The Science of Music

How does Music affect our Brain?

  1. We are all good at recognizing music even at a very early age because music is hard-wired into our brains.
  2. Music has an intense effect on us – watching a musician perform affects brain chemistry differently from listening to a recording.
    • This has been proven through an interesting experiment. Researchers took two clarinet performances and played them for three groups of listeners:
      • one that heard audio only;
      • one that saw a video only;
      • and one that had audio and video.
    • One rapid, complex passage caused tension in all groups, but less in the one watching and listening simultaneously. Why?
    • Possibly, because of the performer’s body language: the clarinetist appeared to be relaxed even during that rapid-fire passage, and the audience picked up on his visual cues.
    • The reverse was also true: when the clarinetist played in a subdued way but appeared animated, the people with only video felt more tension than those with only audio.
    • In another, similar experiment the clarinetist fell silent for a few bars. This time the viewers watching the video maintained a higher level of excitement because they could see that he was gearing up to launch into a new passage. The audio-only listeners had no such visual cues, and they regarded the silence as much less exciting.
  3. Dr. Levitin, a cognitive psychologist, has conducted an experiment to determine how much emotion is conveyed by live performers – there’s a domino effect: the conductor becomes particularly animated, transmits this to the orchestra and then to the audience, in a matter of seconds.
  4. Why is music such an emotional experience? Why did our ancestors pick up instruments and began to play, tens of thousands of years ago? Most memories degrade and distort with time; but pop music memories are seen to be sharply encoded. Because music triggers reward centers in our brains. There is a cascade of brain-chemical activity – first the music triggers the forebrain, as it analyzes the structure and meaning of the tune. Then the nucleus accumbus and ventral tegmental area activate to release dopamine, a chemical that triggers the brain’s sense of reward. The cerebellum, an area normally associated with physical movement, reacts too, responding to the brain’s predictions of where the song was going to go. As the brain internalizes the tempo, rhythm and emotional peaks of a song, the cerebellum begins reacting every time the song produces tension (that is, subtle deviations from its normal melody or tempo). This also explains precisely how music is good for improving our mood.
  5. Pop music relies strongly on timbre, a peculiar blend of tones in any sound; it is why a tuba sounds so different from a flute even when they are playing the same melody in the same key.

What is the Physics behind Music?

  1. If different civilizations across the globe have arrived at the same results through the centuries there must be some very fundamental relationship or truth underlying music. What is that relationship?
  2. The following are notes mostly excerpted from a series of highly informative & educative articles by Anjum Altaf. You can read the original here: An Idiot’s Guide to Music.

What is Pitch? What is Frequency?

