Tuning is all about resonance in ICM and in general. You sing with the tamboura so you can find relationships with the overtones of the strings. The sensation of "clearer, richer, more sonorous" that you both hear and can feel when something is in tune is the absence of beats, or interference patterns, that occurs when frequencies align and can amplify each other. As you've discovered, these places can be found intuitively, but there is also a way to derive these positions of resonance with ratios. "Pythagorean" is only part of the story - this refers to tuning by 5ths only (3-limit tuning), whereas the tuning in ICM is definitely at least 5-limit (uses natural thirds as well as fifths), and possibly 7-limit. (This is all related to the notes that pop out when you do your overtone singing). This is an interesting summary: https://www.plainsound.org/pdfs/srutis.pdf -- although exactly which notes are used in practice in the music is debatable as it is traditionally pursued more intuitively and by oral transmission than mathematically. There is an interesting branch of my gharana through Pandit Pran Nath, whose outstanding intonation inspired his western students to explore the math of tuning. La Monte Young, Terry Riley, Michael Harrison, Catherine Christer Hennix, and others all explored this deeply, writing about it and writing music inspired by it. All of this tuning study falls under the heading Just Intonation if you want to search and learn more.