Eastern Tunings

A rāga (राग) is a melody type: which notes are used, how they move, and the mood that movement makes. This page follows Hindustani (हिन्दुस्तानी) music, the classical music of North India. A rāga (राग) is sung and played against one held pitch, the drone. That pitch is called Sa. Its full name is ṣaḍja (षड्ज), and as the drone it is the ādhāra (आधार), the foundation. Sa does not change during a piece. The music does not change key.

The other notes are named from Sa, in rising order: Re, Ga, Ma, Pa, Dha, Ni, and then Sa again. The second Sa is the same note an octave higher, meaning twice the frequency. A svara (स्वर) is any one of these named notes. The whole question of this page is how far apart those svaras (स्वर) sit.

The story has four stops. Bharata (भरत), around the beginning of the common era, counts the gaps and stops. A line of later books, from 1210 to 1665, gives the notes names and then lengths of string. Srinivasa (श्रीनिवास), late in the 1600s, builds all twelve notes by cutting one string. Bhatkhande (भातखंडे), early in the 1900s, writes the scale a student still meets in a lesson. After those two are both on the page, a table sets them side by side.

1.2 The books between him and the twelve notes

For about a thousand years the count stands. Then writers start doing two new things: they name every one of the 22 steps, and they mark the notes as places on a string. The long essays for the four medieval books are on Other tunings. What each one adds, in year order:

• Śārṅgadeva (शार्ङ्गदेव), 1210, Saṅgītaratnākara (सङ्गीतरत्नाकर). Gives the 22 śrutis (श्रुति) individual names, and lists 19 svaras (स्वर) instead of Bharata's (भरत) nine. The essay.
• Rāmāmātya (रामामात्य), 1550, Svaramelakalānidhi (स्वरमेलकलानिधि). Puts fixed frets on the Sarasvatī (सरस्वती) vīṇā (वीणा), so a note is a place on the neck rather than a count in the air. The essay.
• Veṅkaṭamakhin (वेङ्कटमखिन्), 1620, Caturdaṇḍīprakāśikā (चतुर्दण्डीप्रकाशिका). A svarasthāna (स्वरस्थान) is a seat: one of twelve places a note can occupy in the octave. His 72 melakarta (मेलकर्ता) scales are a map of which seats a scale uses. The seats themselves do not move. It is not a new tuning. The essay.
• Ahobala (अहोबल), 1665, Saṅgītapārijāta (सङ्गीतपारिजात). Measures each svara (स्वर) as a length of wire. This is the step Srinivasa (श्रीनिवास) will turn into a construction. The essay.
• Srinivasa (श्रीनिवास), late 1600s, Rāgatattvavibodha (रागतत्त्वविबोध). One string, cut in half and in thirds. The next section.
• Bhatkhande (भातखंडे), early 1900s. A thāṭ (थाट) is a parent scale: a choice of which form of each note is the plain one for a family of rāgas (राग). He writes ten of them. After Srinivasa (श्रीनिवास).

Pandit Srinivasa (श्रीनिवास), late 1600s, wrote Rāgatattvavibodha (रागतत्त्वविबोध). This section follows its third chapter, Vīṇāvādanādhyāya (वीणावादनाध्याय), the chapter on playing the vīṇā (वीणा). The text used here is the edition of Pandit Vibhukumar S. Shastri, in the Gaekwad's Oriental Series from Baroda.

Bharata (भरत) counted the gaps in śrutis (श्रुति) and never marked them on a string. Ahobala (अहोबल), in Saṅgītapārijāta (सङ्गीतपारिजात) around 1665, measured each svara (स्वर) as a length of wire. Srinivasa (श्रीनिवास), later in that century, makes the measurement a construction. He takes one open string, from the nut, Meru (मेरु), to the bridge, Ghudach (घुड़च), and calls that length 36. Every later note is a half or a third of a length he has already marked. Thirty-six is the length that lets those cuts fall on a unit he can name: 18, 12, 9, and the fractions that follow. A player can find the next fret by folding a span he can already see. He does not need a new measuring rod for each note.

Three of the fourteen steps are Sa itself: the open string, the octave, and the octave above that. The other eleven place the notes in between. Komal (कोमल) means lowered. Tīvra (तीव्र) means raised. In the list below, the Ga and the Ni he marks without the word tīvra (तीव्र) are the ones a modern student calls komal (कोमल). That set, lowered Ga and lowered Ni, is the older plain scale. Later it is named Kāfī (काफी). Bilawal (बिलावल), the scale with every note plain, comes into the story with Bhatkhande (भातखंडे), not here. Where the two pitches differ, the comparison table sets them side by side.

Read a step as a cut, not as a new theory. Tāra (तार) Sa is the octave, the midpoint of the wire. Madhya (मध्य) Sa is the open string, the middle register. Ati-tāra (अतितार) Sa is the octave above the octave. A ratio is the note divided by Sa. With Sa at 240 Hz, multiply the ratio by 240 to get the frequency. Cents, defined above, say how large the gap feels: 1200 is an octave.

Pandit Vishnu Narayan Bhatkhande (विष्णु नारायण भातखंडे) (1860–1936) wrote from Bombay in the early twentieth century. The Sanskrit (संस्कृत) books and the music being sung had drifted apart, and he wrote down the practice. The record is Hindustani Sangeet Paddhati (हिन्दुस्तानी सङ्गीत पद्धति), four volumes published in Bombay from 1910 to 1932, and Lakṣya-Saṅgītam (लक्ष्य-सङ्गीतम्) (1910), which sets what singers were doing beside the old theory.

Srinivasa (श्रीनिवास), in the section above, finds each note by halving and trisecting a string. The plain scale those cuts start from is the older śuddha (शुद्ध) one, Kāfī (काफी): komal (कोमल) Ga and komal (कोमल) Ni. By Bhatkhande's (भातखंडे) time the notes treated as plain were the other set, Bilawal (बिलावल), all śuddha (शुद्ध), the same notes as a major scale. He took that as the reference, so a printed Sa Re Ga would mean the scale a student was actually hearing.

He does not cut the wire into halves and thirds. He builds the twelve notes from three pure intervals: a fifth (3/2), a fourth (4/3), and a major third (5/4). Srinivasa's (श्रीनिवास) halfway cut for śuddha (शुद्ध) Ga does not land on that third. The notes where the two systems disagree are the ones the comparison table measures. The three intervals are named below, then each note is derived from them. A thāṭ (थाट) does not retune those twelve notes. It chooses which form of each one a family of rāgas (राग) treats as home. He wrote ten, and the one a printed lesson starts from is Bilawal (बिलावल). The ten lists are on the rāga (राग) page.

The three intervals he builds from

A fifth is the 3/2 already met above: Pa against Sa. A fourth is the flip of that fifth back down into the same octave, 4/3, which is Ma against Sa. The new ingredient is a major third, 5/4. It is the fifth harmonic of a string, brought down two octaves so it sits between Sa and Ma. Srinivasa's (श्रीनिवास) halfway cut for plain Ga does not land on it. He names the third svayambhū gāndhāra (स्वयंभू गान्धार), the Ga that arises on its own.

The twelve notes, one at a time

The wire is the same 36 units, so his notes can be set next to Srinivasa's (श्रीनिवास). Sounding length is 36 divided by the ratio. Frequency is 240 Hz times the ratio. Where a line mentions Srinivasa (श्रीनिवास), the gap between them is 81/80, about 22 cents, a fifth of a piano step. That comparison is gathered in the next section.

A singer does not park every svara (स्वर) on one of twelve fixed seats. Inside the gaps, the same name moves. It may lean up as it approaches the next note, rest, or sway. A resting note is a nyāsa (न्यास). A slow sway is an āndolana (आन्दोलन). Section 6 shows four rāgas (राग) where that movement is the point.

Much later, writers tried to give the small distances their own ratios. One such description uses four sizes. They do not add up to 22, and Bharata (भरत) did not list them. The pramāṇa śruti (प्रमाण श्रुति) row uses 81/80 because later writers identify his unit with the comma from the table above. The other three rows are sizes those writers use when they talk about steps larger than that unit.

The drone instrument is the tanpura (तानपुरा). Its strings hold Sa, and usually Pa or Ma, for the whole piece. Because Sa never moves, each svara (स्वर) is judged against that one pitch. A temperament is a way of slightly mistuning the fifths on a keyboard so that the instrument can change key and still sound acceptable. A rāga (राग) does not change key, so it does not need that compromise. The arithmetic of equal temperament, where the octave is sliced into twelve equal piano steps, is on Western tunings.

The harmonium's reeds are those twelve equal steps. Two things follow.

• Komal (कोमल) Re in Bhairav (भैरव) and komal (कोमल) Re in Todi (तोडी) are different seats, as the table above shows. The harmonium has one reed for both.
• A reed cannot make a mīṇḍ (मींड), the glide from one note to the next. A great deal of a rāga (राग) lives in that glide.

Rabindranath Tagore called the harmonium the bane of Indian music and would not have it at Santiniketan. In 1940 All India Radio stopped using it in classical broadcasts. The restriction was lifted in 1971, so it ran from 1940 to 1971. The longer quotation sometimes printed beside his name is a paraphrase. The ban, and the Santiniketan rule, are the record.

Primary Sanskrit (संस्कृत) Treatises

How the equal-tempered keyboard was calculated

Modern Acoustic & Musicological Scholarship