Notes, Octaves and Scale
by on February 19, 2015 in Music

In my previous post, I described “Raga” the backbone of Indian Classical Music. Today I would like to delve deeper into Notes, Octaves and Scales used in Indian Music.

Notes and Octaves:
Before we proceed to ragas, let us first examine the most basic notes of Indian Music. The notes used in Indian music are Sa/ Shadaj, Re/ Rishab, Ga/Gandhar, Ma/Madhyam, Pa/Pancham, Dha/Dhaiwat and Ni/Nishad. This corresponds to the western diatonic scale. In Indian music, Sa and Pa (1st and the perfect 5th) have a fixed pitch. The 2nd, 3rd, 4th, 6th and 7th notes are variables. An octave consists of seven notes and is called a “Saptak.” The eight note is double the frequency of the first note and thus is an octave higher. Thus, a ratio of 2:1 frequency yields an octave. There are three main octaves used in Indian music. The Lower octave / Mandra Saptak, Middle octave/Madhya saptak and Higher octave/ Taar saptak. If the Madhya saptak “Sa” were at 240 Hz, the Mandra saptak “Sa” would be at 120 Hz and Taar saptak “Sa” at 480 Hz. In Indian music system the seven natural notes are derived according to the ratio of 3:2, 4:3, 5:3, 5:4, 9:8 and 15:8 ,which can be also be expressed in terms of ratios as – 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8. However, Indian Music uses more than seven notes. Western music uses 12 notes in an octave, whereas Indian music uses 22 microtones called Shrutis, since it was thought that 22 distinguishable notes exist in an octave. However, the 22 shruthis have been approximated to 12 notes by musicologists.

Shruti (microtones) and Scale:
Indian Music scale can be derived starting with Sa of 240Hz. For the sake of easy arithmetic, using the ratios as stated above, the nominal frequencies of Re, Ga, Ma, Pa, Dha and Ni come to 270Hz, 300Hz, 320Hz, 360Hz, 405Hz and 450Hz, in the Just or Pure (shudha) scale used in Hindustani Music. There is a geometric progression of scales with a note being 1.5 times the fifth earlier note. So, Pa(360Hz)/Sa(240Hz) = Dha(405Hz)/Re(270Hz) = Ni(450Hz)/Ga(300Hz) = Sa'(480Hz)/Ma(320Hz) = 1.5. In the west, this is called the perfect fifths and attributed to Pythagoras. We get additional notes by lowering the pitch of Re, Ga, Dha and Ni by one or two shruthis (microtones) to get Komal (flat) (R1), G1, D1 and N1. However, Ma is slightly moved up to get Teevra Madhyam (M2). Thus, we have 12 notes (Sa + 2 Re + 2 Ga + 2 Ma + Pa + 2 Dha + 2 Ni) in an octave, just like western music. The associated frequencies (nominal) are slightly different because an equal tempered scale is used in western music, instead of the pure scale. Out of the twelve notes, ten notes can be moved a microtone or two. The two notes that are excluded are “Sa and Pa”. These microtones are called “Shrutis” and are 22 in number. These shrutis have particular names. The Shrutis, their frequencies, the equivalent western note, and Indian note are outlined in the table below:

Shruti Name Indian Note Western note Hz
1 . Teevra Sa C 261. 63
2. Kumudvati re 273. 38
3. Manda re +(komal Re) D b 279. 07
4. Chandovati Re- 290. 7
5. Dayawati Re(Shudha Re) D 294. 33
6. Ranjani ga 310. 08
7. Ratika ga+(Komal Ga) E b 313. 96
8. Raudri Ga(shudha) E 327. 03
9. Krodhi Ga + 331. 12
10. Vajrika ma(Shudha ma) F 348. 84
11. Prasarini ma+ 353. 20
12. Preeti Ma(Teevra Ma) F# 367. 92
13. Marjani MA+ 372. 52
14. KShiti Pa G 392. 52
15. Rakta dha 413. 44
16. Sandipani dha+(Komal dha) Ab 418. 61
17. Aalaapini Dha-(shudha) A 436. 05
18. Madanti Dha 441. 50
19. Rohini ni 465. 12
20. Ramya ni+ (Komal ni) Bb 470. 93
21. Ugra Ni(Shudha) B 490. 56
22. Kshobhini Ni+ 496. 69
1. Teevra Sa’(Taar Saptak) C 523. 26

Thus we have two microtones for each of re, Re, ga, Ga, ma, Ma, dha, Dha and ni, Ni. The notes starting with lower case are “Komal” or flat notes, except for Ma, where ma is Shudha and Ma is sharp / Teevra.

Carnatic Indian Music, which is prevalent in southern India, is different from Hindustani music, mainly in nomenclature. It also has fixed Sa and Pa, 22 shruthis for an octave and 12 notes in an octave, but they are referred to by different names. The Carnatic music scale was defined by Venkatamakhin and has been followed thereafter. The classification of ragas is different from Hindustani music.

Western music, on the other hand, has the equal tempered scale, which was created around 19th century. Since there are 12 notes, and the octave is to be divided equally (in a logarithmic sense), each note is obtained by multiplying the previous note by the twelfth root of 2 (which is about 1.059). Thus, the actual frequencies used are slightly different from the pure scale used in Hindustani. The keys of a harmonium, piano, or an electronic keyboard are tuned to this equal tempered scale. Some notes are very close to Indian music notes and some are slightly different. Only very trained ears are able to distinguish the difference.

Next up would be a write up on Classifications of Ragas.

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