To get a feel of Aadhara Sruthi listen to the same music in 2 different Sruthis. By listening to the music, the Thamboora sound and the Shadjam note of the same sruthi you can appreciate how these are aligned.
Listen to song Ennathavam seidanai with Aadhara Sruthi of C or 1 'Kattai' (more on Kattai system later). Listen to a Thamboora sound in the same Sruthi and the Shadjam of the same Sruthi.
Now listen to the same piece of music played with Aadhara Sruthi of D or 3 Kattai and Thamboora and Shadjam in the same Sruthi.
Unlike in western music even when the ferquency of the Aadhara Sruthi is changed, the basic note is called Shadjam and denoted by the symbol 'sa'. What happens if we shift the Aadhaara Sruthi further up? After a few steps (when the frequencies are double) the music sounds almost identical and the two could be played together. Listen to the first line of Endaro Mahanubhavulu played in two Sruthis one having double the frequency of the other. The two phrases are an 'octave' apart, the term obviously referring to 8 notes (incluiding the 8th note with double the frequency of the first) covering the octave. They can be played together without disturbing the Aadhara Sruthi foundation. In duets the female voice is usually an octave higher. In the samples of music given in the first page, having the same pitch but produced on different instruments, the Violin's frequencies are double those of Veena and the Flute's are 4 times the Veena. But for a Carnatic musician, they are all in the same 'Sruthi'.
In Carnatic music the term for octave is Sthaayi.