Musical Scales: Thāṭ and Rāga Shrikant G. Talageri [This article is a short(!) tribute to the incomparable greatness of Indian music. A few points: 1. If the article contains ambiguities or errors, particularly in respect of the Chinese scales (where I had to choose from different ambiguous sources), I beg not only the indulgence of the readers but also that the reader should point out these errors in comments. If necessary, they will be corrected. 2. The reader must excuse my arbitrariness or idiosyncracy in the use of general spellings versus phonetic or strictly Sanskritic spellings: thus, I have used rāga rather than rāg, but tāl rather than tāla. 3. In the few places where I have given the URLs of youtube videos, the reader must be prepared for the peculiar habit of the youtube site of often arbitrarily deleting videos from their site - in which case some particular video may not be available]. The two basic components of music are melody and rhythm (or, in common Indian parlance sur and tāl). Here in this article we will only discuss some of the basic aspects of the melody or sur aspect of music. Pitch is the highness or lowness of any sound. Now this is not a technical scientific article in that sense, so it will be assumed that the reader understands what is "high" and "low" in pitch without any scientific explanations provided for understanding the terms, and we will not discuss the scientific technicalities and physics of sound relationships and production, but only the actual notes. If pitch is represented on a long vertical line so that various points higher or lower on that line depict higher and lower pitches respectively, then there is a certain fixed distance/length on that line which represents what is known as an "octave": if we start with a sound at a certain pitch and mark it as a point on that line, and then keep taking the voice higher and higher, we will reach another point further up where we find what is clearly the same sound at a higher pitch: (technically this is because the second sound is formed out of twice the number of wave cycles per second, measured in hertz, as the first sound, but we will not concern ourselves with these technicalities). This length, or distance between the two points, is what is called an "octave". An octave is a natural division of sound, and a natural phenomenon which is discovered in every civilization which develops a musical culture. This "octave" can be illustrated with a musical instrument. Take for example the easiest instrument to illustrate the octave: a harmonium. We will find that the keys on a harmonium are in two rows, a lower row of white keys and a higher row of black keys, in the following form: As we can see, the pattern of keys (taking both rows) is as follows: white-black-white-black-white, white-black-white-black-white-black-white. Let us number the keys 1 to 12. Each key one after the other produces a sound which keeps rising by one note over the previous key. In the above picture, the first 12 keys represent (at least on the harmonium) what we call the mandra saptak (low octave), the next 12 keys represent the madhya saptak (middle octave) and the last 12 keys represent the tār saptak (high octave). If we press any two keys at the same time, we will generally hear a discordant medley of two sounds. But if we press key 1 and key 13 (i.e. the first key in the first series of 12, and the first key in the second series of 12) together, we will hear a composite sound in what is called "absolute harmony" because it is actually the same sound at two different pitches: it will be as if we are hearing the same sound moving like a wave between a high pitch and a low pitch. Similarly, if we press any other two keys which are at a distance of 12 (or multiples of the same) from each other (2 and 14, 3 and 15, or even 1 and 25, 2 and 26, etc), the same effect of "one sound at two pitches" will be produced. The octave is the length or distance, on the "pitch" line, between a given sound and the same sound at a (i.e. at the next) higher pitch, and this distance has been theoretically divided by musicologists into fixed smaller divisions known as "cents", where one octave is 1200 cents. In ancient India with its unique oral tradition (as shown in the oral transmission of the Rigveda in oral form for millenniums without the slightest change), the various notes were distinguished on the basis of the performer's highly-trained voice and ears, and passed on from guru to śiṣya in that form, and musical instruments were also tuned on that basis, and the notes and the natural scale were based on pure acoustics, leading to very subtle nuances in sounds. In Western music, the octave is divided into 12 equal notes of 100 cents each. This is known as the "tempered scale" because of this uniform equal division into 100 cents. Because of the dominant use of the harmonium in learning Indian classical music, and consequent laxity, modern day Indian music has also generally leveled out the notes into equal divisions. Apart from the octave, there is another very important distance between two sounds: the fifth. The different notes of the scale within an octave are in fact possible on the basis of this relationship between two sounds: just as we get one sound in the form of an undulating wave between two pitches when we press two keys at a distance of 12 (i.e. at 1200 cents) from one another, and this distance is called an "octave" with the resulting composite sound producing "absolute harmony"; similarly we get another combined sound which is extremely musical when we press two keys at a distance of 7 (i.e. 700 cents) from one another (e.g. key 1 and key 8, key 2 and key 9, etc.), and this distance is known as a "fifth", and the resulting composite sound produces what is described as two different sounds in "perfect harmony". In the above picture of the harmonium keys, if the first white key represents the starting note called ṣaḍja or SA, the eighth white key represents the ṣaḍja or SA in the higher octave, and the fifth white key represents the pañcam or PA. These two notes SA and PA are considered the two basic and unalterable pillars of the octave or saptak. From these two are produced the other notes. We will examine this subject under the following heads: I. The Formation of the Notes of the Octave. II. The Classification of Parent-Scales or Thāṭs and Meḷas. III. The Rāgas of Indian Music. IV. India's Unparalleled Musical Wealth and Contribution to World Music. I. The Formation of the Notes of the Octave As we saw: 1. Once the starting-point pitch is chosen, it becomes the note SA, and a sound which is 1200 cents higher than this SA becomes the next SA in a higher pitch, and the distance (of absolute harmony) between the two sounds produces the octave of 1200 cents. 2. The next note, produced by perfect harmony within the octave, is 700 cents higher than SA, and this is called PA. How do the other sounds of the scale arise? 1. Just as any note is in absolute harmony with the note 1200 cents higher than it, it is therefore also in absolute harmony with the note 1200 cents lower than it. All the three notes are the same note, e.g. SA, in three different octaves (and of course also in all other octaves extending further into higher pitches as well as into lower pitches), since they all represent the starting points of the respective octaves. In the above picture of the keyboard of a harmonium, the first, the eighth and the fifteenth white keys represent SA in the three octaves. SA is in perfect harmony with PA which is 700 cents higher within the octave: so the fifth, twelfth and nineteenth white keys represent PA in the three octaves. But if SA is in perfect harmony with the note 700 cents above it, it is also in perfect harmony with the note 700 cents below it. In the above diagram, this note would be represented by the fourth, eleventh and eighteenth white keys (the eighteenth key being 700 cents below the next SA, not shown in the picture). Now, since all the three octaves already have notes named PA, this note, which is 500 cents above the lower SA, has to be given another name: madhyam or MA. So each SA is in perfect harmony with the PA higher than it, and with the MA lower than it. So now, within each octave, we have three notes in harmony with each other: SA, MA and PA. 2. In each octave, the MA is in perfect harmony with the higher SA (700 cents above it), and the PA is in perfect harmony with the lower SA (700 cents below it). Therefore MA and PA also are in harmony with each other. The distance between MA and the PA above it is 200 cents: this distance is called a tone (or a second, but this word used here would be confusing, so let us just call it a tone here).