## Sounds Of Music C

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### Re: Sounds Of Music C

epicdragon44 wrote:[img]http://latex.codecogs.com/png.latex?\fr ... }=361%20Hz[/img]
Regarding this equation, could anyone link me to the original equation! That would be much appreciated.
Is that what showed up on your screen?
(340 m/s)/(2pi) * sqrt((2 cm^2)/(450 cm^3 * 1 cm)) * (100 cm)/(1 m) = 361 Hz
(Based on the LaTeX code)

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### Re: Sounds Of Music C

Lol no I meant, what's the original formula, and where did you get it from? I'm just wondering, because I was unaware of the existence of this formula.

An example of my "original formula" would be T = 2pi(L/g), which relates the period of a pendulum to its length L and the gravity of the planet it is on.

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### Re: Sounds Of Music C

epicdragon44 wrote:Lol no I meant, what's the original formula, and where did you get it from? I'm just wondering, because I was unaware of the existence of this formula.

An example of my "original formula" would be T = 2pi(L/g), which relates the period of a pendulum to its length L and the gravity of the planet it is on.
Oh, ok

It's from http://newt.phys.unsw.edu.au/jw/Helmholtz.html

That website also has a ton of other great resources!

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### Re: Sounds Of Music C

Cool, thanks!

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### Re: Sounds Of Music C

I'll go ahead and ask another question since it's been a while...

Name the five major types of instruments based on the Hornbostel-Sachs system and give a brief description for each.

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### Re: Sounds Of Music C

UTF-8 U+6211 U+662F wrote:I'll go ahead and ask another question since it's been a while...

Name the five major types of instruments based on the Hornbostel-Sachs system and give a brief description for each.
Idiophone: a solid body vibrates
Membranophone: a flexible membrane vibrates
Chordophone: a string vibrates
Aerophone: a column of air vibrates
Electrophone: an instrument in which electricity is used to produce or amplify sound
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### Re: Sounds Of Music C

mjcox2000 wrote:
UTF-8 U+6211 U+662F wrote:I'll go ahead and ask another question since it's been a while...

Name the five major types of instruments based on the Hornbostel-Sachs system and give a brief description for each.
Idiophone: a solid body vibrates
Membranophone: a flexible membrane vibrates
Chordophone: a string vibrates
Aerophone: a column of air vibrates
Electrophone: an instrument in which electricity is used to produce or amplify sound

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### Re: Sounds Of Music C

I hope this isn't too many subparts:

Ryan and Josh are trying to play a perfect fifth on their instruments. Ryan plays open (nominal) C on his Bb trumpet, and Josh plays open (nominal) G on his Bb clarinet. Assume that the instruments start out so that the notes they play are tuned to equal temperament using A440.
1. What is the trumpet note's frequency? How would it be notated in concert pitch (e.g. A4)?
2. What is the clarinet note's frequency? How would it be notated in concert pitch?
3. What beat frequency (Tartini tone) is heard between the instruments?
4. How many cents sharp or flat is Ryan (compared to Josh's note)?
5. How many cents sharp or flat is Josh (compared to Ryan's note)?
6. Assume that Josh stays at the initial frequency of his note, and Ryan must adjust to get in tune with him.
i. What piece of his trumpet can Ryan adjust to change hs intonation?
ii. If Ryan's trumpet is initially 58" long, how far must he push in or pull out this instrument part in order to be in tune with Josh? (Assume that the effect of changing the tubing length in this manner is perfectly linear: a 1% increase in tubing length corresponds to dividing the note's frequency by 1.01.)
7. Now assume that Ryan stays at the initial frequency of his note, and Josh must adjust to get in tune with him.
i. What piece of his clarinet can Josh adjust to change hs intonation?
ii. If Josh's clarinet initially has an effective length of 10", how far must he push in or pull out this instrument part in order to be in tune with Josh? (Again, assume linearity in tuning.)
8. If Ryan and Josh discover that they are out of tune with one another in the middle of a performance, and they have no opportunity to adjust their instruments, can they still alter their playing to be in tune with one another? If so, how?
9. Anna, on her vibraphone tuned to A442, joins in to make a major chord with the trumpet and clarinet.
i. What note must Anna hit to fill in the major chord (e.g. A4)? In concert pitch, what chord is it (e.g. F major)?
ii. If Ryan and Josh stay at their initial equal temperament tunings, how many Tartini tones are heard? What are their frequencies?
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### Re: Sounds Of Music C

mjcox2000 wrote:I hope this isn't too many subparts:

