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| Just scale: | 1 | 9/8 | 5/4 | 4/3 | 3/2 | 5/3 | 15/8 | 2 | |
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NAME: _______________________, Sect. #_______
Physics 109 Homework # 6
due Monday, October 22, 2001
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| Just scale: | 1 | 9/8 | 5/4 | 4/3 | 3/2 | 5/3 | 15/8 | 2 | |
Reminder: for the next octave above, you would need to multiply all the numbers by two. For the next octave below, you would need to multiply at the numbers by 1/2.
Reminder: to divide by a fraction, you multiply by the reciprocal.
Reminder: the freq. ratios 5/4 and it's reciprocal 4/5 represent the same interval
1a) Standard A = 440 Hz is called A4. One octave above is called A5 etc.
What is the frequency of A5 ? ______________ Hz
What is the frequency of A6, two octaves above A4 ? ________________ Hz
What is the frequency of A2 two octaves below A4 ? ________________ Hz
b) A tone is said to be "a fifth" above the other, when it’s frequency is (3/2)-times greater.
What is the frequency of a tone a fifth above A4 ? _________________ Hz
What is the name of this tone? ________
What is the frequency of a tone a fifth below A4 ? ________________ Hz
show work:
What is the name of this tone? ________
2. In just tuning, if A4 is tuned to 440 Hz, to what frequency should D4 be tuned?
(Hint: first find the frequency ratio between the two tones in the just scale)
f(D4) = ____________ Hz
3. This exercise shows that in the so-called just tuning not all intervals are just
("just" means a simple number ratio like 3/2 = 1.500)
interval C4 - G4 has a frequency ratio ____________. Is it "just"? ___________
work here:
interval D4 - A4 has a frequency ratio ____________. Is it "just"? ___________
work here:
interval G4 - C5 has a frequency ratio ____________. Is it "just"? ___________
what is this interval called? __________________
4. If you start on G4 = 3/2 (relative to C4 = 1) and ascend (i.e. go up in frequency) by a fifth,
what frequency do you get to (relative to C4 =1) ? _______________
what is the name of this tone? _______________.
If you go another fifth, what frequency ratio do you get to? _______________
what is the name of this tone? _______________.
5. The bugle and the trumpet played in Bach's time have no keys, and thus play only the "natural scale"
(i.e. frequencies which are multiples of the fundamental.)
Suppose the trumpet plays C1 in the fundamental mode, what other notes can you play?
Mark an X when a mode does not fit into the just scale.
| mode: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| tone | C1 , | C2 , | _____ , | _____ , | _____ , | _____ , | _____ , | _____ , | _____ , | _____ |
(hint: go down from the higher modes in octaves (multiply by 1/2) until you can identify the tone on the just frequency table given on top of this homework. Then decide what the tome is called).
work here: