Other Tuning Systems

For fifteen centuries following Bharata Muni's Nāṭyaśāstra, Indian musical intervals were communicated orally and verified by comparing two side-by-side harps (Cala and Dhruva Vīṇās). While this captured the auditory truth of the 22 śrutis, it lacked a repeatable mechanical measurement.

In 1665 CE, Pandit Ahobala published Saṅgīta Pārijāta in northern India. Ahobala performed the first explicit physical monochord string measurements in Indian history:

Ahobala's work proved that Indian ragas did not rely on arbitrary microtonal mysticism—they rested upon the universal harmonic laws of physical vibrating strings.

In 53-Equal Divisions of the Octave (53-EDO), each step is:

1 Step = 1200 / 53 ≈ 22.6415 cents (Holder's Comma)

Notice how miraculously close this is to the fundamental acoustic commas of music theory:

• Syntonic Comma (Pramāṇa Śruti, 81:80): $21.506 \text{ cents}$ (error: only 1.13 cents from 1 step of 53-EDO).
• Pythagorean Comma (531441:524288): $23.460 \text{ cents}$ (error: only 0.82 cents from 1 step of 53-EDO).
• Pure 3:2 Fifth: $701.955 \text{ cents}$. In 53-EDO, $31 \text{ steps} = 31 \times 22.6415 = \mathbf{701.887 \text{ cents}}$ (error: an undetectable 0.068 cents!).
• Pure 5:4 Third: $386.314 \text{ cents}$. In 53-EDO, $17 \text{ steps} = 17 \times 22.6415 = \mathbf{384.906 \text{ cents}}$ (error: 1.4 cents).

In the 1910s, British civil servant Ernest Clements and Indian musicologist K. B. Deval published The Indian Temperament. They demonstrated that Bharata's three interval step sizes correspond exactly to integer steps in 53-EDO:

When European missionaries brought the hand-pumped harmonium to India in the late 19th century, it took the subcontinent by storm because of its loud, steady drone and portability. However, its fixed 12-TET tuning created severe harmonic dissonance:

• The 12-TET Major Third (400.0 ¢) is 13.7 cents sharper than the pure 5:4 third (386.3 ¢) vibrating naturally in the tanpura's upper harmonics.
• The resulting acoustic flutter (beating at 10–14 Hz) ruined the contemplative stillness (*Shanti*) of Indian classical vocal performances.
• This led All India Radio (AIR) to ban the harmonium from national broadcast for over 30 years (1940–1971).

In 2007, Mumbai physician and musicologist Dr. Vidyadhar Oke was granted a patent for the 22-Shruti Melodium. Dr. Oke fitted custom tuned dual-reeds to each key with an external micro-lever. The performer can toggle each black and white key between its higher and lower śruti on the fly (for example, switching between the sharp Komal Re of Raga Marwa and the flat Komal Re of Raga Bhairav), restoring pure, beatless consonance against the tanpura.

In the Near East, modal improvisation (*Taqsim*) and melodic development (*Maqam*) operate on an interval that does not exist in standard Western theory: the Neutral Third (also called the Wustā Zalzal after the 8th-century lutenist Mansur Zalzal).

In the 13th century, Persian polymath Safi al-Din al-Urmawi derived a 17-tone scale using cycles of pure fifths (3:2) and limmas (256:243). In the 19th century, Syrian musicologist Mikha'il Mishaqa and the 1932 Cairo Congress of Arab Music codified modern practice into 24-EDO (24 Equal Divisions of the Octave), dividing the octave into 50-cent quartertones.

In Java and Bali, the magnificent bronze gong-chime ensembles known as Gamelan use two completely distinct tuning systems that defy Western harmonic expectations:

In his 1949 magnum opus Genesis of a Music, American composer Harry Partch declared 12-TET an acoustic tragedy that severed Western humanity from natural consonance. Partch expanded pure tuning from the Renaissance 5-limit all the way to an 11-limit Tonality Diamond:

Discovered independently in the 1970s and 1980s by German microwave engineer Heinz Bohlen, Dutch musicologist Kees van Prooijen, and American computer music pioneer John R. Pierce, the Bohlen-Pierce scale is one of the most radical experiments in psychoacoustics:

In live classical performance, Indian vocalists and instrumentalists never treat Komal Re or Komal Ga as fixed points. The notes are fluid, living entities: