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?
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?