system.
Thus, the expression 'they are to be sung', refers not merely to the
basic scales of the grāma-s, but all those melodic structures or musical
forms that are set into their basic pattern.
Accordingly, the text is suggestive of another function of the
three grāma-s viz., their individual suitability to a particular season.
The traditional six Indian seasons have been compressed into three for
functional purposes ; and on this basis one is led to infer that even
gāndhāra-grāma might have been prevalent sometimes in the forgotten
past All that the text implies is that the three grāma-s are more
suitable for the three respective seasons and the divisions for the day,
but not that they are exclusively to be employed on restricted basis.
ख. मूर्च्छनाः क्रमाश्च
(i) मूर्च्छनालक्षणम्
क्रमात्स्वराणां सप्तानामारोहश्चावरोहणम् ।
मूर्च्छनेत्युच्यते ग्रामद्वये ताः सप्त सप्त च ॥९॥
The mūrcchanā-s and krama-s : 9-26b.
(i) The definition of mūrcchanā: 9
The ascending and the descending movement of the
seven notes in successive order is called mūrcchanā. There¹
are seven mūrcchanā-s in each of the two² grāma-s. (9)
The concept of mūrcchanā is quite important in this system of
music, and should therefore be understood quite adequately.
The word 'mūrcchanā' is derived by Mataṅga from the Sanskrit
root mūrcch—to faint or to increase. Thus he defined mūrcchanā as :
"mūrcchyate yena rāgo hi mūrcchanā-ityabhisañjñitā" i.e., "That by which
the rāga develops is called mūrcchanā." Basically it is the movement,
ascending as well as descending of the seven notes which is called
mūrcchanā in the text. However, 'S' quoting Mataṅga in his support

1. That is, in this world excluding heaven.
2. That is, the ṣaḍja-grāma and the madhyama- grāma.

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168 Treatment of Svara
makes it clear that it is in fact the seven notes arranged in regular order
of ascent and descent which stand to be called as mūrcchanā i.e., in other
words, the action of ascent and descent, that is, the tonal movement is
not to be called mūrcchanā, as it is said by Mataṅga :
"The unit of seven notes in regular order of ascent and descent is
known to be the referent of the word mūrcchanā by the experts of the
subject."
Obviously a very subtle distinction has been made; for indeed, it
is the seven notes in the ascending or the descending movement in their
successive order that constitute mūrcchanā. The movement is quite
inherent in the tones if they are to form a mūrcchanā. Thus, the distinc-
tion is rather formal and may be construed as helpful in placing the
emphasis rightly on the tones, rather than on their movement. Ravi
Shankar defines mūrcchanā as, "scale-wise progressions in descending
motion from the fundamental notes." (cf. Glossary of Technical Words
'My Music, My Life').
The function of mūrcchanā is to develop, to enlarge and to spread
the rāga. Obviously, it is not possible to restrict the arrangement of
mūrcchanā-s to any one register, and as pointed out by 'K' in order to
show their range to be co-extensive with the three registers, Mataṅga,
speaks of mūrcchanā-s of twelve notes as well, but this seems unnecessary
in view of the two grāma-s being used conjointly, covering the three
registers. Kumbhā mentions Kohala and Nandikeśvara as supporting
Mataṅga in his view, but he totally rejects it by himself as technically
uncalled for (cf. S. Raj. 2.1.1. 352-357).
Thus it is settled, as per the text that there are seven mūrcchanā-s
in each grāma.

(ii) षड्जमध्यमग्रामस्थमूर्च्छनानां संज्ञाः
षड्जे तूत्तरमन्द्रा ऽऽदौ रजनी चोत्तरायता ।
शुद्धषड्जा मत्सरीकृदश्वक्रान्ता ऽभिरुद्गता ।।१०।।
मध्यमे स्यात् सौवीरी हरिणाश्वा ततः परम् ।
स्यात्कलोपनता शुद्धमध्या मार्गी च पौरवी ।।११।।
हृष्यकेति,
(ii) The names of the mūrcchanā-s of the ṣaḍja and madhyama-
grāma-s : 10-12a
The first in ṣaḍja-grāma is uttaramandrā which is followed
[by rajanī, uttarāyatā, śuddha-ṣaḍjā,] matsarīkṛtā, aśvakrāntā and

Page 169

Section 4 : Grāma, Mūrcchanā, Krama and Tāna 169
abhirudgatā. Madhyama-grāma has sauvīrī, hariṇāśvā, kalopanatā,
śuddhamadhyā, mārgī, pauravī and hṛṣyakā. (10-12a)
The names of these fourteen mūrcchanā-s seem to be quite significant
and some scholars have even ventured to speculate regarding their
literal signification as related to their musical content and aesthetic effect;
for example, the name of the first mūrcchanā of the ṣaḍja-grāma uttara-
mandrā, literally means, "the one that follows the mandra i. e., the lower
(heptad)" and this exactly tallies with its tonal position, since it com-
mences with the ṣaḍja of the middle heptad.
Now, the question (as raised by 'K') is, 'Why should the mūrcchanās
of the ṣaḍja-grāma begin with the ṣaḍja of the middle register?' i. e., why
not with some other note of, say, the lower register? And 'K' explains,
"that is so, because Bharata has ordained it that way," quoting him,
"mūrcchanā should be demonstrated on vīṇā with the tone madhyama
(madhyama svareṇa vaiṇavena mūrcchanā-nirdeśaḥ)". And then 'K' goes on
to quote Mataṅga in his interpretation of Bharata : "Mūrcchanā should
commence with the middle register in order to establish the lower and
the higher registers (madhya-saptakena mūrcchanā-nirdeśaḥ kāryo mandratāra-
sidhyartham)."
As far as the literal meaning is concerned, Bharata has spoken of
madhyama as the tone and not of madhya saptaka. However, Bharata
also lays down uttaramandrā as the first mūrcchanā, "ādya-hyuttaramandrā
syād etc." (cf. N. S. Ka. ed. XXVIII. 27). So in fact Śāṅgadeva follows
the tradition of Bharata and Mataṅga. Mataṅga however, seems to have
correctly elucidated Bharata, why uttaramandrā is taken as the first
mūrcchanā.

(iii) मूर्छनानामारम्भकस्वराः
, अथ तासां तु लक्षणं प्रतिपाद्यते ।
मध्यस्थानस्थषड्जेन मूर्छना ऽऽरभ्यते ऽग्रिमा ।।१२।।
(iii) The tonal form of the mūrcchanā-s : 12b-15
Their distinguishing character¹ is (now) being out-
lined.² The first mūrcchanā is commenced with the ṣaḍja of
'S' reproduces the mūrcchanā-s (in the ascending form) of the two
grāma-s in accordance with the text as under :

1. Lakṣaṇa, literally means a characteristic mark.
2. Lit. 'established' by demonstration.

170 Treatment of Svara
अधस्तनैर्निषादाद्यैः षडन्या मूर्च्छनाः क्रमात् ।
मध्यममध्यमारभ्य सौवीरी मूर्च्छना भवेत् ॥१३॥
षडन्यास्तदधोधःस्थस्वरानारभ्य तु क्रमात् ।
षड्जस्थानस्थितैरन्याँ रजन्याद्याः परे विदुः ॥१४॥
हारिणाश्वादिका गान्धैर्मध्यमस्थानसंस्थितैः ।
षड्जादीन्मध्यमादींश्च तदूर्ध्वं सारयेत्क्रमात् ॥१५॥
the middle register; and the six other mūrcchanā-s with niṣāda
etc. (placed) one below another in regular order. Sauvīrī
commences with the madhyama of the middle register, and
the six others³ with the notes coming one below another in
successive order. (12b-14b)
According to another version, rajanī etc.⁴ are formed
by niṣāda etc.⁵ that are placed on ṣaḍja⁶ and hāriṇāśvā etc.⁷
Mūrcchanā-s of the two grāma-s

• The tonal form of śuddha-madhyā, mārgī, pauravī and hṛṣyakā
  may appear to be identical with that of uttaramandrā, rajanī, uttarāyatā
  and śuddha-ṣaḍja respectively, due to the same tones employed; but

3. That is, other mūrcchanā-s.
4. That is, from rañjanī, uttarāyatā etc. onwards upto abhirudgatā.
5. That is, ni dha pa backwards upto ri.
6. Ṣaḍja of the middle register.
7. That is, from hāriṇāśva, kalopanatā onwards upto hṛṣyakā.

Section 4 : Grama, Mūrcchanā, Krama and Tāna 171
are formed by gāndhāra etc.⁸ that are placed on madhyama;
the subsequent notes ṣaḍja etc.⁹ and madhyama etc.¹⁰ respecti-
vely may be tuned accordingly. (14c-15)
actually it is not so, because the pañcama of the madhyama-grāma is of
three śruti-s, whereas in the ṣaḍja-grāma it has four; therefore, these
mūrcchanā-s, though similar in appearance, are yet different in content.
Signs . and ˈ (not used here) are respectively indicative of the lower
and the higher register. (12b-14b)
Then the author describes the same phenomenon of the formation
of mūrcchanā-s in quite a different way. The phenomenon remains the
same, only the technique of relating it differs.
As already explained in the previous verse, by the first method
the mūrcchanā-s are formed by placing their initial notes one below the
other. This involves a change of range (sthāna) in the same vīṇā which
has to be mattakokilā, that is provided with 21 strings and has the range
of three registers (cf. Ab. Bh., G. O. S. Vol. IV, p. 122). By this method
the mūrcchanā-s can be worked out as under, either in the range of the
lower and the middle registers, or the middle or the higher registers.
While in the second method explained above, the mūrcchanā-s are
obtained in the same register, but every time the strings have to be
tuned accordingly. Chart 13 (a & b) illustrates the first method and
Chart 13 (c) illustrates the second.
Formation of mūrcchanā-s of the ṣaḍja-grāma
Method I (a)

8. That is, from ga ri backwards upto pa.
9. That is, ṣaḍja and the higher notes.
10. That is, madhyama and the higher notes.

