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The Positive Sciences of the Ancient Hindus c6: Chapter III. Hindu Ideas on Acoustics

The Positive Sciences of the Ancient Hindus c6

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Chapter III. Hindu Ideas on Acoustics

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ANALYSIS OF SOUND.

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*The Mîmâmsakas.*—In their analysis of Sound, the Mîmâmsakas distinguish between three elements: (1) Nâda, a quality of Vâyu (air), which is the physical basis of audible sound; (2) Dhvani, sound as heard, audible sound; and (3) in the case of significant sound, Sphota, "transcendental" or "intelligible" sound, representing the Platonic ideas or *logoi*, which are eternal (नित्य,) ubiquitous (व्यापक), and noumenal (निराधार, *lit.*, without substrate or ground—Kumârila). The Sphotas are manifested by the Dhvanis (audible sounds), of course only in the case of words (शब्द, संज्ञा). Upavarṣa, the teacher of Panini, rejected the Sphotas in favour of the Varnas, which were conceived to be "phonetic moulds" with natural significance.

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As regards sound in its physical aspect and the mode of its propagation, some of the Mîmâmsakas content themselves with saying that Vâyu (air) has a special quality (Nâda) which causes audible sound (नादो वायुगुणः वायुर्वा यदि कल्प्येत—Kumârila, Śloka-Vârtika; वायुरेव ताल्वादिस्थानसंयोगात् शब्दगुणको निष्पद्यते, शब्दस्यापि वायुगुणत्वं वेदितव्यम् — Pârtha-Sârathi Miśra, Nyâyaratnâkara).

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Others, including the teachers of the Śikṣâ (Vedic chanting), hold that the physical basis of sound is a series of air movements (वायुसन्तान, *cf.* Udyotakara's and Vâchaspati's reports); in other words, the air-particles themselves flow in a current in all directions, being obstructed in their path by the impact of tangible objects (*i.e.* material bodies), and the movement ceases, as in the arrow, when the moving force is thus exhausted (*e.g.* स गच्छन्सर्वतोदिक्षु उद्दामवेगाहितक्रियः शरवत् वेगक्षान्नेव न दूरं गन्तुमर्हति . . . शिक्षाविदस्तु पवनात्मकमेव शब्दमाचक्षते—Jayanta, Nyâya-Manjarî). But the orthodox Mîmâmsâ view is that of the Mîmâmsâ doctor, Śabara Svâmi, who holds that Nâda (the physical basis of sound) is a wave-motion of air, being the transmission of conjunctions and disjunctions in the minute particles of air, the wave originating in the first impact, and being continued by the successive impacts of the minute particles (*e.g.* संयोगविभागानैरन्तर्येण क्रियमाणाः शब्दमभिव्यञ्जन्तो नादशब्दवाच्याः (17-1-1) अभिघातेन हि प्रेरिता वायवः स्तिमित्तानि वाय्वन्तराणि प्रतिबाधमानाः सर्वतो दिक्कान् संयोगविभागान् उत्पादयन्ति यावद्वेगं अभिप्रतिष्ठन्ते । ते च वायोरप्रत्यक्षत्वात् संयोगविभागा नोपलभ्यन्ते । अनुपरतेषु एव तेषु शब्द उपलभ्यते । नोपरतेषु अतएव च अनुवातं दूरात् उपलभ्यते शब्दः—Śabara-Bhâṣya, Sûtra 13, Pâda 1, Adhyâya 1). In this view, the particles of air (वाय्ववयवाः) are subject to a vibratory motion (a sort of *parispanda*) in the production of sound (परिस्पन्दाविलक्षण —Jayanta, Nyâya-Manjarî). The Vâkyapadîya describes articulate sounds (*varnas*), and indeed all sounds (*sabdas*), as only forms of air set in motion, with rarefaction and condensation (प्रचय), and capable of variations of velocity and configuration (लब्धक्रियः प्रयत्नेन वक्त्रेरव्यानु- वर्त्तिना स्थानेष्वभिहतो वायुः शब्दत्वं प्रतिपद्यते । तस्य कारणसामर्थ्यात् वेगप्रचयधर्म्मिणः संनिपातात् विभज्यन्ते सारवत्योऽपि मूर्त्तयः । Vâkyapadîya, Kâṇḍa 1, Śloka 109).

