▁involve ▁some ▁stretch ing ▁of ▁the ▁higher ▁notes ▁up ward ▁and ▁the ▁lower ▁notes ▁down ward ▁from ▁their ▁theoretical ▁frequencies . ▁In ▁shorter ▁pian os ▁the ▁wire ▁st iff ness ▁in ▁the ▁bass ▁register ▁is ▁proportion ately ▁high ▁and ▁therefore ▁causes ▁greater ▁stretch ; ▁on ▁larger ▁concert ▁grand ▁pian os ▁this ▁effect ▁is ▁reduced . ▁Online ▁sources ▁suggest ▁that ▁the ▁total ▁amount ▁of ▁" st retch " ▁over ▁the ▁full ▁range ▁of ▁a ▁small ▁piano ▁may ▁be ▁on ▁the ▁order ▁of ▁ ± 3 5 ▁c ents : ▁this ▁also ▁appears ▁in ▁the ▁empir ical ▁Rails back ▁curve . ▁ ▁See ▁also ▁▁ ▁Electron ic ▁tun er ▁ ▁P iano ▁ac oust ics ▁ ▁P iano ▁tun ing ▁ ▁References ▁ ▁Further ▁information ▁ ▁Five ▁lect ures ▁on ▁the ▁ac oust ics ▁of ▁the ▁piano ▁In harm onic ity ▁in ▁piano ▁tun ing ▁ ▁External ▁links ▁" Oct ave ▁Types ", ▁Bill B rem mer . com . ▁ ▁Category : Ac oust ics ▁Category : Mus ical ▁tun ing <0x0A> </s> ▁Daniel ▁Alan ▁He if etz ▁( born ▁November ▁ 2 0 , ▁ 1 9 4 8 ) ▁is ▁an ▁American ▁concert ▁viol in ist ▁and ▁ped agog e ▁best ▁known ▁as ▁the ▁Found er ▁of ▁the ▁He if etz ▁International ▁Music ▁Institute . ▁His ▁career ▁has ▁been ▁focused ▁on ▁education ▁and ▁the ▁art ▁of ▁communication ▁through ▁performance . ▁ ▁Early ▁life ▁Daniel ▁He if etz ▁was ▁raised ▁in ▁Southern ▁California , ▁the ▁son ▁of ▁Dr . ▁Mil ton ▁He if