“O, Mind! Betake thou to the Eternal Bliss of
Nadavidya;
Know ye not that Shiva and Brahma, Indra and Vishnu
Perceive in Nadopasana the Everlasting?”1
SHAKESPEARE spelt curses to him who is not moved by
the concord of sweet sounds; we really wonder if he realised how he had
unconsciously crystallised the purpose of creation in that couplet. Harmony is
not merely the panacea of all human ailments, it is the keynote of cosmic
existence. The apparently mad gyrations of the celestial spheres follow a
mathematical law of harmony, difficult to conceive of, but nevertheless
existing. The unceasing rising and setting of the sun, the almost taxing
regularity of occurrence of the seasons, the innumerable cycles of existence
that go on day after day, all make it clear that harmony is the sole purpose,
not the bye-product of creation. Thus it is that our ancients symbolised the
creator as a Dancer, rising to the tune of the Damaru, and sending forth quivering
the message of harmony through the rhythm of Natya.
Is it surprising therefore, that music which lives
on harmony, should have a greater appeal to the human, than any other form of
aesthetic manifestation? Von Helmholtz once said: “It always struck me as
wonderful and peculiarly interesting mystery, that in the physical and
technical foundations of music, which above all other arts seems in its action
on the mind most unmaterial, evanescent and tender creator of incalculable and
indescribable states of consciousness, that here in especial the science of
purest and strictest thought–mathematics–should prove pre-eminently fertile.”2
Music and mathematics, which the unknowing place at antipodes, are nearer each
other than any two other achievements of the human intellect.
Other forms of art draw from the world of
experience for their delineations. A picturesque scenery might inspire
painting, a sublime act, poetry, and a form of beauty, sculpture. But music is
self-sustaining and “not attempting to describe and only exceptionally to
imitate the outer world, necessarily withdraws from scientific considerations
the chief points of attack which other arts present and hence seems to be as
incomprehensible and wonderful as it is certainly powerful in its effects.”3
It is no wonder therefore that the enormous lot of written and spoken material
on the science and art of music is both vague and inaccurate. No attempt shall
therefore be made to give the reader a concept of music as an art and its
claims to be classed a science, our purpose being solely to analyse the merest
scientific principles of harmony in music.
Harmony is an intellectual necessity, not an
emotion of luxury. The child, whose mental agony it is possible to understand,
is transported to the realms of super-consciousness under the harmony of a
lullaby. The venomous cobra subjects its wickedness to the supreme order
brought about by the harmony of the flute. The hardest amongst us melts at the
strains of meaningless verse doled out by the street singer. Was it the Mogul
Emperor Aurangzeb who wanted music to be buried waist-deep? That is only an
example of the rare mastery of the flesh over the mind. Harmony unlike a
perfume, never satiates. A sweet dish may be unnecessary for body-building, but
harmony is essential for the process of mind-building; nay it is one of the
components of the mind. Disharmony is no doubt present on this good earth, but
only for enhancing the value of the subsequent harmony.
Harmony is the result of one or more simple
undulations in air, mathematically related to one another. But perception of
harmony is a peculiar faculty of the ear. Paradoxical though it may appear,
mere air vibrations do not become sound until they fall on a hearing eat. A
sufficiently strong air vibration may even be felt by the skin, but it does not
become sound. A deaf mute might feel it, but not hear it. Apart from this, the
undulations have to take place within certain limits of rapidity, to be
perceived as sound even by a good ear. These limits, for mere hearing, have
been found to be 32 and 10,000 undulations per second. But harmony ceases after
about 5,000. This depends on the compass of the particular instrument producing
a note. The piano goes up to 4224, the violin 2640 and the normal human voice jars
if it reaches beyond 1,200. The deepest C, called the contra-C in the piano
goes down to 33. But our musicians realise that such deep tones become dull and
indistinguishable drones and seldom pass an octave below the basic. Low notes
are not gathered up as whole tones by the ear.