172 Treatment of Svara
Formation of mūrcchanā-s of the ṣaḍja-grāma
Method I (b)
Section 4 : Grāma, Mūrcchanā, Krama and Tāna
(iv) मूर्च्छना-भेदाः
चतुर्धा ताः पृथक् शुद्धाः काकलीकलितास्तथा ।
सान्तरास्तद्द्द्वयोपेताः षट्पञ्चाशदितीरिताः ॥१६॥
श्रुतिद्वयं चेत्षड्जस्य निषादः संश्रयेत्तदा ।
स काकली, मध्यमस्य गान्धारस्त्वन्तरः स्वरः ॥१७॥
(iv) The classification of the mūrcchanā-s : 16-17
These are fourfold, viz. śuddhā¹ (standard), kākalī-inclu-
sive², antara-inclusive³ and inclusive of both⁴; thus, they are
The mūrcchanā-s are classified on the basis of their being inclusive
or exclusive of either of the two notes called kākalī and antara or both of
them. First of all the author defines these two terms. He says, if
niṣāda absorbs two śruti-s of ṣaḍja and is thus established on the 24th
(22+2) or the 2nd śruti (of the next register), being in effect constituted
of four śruti-s, then it is called kākalī niṣāda and also merely as kākalī for
the sake of convenience. Similarly, if gāndhāra incorporates two śruti-s
of madhyama and is thereafter established on the 2nd śruti of madhyama,
being constituted in effect of four śruti-s, then it is called antara-gāndhāra
or merely as antara for the sake of convenience. Both these notes are
considered to be the modified forms of niṣāda and gāndhāra respectively
and are not counted as independent notes by themselves.
Now, he says there are four classes of mūrcchanā-s, viz. (i) those
that are composed exclusively of the standard notes, i. e. the śuddha-
svara-s, (ii) those incorporating kākalī-niṣāda, (iii) those incorporating

1. Śuddhā literally means pure or natural, the term is suggestive
   of the fact that the mūrcchanā-s of this type are composed of
   tones in the standard śruti-relation i. e., 4-3-2-4-4-3-2 or 4-7-
   9-13-17-20-22.
2. Kākalī-inclusive is the one that takes kākalī-niṣāda instead of
   śuddha-niṣāda, the śruti-relation being 4-7-9-13-17-20-2 (i. e.

24. taking 2 śruti-s from the ṣa of the next register.

3. Antara inclusive is that which takes antara-gāndhāra instead
   of śuddha-gāndhāra, the śruti-relation being 4-7-11-13-17-20-22.
4. The fourth type is such that it takes antara-gāndhāra and
   kākalī niṣāda instead of śuddha ga and ni; the śruti-relation
   being 4-7-11-13-17-20-2 (i e. 24).
   However, the śruti relations indicated here pertain to the
   ṣaḍja-grāma; in madhyama grāma pa will be on the 16th śruti
   instead of the 17th.
   Name of the mūrcchanā | 8 9 10 11 12 13 14 | 15 16 17 18 19 20 21
   Uttaramandrā | sa ri ga ma pa dha ni |
   Rajanī | ni | sa ri ga ma pa dha
   Uttarāyatā | dha ni | sa ri ga ma pa
   Śuddha-ṣaḍjā | pa dha ni | sa ri ga ma
   Matsarīkṛtā | ma pa dha ni | sa ri ga
   Aśvakrāntā | ga ma pa dha ni | sa ri
   Abhirudgatā | ri ga ma pa dha ni | sa
   Chart 13 (b)
   Formation of mūrcchanā-s of the ṣaḍja-grāma
   Method II
   Name of the mūrcchanā | Notes and their śruti-intervals
   Uttaramandrā : — sa — ri — ga — ma — pa — dha — ni
   4 3 2 4 4 3 2
   Rajanī : — ni — sa — ri — ga — ma — pa — dha —
   2 4 3 2 4 4 3
   Uttarāyatā : — dha — ni — sa — ri — ga — ma — pa
   3 2 4 3 2 4 4
   Śuddha-ṣaḍjā : — pa — dha — ni — sa — ri — ga — ma
   4 3 2 4 3 2 4
   Matsarīkṛt : — ma — pa — dha — ni — sa — ri — ga
   4 4 3 2 4 3 2
   Aśvakrāntā : — ga — ma — pa — dha — ni — sa — ri
   2 4 4 3 2 4 3
   Abhirudgatā : — ri — ga — ma — pa — dha — ni — sa
   3 2 4 4 3 2 4
   Chart 13 (c)
   These illustrations clearly make out the difference between the two
   methods of mūrcchanā-formation. The one (I) involves change of range
   and therefore requires the mattakokilā vīṇā and the other is done in the
   same register and involves tuning of the vīṇā according to the mūrcchanā-s.
   (14c-15)

174 Treatment of Svara
known to be fiftysix in all. If niṣāda takes two śruti-s of ṣaḍja,
it becomes kākalī⁵, but if gāndhāra appropriates two śruti-s of
madhyama it becomes antara⁶. (16-17)
antara gāndhāra and (iv) those incorporating both kākalī and antara.
Each of the two grāma-s has seven mūrcchanā-s, so both have fourteen;
and then, each of the fourteen is of four types described above. Thus
(14×4=56), altogether we get fiftysix mūrcchanā-s. The four types of
the mūrcchanā-s of the ṣaḍja-grāma are illustrated as under, along with
their śruti-relations.
The four types of mūrcchanā-s

5. The short form of kākalī-niṣāda.
6. The short form of antara gāndhāra.
   Section 4 : Grāma, Mūrcchanā, Krama and ...
   (v) मूर्च्छनासङ्ख्या-परिज्ञानोपायः
   यस्यां यावतियो षड्जमध्यमौ ग्रामयोः क्रमात् ।
   मूर्च्छना तावतित्येव सा निःशङ्केन कीर्तिता ॥१८॥
   (v) The method of indicating the serial number of a
   mūrcchanā : 18
   In the two grāma-s the serial number of a mūrcchanā, as
   pointed out by Śārṅgadeva¹, is that which corresponds to the
   position of ṣaḍja or madhyama in it². (18)
   This is rather a very faithful rendering of the text which in fact
   implies that, since there are fourteen mūrcchanā-s in the two grāma-s,
   seven in each, the question is how to recognise a particular mūrcchanā in
   terms of its being first, second, third, and so on. The author here
   points out that the serial number of a mūrcchanā is indicated by the
   position of ṣaḍja or madhyama in it in the ṣaḍja or madhyama grāma as the
   case may be. For instance, in uttaramandrā a mūrcchanā of the ṣaḍja-
   grāma 'sa ri ga ma pa dha ni' the position of the sa is first, and there-
   fore it indicates that uttaramandrā is the first mūrcchanā of the ṣaḍja-grāma.
   Similarly ṣaḍja being the sixth note in avakrāntā, it indicates it to be
   the sixth mūrcchanā. Also in the case of madhyama-grāma, hāriṇāśva for
   instance has madhyama in the second position (ga ma pa dha ni sa ri)
   and is thereby the second mūrcchanā of the madhyama-grāma.
   (vi) मूर्च्छना-क्रमाः, तेषां सङ्ख्या च
   प्रथमादिस्वरारम्भादेकैका सप्तधा भवेत् ।
   तासुच्चार्यान्त्यस्वरांतान्पूर्वानुच्चारयेत्क्रमात् ॥१९½॥
   ते क्रमास्तेषु संख्या स्याद् द्वानवत्या शतत्रयम् ।
   (vi) The mūrcchanā-series (krama-s) and their number: 19-20b.
   Each one of them¹ becomes sevenfold by commencing
   with the first note and so on². In these³, the last notes hav-
   ing been sung, initial notes may be sung in their respective
7. Niḥśaṅka is the appelation of Śārṅgadeva.
   2, Cf. Dattilam 21.
8. 'Them' refers to the fiftysix mūrcchanā-s of four types described
   in verse 16.
9. That is, from the first to the seventh note.
   3.&4. 'These' refers to the seven mūrcchanā-series, formed as per

