The that (thaat) is the specification as to which of the alternate forms of swar will be chosen. It has been pointed out elsewhere that several of the swar have alternate forms. The permutations of the various forms give rise to numerous scales with vastly differing intervals. Therefore the concept of that is essentially the same as the Western concept of a mode.
(note - The above notation has been normalised to the tonic of C. No absolute pitch is implied)
There are problems whenever one is talking about the number of thats. Generally only ten are acknowledged; twenty are in common usage; while 32 are possible given present concepts of scale construction. This has created a lot of confusion in north Indian pedagogy. Three common scales which are not part of the ten thats are Ahir Bhairav, Charukesi, or Kiruvani.
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