The undulations so limited go down the auditory
canal, to the petrous bone out of which is hollowed out, the inner ear. This
cavity accommodates the cochlea or snail-shell, a peculiar organ of hearing
divided into three longitudinal sections. In the middle sections are the
extraordinary formations of sound perception, the rods of corti. These
microscopically tiny plates are arranged like the keys of a musical instrument
and tuned to a particular modulation. The principle of resonance will show us
how a particular undulation is picked up by a rod tuned to it. Hence the
sensations are transmitted by the auditory nerves, to the centre of
interpretation, the brain.
A harmonic impulse, single or composite, is seldom
pure in a physical sense. It is made up of undulations of different rapidities,
the individual components being pure no doubt. Experience and experiment show
that the ear not only perceives, but also analyses the air waves into their
elementary forms. Both the analysis of the “wave confusions” and their
subsequent synthesis in the brain with a view to re-interpretation of harmony,
have bewildered both physicists and physiologists. At any rate, this latter
faculty seems to be a rare acquisition of man and the higher animals.
This takes us to the problem of harmonic perception
by the brain. The material available at the disposal of the scientist is so
subjective, that a lot of speculation has set in on the analysis of the mode of
actual perception. To describe poetry and music, “two of the noblest arts,” as
revealing “little to the sense and suggesting much for imagination” or to say
that they “transcend all physical perceptions and take a glimpse of the
unknown”4 is probably only an escape from the inexplicable. Perhaps
this cannot be helped, or perhaps our scientific methods are not quite perfect
for tackling the more of action of the little grey cells. Suffice it to say
that art perceptions the result of mental training, something which cannot be
written down in the form of a mathematical equation. As Tagore would have it
“those of the audience who are appreciative are content to perfect the song in
their own minds by the force of their own feeling.” 5 In saying
this, we are not forgetting the classic contributions of Huxley and Darwin to
the understanding of mental functioning. Nor do we discredit Huxley’s division
of the mind into the “receptor” or sense receiver, the “effector” or motive
organiser, and “the adjustor” or the central nervous system.6 We
only express the fear that the mere physiological functioning of these regions
alone might not result in harmony perception. The co-relation of physical facts
to biological theories is fraught with dangerous speculation and we are not
anxious to step into an unconscious error.
It is a matter of common observation that sounding
bodies are in a state of vibration. Physics has established that if these
vibrations are within the limits of rapidity referred to above, they will
generate sound. For this sound to become a musical tone the impulses have to
recur with perfect regularity and in precisely equal times. Irregular agitation
leads to noise, like harmonious blending of colour leading to multifarious
shades and a haphazard mixture becoming dark. Such regular impulses have two very
distinct properties depending on two physical facts, the rapidity of the
vibrations and the extent of vibrations. The former which is called “frequency”
of undulation, controls the pitch of the note and the latter called
“amplitude,” controls loudness. A veena string of constant length,
plucked a little more vigorously, might produce a “louder” note but not one of
different “pitch.” Pitch depends solely on the number of vibrations per second,
whether the note is produced by the vibrating strings of the violin or veena,
or the vocal chords of the larynx or the trembling lips of the trumpeter.
Quite apart from the pitch and loudness of a
musical tone, there is the third characteristic quality which enables us to
distinguish a tone equally high and equally loud, but produced by different
musical instruments. We shall presently refer to the physical causes of varying
musical quality, but it is here necessary to state that this is controlled by
the nature of the vibrating mechanism (the string or plate or air colunm that
vibrates), the nature of the exciting mechanism (the finger of the player or
his bow or the hammer), and the general build of the musical instrument. There
is, however, no doubt about the fact that these variations affect, not the
quality of the individual notes uttered but the harmony of their blending. The
study of musical quality was itself therefore called “harmonic analysis” by the
pioneer in the field, Von Helmholtz.
Authorities on music hold that the eastern systems
of music are of the melodic type and the western harmonic, distinctly different
from each other.7 Actually, the physicist is compelled to argue that
the two terms are much misused, from his point of view. Harmony and melody are
so much allied that it is here necessary to state what they refer to from a
purely physical analysis. When a single tone is emitted, its melody is
controlled by other tones attendant on it and hence melody is what we might
call “mono-tone harmony.” When an individual singer utters a series of tones in
a ‘strain’ of music, we have one type of “multi- tone harmony,” leading thereon
to the development of scales of music. When a number of singers perform
simultaneously, we have the second type of multi-tone harmony, popularly called
orchestral harmony or chorus harmony.