176 Treatment of Svara Section 4 : Grāma, Mūrcchanā, Krama and Tāna 177
order. These⁴ are mūrcchanā-series (krama-s) and their num-
ber is three hundred and ninetytwo. (19-20b).
These series of tonal order do not stand in the descending order and
are therefore called krama-s or mūrcchanā-krama-s-i.e., mūrcchanā-series.
Since each of the fiftysix mūrcchanā-s has seven series, the total number of
such sub-varieties comes to (56 x 7 = 392) three hundred and ninetytwo.
The purport is that each one of the fiftysix mūrcchanā-s spoken of
above, has seven series of mūrcchanā-s of its own which are formed by
commencing the mūrcchanā with the first, the second, the third, the
fourth, the fifth, the sixth and the seventh note, keeping the śruti-value
of the notes unaltered. Now, 'S' poses the problem that, if the mūrc-
chanā is commenced with the second note and so on, how can it have
seven notes in it ? The text resolves the difficulty by suggesting that
the last notes may be sung in the first instance and the preceding notes
may be sung in their respective order. Moreover, it is notable that in
this scheme the basic scale is not altered and so the mūrcchanā does not
change, what changes is the order of notes in it, and actually each
mūrcchanā has seven possibilities of such a variety in the order. These
series are therefore called krama-s, literally 'orders'; they are useful in
the computation of kūṭatāna-s (permutational note-series). The series of
mūrcchanā-s are therefore sub-varieties of the mūrcchanā-s and are distin-
guished from the mūrcchanā-s proper by the fact that they are formed only
in the ascending order of notes, whereas the mūrcchanā-s are formed in
the descending order as well. For instance uttaramandrā, the first
mūrcchanā, of the ṣaḍja-grāma is sa ri ga ma pa dha ni : ni dha pa ma
ga ri sa; but the series of this mūrcchanā are recorded as follows :-
These krama-s, named as mūrcchanā-series are considered to be
mūrcchanā-s only in so far as the notes in their ascending order are placed
consecutively and exhibit some sort of order in their arrangement.
Mataṅga, following Bharata, classifies the seven-tonal mūrcchanā-s
in slightly a different way, viz. pūrṇā (complete), ṣāḍavitā (hexatonic),
auḍuvitā (pentatonic) and sādhāraṇī (mixed), the first one of which
incorporates all the seven notes, the second is composed of six notes, the
third is formed with five notes only, while the fourth includes kākalī
or/and antara forms of niṣāda and gāndhāra.
Bharata has defined mūrcchanā as a group of seven notes placed
in order, and he derives mūrcchanā-tāna-s (also called only tāna) from
them by the omission of one or two notes (cf. N. S., G. O. S. IV.
32-33, p. 25). Śārṅgadeva too, basically follows this classification
but technically he applies the term tāna to all those modifications of
mūrcchanā-s that are formed by the omission of one to six notes in the
combinational and permutational note-series (śuddha and kūṭa tāna-s).
(vii) मूर्च्छनानां देवताः
यक्षरक्षोनारदाब्जभवनागाश्विपाशिनः ॥२०॥
षड्जग्रामे मूर्च्छनानामेताः स्युर्देवताः क्रमात् ।
ब्रहेन्द्रवायुगन्धर्वसिद्धद्रुहिणभानवः ॥२१॥
स्युरिमा मध्यमग्राममूर्च्छनादेवताः क्रमात् ।
(vii) The presiding deities of the mūrcchanā-s : 20c-22b
The presiding deities of the mūrcchanā-s of the ṣaḍja-
grāma respectively¹ are yakṣa², rakṣa³, Nārada⁴, Brahmā⁵,

1. That is, from the first mūrcchanā-series to the seventh series.
2. Yakṣa is a class of demigods who are considered to be the
   guards of the treasures of Kubera, the god of wealth.
3. Rakṣa is the name given to evil spirits 'K. R.' in his note
   on verse 20 considers rakṣa-s along with yakṣa-s to be semi-
   celestial beings. He does not elaborate on their function.
4. Nārada is a celestial figure, a sage elevated to be a divine
   roaming minstrel of the three worlds (i.e. the heaven being the
   abode of gods, the earth being the abode of mortals and the un-
   der world below the earth, being the abode of nāga-s or reptiles).
5. The creative aspect of the Hindu trinity.
   this verse; they may be understood as subvarieties of the seven
   mūrcchanā-s, called krama-s in the text. The word krama is used
   in the sense of series in this particular context.
   12

178 Treatment of Svara
nāga,⁶ aśvin⁷ and Varuṇa⁸; and those of the madhyama-grāma
respectively are Brahmā, Indra⁹, Vāyu¹⁰, gandharva,¹¹ siddha¹²
Śiva and sun.¹³ (20c-22b)
(viii) नारदकथितानि मूर्च्छना-नामानि
तासामन्यानि नामानि नारदो मुनिरब्रवीत् ॥२२॥
मूर्च्छनोत्तरवर्णा ऽऽद्या षड्जग्रामे ऽभिरुद्गता ।
अश्वक्रान्ता च सौवीरी हृष्यका चोत्तरायता ॥२३॥
रजनीति समाख्याता ऋषीणां सप्त मूर्च्छनाः ।
आप्यायनी विश्वकृता चन्द्रा हेमा कपर्दिनी ॥२४॥
मैत्री चान्द्रमसी पित्र्या मध्यमे मूर्च्छना इमाः ।
नन्दा विशाला सुमुखी चित्रा चित्रवती सुखा ॥२५॥
आलापा चेति गान्धारग्रामे स्युः सप्त मूर्च्छनाः ।
ताश्च स्वर्गे प्रयोक्तव्या विशेषान्न नोदिताः ॥२६॥
(viii) Nārada's nomenclature for the mūrcchanā-s : 22c-26
The sage Nārada has given¹ another nomenclature for
them² viz. the first in the ṣaḍja-grāma is uttara-varṇā and
then³ abhirudgatā, aśvakrāntā, sauvīrī, hṛṣyakā, uttarāyatā and
Nārada is a celebrated authority of ancient India and this
subject is dealt with in two works ascribed to him, viz. Nāradīya-śikṣā
and Saṅgīta-makaranda. The nomenclature ascribed to Nārada in the
text tallies more or less with the one given in Nāradīya-śikṣā, but is
slightly different from that of Saṅgīta-makaranda (cf. N. Śikṣā 1.2.9-14
6. Nāga, a class of beings inhabiting the world below the earth,
who are likened to serpents.
7. Aśvins are the twin brothers, the sons of the sun and the physi-
cians of the gods.
8. A god of the vedic pantheon and puranic mythology.
9. The chief of the gods.
10. The god of wind.
11. Celestial chorister, a singer in general.
12. A class of demi-gods with supernatural powers, or a perfected
human being.

1. Literally, it would be translated as 'said'.
2. 'Them' refers to the seven mūrcchanā-s of each of the grāma-s.
3. The sense of 'then' is implied in the context.
   Section 4 : Grāma, Mūrcchanā, Krama and Tāna 179
   rajanī; these are the seven mūrcchanā-s of the seers. In the
   madhyama-grāma the mūrcchanā-s are: āpyāyanī, viśvakṛtā, candrā,
   hemā, kapardinī, maitrī and cāndramasī belonging to the manes.
   Nandā, viśālā, sumukhī, citrā, citravatī, sukhā and ālāpā are the
   seven mūrcchanā-s of gāndhāra-grāma; but they have not been
   spoken of in detail as they are to be employed in heaven
   only. (22c-26)
   and S. Mak. 1.2.10-15). However, it is notable that the name uttara-
   varṇā given to the very first mūrcchanā of the ṣaḍja-grāma is not found in
   both of them ; and what is found in its place is uttara-mandra. Besides,
   there are a few other minor variations. That shows that Śārṅgadeva
   probably had access to a different MS. of Nāradīya-śikṣā.
   Another notable point is the distribution of the mūrcchanā-s of the
   three grāma-s among the gods, the seers (who are human beings) and
   the manes. This is in keeping with the Brahminical tradition of
   symbolic characterisation already spoken of. It may however be
   mentioned that, since the seven mūrcchanā-s of the ṣaḍja-grāma only are
   allocated to the seers (ṛṣi-s) these mūrcchanā-s only are considered to
   be of use in this world by the Nāradīya-śikṣā (cf. 1.2.13-14).
   ग. तानाः
   (i) शुद्धताननिर्माणविधिः, सङ्ख्या च
4. शुद्धतानलक्षणम्
   तानाः स्युर्मूर्च्छनाः शुद्धाः षाडवौडुवितीकृताः ।
   C. The tāna-s : 27-90
   (i) The formation and the number of the śuddha-tāna-s
   (specific combinational note-series) : 27-30
   (1) The definition of the śuddha-tāna : (27ab)
   The śuddha¹ (standard) mūrcchanā-s, by dropping one
   Tāna, which has been rendered as 'note-series' is essentially a
   mūrcchanā. The word tāna is derived from the Sanskrit root tan 'to
   spread, to stretch, or to expand, enlarge, develop.
5. Śuddha literally means pure i. e., unmodified or natural. In
   this context, śuddha implies an ascending and descending
   series of seven standard notes placed in their regular order in
   the ṣaḍja or madhyama grāma; and that is why it has been
   rendered here as 'standard'.

Page 180

180 Treatment of Svara
or two notes become śuddha-tāna-s² (specific combinational
note-series). (27ab)
The mūrcchanā-s have been classified into four types (cf. verse 16
ante), viz. standard (śuddha, kākalī-inclusive, antara-inclusive and
inclusive of both. Broadly speaking, these four types fall into two
categories, viz. composed of standard notes only and composed of
standard and modified notes. A tāna is formed by dropping one or
two notes from any standard mūrcchanā. Thus, a śuddha-tāna is nothing
but a standard mūrcchanā deprived of one or two notes.
The word śuddha qualifies both the words mūrcchanā and tāna.
Tāna-s are also of two types śuddha and kūṭa, i. e. combinational and
permutational. 'K' argues that if the word śuddha of the text is taken
merely to qualify the word tāna, then śuddha-tāna-s would proceed from
all the fiftysix mūrcchanā-s already described, and in that case the
number of hexatonic and pentatonic tāna-s would not tally with the
text; while on the other hand, if it qualifies only 'mūrcchanā' then even
kūṭa i. e. permutational tāna-s would also be possible from the standard
mūrcchanā-s, which is contrary to the fact. Thus it is that, śuddha
(standard) mūrcchanā-s when deprived of one or two notes become what
is called the hexatonic and the pentatonic combinational note-series.
Mataṅga, however, points out another difference between mūrcchanā and
tāna. He says : "mūrcchanā proceeds in the ascending order, while tāna
proceeds in the descending order only." So tāna, as differentiated by
him, is restricted to the descending order of notes only.

