Learning Object 6 - Harmonics and music

1. JordanLy
LF2 – red
33714149
Learning object 6
Question:
Harmonyis an integral elementof music.Composedof differentchords,notesandtones,
harmonycan be utilizedtocreate elegantsounds.The processof harmonizingusuallyinvolvesnotes
that are thirds,fifth,andoctavesapart.
JohanssonandWorthingtonare twoguitaristsaspiringtocreate a guitar duobandcalled
“JohanssonandFriend”.Theyare experimentingwithharmonizingasthe skill isparamounttoany guitar
duo. They are experimentingwithcapos,whichclose off guitarstringsatdifferentlengthstoaugment
the emittedsound.Let’ssaythatJohanssonhasa stringthat playsa middle C,whichemitsafrequency
of about261 hz.Worthington,inhopesof creatinga majorthirdchord, wantsto change the lengthof
hisstring(let’sassume theyare usingthe same stringontwo differentguitars) usingacapo to playa
middle E,whichemitsafrequencyof about329 hz. What isthe ratio that Worthingtonmustreduce his
stringby to create thismajorthird? Rememberthatthe stringisfixedatboth ends.
Solution:
The frequencyemittedbythe closedstringsis denotedbythe equation:
𝑓 =
1
2𝐿
√
𝑇
𝜇
Where L is the lengthof the string,T is the tension,and μis the mass density.
Since we are usingthe same string,the tensionandmassdensitiesare the same,andwe can
compare the stringsbasedon justtheirlengthsuchthat:
𝑓1 =
1
2𝐿1
𝑓2 =
1
2𝐿2
261 ℎ𝑧 =
1
2𝐿1
329 ℎ𝑧 =
1
2𝐿2
Solvingforthe ratioof L2 overL1 yieldsa0.79 ratio or about1/8th
of the original stringlength.