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*Nyâya-Vaiśeṣika.*—The early Nyâya writers hold that the sound-wave (शब्दसन्तान) has its substrate in Âkâśa (ether) and not Vâyu (air). Later writers (*e.g.* Vâchaspati in the Tattvavindu) add that sound itself as a phenomenon is not to be conceived as a mode of motion (*parispanda*), for Âkâśa, the substrate, is, in the Nyâya view, incapable of motion (न तावत् परिस्पन्दस्तस्य मूर्त्तनुविधायिनो द्रव्ये विभुनि विभुगुणे वा शब्दे मूर्त्तभावेनासम्भवात्—Tattvavindu). At the same time the propagation of sound must be conceived on the analogy of waves in water (वीचितरङ्गन्याय). Udyotakara in the Vârtika, Vâchaspati in the Tâtparyyaṭîkâ, and Jayanta in the Nyâya-Manjarî controvert the three views current in the Mîmâmsâ school—(1) that Nâda, the physical basis of audible sound, is a specific quality of Vâyu (air), (2) that sound, in its physical aspect, is constituted by a series of air movements of the nature of a current (वायुसन्तान), and (3) that it is not air-currents but air-waves, series of conjunctions and disjunctions of the air-particles or molecules (वाय्ववयवाः, वायुपरमाणवः), that constitute the Nâda, the sound physical, to which, in the case of significant sounds, the Mîmâmsakas assign the function of manifesting the Sphoṭa, "transcendental" or "intelligible" sound (*logos*, the word). *Vide* Udyotakara Vârtika, Adhyâya 2, Âhnika 2, Sûtra 14; also Tâtparyyaṭîkâ, माभूत् वायुसन्तानो मा च भूततद्गुणो नादः शब्दस्य व्यञ्जकः वायवीयास्तु संयोगविभागव्यञ्जका भवन्ति इत्यतआह, etc., *loc. cit.* Against these views the early Nyâya doctors maintain that sound is a specific quality of Âkâśa (ether) and not of Vâyu (air). At the same time they admit that the impact which originates the sound phenomenon (अव्याप्यवृत्ति अयावद्द्रव्यभावि विशेषगुण) in Âkâśa does so by setting up a vibration in the molecules of the object struck (*e.g.* a bell), and that these vibrating molecules impinge against the air-molecules in contact (वायुपरमाणवः, प्रत्यासन्नवायुः). In other words, though Âkâśa is the substrate (आश्रय), the efficient cause of sound (निमित्तकारण) is to be found in the mechanical impact (अभिघात) of vibrating molecules of sonorous bodies against contiguous molecules of air. As to the propagation of sound, the early Nyâya-Vaiśeṣika writers content themselves with stating that the first sound thus produced in the substrate Âkâśa by the impact of the vibrating molecules (*e.g.* of a bell) against the contiguous molecules of air, produces a second sound in the contiguous Âkâśa, and the second sound a third, and so on, in the same way as waves are generated in water, until the last sound sets up a vibration in the ear-drum (कर्णशष्कुलि). Of course, this propagation of sound-wave in Âkâśa (ether) is effected by means of the air-wave as its vehicle. This is the Nyâya-Vaiśeṣika hypothesis (कल्पना) of an independent sound-wave (शब्द-सन्तान). Âkâśa (ether) is motionless, but the air-wave would not be transmitted if the air-molecules were not interconnected by Âkâśa. Praśastapâda, the Vaiśeṣika doctor, for example, describes the first sound as giving off a second, the second a third, and so on, expanding in Âkâśa, in the same way as waves are supposed to propagate themselves in the ocean.

