A Modern Introduction to Music – 8

By Anjum Altaf

When I discovered ‘frequency’ I felt empowered and reacted much as Archimedes did by letting out a high-pitched shriek – Eureka (“I have found it”). At least for me it was an empowering feeling to finally figure out what I had been talking about.

Let us get two things out of the way before we forge ahead. First, the term ‘high-pitched shriek’ is really a tautology: a shriek, by definition, is high-pitched. If you don’t believe me, try and emit a low-pitched shriek. What you might succeed in emitting would be a low-volume shriek but the shriek itself would retain a high pitch. This is a useful exercise because it would help you distinguish clearly between the two attributes of sound we have learnt so far – volume and frequency. To be absolutely sure you know what you are going to talk about, try and emit sounds corresponding to all the four possible combinations of volume and frequency: Low Volume, Low Frequency; Low Volume, High Frequency; High Volume, Low Frequency; High Volume; High Frequency.

Second, we had mentioned that what physicists call ‘frequency’ is termed ‘pitch’ by musicians. Keep in mind that frequency is an objective indicator – it is nothing more than a quantitative measure indicating the number of cycles per second of a particular sound wave. Pitch, on the other hand, is a subjective measure of how the ear responds to the sound. All subjective measures are richer and more nuanced than objective measures – pitch is more than just frequency. But for the moment, it is enough to know that there is a great degree of overlap – a higher pitch reflects a higher frequency; a lower pitch reflects a lower frequency.

Now that we know frequency, where do we go from here? We have mentioned that the frequency of a sound is a measure of the number of cycles of the sound wave that pass a given point in a second – the higher the number, the higher the frequency (recall that this means the waves are packed tightly together and therefore the wavelength is small). This measure, cycles per second, has been given the name Hertz in honor of the German physicist Heinrich Hertz and is denoted by the symbol Hz. Thus you will see a frequency of X cycles per second referred to as X Hz. Larger units like Kilohertz (KHz) and Megahertz (MHz) are commonly used and some of you may associate them with broadcast frequencies used for the transmission of sound to radios.

One of the important facts to know is that the human ear can only pick up sounds that range from about 20 Hz to about 17,000 Hz. An interesting detail is that many animals have a more acute hearing than humans. Thus, dogs can hear frequencies as high as 22,000 Hz. This discovery (by Galton in 1883) led to the invention of the ‘silent’ dog whistle that can be used to attract the attention of dogs without inflicting any pain on human ears.

Another interesting detail is that the old style telephones had a limited frequency range between 300 and 3,400 Hz. This range was adequate for ordinary conversation but if a friend attempted to use the telephone to sing you a song that was rich in high frequencies, most of them would be cut off and the song would sound flat to you. The faithfulness with which audio devices reproduce sounds is referred to as fidelity. This is the reason why hi-fi devices (devices with high fidelity) cost more than run-of-the-mill ones.

Equipped with this knowledge, some of you might find it ironic that we will be taking a huge step back but it is often the case that new knowledge helps makes sense of the past. Now that we know what frequency is, I am going to take you all the way back to the origin of music.

Recall that in a previous installment we had stretched a rubber band between the thumb and forefinger and plucked it to cause it to vibrate and produce a sound. Many people surmise that this was the way human beings stumbled upon music and on how to create music. The conjecture is that it was hunters using bows and arrows who noted that drawing and releasing the tightly strung bow in the act of shooting an arrow produced a sound that was different from noise. And this started a process of experimentation by the curious or the idle (perhaps this was the rationale for Russell’s celebrated essay In Praise of Idleness). What would happen if another string was stretched along the frame and the two plucked one after the other?

It was such experimentation that led to the emergence of the harp, widely credited as the first human-made musical instrument. Now, look at the shape of the harp. The most obvious thing to note is that the harp has many strings and that all the strings are different in length – the frame is designed in a way that ensures that no two strings can have the same length.

The questions to explore next would be the following: Why, in this first musical instrument, do the strings have different lengths? And, more importantly, how are the lengths of the different strings related to each other? Do the relative lengths of the strings matter or would any random choice be equally good?

An exploration of these questions would reveal to us how music is really made. This big step back to the origin of music would return us to the present armed with all the tools we need to understand the language of music. Don’t forget what we are after: What is Sa and how is Sa related to Re?

More soon.

Give yourself a break and listen to the harp being played here. Try and figure out the relative relationship between the length of the string and the frequency of sound it produces. How do the sounds produced by plucking longer or shorter strings differ?


  • Vinod
    Posted at 07:31h, 16 August Reply

    You are going back to A levels physics. I like it. I was good at that. Let me answer the question in your last couple of paras and show off a bit.
    The length of the string determines the wavelength (in a sinusoidal wave), a half wave length to be precise. The ends of the string are the nodes. And the well known formula relating length to frequency and speed of wave is

    speed = frequency x wavelength

    Since speed is a constant one can play with length to get the desired frequency.

    • Anjum Altaf
      Posted at 16:13h, 16 August

      Vinod: In earlier years this really was O level physics. It is a pity teachers did not motivate the students by relating it to music. I guess most science teachers were not musically inclined and most musically inclined students did not study science. You are quite right, one can play with length to vary frequency. I will use that to relate Re to Sa.

  • Anil Kala
    Posted at 17:07h, 16 August Reply

    This is becoming very tedious. In fact as bad as the traditional instructors rushing through basics. Imagine eight installments just to tell us what frequency is.

    I only want to know what are these special frequencies ( sa re ga…..) what is the relationship between them and how have we arrived at these frequencies.

    • Anjum Altaf
      Posted at 18:22h, 16 August

      Anil: I am not sure which way you are pushing. The second and third sentences in the first paragraph contradict each other. If I do understand you right, an easy solution would be to skip all the installments till what you are looking for is described – I will send you an alert. You might find it puzzling that sa re ga are not special frequencies at all.

    • Umair
      Posted at 08:45h, 18 August

      I agree with Anil that it is getting a little tedious, but i think there is no other way to reach our goal unless we have a strong foundation.
      Being patient would be the best way to go forward.
      I like the little treat at the end where we get to listen to a nice piece and try implementing our new found knowledge. This makes it more interactive. It would help if somehow the level of interaction is increased.

    • Anjum Altaf
      Posted at 09:39h, 18 August

      Umair: I wish there was a way to proceed faster. If I could assume that most readers had the equivalent of O level physics an remembered some of it, I could speed up considerably but I feel that assumption would not be justified. I could also proceed much faster if I could do this on YouTube but I don’t have the expertise to move to that medium. Explaining something about sound is very difficult when one is restricted to descriptions in words.

      In any case, this is a difficult task. If it were really easy you would find the explanations in an existing textbook. I haven’t been able to locate one yet that works for beginners although I could have certainly have missed something.

      By necessity this has become a series for the patient reader who enjoys the byways and diversions as much as the thrill of getting to the end of the journey. I try and ensure in every installment that something new is added to the stock of knowledge of the beginner without overloading him or her.

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