2. Tāna, in the ancient terminology, is a series of five to six notes
   in a specific combinational order called śuddha-tāna (specific
   combinational note-series). Though śuddha-tāna is the full
   expression, when writing about it in its context, the word
   śuddha is taken for granted and mere tāna is used instead.
   Accor dingly, the expression specific combinational note-series
   is also sometimes replaced by the simple term note-series (in
   due context). But tāna as such has to be distinguished from
   kūṭa-tāna (permutational note-series) to be defined presently.
   However, in modern music tāna, as defined by Ravi Shankar,
   is a musical phrase sung on vowels, syllables or words drawn
   out or stretched by expressive passages. (cf. Glossary of
   technical words, My Music My Life).

Page 181

Section 4 : Grāma, Mūrcchanā, Krama and Tāna 181

2. षाडवतानाः

षड्जगाः सप्त हीनाश्चेत्क्रमात्स्रिरिपसप्तमैः ॥२७॥
तदा ऽष्टाविंशतिस्ताना मध्यमे सरिगोर्झताः ।
सप्त क्रमाद्यदा तानाः स्युस्तदा त्वेकविंशतिः ॥२८॥
एते चैकोनपञ्चाशदुभये षाडवा मताः ।
(2) The hexatonic note-series : (27c-29b)
The seven (mūrcchanā-s) of the ṣaḍja-grāma, by an indi-
vidual omission of sa, ri, pa and ni¹ in their respective turn,
make twenty-eight (note-series). Similarly, the seven
(mūrcchanā-s) of the madhyama-grāma, by the omission of sa, ri
and ga in turn respectively form twentyone (note-series).
Both of them put together, are considered to be fortynine
hexatonic note-series.² (27c-29b)
Though the combinational (śuddha) note-series (tāna-s) are derived
from the standard (śuddha) mūrcchanā-s, the latter is distinguished by the
absence of modified notes, the former is distinguished not only
by the absence of kākalī and antara notes, but also by the absence
of any change in the regular arrangement of notes. If the note-series
is set in the permutational form then it is called kūṭa-tāna i. e. permu-
tational note-series. The note-series are formed by the omission of one
or two notes. If one of the seven notes is omitted, what we get is a
hexatonic note-series and if two out of the seven are omitted we get
pentatonic note-series.
'K' raises the question that, "since pañcama determines the grāma,
if it is omitted, how can it discharge this function ?" He resolves the
difficulty by pointing out that the pañcama can only be omitted in the
ṣaḍja-grāma; therefore, even its omission is indicative of that particular
grāma.
'S' explains at length how we get twentyeight note-series in the
ṣaḍja-grāma and twentyone note-series in the madhyama-grāma. When
the seven mūrcchanā-s of the ṣaḍja-grāma are deprived of ṣaḍja, then we
get seven hexatonic note-series, likewise when deprived of ri, pa and ni
respectively, we get seven other such series in each case, making twenty-
eight in all. Similarly, in the madhyama-grāma when the standard

1. Saptama—literally means the seventh (note) i. e. ni.
2. That is, 'ṣāḍava-tāna-s'.

182 Treatment of Svara
mūrcchanā-s are deprived of sa, ri and ga respectively, they form into
twentyone note-series. Taken together, we get forty-nine hexatonic
note-series. That is how the standard mūrcchanā-s being deprived of
one or two notes become combinational note-series.
An illustration of the hexatonic note-series with the omission of
sa in the ṣaḍja-grāma
No. Name of the mūrcchanā Form of the mūrcchanā
1 Uttaramandrā x ri ga ma pa dha ni
2 Rajanī ni x ri ga ma pa dha
3 Uttarāyatā dha ni x ri ga ma pa
4 Śuddhaṣaḍjā pa dha ni x ri ga ma
5 Matsarīkṛtā ma pa dha ni x ri ga
6 Aśvakrāntā ga ma pa dha ni x ri
7 Abhirudgatā ri ga ma pa dha ni x
(Chart 16*)
Note :—x denotes omitted sa.
* Adopted from S. Raj. Vol. I, p. 132.
3. औडुवतानाः
सपाभ्यां द्विश्रुतिभ्यां च रिपाभ्यां सप्त वर्जिताः ॥२९॥
षड्जग्रामे पृथक्ताना एकविंशतिरोडुवाः ।
रिधाभ्यां द्विश्रुतिभ्यां च मध्यमग्रामगास्तु ते ॥३०॥
हीनाश्चतुर्दशैव स्युः पञ्चत्रिंशत्तु ते युताः ।
(3) The pentatonic note-series : (29c-31b)
Besides, the seven (standard mūrcchanā-s) of the ṣaḍja-
-grāma being deprived of sa and pa, ga and ni¹ and ri and pa
respectively form twentyone pentatonic note-series; while
those of the madhyama-grāma being short of ri and dha and ga
and ni² respectively become fourteen (tāna-s): altogether,
they make thirtyfive. (29c-31b)
Just as the standard mūrcchanā-s by dropping one note become
hexatonic note-series, by dropping two notes they become pentatonic
note-series. In ṣaḍja-grāma, by the omission of sa and pa we get one set
of seven pentatonic note-series, by the omission of ga and ni, another set
of seven and by the omission of ri and pa the third set of seven, making
twentyone in all. Similarly, in the madhyama-grāma by the omission of
1 & 2. Dviśruti of the text literally means a bi-śrutic note; ga
and ni are the two notes with two śruti-s each.
Section 4 : Grāma, Mūrcchanā, Krama and Tāna 183
4. षाडवौडुवतान-मिलितसङ्ख्या
सर्वे चतुरशीतिः स्युर्मिलिताः षाडवौडुवाः ॥३१॥
(ii) कूटताननिर्माणं, तेषां सङ्ख्या च

1. कूटतानलक्षणम्
   असम्पूर्णाश्च सम्पूर्णा व्युत्क्रमोच्चारितस्वराः ।
   मूर्च्छनाः कूटतानाः स्युः,
   (1) Total number of hexatonic and pentatonic combinational
   note series (śuddha-tāna-s) : (31cd)
   However, the hexatonic and the pentatonic (specific
   combinational) note-series make eightyfour in all. (31cd)
   (ii) The formation and the number of kūṭa (permutational)
   tāna-s (note-series) : 32-49
   (1) The definition of kūṭa-tāna (permutational) note-
   series) : (32 abc)
   The complete or incomplete mūrcchanā-s with their notes
   produced in a permuted form become permutational note-
   series (kūṭa-tāna-s). (32a-32c)
   ri and dha we get one set of seven pentatonic series, and by the omission
   of ga and ni, the second set, making fourteen in all. Thus the pentatonic
   note-series in both the grāma-s are counted as thirtyfive and the number
   of both the hexatonic and the pentatonic note-series in both the grāma-s
   is considered to be (49+35 = 84) eightyfour. An illustration of a penta-
   tonic note-series is given as under. We know that mūrcchanā is in the
   ascending as well as in the descending order of notes.
   An illustration of the pentatonic note-series with the omission
   of sa and pa in the ṣaḍja-grāma
   No | Name of the mūrcchanā | Form of the mūrcchanā
   1 | Uttaramandrā | x ri ga ma • dha ni
   2 | Rajanī | ni x ri ga ma • dha
   3 | Uttarāyatā | dha ni x ri ga ma •
   4 | Śuddha-ṣaḍjā | • dha ni x ri ga ma
   5 | Matsarīkṛt | ma • dha ni x ri ga
   6 | Aśvakrāntā | ga ma • dha ni x ri
   7 | Abhirudgatā | ri ga ma • dha ni x
   (Chart 17*)
   Note:—x denotes sa and • denotes pa.
   *Adopted from S. Raj. Vol. I, p. 136.

184 Treatment of Svara
A mūrcchanā is said to be complete when it has seven notes, and it
is considered incomplete when it has less than seven notes i.e. from six
to one; although one note does not make a series, but that is theoretical.
Actually, when one or more 'notes are omitted from a mūrcchanā, it
becomes a tāna (as already explained in the comments on 19-20b ante),
a note-series. But, here, the author is talking in terms of incomplete
mūrcchanā-s (as well) giving rise to permutational note-series, because
such note-series are derived from the mūrcchanā-series, and not because
on this account, they continue to be mūrcchanā-s. It has already been
said that Bharata has used the expression mūrcchanā-tāna for hexatonic
and pentatonic combinational note-series.
We have already come across the fourfold classification of mūr-
cchanā-s and this is a twofold classification viz. complete and incom-
plete. Now, the purport of the text is that, a mūrcchanā, whether
complete or incomplete, becomes a permutational note-series if the
normal order of its notes is disturbed, and in that case even a descend-
ing movement to a certain extent is no bar. It may be pointed out that
ordinarily the notes of the mūrcchanā-series (krama-s) from which the
note-series are derived are in the ascending order.
2. पूर्णकूटतानानां सङ्ख्या
तत्सङ्ख्यामभिदध्महे ॥३२॥
पूर्णाः पञ्च सहस्राणि चत्वारिंशद्युतानि तु ।
एकैकस्यां मूर्च्छनायां कूटतानाः सह क्रमैः ॥३३॥
षट्पञ्चाशन्मूर्च्छनास्थाः पूर्णाः कूटास्तु योजिताः ।
लक्षद्वयं सहस्राणि द्व्यशीतिर्द्वे शते तथा ॥३४॥
चत्वारिंशच्च सङ्ख्याता
(2) The enumeration of the complete permutational note-
series : (32d-35a)
We calculate their number as follows. Including the
mūrcchanā-series (krama-s) there are five thousand and forty
(5040) complete permutational note-series in each of the
Mataṅga has spoken of five thousand thirtythree permutational
note-series, and Śārṅgadeva has added the seven mūrcchanā-series to
this number, for each of the fiftysix mūrcchanā-s does have seven series
of its own. Dattila also does not include the seven mūrcchanā-series
(krama-s) in the total number of permutational note-series, but that
Section 4 : Grāma, Mūrcchanā, Krama and Tāna 185
mūrcchanā-s. Thus, the total number of the complete permu-
tational note-series subsisting in the fiftysix mūrcchanā-s comes
to two lakh eightytwo thousand and two hundred forty
(2,82,240). (32d-35a)
makes no difference in principle. The number 5040 is arrived at in
the following manner :
With 1 note the number of possible permutational series of
of the notes will be 1 × 1 = 1
With 2 notes ,, ,, ,, ,, 1 × 2 = 2
With 3 ,, ,, ,, ,, ,, 2 × 3 = 6
With 4 ,, ,, ,, ,, ,, 6 × 4 = 24
With 5 ,, ,, ,, ,, ,, 24 × 5 = 120
With 6 ,, ,, ,, ,, ,, 120 × 6 = 720
With 7 ,, ,, ,, ,, ,, 720 × 7 = 5040
To demonstrate let us take items with 2 and 3 notes to begin
with :—

