Octaves, semitones

 
Table 2: Properties of the diatonic scale of C major

Projects:

1. Take a cylindrical wine bottle, generate a note by blowing into it and compare it with a piano or keyboard to determine the frequency. Then fill the bottle half full and repeat. What notes do these frequencies correspond to?
2. Take a string instrument (guitar, ukulele, banjo, violin) and measure exactly half the length of the string between bridge and nut. Pluck a note on the open string, then press the string at the half-way point. What is the relationship between the notes?