▁stretch ed ▁oct ave ). ▁" For ▁a ▁stretch ed ▁tun ing ▁the ▁oct ave ▁is ▁greater ▁than ▁a ▁factor ▁of ▁ 2 ; ▁for ▁a ▁com pressed ▁tun ing ▁the ▁oct ave ▁is ▁smaller ▁than ▁a ▁factor ▁of ▁ 2 ." ▁ ▁Mel od ic ▁stretch ▁refers ▁to ▁tun ings ▁with ▁fund ament als ▁stretch ed ▁relative ▁to ▁each ▁other , ▁while ▁harm onic ▁stretch ▁refers ▁to ▁tun ings ▁with ▁harm on ics ▁stretch ed ▁relative ▁to ▁fund ament als ▁which ▁are ▁not ▁stretch ed . ▁For ▁example , ▁the ▁piano ▁features ▁both ▁stretch ed ▁harm on ics ▁and , ▁to ▁accommod ate ▁those , ▁stretch ed ▁fund ament als . ▁ ▁Fund ament als ▁and ▁harm on ics ▁▁ ▁In ▁most ▁musical ▁instruments , ▁the ▁tone - gener ating ▁component ▁( a ▁string ▁or ▁reson ant ▁column ▁of ▁air ) ▁v ibr ates ▁at ▁many ▁frequencies ▁simultaneously : ▁a ▁fundamental ▁frequency ▁that ▁is ▁usually ▁perce ived ▁as ▁the ▁pitch ▁of ▁the ▁note , ▁and ▁harm on ics ▁or ▁over ton es ▁that ▁are ▁multi ples ▁of ▁the ▁fundamental ▁frequency ▁and ▁whose ▁w avel ength s ▁therefore ▁divide ▁the ▁tone - gener ating ▁region ▁into ▁simple ▁fraction al ▁segments ▁( 1 / 2 , ▁ 1 / 3 , ▁ 1 / 4 , ▁etc .). ▁( See ▁harm onic ▁series .) ▁The ▁fundamental ▁note ▁and ▁its ▁harm on ics ▁sound ▁together , ▁and ▁the ▁amplitude ▁relationships ▁among ▁them ▁strongly ▁affect ▁the ▁perce ived ▁tone ▁or ▁tim bre ▁of ▁the ▁instrument .