  1. Pitch, in music, is the position of a single sound in the complete range of sound. Sounds are higher or lower in pitch according to the frequency of vibration of the sound waves producing them. A high frequency (e.g., 880 hertz [Hz; cycles per second]) is perceived as a high pitch and a low frequency (e.g., 55 Hz) as a low pitch. Frequency is the term used by physicists. Musicians refer to the same concept as ‘pitch’.
  2. How Sound Waves Work shows us that a wave has a frequency and different waves have different frequencies. A longer wavelength (equivalent to lower frequency or pitch) sounds flat to the ear; a shorter wavelength (equivalent to higher frequency or pitch) sounds sharp to the ear.
  3. Frequency is an objective indicator indicating 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 – so a pitch is more than just frequency, even though a higher pitch reflects a higher frequency; a lower pitch reflects a lower frequency.
  4. A typical female voice has a higher pitch than a typical male voice. Listen to aaj jaane kii zid na karo by Asha Bhosle and by Farida Khanum and be able to distinguish between them by the difference in the pitch of their voices. Here are two great and atypical female and male voices – Gangubai Hangal [low pitch] and Abdul Karim Khan [high pitch].
  5. The range of frequencies that are audible to the human ear extends from about 20 Hz to about 17,000 Hz – a huge continuous range that can accommodate an infinite number of stopping points. 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.
  6. The human ear cannot distinguish very small differences in frequencies and of those that it can distinguish, not all combinations are musical or pleasing to hear.
  7. Consonant frequencies (those that sound pleasant together) are related to each other by the ratios of small integers.
  8. Relative to any arbitrary starting frequency (which is normalized to 1 in order to keep the exposition general), the sequence of frequencies is as follows:
    1. 1,
    2. 9/8,
    3. 5/4,
    4. 4/3,
    5. 3/2,
    6. 5/3,
    7. 15/8 and
    8. 2
    9. So if we take the starting frequency to be 200 Hz, the adjacent frequency would be 200*9/8 = 225 Hz, and so on.
  9. Note a very important feature here: The final frequency in the normalized sequence is 2 – an exact multiple of the starting frequency (its second harmonic), after which the same sequence of ratios would repeat. Thus, in our numerical example, the next frequency after 400 Hz would be 400*9/8 = 450 Hz. We can also see from this that the repeating sequence can begin with any frequency: if our starting frequency had been 225 Hz instead of 200 Hz the sequence of consonant frequencies would have ended at 2*225 = 450 Hz instead of at 400 Hz.
  10. Now strings vibrate in the same way everywhere and sound travels in the same way everywhere (on earth, at least) and the construction of the human ear is the same everywhere. Therefore, it is no surprise that widely separated civilizations discovered this same sequence of relative frequencies that sound pleasing to the human ear.
  11. The identification tags or names of these relative frequencies is the sargam; frequency of Pa is exactly one-and-a-half times the frequency of Sa, the frequency of Re is related to the frequency of Sa in a ratio of 9/8.
  12. From one octave to the next, the frequency doubles. That’s why we can recognize it to be the same note, but one octave higher. Its the ratios that are important, not the absolute frequencies – the lower note generates a strong second harmonic which has the same frequency as the second note = same tonal quality, different frequencies.
  13. After Ni – we arrive at a frequency that is 2*Sa = Sa of next higher taar saptak 400 Hz & in the reverse direction, we reach the Sa of lower mandra saptak – 100 Hz [See Notations or Svar Mapping].
  14. The typical human can vocalize the range of svaras from the M or P of the mandra saptak to the M or P of the taar saptak when the reference svar is the S of the middle or madhya saptak – so the human voice can handle with most ease the madhya saptak.
  15. It is considered a great achievement for a vocalist to have a range spanning the entire three saptaks – Ustad Bade Ghulam Ali Khan sahib was reputed to have this ability.
  16. A piano has eight saptaks, a regular keyboard four. This is because instruments can generate frequencies both higher and lower than the human throat can.
  17. The names in the Western tradition: Do, Re, Mi, Fa, So, La, Ti, Do (abbreviated for notation as C, D, E, F, G, A, B, C – the higher Do is included in the sequence and the set is known as an octave (a collection of eight notes). Listen to Julie Andrews in The Sound of Music teaching children the alphabet of music.

Why do we need to tune Indian musical instruments? Because the reference frequency, Sa, is arbitrary and not fixed!

  1. Spacing the notes uniformly is convenient but it comes at the cost of purity of sound. Most Indian accompanying instruments are stringed and can be re-tuned relatively easily – so Indian artists prefer the pure, just-tempered scale.
  2. Many Western instruments use the keyboard (like the piano) which are very cumbersome to re-tune. They work better with the equally-tempered scale.
  3. Every individual’s reference frequency (the frequency that he/she finds most comfortable to anchor his/her singing around) would differ to some extent – this is the reason for not assigning Sa a pre-determined absolute frequency.
  4. Vocalists needed a range from P of lower saptak to P of the upper saptak, covering 15 svaras; someone with a deep voice would have no problem with the lower notes but find it difficult to reach the higher ones while one with a high-pitched voice would face the reverse situation. Such individuals adapt by picking a convenient reference frequency that enables them to cover the entire range. Thus the reference note of the first individual would have a higher frequency than the reference note of the second.
  5. Typically, men choose a higher reference frequency than women. One can now appreciate the logic of having relative frequencies – both singers would be vocalizing the lower P but the two P’s would not have the same frequency.
  6. The human ear recognizes a svar not as an absolute frequency but only on the basis of its relative distance from the reference svar. Once the performer has made the choice of his/her reference note, the accompanying instruments (taanpura, sarangi or violin, and tabla in the case of vocal music) are tuned in accordance with the frequency of this reference note Sa. The frequencies of rest of the svaras are now fixed in keeping with the ratios mentioned earlier and they are tuned accordingly.
  7. Now imagine what happens when the instruments are tuned for one individual and he/she is followed on the stage by another. Since the reference frequency would change, every string of the instruments would need to be re-tuned.

What are the Black & White Keys in a Keyboard?

