Quiz 9 Answers
A.
1= G' , 2= G , 3= D , 4= g , 5= b , 6= d , 7= f , 8= g'
B.
1= D' , 2= D , 3= A , 4= d , 5= f# , 6= a , 7= c , 8= d'
C.
1= A' , 2= A , 3= E , 4= a , 5= c# , 6= e , 7= g , 8= a'
D.
The wavelength of Overtone No.256 = 1/256 x 1280 mm = 1280/256 = 5 mm
No. 256 is a multiple magnitude of 2 :
1 - 2 - 4 - 8 - 16 - 32 - 64 - 128 - 256.
The pitch of Overtone No.256 is therefore also a B , but 8 octaves higher than the Fundamental tone.
E.
The complete Diagram is :
Audio 6
| Child
| Parent
| Grandparent
|
| G
| C
| F
|
| C
| F
| Bb
|
| F
| Bb
| Eb
|
| Bb
| Eb
| Ab
|
| Eb
| Ab
| Db
|
| Ab
| Db
| Gb
|
| Db
| Gb
| B
|
| Gb
| B
| E
|
| B
| E
| A
|
| E
| A
| D
|
| A
| D
| G
|
| D
| G
| C
|
| G
| C
| F
|
How can F be an 11x great-grandparent of him- (or her-)self you might ask ?
Impossible ? No !!!!
Calculated correctly the F after 12 generations is in fact a quarter tone sharp.
This discrepancy, known as the Pythagorean Comma, has plagued Western musicians for
many hundreds of years.
It was finally resolved by the introduction of the Equal Temperament tuning system (much promoted by J.S Bach in his time). This made all semitones equal, and modulation from key to key possible.
So young F may very much look like his ancient ancestor, but he is (in the world of natural acoustics at least) just a little different.
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© 1998 Michael Furstner (Jazclass)