Okay, cool.mjcox2000 wrote:UTF-8 U+6211 U+662F wrote:I just started on this event, but I'll give it a shot...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.

- What is the trumpet note's frequency? How would it be notated in concert pitch (e.g. A4)?
- What is the clarinet note's frequency? How would it be notated in concert pitch?
- What beat frequency (Tartini tone) is heard between the instruments?
- How many cents sharp or flat is Ryan (compared to Josh's note)?
- How many cents sharp or flat is Josh (compared to Ryan's note)?
- 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.)- 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.)- 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?
- 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?

[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.

[*]

[*]

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]Your turn!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.)

My friend plays a nominal G5 on his B-flat trumpet tuned at A440. Unfortunately, I arrive late at the recital running into the room towards him at 5 m/s. Suppose he is walking toward me at 1.3 m/s when I arrive. What frequency pitch do I hear, and what concert pitch note is that closest to?