  1. The intervals between svaras are not equal
    • the interval between S and R is 9/8 = 1.125;
    • the interval between R and G is 10/9 = 1.111; and
    • the interval between G and M is 16/15 = 1.067.
  2. From the auditory perspective,
    • 1.125 and 1.111 are reasonably close to be treated similarly – they are both termed as one full step (or just a step) between svaras.
    • 1.067 is too small to be treated as a full step. But 1.067×1.067 = 1.137 which is just over one full step.
    • So two intervals of 16/15 raise the frequency as much as one full step. It is therefore natural to term the interval 16/15 as a half-step.
  3. Now we can write the sequence of intervals of consonant svaras in simplified form as follows:
    1. STEP,
    2. STEP,
    3. HALF-STEP,
    4. STEP,
    5. STEP,
    6. STEP,
    7. HALF-STEP
  4. This is how we get from the reference S to the S of the next saptak:
    1. S to R      One Full Step
    2. R to G     One Full Step
    3. G to M    One Half Step
    4. M to P    One Full Step
    5. P to D     One Full Step
    6. D to N    One Full Step
    7. N to S    One Half Step
  1. Imagine that the black keys don’t exist for the moment. If one begins with the 1st Sa on the left, one can proceed to the higher Sa using just the white keys. In order for the intervals to be in accordance with the requirements of consonance, these white keys would follow the tuning pattern
    1. Step-
    2. Step-
    3. Half Step-
    4. Step-
    5. Step-
    6. Step-
    7. Half Step.
  2. Thus the intervals between keys 3 Ga and 4 Ma and 7 Ni and 8 Sa are half steps; all the other intervals are full steps.
  3. Now suppose a vocalist comes along and decides that for his / her accompaniment Pa would be his/her reference note, i.e., what was Pa for the previous individual will be the Sa for the new one (remember what is critical to music are the intervals between svaras not the absolute frequencies).
  4. Let us take Pa as our starting point and see what sequence of steps and half steps we encounter as we move up the keyboard:
    1. Pa to Dha = One Full Step
    2. Dha to Ni = One Full Step
    3. Ni to Sa = One Half Step
    4. Sa to Re = One Full Step (Sa is the same as Sa of the next octave)
    5. Re to Ga = One Full Step
    6. Ga to Ma = One Half Step
    7. Ma to Pa = One Full Step
  5. The required interval sequence is:
    1. STEP,
    2. STEP,
    3. HALF-STEP,
    4. STEP,
    5. STEP,
    6. STEP,
    7. HALF-STEP
  6. The sequence that results when we start from Pa as Sa is:
    1. STEP,
    2. STEP,
    3. HALF STEP,
    4. STEP,
    5. STEP,
    6. HALF STEP,
    7. STEP
  7. We are fine till the fifth interval – the two sequences are identical. Then instead of {STEP, HALF STEP} we get {HALF STEP, STEP}. How can this problem be resolved? The black keys represent a solution to this problem.
  8. The interval between the white keys Ga and Ma is a half step. But now, with the changed reference note, we need a full step here. The solution is to insert a new key (marked in black) at a half step above the white key. Now if we go from key Ga to this new black key we would move the frequency up by a full step. And from this new black key to the white Ma is now a half step. So, by inserting this black key and using it, we convert the {HALF STEP, STEP} sequence to a {STEP, HALF STEP} one and thereby fulfill the interval requirement for consonance.
  9. Proceeding in a similar way by choosing other keys as starting points, we will discover where additional keys have to be inserted in order to have a consonant sequence no matter what the starting point.
  10. What is happening in effect, if you look at the schematic, is that a new half step is being added between every full step. These additional half step keys are the new black keys. Note that there are no black keys between the white keys Ga and Ma and Ni and Sa because they were half steps in the first place.
  11. This can also provide an explanation for the distinctive 2-3 pattern of the black keys. It simply follows from the pattern of the white keys: STEP, STEP, HALF-STEP, STEP, STEP, STEP, HALF-STEP
    • The first set of two full steps get two black half step keys;
    • the second set of three full steps gets three black half step keys.

What is a Saptak?