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शब्दोऽम्बरगुणः संयोगविभागशब्दजः . . . . स्थानवायुसंयोगापेक्षमाणात् स्थानाकाशसंयोगात् वर्णोत्पत्तिः । अव्यक्तशब्दोऽपि भेरीदण्डसंयोगापेक्षात् भेर्य्याकाशसंयोगात् उत्पद्यते । वेणुपूर्व्वविभागात् वेण्वाकाशविभागाच्च शब्दाच्च शब्दाच्च संयोगविभागनिष्पन्नात् वीचिसन्तानवत् शब्दसन्तान इत्येकं सन्तानेन श्रोत्रप्रदेशमागतस्य ग्रहणम्। Praśastapâda, यथा जलवीच्या तदव्यवहिते देशे वीच्यान्तरमुपजायते ततोऽप्यन्यत् ततोऽप्यन्यदित्यनेन क्रमेण वीचिसन्तानो भवति तथा क्रमेण शब्दसन्तानो भवति । नन्वेषा कल्पना कुतः सिद्धतीत्याह etc. (*Śrîdhara*, *ibid.*). On this hypothesis the locus of the sound at any moment forms a circle in Âkâśa, and the propagation is carried on in the air by means of ever-expanding circles, as in the case of waves in water. But this analogy is rejected by some (*e.g.* Udyotakara), who hold that the first sound gives off not one sound in a circle, but an indefinite number of sounds in all directions, and each of these again gives off another, and so on, so that sound may be said to expand by successive concentric spherical layers, even as the Kadambakoraka (the so-called bud of the *Nauclea Kadamba*) expands by successive concentric spherical layers of filaments which shoot forth from one another. On the first of these two hypotheses, the air-wave implied in the transmission of sound is of the nature of what we call transverse waves; on the second, of the nature apparently of longitudinal waves. In any case, it is clear that the orthodox Mimâmsa view of Śabara Svâmi, that the air-wave constituting physical sound means a series of mere conjunctions and disjunctions of air-particles with rarefaction and condensation (*e.g.*, सर्व्वतोदिक्षान्-संयोगविभागानैरन्तर्य्येण, Śabara, प्रवय, Vâkyapadîya), implies longitudinal waves, वीचितरङ्गन्ययेन तदुत्पत्तिस्तु कीर्त्तिता कदम्बकोरक न्यायादुत्पत्तिः कस्यचिन्मते (Viśvanâtha, Bhâshâ Parichheda, Śloka 165); **परिशेषेषु सन्तानसिद्धिः। तत्राद्यः शब्दः संयोग-विभाग-हेतुकः। तस्मात् शब्दान्तराणि कदम्बगोलकन्यायेन सर्वदिक्कानि। तेभ्यः प्रत्येकमेकैकः शब्दः मन्दतरतमादिभावेनान्यप्रतियन्धमनुविधीयमानः प्रादुर्भास्त। ततोऽन्यस्यातिमान्द्यात् शब्दान्तरोत्पत्तिः—शक्तिविधातो येन केनचित् प्रतिबन्धात् भवति** (Udyotakara, II., 2, 14). As the momentum of the impact series (which constitutes the efficient cause of the sound-wave) grows feebler and feebler in the course of transmission through the air-particles, the sound at last dies away. Gangeśa, in the Chintâmaṇi, holds that the propagation is not from molecule to molecule, but travels in ever-expanding circles as in water-waves, perhaps in spherical layers by compression of masses of air; and these air-waves, the vehicles of sound, are exceedingly swift.. This explains the velocity of sound. **शब्देन च अव्यवहितपरमाणुदेशोत्पादक्रमेण न शब्दारम्भो येन मेघज्ञादि शब्दानां भूलोकप्राप्तिर्युगान्तरेऽपि न स्यात्। किन्तु मेघाद्यभिहतं सर्वतोगामि-महावायोगंहति देशे संयोग-निमित्तमासाद्य आद्यशब्देन सर्वदिग्वत्शब्दः एक एव जन्यते उत्तरोत्तरेणापि अधिकाधिकदेशतः सर्वत्र एकैक एव शब्दः वीचितरङ्गवदुपपद्यते वायोरेव नयनवत, महावेगतया शीघ्रगामित्वेन चरमशब्दारम्भात् आद्यशब्दानन्तरं अचिरेणैव शब्दोपलम्भः। वायोरेव च मन्दतरतमादिक्रमेण मन्दादिशब्दोत्पत्तिः यथा आद्य शब्देन कदम्बगोलकवद् दशदिशि दशशब्दा आरभ्यन्ते तैश्च दशशब्द सन्ताना इति** (Gangeśa, Tattva Chintâmaṇi).

