The Octave

Every year when I start teaching strings, the first notes we learn are the open strings.  Soon the students are ready to put down their left fingers, and when I say something like, "Let's play E", some of the violin students play the open E string.  Then I need to explain that there are 2 Es on their instruments.  (Yes there are more than 2, but I don't want to freak any of them out).

Yesterday I was working with one of my private students.  She is working on her intonation, so I thought we should work on 4-note scales.  A-B-C#-D on the A string, and then check the third finger D with the open string D to see if it is in tune.  I made some comment about them both being a D - basically the same note.  She looked at me and said, "how can they be the same note?"

Yes, I know there is an explanation that has a physics background, and it has to do with ratios and wavelengths, but I can't go into that (I don't completely understand it, and neither will my young students).  I like to show the piano keyboard and play various octaves of the same note to see if the students think they are the same note, and at first they don't.  Then I play a 7th and ask if those notes sound the same.  Of course they don't.  Then I play the octave again, and they seem to get that they are the same notes, one higher, one lower.

I don't remember ever wondering about it when I first started learning music.