A single musical tone is always accompanied by a
series of “overtones” weak in themselves, but nevertheless playing a very
important part in determining the quality of the tone. Helmholtz, as a result
of very laborius work, established that the nature, number, and relative
intensities of these overtones determine musical quality.
By “nature” is meant the relationship between the
overtone frequency and the fundamental or tone-frequency. Where the overtones
happen to be exact multiples of the fundamental, they are called “harmonies”
and the tone acquires musical harmony. In pronouncing vowels, or in what is
termed articulation of speech, these overtones have no integral relation to the
fundamental. We are not concerned with this, but with the problem of synthesis
of harmonies with the fundamental, leading to melody. That the ear has the
capacity to analyse and absorb even the weak harmonies has been established
beyond any possible doubt.
A simple illustration might be relevant. Let us
imagine a serene lake in which there is an incessant undulation due to the
draughts of air. A bird suddenly pecking at a fish or a stone dropped in, might
set up other undulations so that an observer would see a complicated wave- form
floating along. But on the surface of water, the different individual waves
travel with different velocities, so that in a short while we might observe the
simpler vibrations left behind. In air, however, the undulations travel with
the same velocity and the ear has to receive the waveform as a whole. It is the
nature of such waveforms that produces the difference in harmonic blending. The
more rounded off and smooth the resultant waveform, the softer is the resultant
tone; the more angular or jerky, the harsher is the quality. That probably is a
very unscientific manner of putting it. But that illustrates what we understand
by monotone harmony. Other investigations have ventured to suggest that not
merely harmonics, but overtones bearing ratios 5/4, 3/2, 4/3, etc., to the
fundamental produce very harmonious combinations. They draw their inferences
from multi-tone harmony, where these intervals are found to produce great
concord.
The number of harmonics present controls the
richness of the tone. If the nagaswaram music is rich as compared to the
flute music, it is not because of the relative strength of its notes, but
because of the full retinue of harmonics following them. No one would assert
that melody in absent in flute music, for richness is not melody. The former
depends on the number of harmonics present and the latter on their relative
strength. For example, let us assume that the intensity associated with all the
harmonics is only one per cent. If the greater part of this one per cent is
associated with a harmonic seven times the fundamental, it is found that melody
is lacking. But if the reinforced harmonic is five times, there is very good
melody. All the while there would be richness, as in a harsh but rich violin
note. The statements about the relative strength of the melodious and
un-melodious harmonics should not be taken as theoretically sound. They are
facts of experimental observation with quite a volume of corroborative
evidence.
The overtones show themselves out more easily when
they are not in tune with the fundamental, than when they are in harmony, like
our becoming aware of an organism when it goes ill. The perfect artist is one
who suppresses these inharmonious and out-of-tune overtones and reinforces the
others. “The art of a bell-founder consists precisely in giving bells such a
form that the deeper and stronger particles shall be in harmony with the
fundamental tone, as otherwise the bell would be unmusical, tinkling like a
kettles.8
The problem of multi-tone harmony would become
simple once we analyse the physical nature of the combination of two tones.
When two tones are of slightly varying rapidity of undulations, a remalleable
phenomenon takes place. The elevations of one of the undulations might
superimpose on the elevations of the other and then we hear the sum total
effect. Very soon, one of the waves outstripping the other, the elevations of
one might coincide with the depressions of the other. We have momentarily no
sound at all. Thus we hear a sort of waxing and waning of sound which the
physicist calls “beats”.
Beats are generally very unpleasant to experience,
unless the rapidity of waxings and wanings itself gives the character of a
“beat-tone” to the combination like flickering light which irritates the eye
unless the flicker is very quick and by persistence of vision we feel to
observe it. This leads us to the theory of concord and discord between musical
tones.
