1. History: 

Ancient Indians were not only great Musicians, but Mathematicians too.

For few thousand years, the Indian Classical Music employed 22 Shrutis with a strong mathematical base. Over the centuries however, the mathematics became obscure and the musical notes persisted by teachings in the Guru-Shishya Parampara.

In the last 150 years or so, especially after the European musical instruments tuned to the European 12-Tone Equi-Tempered scale (such as Organ or the Harmonium) reached India, they invaded the Indian musical scene and most Indian musicians overlooked the minute though musically significant differences in the Indian Shrutis and preferred the convenience of these readily tuned instruments to the age-old instruments for accompaniment such as the Dilruba, Sarangi, or Violin in India.

This diluted the purity of Indian musical notes.

Few puritans in India, however, rightly ignored the ET tuned instruments and did not compromise by taking them (Harmoniums/Organs) for accompaniment.

Harmoniums were actually banned on the All India Radio from 1940 to 1971, although it's popularity never decelerated since there existence from 1860, despite the ET scale.

2. Problem: 

There was no uniform documentation of the differences between the Indian 22 Shrutis and the ET scale.

There were discrepancies between the work of different Indian authors as regards the 22 Shrutis and their positions across the length of the Saptak, only due to the fact that the underlying principle and the mathematical rules governing the division of the Saptak were not discovered.

Listening to the ET tuned Harmoniums spoiled the ears of the Performers and the Listeners, spoiling any effort on the research and clarity on the 22 Shrutis. All the 12 notes of the ET tuned Harmonium are completely different from 22 Shrutis.

To show this difference mathematically and irrefutably and to play the 22 Shrutis precisely, was the problem.

3. Solution:

 This research work clarified the differences in '(Innumerable) Nadas', '22 Shrutis (selected from Nadas)', and 'Swaras (Selected shrutis in a Raga)', and provided the logic and the pucca mathematical principle with a combination of 3 ratios of numbers (1.0535, 1.0125, 1.04166) or 4 percentages (5.35%, 6.66%, 11.11%, 12.5%) which sequentially and accurately provide the precise positions of all the Indian 22 Shrutis.

The Shrutis come sequentially, giving accurate positions on the way of the principle natural notes such as the Gandhar (at 25 %), Madhyam (at 33.33 %), Pancham(at 50 %), Dhaivat (at 66.66 %), and also eliciting all the 22 Shrutis in between, and ending in the upper Shadja (at 100 %).

Thus, all but the stable notes, namely, Shadja and Pancham have 1 variant each, forming 10 x 2 = 20 Shrutis, plus Shadja and Pancham, totalling to 22 Shrutis. 

Furthermore, all the Shrutis demonstrate Shadja:Madhyam and Shadja:Pancham Bhava, providing the fundamental consonances or Samvad in Indian Classical Music. Moreover, all 22 Shrutis are at "Equiratioal" distances between S-S', S-P, S-M, and S-g.

The 22 shrutis are interconnected only by Shadja-Gandhar or Shadja-Pancham relationship, and this natural arrangement is useful in the selection of Shrutis in a Raga.

4. Creation of 22-Shruti-Harmonium: 

Later part of work involved accurately tuning these 22 Shrutis in Harmonium. For this, there were 2 hurdles.

The first was to create the sound of every Shruti accurately, and the second was how to accommodate 22 Shrutis within 12 notes of Harmonium.

I resolved the first hurdle by synthesizing the sound of Shrutis on the Synthesizer, and the second hurdle by providing additional reedboards for accommodating additional Shrutis, and invented a new mechanical modification to select the 12 Shrutis to be played out of the 22.

The patented Harmonium is thus tuned with these 22 Shrutis, completely transforming the European tuning and nature of the instrument, to suit the Indian Classical Music requirement.

5. Creation of 22-Shruti-Metallophone:

There was a need to create a simple musical instrument which will be able to play 22 Shrutis accurately even in the hands of a novice.

The instrument needed to have a pre-set accurate tuning of 22 Shrutis without a chance of any disturbance in tuning over time or due to handling of the instrument, or due to changes in electrical voltage etc. 22-Shruti-Metallophone using metal plates provided a perfect solution.

6. Creation of 22-Shruti-Veena:

 This was necessary to actually demonstrate the interrelationship of Mathematics, Physics and Music. This was made possible by this world's first calibrated string instrument.

7. Creation of Musical Frequency Analyzer: 

As questions were being raised about the accuracy of this work, this novel instrument helped tremendously, as it can continuously and accurately analyze and give digital frequency of any incoming sound.

8. Revealing a simple method to play 22 Shrutis on a string:

Finally, I have unearthed the simple formula of Galileo with the help of which, we can very accurately play these 22 Shrutis on any string (even Tanpura).

9. Rationale of using shrutis in various Indian Ragas:

 The scientific rationale for the selection of shrutis in various Indian Ragas according to the S-G-P relationship of selected shrutis is now demonstrated clearly, with their moorchhana relationship with many other Ragas also.

10. The Benefit: 

The development of the Shruti-system in India is a well controlled exercise where the physical sounds arising from mathematical precision have been converted to an aesthetic division of the Saptak, enabling the development of the conceptual content of the music (Ragas), and it pleases the soul.

22 Shrutis are therefore a "Musico-Mathematical Miracle".

This work has so far created 3 new musical instruments, a 22-Shruti–Harmonium, a 22-Shruti-Metallophone, and 22-Shruti-Veena, a Musical Frequency Analyzer.

The effort has been very satisfactory, soul-pleasing, and it surely will supplement and augment the purity of Indian Classical Music.