The Samaveda is one of the four Vedas, the sacred texts of Hinduism. It contains melodies and chants that were used in ancient Indian rituals and ceremonies.

The Pythagorean theorem, which relates the lengths of the sides of a right triangle, is used to determine the intervals and scales in Indian classical music.

Bharata Muni, the author of the Natya Shastra, is credited with developing the concept of shrutis, the 22 microtones that form the basis of Indian classical music.

The perfect fifth interval, known as the 'pancham', is defined by the mathematical ratio of 3:2. This ratio is found in many natural phenomena and is considered pleasing to the ear.

The Veena, a string instrument, is known for its complex mathematical design. The placement of the frets and the proportions of the instrument are based on mathematical principles to achieve specific musical intervals and tones.

The frequency of a note (f) is calculated using the formula f = 2 * pi * sqrt(T), where T is the period of the wave.

Venkatamakhin, a 17th-century musician and musicologist, developed the 'melakarta' system, which categorizes the 72 fundamental scales used in Carnatic music.

The tonic and the dominant notes in Indian classical music are related by the mathematical ratio of 5:4. This ratio is known as the 'shadja-pancham' relationship.

The Sarangi, a bowed string instrument, is known for its logarithmic scale. This scale allows musicians to tune the instrument precisely to different pitches.

The Fibonacci sequence, a series of numbers where each number is the sum of the two preceding ones, is used to determine the rhythmic cycles in Indian classical music.

Bharata Muni, the author of the Natya Shastra, also developed the concept of 'grahas', the seven notes of the Indian musical scale.

The perfect fourth interval, known as the 'madhyama', is defined by the mathematical ratio of 4:3. This ratio is found in many natural phenomena and is considered pleasing to the ear.

The Tampura, a drone instrument, is known for its use of just intonation. This tuning system produces pure and harmonious intervals.

The tonic and the subdominant notes in Indian classical music are related by the mathematical ratio of 4:3. This ratio is known as the 'shadja-madhyama' relationship.

Bharata Muni, the author of the Natya Shastra, also developed the concept of 'jati', the seven basic melodic structures in Indian music.