1. Two-note-series : sa ri, ri sa
2. Three-note-series : sa ri ga } group A with ga constant
   ri sa ga }
   sa ga ri } group B with ri constant
   ga sa ri }
   ri ga sa } group C with sa constant
   ga ri sa }
   Now, it will be observed that the two-note-series is a simple one
   and does not involve any complicated procedure in the working out of
   the different permutations as in the case of the three-note-series, and
   much more so in all the subsequent series. The permutations in the
   three-note-series are so arranged that an attempt is made as a rule to
   keep the last note of the series constant as long as possible. This is
   demonstrated in the four-note-series worked out hereunder.
   S. No. Group A Group B Group C Group D
3. sa ri ga ma sa ri ma ga sa ga ma ri ri ga ma sa
4. ri sa ga ma ri sa ma ga ga sa ma ri ga ri ma sa
5. sa ga ri ma sa ma ri ga sa ma ga ri ri ma ga sa
6. ga sa ri ma ma sa ri ga ma sa ga ri ma ri ga sa
7. ri ga sa ma ri ma sa ga ga ma sa ri ga ma ri sa
8. ga ri sa ma ma ri sa ga ma ga sa ri ma ga ri sa
   It will be observed that on the basis of the above principle, the
   24 permutations of the four-note series have been classified and arranged

186 Treatment of Svara
in four groups in each of which the notes ma, ga, ri and sa respectively
are constant, while the position of other notes keeps on changing. This
gives us the clue to find out the number of possible permutations.
Similarly the 120 permutations of the pentatonic series, 720 of the
hexatonic series and 5040 of the complete series can be worked out
easily. Another principle involved in these calculations is that the
number of permutations of the preceding series denotes the number of
times each note of the succeeding series can be kept constant. Thus, for
example, the permutations of the two-note-series are 2, therefore in the
three-note-series all the three notes can be kept constant twice, leading
us to (2 × 3 = 6) six permutations in all. Likewise, in the four-note-
series, each note can be kept constant for 6 times since the preceding
three-note series has six permutations, leading us to (4 × 6 = 24) twenty-
four permutations in all. That is how the pentatonics are 5 × 24 = 120,
the hexatonics are 6 × 120 = 720, and the complete series are
7 × 720 = 5040.
3. अपूर्णकूटतान-निर्माणम्
,अथापूर्णान्प्रचक्ष्महे ।
एकैकान्त्यान्त्यविरहाद्भेदाः षट् षट्स्वरादयः ॥३५॥
एकस्वरो ऽत्र निर्भेदो ऽप्युक्तो नष्टादिसिद्धये ।
क्रमा अकूटतानत्वे ऽप्युक्तास्तेषूपयोगिनः ॥३६॥
(3) The formation of the incomplete permutational
note-series : (35b-36)
Now, we are to describe the incomplete (permutational
note-series). In each (of the mūrcchanā-s) six varieties are
formed, viz. hexatonic¹ etc. by successively dropping the
last note step by step. Although the monotone has no sub-
The incomplete permutational note-series are formed by the simple
device of dropping the last note from seventh to the second; thus, by
dropping the seventh we get a hexatonic tāna, by dropping the sixth we
get a pentatonic tāna, by dropping the fifth we get a tetratonic note-
series, by dropping the fourth we get a tri-tone note-series, by dropping
the third we get bi-tone series and by dropping the second we get the
mono-tone: these are the six varieties.

1. Hexatonic, i. e., having six tones, the other varieties being
   pentatonic, tetra-tonic series, tritone-series, bitone-series and
   monotone-series.
   Section 4 : Grāma, Mūrcchanā, Krama and Tāna 187
   varieties, it is also counted for the working of naṣṭa.² The
   original-series (krama-s³) which are unrelated to the permu-
   tational note-series have also been included as they will be
   useful with regard to them. (35b-36)
   The number of note-series in each of them will now be described.
   The terms naṣṭa and uddiṣṭa will shortly be explained in their proper
   context, but for the time being the author has pointed out the reason
   for enumerating the mono-tone as a note-series even though it can have
   obviously, no varieties. Similarly, the krama-s or the mūrcchanā-series
   (precisely called here as, the original-series) too have been enumerated
   for technical reasons which will soon be clear.
2. अपूर्ण कूटतानानां सङ्ख्या
   स्युः षाडवानां विशत्या सह सप्त शतानि तु ।
   औडुवानां तु विशत्या सहितं शतमिष्यते ॥३७॥
   चतुःस्वराणां कूटानां चतुर्विंशतिरीरिताः ।
   त्रिस्वराः षड् द्विस्वरौ द्वावेकस्त्वेकस्वरो मतः ॥३८॥
   (4) The enumeration of the different permutational
   note-series : 37-38
   The hexatonic series formed are seven hundred and
   twenty¹, and the pentatonic series are one hundred and
   Ārcika literally means relating to the Ṛgveda (Ṛc + veda). Ṛc is a
   hymn, and the hymns employed in the performance of sacrifices, it
   seems, were sung in the monotone, though the accent system was also
   there with its three accents viz., udātta (raised), anudātta (unraised) and
   svarita (intermediate note). 'K' also says, "Yajñaprayogeṣu ṛcamekasvara-
   śrayatvāt, tatsambandhād ārcikaḥ" i. e., hymns while they are employed in
   (2. Naṣṭa will be explained later.
3. Krama in this context refers to the original (mūla) form of the
   mūrcchanā-s in their ascent i. e., ‘sa ri ga ma pa dha ni’ for
   uttamamandrā. However, the term mūrcchanā-series applied to the
   392 series spoken of vide 19-20 ab ante is not precisely appli-
   cable in the context of the calculation of permutational note-
   series, the krama-s for which may consist of six to one notes
   each in the original order of the mūrcchanā-series concerned.
   Thus, the krama-s in this context have been rendered as the
   original series, as the author himself names them as mūla-
   krama-s somewhere else (verse 40 of this section).
4. This includes the original series (krama-s) as well.