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But how does the first sound produce the second, the second the third, and so on? At every step the efficient cause, the impact of some vibrating molecule against a contiguous molecule of air, must be posited, and this is equally applicable to a sound produced by a sound (**शब्दजशब्द**) as to one produced by conjunction and disjunction (**संयोगज** or **विभागज**). In other words, the sound-wave (**शब्दसन्तान**) in Âkâśa necessarily implies an air-wave. The Mimâmsaka view, then, that explains the propagation of sound by the transmission of the original oscillatory motion through the successive layers of air by means of successive impacts or pressures producing conjunction and disjunction of air-molecules (वायवीयाः संयोगविभागाः—Śabarabhâṣya), or rarefaction and condensation (प्रचय—Vâkyapadîya), is also implied in the Nyâya-Vaiśeṣika doctrine of the sound-wave (शब्दसन्तान), the difference being that in the latter the air-wave, which is conceived as a mode of serial motion (गति-सन्तान), is only the vehicle or medium of propagation of a so-called sound-wave in Âkâśa, which is not itself a mode of motion. This is what we find expressly and elaborately formulated in the later Nyâya-Vaiśeṣika (*vide* Gangeśa, Chintâmaṇi, *supra*).

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ANALYSIS OF VIBRATORY MOTION, *e.g.* OF A BELL (IN AIR).

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The molecules of a bell vibrate when the bell is struck. The question is—what is the nature of this vibratory movement? Vâtsyâyana and Udyotakara answer that, when the hand strikes the bell, some of the molecules are displaced (from their stable position—*i.e.* there is *karma* in the molecules), and thus a Sanskâra (here a kinetic Sanskâra, momentum) is generated (संस्कार, कम्पसन्तानसंस्कार—Vâtsyâyana and Vâchaspati), and the molecules swing forward under the action of this Sanskâra until they strike the contiguous molecules of air. This now is a case of mutual impact, which divides the momentum between the colliding masses, and the bell-molecules begin to swing backward, the motion continuing under the action of the diminished Sanskâra until they come in collision again with other air-molecules; and then the process is repeated, and the bell-molecules begin to swing forward and backward until the original energy which is parted with in some measure at each impact becomes so feeble as to be unable to produce any kinetic disturbance (कर्म). Similarly, the air-molecules themselves are set vibrating by means of these impacts, and the transmission of the motion would form the wave of air, which the later Nyâya-Vaiśeṣika expressly posit as the vehicle of the sound-wave. But Udyotakara never conceived vibration *in vacuo*, nor does it appear if he meant to include the second species of Sanskâra (elasticity, Sthitisthâpaka-sanskâra) as converted from its potential state (अतीन्द्रियता) into kinetic energy, and thus contributing to the momentum (*vega*). He uses the generic term Sanskâra, which comprehends elasticity as well as momentum due to impressed force. His commentator, Vâchaspati, does not go into details, and does not analyse the momentum. Later writers, however, expressly state that elasticity (Sthitisthâpaka-sanskâra) is one of the causes of vibration, and that elasticity resides not only in the element of earth, but also in air, water, and *tejas* (*cf.* Viśvanâtha).

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घण्टायामभिहन्यमानायां तारस्तारतरो मन्दो मन्दतर इति श्रुतिभेदानाना-शब्दसन्तानोहि अविच्छेदेन श्रूयते (Vâtsyâyana, II., 2, 3, 6) पाणिसंश्लेष-मपेक्षमाणात्कम्प्येभ्यः पाणि-घण्टासंश्लेषात् पाणिगतवेगापेक्षात् घण्टायां कर्म्म तत्कर्म्म पाण्यभिघातमपेक्षमाणं विभागसमकालं संस्कारं करोति । सा चलन्त्याभ्यन्तरिकं वायुमुपगृह्णाति सा च वायुनाभिहता पुनः कर्म्म करोति ।