Ryan and Josh are trying to play a perfect fifth on their instruments. Ryan plays open (nominal) C on his Bb trumpet, and Josh plays open (nominal) G on his Bb clarinet. Assume that the instruments start out so that the notes they play are tuned to equal temperament using A440.
1. What is the trumpet note's frequency? How would it be notated in concert pitch (e.g. A4)?
2. What is the clarinet note's frequency? How would it be notated in concert pitch?
3. What beat frequency (Tartini tone) is heard between the instruments?
4. How many cents sharp or flat is Ryan (compared to Josh's note)?
5. How many cents sharp or flat is Josh (compared to Ryan's note)?
6. Assume that Josh stays at the initial frequency of his note, and Ryan must adjust to get in tune with him.
i. What piece of his trumpet can Ryan adjust to change hs intonation?
ii. If Ryan's trumpet is initially 58" long, how far must he push in or pull out this instrument part in order to be in tune with Josh? (Assume that the effect of changing the tubing length in this manner is perfectly linear: a 1% increase in tubing length corresponds to dividing the note's frequency by 1.01.)
7. Now assume that Ryan stays at the initial frequency of his note, and Josh must adjust to get in tune with him.
i. What piece of his clarinet can Josh adjust to change hs intonation?
ii. If Josh's clarinet initially has an effective length of 10", how far must he push in or pull out this instrument part in order to be in tune with Josh? (Again, assume linearity in tuning.)
8. If Ryan and Josh discover that they are out of tune with one another in the middle of a performance, and they have no opportunity to adjust their instruments, can they still alter their playing to be in tune with one another? If so, how?
9. Anna, on her vibraphone tuned to A442, joins in to make a major chord with the trumpet and clarinet.
i. What note must Anna hit to fill in the major chord (e.g. A4)? In concert pitch, what chord is it (e.g. F major)?
ii. If Ryan and Josh stay at their initial equal temperament tunings, how many Tartini tones are heard? What are their frequencies?
I just started on this event, but I'll give it a shot...
[list=a]
[*]233.08 Hz and B-flat3
[*]349.23 Hz and F4 (not quite sure about the octave)
[*]349.23 Hz - 233.08 Hz = 116.15 Hz
[*]With just tuning, the ratio for a perfect fifth is 3:2.

$349.23 Hz * \frac23 = 232.82 Hz$

$1200\log_2\frac{233.08 Hz}{232.82 Hz} = 1.9323\ \textrm{cents sharp}$

[*]

$233.08 Hz * \frac32 = 349.62 Hz$

$1200\log_2\frac{349.62 Hz}{349.23 Hz} = 1.9323\ \textrm{cents flat}$

[*]

i. The slide
ii. This question isn't clear to me (what's linear in what?)...

[*]

i. The barrel
ii. this question isn't clear to me either...
[*] Both Josh and Ryan can adjust their pitches by changing their voicing, "lipping up or down".
[*]

i. D4 (293.66 Hz), B-flat major
ii. 3:
349.23 Hz - 293.66 Hz = 55.57 Hz
349.23 Hz - 233.08 Hz = 116.15 Hz
293.66 Hz - 233.08 Hz = 60.58 Hz[/list]

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### Re: Sounds Of Music C

UTF-8 U+6211 U+662F wrote:
mjcox2000 wrote:I hope this isn't too many subparts:

