I’m going to bring back up the musical one since no one’s commented.The musical scale has seven notes then the pattern repeats. Calling it an octave brings about all sorts of complications since subsequent scales only have seven i.e. a three octave scale only has 22 notes not 24 also the 13th is the same note as the 6th but an “octave” higher.
Except there are 12 notes in an Octave in western music, or between octave intervals……. You are perhaps confusing Octave with Scale (or they are) The Octave is the distance between harmonic intervals, so yes, in a three Octave scale there are three tonic notes (Doh) because, traditionally and for the sake of our ears, we always want to resolve the scale on a tonic note. There are many different scales, and each one can be subdivided into modes depending on the relationship between the root, (tonic) the third, the fifth, and then the inclusion or omission of various notes in between . So for example a blues scale is based on a pentatonic scale (root, second, third, fifth and sixth notes of the major scale) but to that scale we add one or more chromatic notes to change the mode, so a major blues scale is root, second, flat third, third, fifth and sixth. A minor blues adds in a flat fifth to the minor pentatonic scale to give 1-b3-4-b5-5-b7. In many ways, the resolution from the 7th to the octave tonic determines the feel of the scale.
The important thing for a pianist is to recognise that there is an octave interval every twelve keys, with the 13th key being an octave above the root. The success of a guitarist depends on knowing where the tonic of the key is to be found, and learning the shape of the boxes or positions to be played, depending on the mode of the scale in use.