188 Treatment of Svara Section 1 : Grāma, Mūrcchanā, ...
Although later in the classical period gāthā represents non-vedic
5. एकस्वरादि-कूटतानचतुष्टस्य नामानि religious verse, from the above context and also from the following verse
it seems, here it refers to the Yajur-veda. The fact that this tonal distri-
आर्चिको गाथिकश्चाथ सामिको ऽथ स्वरान्तरः । bution is related only to those hymns that are meant to be employed in
the sacrificial acts is also evidenced by the following verse of this work:
एकस्वरादितानानां चतुर्णामभिधा इमाः ॥३९॥ "Ṛk sāmayajuṣāṅgāni ye yajñeṣu prayuñjate, avijñānāddhi śāstrāṇām
teṣāṁ bhavati visvaraḥ." (1.1.4), i e, 'Those parts of the Ṛg. Yajur and the
twenty, the tetratonic permutational note-series are known Sāma-veda-s that are applied in sacrificial acts, due to the lack of scienti-
to be twentyfour, the tritone series are six, the bitone series fic understanding, are recited in the wrong tone (i. e. in an improper
are two and the monotone is one, of course. (37-38) and unprecise way)' Here, the word Yajur seems to have been used for
gāthā. However, in the Vedic literature the word gāthā is also used in
(5) The names of the first four permutational note-series : 39 the sense of gāna i. e., song Swami Prajñānānanda, after giving the
The names for the first four note-series such an mono- illustrations of its use in the Ṛigveda, concludes that "gāthā is, gīyate-iti
tone etc. respectively are ārcika, gāthika, sāmika and svarāntara. gāthā i. e., that which is sung, or is suitable for singing is gāthā". (cf.
(39) Historical Development of Indian Music, pp. 46, 47).
the sacrifices take resort to the monotone, and so being related to them,
the monotone is called ārcika. 6. षाडवकूटतान-सङ्ख्या
Similarly gāthika, is the one that is related to gāthā, i. e nonvedic उक्ताः शुद्धादिभेदेन निगयुक्ताश्चतुर्विधाः ।
religious verse. Likewise the tritone is associated with the Sāmaveda: तयोरेकैकहीनास्तु द्वेधा मूलक्रमा मताः ॥४०॥
the hymns of this particular veda were sung in three tones when employ- षड्जौ च मध्यमौ च चत्वारः स्युर्द्विधा द्विधा ।
ed for sacrificial purposes. However, the Sāmaveda otherwise bears ample
evidence that its music was based on seven notes, though we need not चतुर्धा ऽन्ये दशेत्यष्टाचत्वारिंशदमी क्रमाः ॥४१॥
go into this subject in this context. But it is worthwhile to quote सविंशतिः सप्तशतो प्रागुक्ता गुणिता क्रमैः ।
Swami Prajñānānanda who writes, "The sāmagāna was of various types चतुस्त्रिंशत्सहस्राणि षष्ट्या पञ्च शतानि च ॥४२॥
with different numbers of tone in different vedic recensions (śākhā-s), इति षाडवसङ्ख्या स्यात्,
and they had different methods of rendering. Usually three, four or
five notes were used in the sāmagāna-s, but in the kauthuma recension (6) The enumeration of the hexatonics : 40-43a
(śākhā) the sāmagāna was presented with seven vedic notes. The vedic The original series, inclusive of ga and ni have been
notes were in the downward movement (avarohaṇa-krameṇa), whereas the mentioned¹ to be fourfold viz. śuddhā (standard) etc., but if
modern classical notes are used in the upward movement (ārohaṇa- deprived of either² of them, they are considered to be two-
krameṇa)", (cf. Historical Development of Indian Music, pp. 46, 47). It
may also be observed that the bulk of the hymns of the Samaveda are The mūrcchanā-s such as 'sa ri ga ma pa dha ni : ni dha pa ma ga ri sa'
taken verbatim from the Ṛgveda with a view to their application in the etc. have been explained as fourfold vide verse 16 ante. The four
context of certain sacrifices. It is interesting to refer to the Nāradīya- types enumerated are the standard, the kākalī-inclusive, the antara-
śikṣā in this context which also gives the four names exactly as in the inclusive and the twin-inclusive (i.e. inclusive of both kākalī and antara).
text : "Ārcikaṁ gāthikaṁ caiva sāmikaṁ ca svarāntaram" (1.1.2), and then Corresponding mūrcchanā-series are derived from out of these, taking the
it goes on to explain as under : seven notes in their ascending order. However, as already explained
"Ekāntaraḥ svaro hyṛkṣu gāthāsu dvyantaraḥ svaraḥ : Samasu tryantaram 1. The fortysix mūrcchanā-series mentioned vide 16-17 ante.
vidyādetavat svarato-antaram" (1.1.3) i. e., 'The hymns of the Ṛigveda are 2. That is, if either ni or ga is dropped.
to be sung with a single-space tone, those of the gāthā with the double-
space-tone, while those of the Sāmaveda with the triple-space tone; such
is the scheme of tonal spacing.'

190 Treatment of Svara
fold⁸. The four⁴ beginning with ṣaḍja⁵ and madhyama⁶ are
twofold each, and the other ten are fourfold; thus, these
original series are forty-eight⁷ in all. (40-41)
The seven hundred and twenty⁸, already enumerated,
when multiplied by the original series make thirty-four thou-
sand five hundred and sixty, which forms the total number
of hexatonics⁹. (42-43a)
(cf. note 3 on 35b-36d), when one or more notes are dropped out of
these series in their original order for making permutational note-series,
these mūrcchanā-series in that modified form are called krama-s or
original series. The author, now onwards, is taking into account the
number of these original series in the hexatonic to monotonic series.
Now, if hexatonic note-series are to be formed out of the mūrcchanā-
series, the last note may be dropped in the process, in each case. Thus
we shall, in effect, have two types of note-series viz. inclusive of either
kākalī or antara or exclusive of either of them.
Fourteen mūrcchanā-s have been spoken of (vide verse 15 ante) in
both of the grāma-s. Out of these fourteen, two in each of the grāma-s
(i.e. four) begin with sa and ma and end in ni and ga respectively. In
their case only two alternate types are possible viz., śuddha (standard)
and antara-inclusive, and śuddha (standard) and kākalī-inclusive. The
rest of the ten mūrcchanā-s will have the usual four varieties. Thus we
have four hexatonic note-series, which are two-fold, making eight varie-
ties in all, and ten hexatonic note-series that are four-fold making forty
varieties in all. The total number of the original series, in this way,
comes to forty-eight. (40-41)
Seven hundred twenty permutational hexatonic note-series have
been enumerated (cf. verse 37 ante) for each mūrcchanā. In all forty-
eight mūrcchanā-series have been counted. Thus the total number of
the permutational hexatonic note-series is worked out (720 × 48 = 34560)
to be thirty-four thousand five hundred and sixty.
3. Viz in case ni is dropped, standard and antara-inclusive; and
in case ga is dropped, standard and kākalī-inclusive.
4. The four mūrcchanā-series.
5. The first mūrcchanā (uttaramandrā) of the ṣaḍja-grāma and the
fourth mūrcchanā (śuddhamadhyā) of the madhyama-grāma.
6. The fifth mūrcchanā (matsarīkṛtā) of the ṣaḍja-grāma and the
first (sauvīrī) of the madhyama-grāma.
7. (4 × 2 = 8) + (10 × 4 = 40) = 8 + 40 = 48.
8. 720 permutational hexatonic note-series, formed out of a given
combination.
9. That is, permutational hexatonic note-series, formed out of
48 hexatonic combinations or original series. This number
also includes the original-series (mūlakrama-s).
Section 4 : Grāma, Mūrcchanā, Kūṭatāna ...
7. औडुवकूटतान-सङ्ख्या
, अथ पञ्चस्वरान्ब्रुवे ।
गाद्यौ धाद्यौ निषादाद्यौ चतुर्भेदाः षडौडुवाः ॥४३॥
अष्टावन्ये द्विधेत्येवं चत्वारिंशदिमे क्रमाः ।
सविंशतौ शते तैश्च गुणिते ऽष्टौ शतानि तु ॥४४॥
चत्वारि च सहस्राणि सङ्ख्या पञ्चस्वरेष्विति ।
(7) The enumeration of the pentatonics : 43b-45b
Now, I am to describe the pentatonics.¹ The six
pentatonics² commencing with ga dha and ni are fourfold,
and the eight others are twofold; thus, these (original) series
are forty in all, which when multiplied by one hundred and
twenty³ bring the total number of the pentatonics⁴ to four
thousand and eight hundred. (43b-45b)
¹The pentatonic permutational note-series are formed by dropping
the last two notes of the mūrcchanā-series. In the two grāma-s we have
six series i. e., three in each beginning with ga, dha and ni in which
naturally neither ga nor ni is dropped. So these six series are fourfold;
but in the case of remaining eight series either ga or ni is dropped, and
so we can have only two types. That is how the total number of pen-
tatonic series is found to be forty, i. e. (6 × 4 = 24) + (8 × 2 = 16) = 24 +
16 = 40.

1. The pentatonic permutational note-series.
2. These six are identified to be from the mūrcchanā-s of the two
   grāma-s as under.
   | Commencing with the note | The mūrcchanā-s in the grāmas: Ṣaḍja-grāma (No.) | The mūrcchanā-s in the grāmas: Ṣaḍja-grāma (Name) | The mūrcchanā-s in the grāmas: Madhyama-grāma (No.) | The mūrcchanā-s in the grāmas: Madhyama-grāma (Name) |
   |---|---|---|---|---|
   | ga | 6th | Aśvakrāntā | 2nd | Hariṇāśvā |
   | dha | 3rd | Uttarāyatā | 6th | Pauravī |
   | ni | 2nd | Rajanī | 5th | Mārgī |
   (Chart 18)
   (Showing pentatonic series inclusive of ga and ni)
3. 120 is the number of permutational pentatonic note-series (kūṭa-
   tāna-s) formed out of a given combination or original-series.
4. That is permutational pentatonic, note-series formed out of 40
   pentatonic combinations or original series. The number also
   includes the original series (mūla-krama-s).

192 Treatment of Svara
Again each of the mūrcchanā-series has been spoken of as having one
hundred and twenty permutational pentatonic note-series. We have
forty mūrcchanā-series for pentatonics, and multiplied by one hundred
and twenty, the total number of the permutational pentatonic note-
series comes to four thousand eight hundred including the original
mūrcchanā-series.
8. चतुःस्वरकूटतान-सङ्ख्या
चतुःस्वरेषु न्याद्यौ द्वौ चतुर्धा द्वादशापरे ॥४५॥
क्रमा द्विधेति द्वात्रिंशच्चतुर्विंशतिताडिता ।
शतानि सप्ताष्टषष्ट्या स्याच्चतुःस्वरसंमितिः ॥४६॥
(8) The enumeration of the tetratonics : 45c-46
Among the tetratonics¹, the two commencing with ni
are fourfold, while the other twelve (original) series are two-
fold; these thirty-two² when multiplied by twenty-four³ make
a sum-total of seven hundred and sixty-eight.⁴ (45c-46)
Of the fourteen mūrcchanā-s of the two grāma-s when the tetratonics
or the series of four notes are derived, two of them that begin with ni
(i. e. from the second of the ṣaḍja-grāma, rajanī) and the fifth of the
madhyama-grāma mārgi), include ga as well, and therefore have four
varieties. The other twelve drop either ni or ga and hence have only
two types. So among the tetratonics we have (2 × 4 = 8) + (12 × 2 = 24) =
8 + 24 = 32 (thirty-two) original series.
Twenty-four permutational note-series of the tetratonics have been
enumerated for each of the original series (vide verse 38 ante). So,
thirty-two multiplied by twenty-four yields seven hundred and sixty-
eight tetratonic series.