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ततः कर्म्मणः संस्कारः संस्कारेण पुनः कर्म्म पुनर्वायुप्रग्रह इत्येवमादिन्यायेन संस्कार उत्पद्यते। तत्र जन्यस्यातिमन्दत्वात्प्रष्टायां महाभूतक्षोभशक्तेरभावः ततो वायुप्रग्रहोच्छेदः ततःसंस्कारक्षय इति (1) Udyotakara Vârtika, Adhyâya 2, Âhnika 2, Sûtra 36. (प्रह्लातदवयवसंयुक्ता वायुपरमाणव एव आध्यात्मिको वायुः—Vâchaspati, Tâtparyyatîkâ, *loc. cit.*, also संस्कारं वेगाख्यं करोति). But *cf.* Viśvanâtha, संस्कारभेदो वेगोऽथ स्थितिस्थापकभावने। मूर्त्तमात्रेतु वेगः स्यात् कर्म्मजो वेगजः क्वचित्। स्थितिस्थापकसंस्कारः क्षितौ केचिच्चतुर्ष्वपि। अतीन्द्रियोऽसौविज्ञेयः क्वचित् स्पन्देऽपि कारणम्—Bhâshâ-parichchheda, Ślokas 157–159.

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As the air-wave forms the vehicle of the sound-wave, if it does not constitute the sound-wave itself, the favourable or retarding influence of currents of wind is easily explained. The presence or absence of water (and other intervening objects) offering greater or less resistance to the transmission of the wave-motion also easily accounts for the greater or less distance to which the sound is carried.

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ECHO.

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प्रतिध्वनि (Echo) was supposed to be a reflection of sound. Some consider it to be an after-sound, a sound generated by sound. Others suppose it to be due to the reflection of sound in the same way as an image in water or in a mirror (प्रतिबिम्ब) is due to the reflection of light. There is an element of hallucination in either case (बुद्धिपरिणामविशेषः)—the image in water is not a real image, neither is the echo the real sound it is taken to be. (रुपवत्त्वं च न सामान्यतः प्रतिबिम्बप्रयोजकं शब्दस्यापि प्रतिध्वनिरूपप्रतिबिम्ब

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दर्शनात् । न च शब्दजन्यशब्दान्तरमेव प्रतिध्वनिरिति वाच्यं स्फटिकलौहित्यादेरपि जपासन्निकर्षजन्यतापत्त्या प्रतिबिम्बमिथ्यात्वसिद्धान्तक्षतेरिति । प्रतिबिम्बश्च बुद्धेरेव परिणामविशेषो बिम्बाकारो जलादिगत इति मन्तव्यम् ।—Vijnânabhikṣu, Pravachana-Bhâṣya, Chap. I., Sutra 87.)

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PITCH, INTENSITY, AND TIMBRE.

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Sounds differ from one another by their pitch (तारमन्दादिभेद), by their intensity (तीव्रमन्दादिभेद), and by their quality or timbre (असाधारण धर्म). When a bell is struck, an indefinite number of notes (श्रुतिभेद, tones and overtones) are emitted, of varying pitches; and the notes die away, becoming less and less intense. Now, we know that the molecules swing to and fro, and that the. Sanskâra (momentum, *vega*) of the vibrations (कम्पसन्तानसंस्कार) grows feebler and feebler. The differences in pitch (tones and overtones) as well as in intensity must be due to variations in the Sanskâras of the vibrations. The distinguishable pitches (called Srutis, श्रुतिभेद) as well as the degrees of intensity (तीव्रमन्दादि) must be ascribed to variations in the *vega* (momentum), and, by implication, the frequency, etc., of the vibrations.

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*Cf.* Vâtsyâyana, II., 2, 36—घण्टास्यं सन्तानवृत्तिसंस्कारभूतं पटुमन्दमिति वर्तते तस्यानुवृत्त्या शब्दसन्तानानुवृत्तिः पटुमन्दभावाच्च तीव्रमन्दता शब्दस्य तत्कृतश्च श्रुतिभेदः *Vide* also Udyotakara's analysis of vibration based on Vâtsyâyana: घण्टायामभिहन्यमानायां तारस्तारतरो मन्दोमन्दतर इति श्रुतिभेदाज्ञानाच्छब्दसन्तानो हि अविच्छेदेन श्रूयते । सन्तानवृत्तित्वात् मन्दतरमन्दतमादिभिरुपानुविधायिनं शब्दमुत्पादयन्ति तत्र कारणं संस्कारः—Udyotakara, Vârtika, Adhyâya 2, Âhnika 2, Sûtra 36. **सन्तानवृत्तिना कारणेन श्रुतिभेदोत्पत्तिः**—Vâchaspati, Tâtparyyatîkâ, *loc. cit.*

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Sounds also differ from one another in volume or massiveness in the case of coalescence (**समानजातीयोपचय**). A sound both loud and massive is called **महान्** (large)—**एवं शब्दसन्तान एव तारः महान् इत्युच्यते तत्राप्यस्ति समानजातीयोपचयः अस्ति च स्फुटतरत्वम् महानपि स्फुटतरः । अयमपि तथा इति महानित्युच्यते**—Vâchaspati, II., 2, 36.