Ryan and Josh are trying to play a perfect fifth on their instruments. Ryan plays open (nominal) C on his Bb trumpet, and Josh plays open (nominal) G on his Bb clarinet. Assume that the instruments start out so that the notes they play are tuned to equal temperament using A440.
1. What is the trumpet note's frequency? How would it be notated in concert pitch (e.g. A4)?
2. What is the clarinet note's frequency? How would it be notated in concert pitch?
3. What beat frequency (Tartini tone) is heard between the instruments?
4. How many cents sharp or flat is Ryan (compared to Josh's note)?
5. How many cents sharp or flat is Josh (compared to Ryan's note)?
6. Assume that Josh stays at the initial frequency of his note, and Ryan must adjust to get in tune with him.
i. What piece of his trumpet can Ryan adjust to change hs intonation?
ii. If Ryan's trumpet is initially 58" long, how far must he push in or pull out this instrument part in order to be in tune with Josh? (Assume that the effect of changing the tubing length in this manner is perfectly linear: a 1% increase in tubing length corresponds to dividing the note's frequency by 1.01.)
7. Now assume that Ryan stays at the initial frequency of his note, and Josh must adjust to get in tune with him.
i. What piece of his clarinet can Josh adjust to change hs intonation?
ii. If Josh's clarinet initially has an effective length of 10", how far must he push in or pull out this instrument part in order to be in tune with Josh? (Again, assume linearity in tuning.)
8. If Ryan and Josh discover that they are out of tune with one another in the middle of a performance, and they have no opportunity to adjust their instruments, can they still alter their playing to be in tune with one another? If so, how?
9. Anna, on her vibraphone tuned to A442, joins in to make a major chord with the trumpet and clarinet.
i. What note must Anna hit to fill in the major chord (e.g. A4)? In concert pitch, what chord is it (e.g. F major)?
ii. If Ryan and Josh stay at their initial equal temperament tunings, how many Tartini tones are heard? What are their frequencies?
I just started on this event, but I'll give it a shot...
[list=a]
[*]233.08 Hz and B-flat3
[*]349.23 Hz and F4 (not quite sure about the octave)
[*]349.23 Hz - 233.08 Hz = 116.15 Hz
[*]With just tuning, the ratio for a perfect fifth is 3:2.

$349.23 Hz * \frac23 = 232.82 Hz$

$1200\log_2\frac{233.08 Hz}{232.82 Hz} = 1.9323\ \textrm{cents sharp}$

[*]

$233.08 Hz * \frac32 = 349.62 Hz$

$1200\log_2\frac{349.62 Hz}{349.23 Hz} = 1.9323\ \textrm{cents flat}$

[*]

i. The slide
ii. This question isn't clear to me (what's linear in what?)...

[*]

i. The barrel
ii. this question isn't clear to me either...
[*] Both Josh and Ryan can adjust their pitches by changing their voicing, "lipping up or down".
[*]

i. D4 (293.66 Hz), B-flat major
ii. 3:
349.23 Hz - 293.66 Hz = 55.57 Hz
349.23 Hz - 233.08 Hz = 116.15 Hz
293.66 Hz - 233.08 Hz = 60.58 Hz[/list]
On parts d and e, it's plus/minus 1.955 cents, not 1.932; I assume that deviation is just because of intermediate rounding error.

On f.ii. and g.ii., I was getting at how much they would have to adjust their instruments to get in tune.
- Ryan has to divide his frequency by 1.00113, which means he must multiply the length of his instrument by 1.00113. He has to increase the tubing length to 58.0655", which means lengthening the tubing 0.0655". Since the tubing length is increased by twice the amount you pull out the tuning slide, Ryan must pull out the slide half that amount, or 0.0327".
- Josh has to multiply his frequency by 1.00113, which means he must divide the length of his instrument by 1.00113. His tubing length must be 9.9887", so he must push in 0.0113".
(Practically, it doesn't make sense to move a trumpet tuning slide 1/32" or a clarinet barrel 1/100", so players would likely just lip these notes up or down; in principle, however, this is how you can adjust the slide/barrel to tune.)

On i.i., you failed to account for the A442 tuning of the vibraphone. With A442 tuning, D4 is 295.00 Hz. I assume you just looked up the frequency of D4 instead of calculating it -- to avoid making this mistake again, you can calculate that since D4 is 7 semitones down from A4, D4 (in an A442 system) is 442*2^(-7/12) Hz=295.00 Hz, or you can take the value you got from a table and multiply by 442/440: 293.66 Hz*442/440=294.99 Hz.
(The Tartini tones in i.ii must also be adjusted to compensate for the 295 Hz D4.)