1. 'Tetratonic' is an abbreviated expression for the permutatio-
   nal note-series of four notes.
2. That is, eight obtained from the two mūrcchanā-s beginning
   with ni and twenty-four from the remaining twelve mūrcchanās,
   having two varieties each.
3. The number of permutational note-series of four tones in each
   combination or original series.
4. That is, permutational tetratonic note-series, formed out of
   32 tetratonic combinations or original series. This number
   also includes the original series (mūla-krama-s).
   SECTION 1 : SVARA
5. त्रिस्वरकूटतान-सङ्ख्या
   त्रिस्वरेषु तु माद्यौ द्वावभेदौ द्वादशापरे ।
   द्विधा षड्विंशतिरिति क्रमास्ते षड्भिराहताः ॥४७॥
   षट्पञ्चाशच्छतं च स्युः,
   (9) The enumeration of the tritones : 47-48a
   But among the tritones¹, the two commencing with ma
   have no variations, while the remaining twelve are twofold :
   thus, these twenty-six (original) series when multiplied by six
   make one hundred and fifty-six² in all. (47-48a)
   When the tritone permutational note-series are formed from the
   fourteen mūrcchanā-s, the last four notes are dropped in each case. In
   this process the two mūrcchanā-s of the two grāma-s beginning with ma,
   i. e., the fifth (matsarīkṛtā) of the ṣaḍja-grāma and the first (sauvīrī) of the
   madhyama-grāma, when deprived of their last four notes, drop out both
   ni and ga, and thus can have no varieties. The other twelve series have
   two varieties each, for they would retain either ni or ga. That is how
   the original series for three tones are counted as twenty-six : 2 + (12 × 2 =

24. = 26.
    Again, each of the original series has six tritone permutational
    note-series (cf. verse 38 ante). Thus, the total number of the tritone
    permutational note-series comes to one hundred and fifty-six (i. e.
    26 × 6 = 156).

10. द्विस्वरैकस्वर-कूटतान-सङ्ख्या
    , द्विस्वरेषु पुनर्द्विधा ।
    रिगधन्यादयो ऽष्टौ स्युः शुद्धास्तदितरे क्रमाः ॥४८॥
    (10) The enumeration of the bitones and the monotones :
    48b-49
    Again among the bitones¹, the (original) series com-
    mencing with ri, ga, dha and ni being twofold are eight, while

1. That is, the permutational note-series of three notes.
2. That is, permutational tritonic note-series, formed out of 26
   tritonic combinations or original series. This number also
   includes the original series (mūla-krama-s).
3. 'Bi-tone' represents the permutational note-series of two notes.
   13

194 Treatment of Svara
द्वाविंशतिस्ते तु चतुश्चत्वारिंशद् द्विताडिताः ।
एकस्वरास्त्वभेदत्वान्मौला एव चतुर्दश ॥४९॥
the others² are śuddha (standard). These twenty-two multi-
plied by two become forty-four³ while the monotones⁴
having no variations are fourteen⁵ krama-s in identity with
the original-series. (48b-49)
The bitone permutational note-series are formed by dropping the
last five notes from the mūrcchanā-series. In this process the bitone series
beginning with ri, ga, dha and ni include either ga or ni and are therefore
twofold, yielding sixteen varieties in the two grāma-s. The remaining
six series, being devoid of both ga and ni, have no variations. Thus the
bitones are twenty-two series. But each mūrcchanā-series has two bitones;
so the total number of bitone permutational note-series is forty-four
(i. e. 16+6=22×2=44).
With the so-called monotone series, there is obviously no question
of variation, so in identity with the fourteen mūrcchanā-s from which
they are derived, they are fourteen in all.
To recapitulate, the total number of the permutational note-series
enumerated hitherto is computed as under :—
(i) The complete series of seven tones each 2,82,240 vide
verse No. 34 ante
(ii) The hexatonic series of six tones each 34,560 ,, ,, 42 ,,
(iii) The pentatonic series of five tones each 4,800 ,, ,, 45 ,,
(iv) The tetratonic series 768 ,, ,, 46 ,,
(v) The tritonic series 156 ,, ,, 48 ,,
(vi) The bitonic series 44 ,, ,, 49 ,,
(vii) The monotones 14 ,, ,, 49 ,,
Total number including original series 3,22,582
2. The remaining six original series i. e., krama-s.
3. This number includes the original series as well.
4. Permutational note series of one note each.
5. That is because the series of mūrcchanā-s are fourteen.

Section 4 : Grāma, Mūrcchanā, Krama and Tāna 195
(iii) पुनरुक्ताः कूटतानाः, तेषामपनये कूटतान-सङ्ख्या
षड्जादेः शुद्धमध्याया भेदकं पञ्चमं विना ।
चतुःस्वरे क्रमद्वन्द्वे ऽष्टाचत्वारिंशदीरिताः ॥५०॥
तानास्त्रिस्वरयोस्त्वेते द्वादश द्विस्वरे द्वयम् ।
एक एकस्वरस्ते त्रिषष्टिरौत्तरमन्द्रकैः ॥५१॥
पुनरुक्ता मतास्तानेन्यादिमार्गीक्रमाः पुनः ।
पञ्चस्वरा ये चत्वारस्तत्तानानां चतुःशती ॥५२॥
अशीत्यभ्यधिका चातुःस्वरी षण्णवतिर्भवेत् ।
द्वादश त्रिस्वरद्वन्द्वे चत्वारो द्विस्वरद्वये ॥५३॥
एक एकस्वरस्तानस्तेषां पञ्चशती त्वियम् ।
त्रिनवत्या युता तानैर्भिन्ना रजनीगतैः ॥५४॥
धैवतादेस्तु पौरव्याश्चत्वारः षट्स्वराः क्रमात् ।
तत्तानानां तु साशीतिः शताष्टाविंशतिर्मता ॥५५॥
औडुवानां चतुर्णां प्रागुक्ता सङ्ख्या चतुःस्वरौ ।
त्रिस्वरौ द्विस्वरावेकस्वरः प्रागुक्तसङ्ख्यकाः ॥५६॥
पञ्चविंशतिसंयुक्ता चतुस्त्रिंशच्छती त्वियम् ।
तानानां सदृशाकारा स्यात्तानैरौत्तरायतैः ॥५७॥
इत्येकाशीतिसंयुक्तं सहस्राणां चतुष्टयम् ।
तानानां पुनरुक्तानां पूर्णपूर्णैः सह क्रमैः ॥५८॥
अपनीयेत चेदेषा कूटतानमितिर्भवेत् ।
लक्षत्रयं सप्तदश सहस्राणि शतानि . च ॥५९॥
नवत्रिंशद्युतानीति,

196 Treatment of Svara
(iii) The repetitions and the total number of permutational
note-series : 50-60
In the absence of the grāma-indicative¹ pañcama of the
śuddha-madhyā² commencing with ṣaḍja, forty-eight note-series
of tetratones, twelve of tritones, two of bitones and one of the
monotone in the two original series,³ making sixty-three in
all are considered to be the repetitions of those pertaining to
uttaramandrā⁴. (50-52a)
In mārgī⁵, which commences with niṣāda, the four⁶
(original-series) provide four hundred and eighty pentatonic
The 3,22,582 permutational series of notes just enumerated not
only include the number of original-series (krama-s) but also many
repetitions in-between the note-series of the two grāma-s. 'K' very ably
introduces this matter as under:
"Even though ni and ga in their kakalī and antara forms determine
and bring about the mūrcchanā-variation, yet while this difference in
relation to other notes is quite notable, it is hardly perceptible within
these notes i. e., with reference to niṣāda and gāndhāra; and that is why
these two (i. e. kākalī and antara) are not considered to be as good as the
standard notes. Again, if as a rule, the different mūrcchanā-s such as
rajanī etc. commencing with ni etc. in the ṣaḍja-grāma come into being by
occupying the position of middle ṣaḍja and those in the madhyama-grāma
such as hariṇāśva etc., commencing with ga etc., occur by occupying the
middle madhyama of the madhyama-grāma, then even where the grāma-
indicator viz. the pañcama is omitted, because of the difference in the

