Sounds Of Music C

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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...

Click to Show Answer

[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.











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[*]



      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]

Very close, but there are a few things you missed. (Click to Show Hidden Text)

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.)

Your turn!

Okay, cool.
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?

[mjcox2000]

Okay, cool.
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?

He's playing a concert F5, at 698.46 Hz in his frame.
Assuming a speed of sound of 343 m/s, the relative speed between you and the sound wave is 349.3 m/s. In your frame, the note has a frequency of 698.46 Hz*(349.3/343)=711.29 Hz.
This note is still closest to concert F5, but in your frame, it's 31.5 cents sharp.

[UTF-8 U+6211 U+662F]

Okay, cool.
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?

He's playing a concert F5, at 698.46 Hz in his frame.
Assuming a speed of sound of 343 m/s, the relative speed between you and the sound wave is 349.3 m/s. In your frame, the note has a frequency of 698.46 Hz*(349.3/343)=711.29 Hz.
This note is still closest to concert F5, but in your frame, it's 31.5 cents sharp.

Yep, your turn! Although I got 711.33 Hz.

[mjcox2000]

Why are brass instruments generally more directional than woodwinds?

[UTF-8 U+6211 U+662F]

Why are brass instruments generally more directional than woodwinds?

Just a guess (Click to Show Hidden Text)

Brass instruments use valves to change the pitch, changing the length of the tube, while woodwinds use holes which, while changing the length of the tube, spread out the sound.

[mjcox2000]

Why are brass instruments generally more directional than woodwinds?

Just a guess (Click to Show Hidden Text)

Brass instruments use valves to change the pitch, changing the length of the tube, while woodwinds use holes which, while changing the length of the tube, spread out the sound.

Generally right (Click to Show Hidden Text)

Sound only has one path to escape from a brass instrument -- straight out the bell. (The flare of the bell also helps direct the sound.) In a woodwind instrument, however, sound also has the opportunity to escape through the holes, escaping through the side of the instrument. (I think this is what you were going for in discussing the holes.)

Your turn.

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What is the term for the quality that differentiates between two different sounds of the same pitch and loudness? What are some aspects of this quality?

[Jacobi]

What is the term for the quality that differentiates between two different sounds of the same pitch and loudness? What are some aspects of this quality?

The Term is... (Click to Show Hidden Text)

Timbre.  Timbre depends on the relative amplitudes of the instrument's harmonics.  Each instrument has its own unique timbre, for example string, woodwind, brass, or drum.

[UTF-8 U+6211 U+662F]

What is the term for the quality that differentiates between two different sounds of the same pitch and loudness? What are some aspects of this quality?

The Term is... (Click to Show Hidden Text)

Timbre.  Timbre depends on the relative amplitudes of the instrument's harmonics.  Each instrument has its own unique timbre, for example string, woodwind, brass, or drum.

Yep, your turn.

Also things like (Click to Show Hidden Text)

attack, duration of pitch, etc.

[Jacobi]

I'm not sure whether this is under the purview of this event, but here it is:

What is the interval between:

1. The 2nd and 6th tones of a major scale?
2. The 4th and 7th tones of a harmonic minor scale?
3. The 3rd and 5th tones of a simple minor scale?
4. The 1st and 8th tones of any scale?