The Samaveda is the third Veda, and it is primarily dedicated to music and chant. It contains melodies and rhythmic patterns that form the basis of Indian classical music.

Svara refers to the musical notes in Indian music. There are seven basic Svara: Sa, Re, Ga, Ma, Pa, Dha, and Ni. These notes form the foundation of Indian ragas and melodies.

Indian mathematicians used mathematical ratios to derive musical scales. They discovered that certain ratios, such as the 3:2 ratio for the perfect fifth, produced harmonious sounds.

The concept of Raga in Indian music is based on Pythagorean tuning. This system of tuning divides the octave into 12 equal semitones, which allows for the creation of various scales and melodic structures.

Indian mathematicians developed complex Tala systems, which are rhythmic cycles that govern the structure and flow of Indian music. These Tala systems involve intricate patterns of beats and subdivisions.

The Drone in Indian music is a continuous, unchanging note that serves as a harmonic foundation. It provides stability and a reference point for the melody and improvisation.

Indian mathematicians played a role in the design of string instruments, such as the Sitar and Veena. They applied mathematical principles to determine the ideal proportions and dimensions of these instruments for optimal sound quality.

Just Intonation in Indian music is based on Mean Tone Temperament, which is a tuning system that aims to preserve the purity of intervals. This system involves adjusting the tuning of certain notes to create more harmonious intervals.

Indian mathematicians contributed to the development of a Solfege system, known as 'Svara-Saptaka,' which uses syllables to represent musical notes. This system aids in the teaching and memorization of melodies.

The Harmonium is a keyboard instrument used in Indian music. It provides harmonic accompaniment to melodies and drones, enriching the overall texture and harmony of the music.

Indian mathematicians played a role in establishing the Gurukul system of education, where students lived with their teachers and learned music through oral tradition and practical training.

Rhythmic Cycles in Indian music are often based on Modular Arithmetic, which involves repeating patterns of beats within a specific cycle. This mathematical concept allows for the creation of complex and intricate rhythmic structures.

Indian mathematicians explored the healing properties of music and its potential to influence emotions and well-being. They recognized the therapeutic value of music in various contexts.

The Tabla is a pair of hand drums used in Indian music. It provides rhythmic accompaniment to melodies and drones, adding depth and complexity to the overall musical texture.

Indian mathematicians played a role in establishing music festivals and competitions, which provided platforms for musicians to showcase their talent and compete for recognition and appreciation.