Two tones of different pitches may mutually disturb
each other and split up into very disagreeable beats. When the frequency ratio
between the two tones is a semitone (about 1.07), in the normal scale, between
20 and 40 beats result, and the sensation is very harsh. When the difference is
a whole tone, the roughness is less and when it is a third, it is altogether
absent. Even when the fundamentals are very widely separated and as such may
not beat, their overtones may interfere and produce beats. For example, if two
tones bearing ratio 2:3 are sounded together, there is one harmonic in each
which is exactly six times the fundamental. These two harmonics will therefore
be in great concord. If one of the basic tones be slightly out of tune, beats
are produced between the harmonics and discord sets in. Actually the tones
referred to above are the shadja and panchama of the scale of
music. We know by experience how harsh it would be if these two important tones
are slightly out of tune. The shadja and madhyama have a ratio
3:4 and will have concord of the twelfth harmonic. It is possible to
work on like this and with a given tone as fundamental, a precisely determinate
number of other degrees of tones which can be sounded at the same time with it
without producing any want of uniformity, could be obtained. Such a sequence
would be called a musical scale. In the very nature of things, a musical scale
could only employ musical intervals or frequency ratios which are best
calculated to avoid discordant beats of any of the harmonics.
It becomes imperative to a single singer performing
a strain of music, to employ only the intervals of any particular scale of
music he chooses to exhibit. The ear can never forget an earlier tone in a
sequence, so that even if at any instant, he emits only a single tone, the ear
cannot fail to recognise its relationship to its predecessor. We in India,
employ a drone (Tambura) to aid the ear in the process of recognition of
the fundamental, fifth, and octave. Sruti, to us, is the life and soul
of harmony as we understand.”
In an orchestra also, the need for avoiding
discordant beats is very paramount. The fundamentals of the different members
of the orchestra or choir have got to bear concordant intervals to one another
and at no time could any two notes uttered produce discord. Harmonious blending
is disturbed if the fundamentals do not agree or any of the other tones of the scales
do not agree, or even if their overtones do not agree. The problem gets even
more complicated when we realise that the interference of two loud waves
results in the production of what are called “combinational tones”. These tones
again have subjective existence and have frequencies, the sum and difference of
the component tones. The combinational tones are capable of producing beats
with the harmonics of the individual tones. For example, if three tones, c,
e, g, having frequency ratios 4:5:6 are sounded together, they produce a
combinational tone c which does not beat with any of the tones or their
harmonics. But if the tones are not thus exactly tuned, this combinational tone
beats and produces disharmony. Only experience could really help us in determining
the good companions in this kind of multi-tone building.
Harmony is thus a physical process capable of a
physical analysis and comprehension. But while we are able to determine the
“causes” of concord and discord, the actual “feeling” of compatibility or
incompatibility is a matter of intellectual experience. “For the attainment of
the higher beauty which appeals to the intellect, harmony and inharmony are
only the means, although essential and powerful means.”9 Reluctantly
we will be compelled to admit that however accurate our analysis of pleasurable
sensations, they suffer from the limitations of the scientific method and its
utter incapacity to describe an emotion. But at the same time what matters is
what we aim at, and when achievement comes “it is no more emotionless than it
must have been to Dalton when he reduced the untidy pile of facts about
chemical composition to the law of constant proportions and atomic theory; or
to Mendel when he swept away a whole rubbish heap of nonsense about heredity
and replaced it by his simple notion of the heredity factor.” 10
1 Saint Thyagayya’s
Kalyanavasanta Kirtana “Nadaloludai,”–a broad rendering.
2 Helmhotz: Address at
Bonn (1857).
3 Helmholtz:Ibid.
4 Quoted by K.
Chandrasekharan, “An approach to Indian Art.” Page 7.
5 Ibid, page 12.
6 For further details
see “Essays of A biologist”: Julian Huxley, page 30.
7 Prof. P. Sambamurti,
South Indian Music Series, Book I, page 3.
8 Helmholtz: Address at
Bonn(1857).
9 Helmholtz: Address at
Bonn(1857).
10 Waddington: “The
Scientific Attitude.” Page 47.