1. Pañcama is considered to be indicative of the grāma in the
   sense that if it is a four-śruti pañcama it indicates the ṣaḍja-
   grāma and if it is a three-śruti pañcama it indicates the
   madhyama-grāma. Literally, the 'bhedaka' of the text means
   'discriminator' implying that it functions to distinguish
   between the two grāma-s.
2. Śuddhamadhyā is the fourth mūrcchanā of the madhyama-grāma
   and runs as 'sa ri ga ma pa dha ni'.
3. The series pertaining respectively to the two types standard
   and antara-inclusive.
4. The first mūrcchanā of the saḍja-grāma which runs as : sa ri ga
   ma pa dha ni.
5. The fifth mūrcchanā of the madhyama-grāma commencing with ni
   and ending with dha.
6. These are—standard, kākalī-inclusive, antra-inclusive and
   inclusive of kākalī-antara.
   Section 4 : Grāma, Mūrcchanā, Krama and Tāna 197
   note-series and ninety-six tetratonic series; the two⁷ (original
   series) produce twelve tritone and four bitone note-series,
   which along with the one monotone altogether make five
   hundred and ninety-three note-series that are identical with
   those of rajanī.⁸ (52-54)
   Pauravī⁹, commencing with dhaivata, with its four¹⁰
   (original series) is found to have two thousand eight hundred
   gramic position of the commencing note of the mūrcchanā, there is no
   question of any repetition being made in the permutational note-series
   proceeding from them, since their parent grāma can easily be traced.
   But however, if as a rule, in the two grāma-s the different mūrcchanā-s
   are formed by placing the commencing notes one below the other then
   the note-series of the śuddha-madhyā, mārgī and pauravī mūrcchanā-s of
   the madhyama-grāma have a necessary correspondence with the note-series
   such as hexatonics etc of the uttaramandrā, rajanī, uttarāyatā etc., the
   mūrcchanā-s of the ṣaḍja-grāma; and thus, due to the lack of difference
   in the gramic position of the commencing notes and also because of the
   omission of pañcama there is a definite possibility of their having been
   repeated. Therefore, the author is now to point out such repetitions in
   the note-series of the madhyama-grāma, in order to exclude them from the
   total number."
   Now, this introduction to the topic of repetitions, significant as it
   is, obviously requires some elucidation. Two ways of forming the
   mūrcchanā-s have been mentioned (verse 12-15 ante) viz. (i) by com-
   mencing the succeeding mūrcchanā-s with their opening notes placed in
   the position of ṣaḍja in the ṣaḍja-grāma and madhyama in the madhyama-
   grāma and (ii) by placing their commencing notes one below the other.
   The commentator points out that in the first case there is no possibility
   of repetitions, for then the grāma-distinction is preserved, but in the
   second case the possibility does exist. After all, the only markable
   difference between the two grāma-s is the number of śruti-s of pañcama,
   the other differences being consequent upon it. The process of forming
   note-series is such that successively the last notes are dropped. In this
   process pa, which is indicative of the grāma, is invariably retained in the
7. These are—standard and kākalī-inclusive.
8. The second mūrcchanā of the ṣaḍja-grāma corresponding to the
   mārgī of the madhyama-grāma.
9. Pauravī is constituted as : dha ni sa ri ga ma pa .
10. The four original series are of the four types, viz. standard,
    kākalī-inclusive, antara-inclusive and inclusive of both kakalī
    and antara.

Left Page (Page 202)

202 Treatment of Svara
The number of repetitions

• 22 + 11 = 179\end{aligned}\right}$ | Hexatonic, pentatonic, tetratonic, tritonic, bitonic and monotone series respectively. |
  | 3. | Repeated note-series | 4081 | $\left.\begin{aligned}63 + 593 + 3425
  = 4081\end{aligned}\right}$ | śuddhamadhyā, mārgi pauravi respectively |
  Total number of repetitions : 392 + 179 + 4081 = 4652
  (Chart 19b)
  The correct number of permutational note-series
  | | | |
  | :--- | :---: | ---: |
  | Total number of note-series | ... .. | 3,22,582 |
  | Total number of repetitions | (-) | 4,652 |
  | Correct number of note-series | ... ... | 3,17,930 |
  (Chart 19c)
  (iv) प्रतिमूर्च्छनं कूटतान-सङ्ख्याज्ञानोपायः
  , ज्ञानोपायो ऽत्र कथ्यते ।
  अङ्कानेकादिसप्तान्तानूर्ध्वमूर्ध्वं लिखेत्क्रमात् ॥६०॥
  हते पूर्वेण पूर्वेण तेषु चाङ्के परे परे ।
  एकस्वरादिसङ्ख्या स्यात्क्रमेण प्रतिमूर्च्छनम् ॥६१॥
  (iv) Determining the number of permutational forms in the note-series of each mūrcchanā : 60b-61
  Now, the method of determining them¹ is herewith described : Let the numbers one to seven be written (verti-
  Since the number of permutations making for the note-series enumerated above is enormous, a mathematical device has been devised to determine the number of a particular permutation of a given form

1. This refers to the permutational note-series i. e., the kūṭatāna-s.

Right Page

Section 4 : Grāma, Mūrcchanā, ... ...
cally) one over² another in consecutive order. Every succeeding³ number multiplied by the preceding⁴ one respectively points out the number of note-series such as monotone etc., in each mūrcchanā. (60b-61)
in a particular series and also the particular form of a certain permutation in a particular series, given its proper number. This device is called khaṇḍa-meru, which will be explained subsequently.
Presently the author is trying to explain the method of working out the precise number of the note series or the permutational form of a particular series of notes such as monotone, bitone, tritone series and so on in each mūrcchanā.
The text directs us to write numbers commencing from one upto seven, one over the other i. e., vertically. These numbers incidentally would represent the particular note-series such as monotone, bitone, etc. Keeping in view the directions of the text the numbers would be written from the bottom to the top. 'S' too interprets the text as such.
Number of permutational forms in different note-series in each mūrcchanā

2. This expression does not suggest that the numbers are not to be written serially, for that direction has explicitly been given immediately in the text, it only implies that they are not to be written horizontally as usual.
3. The successive note.
4. The preceding resultant i. e., the number of the permutations of the previous series.

204 Treatment of Svara
Number of permutational forms in different note-series in each mūrcchanā

1. 'sa ri ga ma pa dha ni' is the original order of the seven notes.
   The word krama which has been rendered as 'the mūrcchanā
   series' or sometimes as the original series has a different shade
   of meaning here, though essentially the connotation of the
   word remains the same. If it is a tetratonic series the order
   would be 'sa ri ga ma' for it, and so on. Thus, in this context,
   krama implies the original combinational order of notes of a
   given note-series. But for the sake of convenience we are to
   use the expression "original order" corresponding to the Skt.
   mūlakrama.
2. The repetition of the term 'pūrva' in the text has been effected
   through this expression, since that is the import of the text.
   Section 4 : Grāma, Mūrchhanā, Tāna and ...
   that³ becomes the succeeding note, the preceding one may
   be advanced keeping the subsequent⁴ notes afterwards; and
   describing the method of placing the notes of various types of note-
   series such as complete, hexatonic etc., in a particular and progressive
   sequence of notes, giving all the possible permutations of the series.
   The essential formula consists in the rule that, while forming the 'permu-
   tational calculus' (prastāra) the notes of the series may, in the first
   instance, be placed in their original order, which may be considered to
   be the first note-series. In order, further to derive the other possible
   permutations the preceding note in each of the series has been placed
   below the succeeding note.
   The question is, 'what to do about the remaining notes'?, and the
   author himself explains that the notes following the succeeding note will
   have to be placed after the note transposed, and the notes preceding it
   will be placed before it in their original order. This much is the action
   that is to be taken.
   The next series, and all the other possible series will be formed
   by applying the above rule to their preceding series. The application
   of the rule is demonstrated by the commentators as under with respect
   to the permutational calculus of the tetratonic series.
   (i) The first series is of the original order viz. sa ri ga ma.
   (ii) To form the series the preceding note viz. sa is to be written
   below the succeeding note, viz. ri. The subsequent notes ga and ma
   will be written after (or in front of) ri as in the overhead line (i. e., the
   preceding series), and ri will naturally be placed before i. e., behind it;
   thus what we get is ri sa ga ma.
   (iii) To form the third series, the second series may be taken as
   the top. Now as per the rule, ri may be placed below sa which will
   result in the series sa ri ga ma, a repetition of the original order. The
   purpose of the permutational calculus being the forming of different
   The implication derived by 'K' is that this action can be taken
   only once in each of the note-series of a particular sequential
   order.
3. The pronoun 'that', according to 'S', refers to the preceding
   note i. e., in the first step. This is the second step being
   explained and accordingly the preceding note of the first step
   becomes the succeeding note of the second step.
4. The subsequent notes are the ones that follow the action taking
   place among the preceding notes with reference to the previous
   note-series.

206                      Treatment of Svara                              Section 4 : Grama, Murchhana, ...
the rest (of the notes in the series) be left behind$^5$ according                      Permutational calculus of the tetratonic series
to the original order; such is the 'permutational calculus'$^6$
(prastāra). (62-63b)

5. 'Behind' the placement of the preceding note i. e., to the left of it on the paper.
6. Prastāra is defined as the extension of the series of note-series in a particular permutational sequence, which has been explained above.
   (Chart 21)
   The process of formation is briefly presented in the following chart
   as per the rule stated in the text, and demonstrated up to seventh note-
   series as explained above.
   The process of formation of the permutational calculus of the
   tetratonic series
   | Sl. No. of the note-series | Notes transposed | Series obtained | Remarks |
   | :--- | :--- | :--- | :--- |
   | 1st series | ............ | sa ri ga ma | This being the 1st series no series precedes it and there is no transposition of notes. |
   | 2nd series | sa for ri | ri sa ga ma | |
   | 3rd series | ri for ga | sa ga ri ma | |
   | 4th series | sa for ga | ga sa ri ma | |
   | 5th series | ga for ri | ri ga sa ma | |
   | 6th series | ri for ga | ga ri sa ma | |
   | 7th series | ga for ma | sa ri ma ga | |
   (Chart 22 a)
   If the notes are 1, 2, 3, 4 we get the following picture of the first six series :
   | No. of series | sa ri ga ma | Remarks |
   | :--- | :---: | :--- |
   | 1st series | 1—2—3—4 | Original order |
   | 2nd series | 2—1—3—4 | 1 transposed for 2 |
   | 3rd series | 1—3—2—4 | 2 transposed for 3 |
   | 4th series | 3—1—2—4 | 1 transposed for 3 |
   | 5th series | 2—3—1—4 | 3 transposed for 2 |
   | 6th series | 3—2—1—4 | 2 transposed for 3 |
   (Chart 22 b)