  1. The saptak has 7 primary svaras – plus there are 5 auxiliary svaras yielding a total of 12 svaras. 
  2. So we can now go from one saptak to the next in 12 half steps. And this clever invention can accommodate all the changes of reference notes possible without losing the consonance of musical sounds. Instead of relying on just the white keys we would be using one or more black keys as needed.
  3. Sequence of svaras in a saptak now appears as follows:
    • S * R * G M * P * D * N S
    • The asterisks denote the five new svaras added in the saptak (the black keys on a keyboard – note the characteristic 2-3 pattern mentioned before). 
  4. The convention adopted in naming them is not to give them independent names but to treat them as altered or vikrit swaras that are auxiliary to the seven principal svaras (in Indian music these are called the pure or shuddh svaras).
  5. In the Indian tradition, the first two auxiliary svaras are treated as variants of R and G; the third as a variant of M; and the fourth and the fifth as variants of D and N.
  6. This leaves S (the reference svar) and P (the svar at an interval of 3/2 to S) as fixed or achala svaras with no variants. In introductions to Indian music it is invariably pointed out that S and P are fixed svaras.
  7. P is said to divide the saptak into two halves – the lower and upper halves of the saptak.
  8. We proceed now to the names of the five auxiliary svaras: those that are a half-step below a shuddh svar are called the komal or soft variants of the respective shuddh svaras. Those that are half-step above a shuddh svar are called tiivra or sharp variants of the respective shuddh svaras.
  9. A look at the sequence above shows that in the Indian tradition there are four komal svaras and one tiivra svar, as follows: S, komal R, R, komal G, G, M, tiivra M, P, komal D, D, komal N, N, S
  10. In notation form these svaras are denoted as follows:
    • S r R g G M m P d D n N S
  11. Read more here:

The Language of Music

  1. We now have the alphabet of the language of Indian music and can discuss the unique characteristics of this language and how the knowledge helps us in both appreciating and learning music.
  2. Consider languages like Hindi, Urdu or English. Each consists of over two dozen letters in its alphabet. Sometimes the letters are given a name (as in Urdu and English) and sometimes not (as in Hindi) but the key function is always to associate a basic sound with the shape of a symbol. For example, the baa sound is associated with the shape B in English and Hindi and Urdu have their own symbolic equivalents.
  3. In these languages each distinct symbol is associated with a different sound (with some exceptions that are not important here). But each sound can be emitted at the same amplitude and the same frequency – one can use a flat and level voice to read out the English alphabet from A to Z.
  4. In the language of music each of the twelve letters (S to N) is associated with the same sound (the sound aaa if vocalized or the sound produced by the plucking of a string or the blowing of a flute).
  5. Each of these sounds can be of the same amplitude but, and this is the crucial difference, each has to be at a different frequency.
  6. Reading out the alphabet S to N in a flat and level voice can be alright for expositional purposes but would be wrong musically. If the alphabet of music has to be expressed correctly, by the time one gets through from a lower S to a higher S, the frequency at which the svar is pronounced has to double. And given the selection of the fundamental svar S, each subsequent letter has a precisely defined frequency. Recall that the frequency of P is one-and-a-half times the frequency of S. Instead of associating a sound with a shape we are associating it with a pitch. [Note: The naming conventions for the auxiliary notes mentioned in this post pertain to the Hindustani variant of ICM. The conventions used in the Carnatic variant are different.]

Western and Indian Musical Traditions

  1. The Western tradition is instrument-oriented in which a keyboard instrument like the piano plays a central role. By contrast, the Indian tradition revolves around vocal music and its accompanying instruments are primarily string instruments (leaving the percussion instruments out of the discussion for the moment).
  2. Now think of the implications for retuning instruments when the reference svar or key is changed. It is relatively easy to retune string instruments but very cumbersome to retune keyboard instruments like the piano. In fact it is impractical to retune a piano repeatedly. A solution for this problem was found by sacrificing a little bit of the integrity of sound for a whole lot of convenience.
  3. The solution was to make each of the 12 half-steps on the keyboard of exactly the same size. With this change it would not matter which key was picked as the starting one because the musical distances would be the same independent of the choice. It is easy to find the interval represented by the size of this modified half-step.
  4. Since all half-steps are now of exactly the same size if we multiply the starting frequency 12 times by the interval of the half-step the resulting frequency should be twice the starting frequency:
    • 1 * (x) ** 12 = 2 where ** signifies that x is raised to the power of 12 or multiplied by itself 12 times.
    • It follows that x = 12th root of 2 and this can be found on a calculator to be 1.0595.
    • It also follows that now the size of every full-step is the same with a value (1.0595 * 1.0595) = 1.1225.
    • Thus the interval between S and R is 1.2225 instead of the true value of 1.125 and the interval between R and G is also 1.2225 instead of the true value of 1.111, and so on.
  5. These variations are too small to affect the consonance of the music although there has to be a subtle loss of integrity. The resulting scale of 12 equal half-steps is called the equally-tempered scale while the scale with true intervals is called the just-tempered scale. The equally-tempered scale is the compromise that allows pianos and keyboards to be played from any key without the need to be retuned for every change.

Some More Interesting Reads:

More on Indian Classical Music:
The Alchemy of Indian Classical Music

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