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Śabara, the Mîmâmsâ doctor, explains massiveness (**महत्त्व**) as due to **नादवृद्धि**, the coalescence of different air-waves, which by their simultaneous impact affect a comparatively large tract of the ear-drum (**यच्चैतत् बहुभिर्भैरीमाध्मानद्भिः शब्दमुच्चारयद्भिर्महान् शब्द उपलभ्यते । न वर्द्धते शब्दः । मृदुरेकेन बहुभिस्तूच्चार्य्यमाणे तान्येव अक्षराणि कर्णशष्कुलीमण्डलस्य सर्वां नेमिं व्यापद्भिः संयोगविभागनैरन्तर्येण अनेकशो ग्रहणात् महान् इव अवयववानिव उपलभ्यते । संयोगविभागनैरन्तर्येण क्रियमाणाः शब्दमभिव्यञ्जन्तो नादशन्दवाच्याः । तेन नादस्यैषा वृद्धिः न शब्दस्य**—Śabara on Jaimini, Sûtra 17, Adhyâya 1, Pâda 1). The Mîmâmsakas, who resolve sounds into air-waves, attribute all differences, whether of pitch, intensity, or massiveness, to differences in the series of conjunctions and disjunctions of air-particles that form the waves (*vide* Vâchaspati's report, **शब्दानां तु संयोगविभागयोनीनां युक्तस्तद्भेदेन रूपभेदः** ; *cf.* also the later Nyâya-Vaiśeṣika, which accepts air-waves as vehicles of sound-waves : **वायोरेव मन्दतरतमादिक्रमेण मन्दादि-शब्दोत्पत्तिः**—Gangeśa, Tattva Chintâmaṇi). It may be noted that the terms **तीव्र** and **मन्द** are occasionally used in a general sense, and applied to express higher and lower degrees of pitch as well as of intensity.

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There are also differences of quality (**शब्दस्य असाधारणधर्म्मः**). The same sound *ga* (**ग**), of the same pitch and intensity, uttered by men and parrots, can be distinguished; so also the sounds, even the same notes of the scale, given out by a wind instrument like the *venu* and a stringed instrument like the *vina*. Similarly, there are sexual and even individual differences of voice (अस्ति हि शुकसारिकामनुष्यवक्त्रप्रभवेष्वककारादिषु स्फुटतरः रूपभेदप्रत्ययः पुंसाम्। एवं स्त्रीपुंसप्रभवेषु स्त्रीपुंसभेदप्रभवेषु च—Vâchaspati, Tâtparyyatîkâ, II., 2, 14. वीणा वाद्यते वेणुः पूर्य्यते वीणावेणुशब्दयोरसाधारणी धर्मः—Udyotakara, II., 1, 15. वेणुवीणामृदङ्गादिप्रभवेषु भेदप्रत्ययः शुकसारिकामनुष्यकण्ठोत्थादिभेदप्रत्ययः—Gangeśa and Mathurânâtha). The sounds emitted by impact of the different Bhûtas (echo from Âkâśa, hissing from the wind, puffing from fire, bubbling from water, and splitting or cracking from earth) are characteristic examples of such differences of timbre (*vide* Panchadaśî, Bhûtaviveka, Śloka 3).

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The Vâkya-padîya (Kânda I, Śloka 109), as we have seen, ascribes all differences (whether of pitch, volume, or timbre) to the characteristic forms of the air-waves, which differ from one another by their configuration (सन्निपातात् विभज्यन्ते मूर्त्तयः), and are capable of variations of velocity (momentum, *vega*) as well as of rarefaction and condensation (कारणसामर्थ्यात् प्रचयापचयैः).

