Question

what are stretched octaves and why are they necessary？

Answer 1

Stretched octaves are those which sound out of tune when played with normal octaves, but sound in tune when played with equivalently stretched octaves. Its frequency ratio is not that of the octave , but slightly higher

These are necessary in real life. In ideal cases, the only tension in the string is the applied tension. However, in practical cases, the material properties of the steel come into play. Upon applying tension either during tuning or playing, the small change in length causes an additional restoring force due to the Young's Modulus, in the form of elastic stiffness.