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There are passing references to the obscuration (अभिभव) of sounds in Vâtsyâyana, Udyotakara and Vâchaspati, but the subject is treated more from a psychological than from a physical point of view. (तीव्रभेरीशब्दः मन्दतन्त्रीशब्दमभिभवति न मन्दः। नानाभूतेषु शब्दसन्तानेषु सत्सु श्रोत्र-प्रत्यासत्तिभावेन कस्यचित् शब्दस्य तीव्रेण मन्दस्य अभिभवो युक्तः—Vâtsyâyana, II., 2, 14; *vide* Udyotakara and Vâchaspati, *loc. cit.* Here तीव्र = loud, and मन्द = low.)

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MUSICAL SOUNDS.

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*Śrutis and Svaras.*—We have already seen that the distinguishable pitches are called Śrutis, and they are proportioned to the *vega* (momentum) of the *kampa-santāna* (vibration). Now the ratio of a note to its octave (in respect of pitch) is given as 1:2; we may therefore conclude that the *vega* of the vibration in the latter case was considered to be twice as great as in the former. An indefinite number of Śrutis could be interposed between a note and its octave (आनन्त्यं हि श्रुतीनां च सूचयन्ति विपश्चितः यथा ध्वनिविशेषाणामानं गगनोदरे । संगीतरत्नाकर । *cf.* संगीतपारिजात । केशाग्रव्यवधानेन बह्व्योऽपि श्रुतयः स्मृताः—संगीतपारिजात, Śloka 40). Twenty-two such are named and recognised for musical purposes. But a Śruti as such cannot constitute a musical tone (Svara). A Śruti is a simple (unmixed) and fundamental tone of a certain pitch, whereas an ordinary musical tone (Svara) is really composed of a fundamental tone (Śruti) and certain partial tones (harmonics, Anurananas, अनुरणन). The musical tones (Svaras), vocal or instrumental, are therefore of the nature of what we call clangs, because, either accompanying or following the Śrutis or simple fundamental tones (ह्रस्त्रादिमात्र), are always found certain partial tones (अनुरणन). व्यवहारे त्वसौ त्रेधा हृदि मन्द्रोऽभिधीयते । कण्ठे मध्यो मूर्ध्निंतारो द्विगुणश्चोत्तरोत्तरः (संगीतरत्नाकर) हृदिमन्द्रोगलेमध्यो मूर्ध्नि तार इति क्रमात् । द्विगुणः पूर्वपूर्वस्मात् —Dâmodara, Sangîtadarpaṇa, Chap. I., Śloka 49. श्रुत्यनन्तरभावी यः स्निग्धोऽनुरणनात्मकः । स स्वरः उच्यते—Sangîta-ratnâkara. स स्वरो यः श्रुतिस्थाने स्वनन् हृदयरञ्जकः (संगीतदामोदर) द्वाविंशतिविधो मन्द्रोध्वनिः सञ्जायते

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हृदि । स एव द्विगुणो मध्यः कण्ठस्थाने यथाक्रमम् । स एव मस्तके तारःस्यान्मध्यात् द्विगुणक्रमात्—Sangîta Samaya Sâra, 1. नादाच्च श्रुतयो जातास्ताः षड्जादयः स्वराः । प्रथमश्रवणाच्छन्दः श्रूयते ह्रस्वमात्रकः सा श्रुतिः सम्परिज्ञेया स्वरावयवलक्षणा । स्वरूपमात्रश्रवणादान्दोलनुरणनं विना । श्रुतिरित्युच्यते—Dâmodara, Sangîta-darpaṇa, Chap. I., Śloka 51. The relation between a Śruti and a Svara is variously conceived as (1) परिणाम modal change; (2) व्यञ्जन manifestation; (3) तादात्म्य जातिव्यक्त्योरिव the relation of genus and species; (4) विवर्त्तन (मुखं यद्वद् दर्पणेषु विवर्त्तितं) reflection; (5) कार्यकारणभाव, the relation of cause and effect; *cf.* संगीतपारिजात by Ahobala, श्रुतयस्तु स्वरा भिन्नाः श्रावणत्वेन हेतुना। अहिकुण्डलवत तत्र भेदोक्तिः शास्त्रसम्मता ।—संगीतपारिजात, Śloka 38.

Section 6. The Notes of the Diatonic Scale: Determination of Their Relative Pitch

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The pitch of a note is inversely proportional to the length of the wire (तन्त्रीतनुस्वरो ज्ञेयः तद्दर्ध्यव्यस्तमानतः—क्षेत्रलीलावती, quoted by Mr. Devala in his "Hindu Musical Scale").

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The pitch of the fundamental note to that of its octave is as 1 : 2 (मध्यस्थानस्यः षड्जः द्विगुणसमः—रागविबोध, quoted by Mr. Devala).

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The pitch of the fourth note (F) to that of the fundamental (C) is as 4 : 3 (उभयोः षड्जयोर्मध्ये मध्यमं स्वरमाचरेत—संगीतपारिजात, quoted by Mr. Devala).

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The vibrations of the fifth note (G) to those of the fundamental (C) are as 3 : 2 (त्रिभागात्मकवीणायां पञ्चमः स्यात्तदग्रिमे ।—संगीतपारिजात, quoted by Mr. Devala).

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Concord (सम्वादित्व) is either perfect or imperfect. The ratio of perfect concord is 3 : 2 ; that of imperfect concord, 4 : 3 (स-प-स-म मुख्याः संवाद्निः स्वराः रक्तसंश्रयाः प्रायः—रागविबोध, quoted by Mr. Devala) ; *e.g.* if D be the Vâdî, A would be a Samvâdî ; if E be the Vâdî, B would be a Samvâdî : in each case a perfect concord. The pitch of D is determined from that of G, and the pitch of A from that of D, in each case, by the rule of perfect concord.

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Determination of the pitches of E and B (after Mr. Devala). This may be done in either of the following ways :—

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(1) E may be determined from A, and B from E, by the rule of perfect concord. This would give 303¾ as the value of the pitch of E, and 455⅝ as that of the pitch of B, if the pitch of C be taken as 240 ; *or*

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(2) E may be determined from C by reduction of the fifth harmonic by two octaves, a sort of imperfect concord ; and then B may be determined from E by the rule of perfect concord. This would give 300 for E, and 450 for B, if C be taken as 240.

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Mr. Devala, in his investigations with the "Sonochord," finds that Hindu musicians (and Sanskrit writers on music) adopted the latter values for E and B, as they tested their notes by harmonics (मेरुगतस्वयम्भूस्वरपंक्तिप्रामाण्येन—रागविबोध, quoted by Mr. Devala). The Hindus therefore followed just intonation.

Section 7. Musical Intervals

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Musical tones are related to one another in four ways as Vâdîs, Samvâdîs, Vivâdîs, and Anuvâdîs. The mediæval compilations explain these in reference to melody, and harmony is altogether unknown, but the terms might be used to indicate relations of harmony as well. The Vâdî might in that case answer to the key-note (or tonic), and the Samvâdîs to the two consonances, the fifth (2 : 3), and the fourth (3 : 4).

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The rule given for the determination of a Samvâdî is 12 or 8 Śrutis intervening, the intervals being, therefore, 13 and 9 Śrutis respectively (giving the ratios ⅔ and ⅓).

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C being the Vâdî, G and F are stated to be the Samvâdîs.

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In the same way, it is stated that if D be the Vâdî, A would be a Samvâdî. If E be the Vâdî, B is given as a Samvâdî.

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On the other hand, a two-Śruti interval (*i.e.* a difference of a semitone) gives a Vivâdî, which would thus answer to a dissonance. This is given as a general rule (द्विश्रुत्यन्तरौस्वरौविवादिनौ Matanga). Other cases are also noticed, *e.g.* E is a Vivâdî to D, and B to A, and *vice versa* (ratio of 9 : 10).

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The notes that do not come under these heads are Anuvâdîs (*e.g.* the sixth); *cf.* Bharata, Nâtya-Śâstra, Chap. XXVIII., Ślokas 23–24.

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Also Sangîta-ratnâkara :—

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चतुर्विधा स्वरा वादी सम्वादी विवायपि अनुवादीति । वादीतु प्रयोगे बहुलस्वरः श्रुतयो द्वादशाष्टौ वा ययोरन्तरगोचराः मिथः सम्वादिनौ तौ स्तो निगावन्यविवादिनौ । रिधयोरेव वा स्यातां तौ तयोर्वारिषावपि । शेषाणामनुवादित्वम् । (स्वराध्याय).

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