Please try without researching
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April 22nd, 2015 at 7:47:31 AM
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Concert pitch in Hz
Pittsburgh Symphony Orchestra 440
Vancouver Symphony Orchestra 440
Mexico City Philharmonic Orchestra 440
Baltimore Symphony Orchestra 440
Cleveland Orchestra 440
Seattle Symphony at Benaroya Hall 440
Detroit Symphony Orchestra 441
Philadelphia Orchestra 441
Boston Symphony Orchestra 442
Sao Paulo Symphony Orchestra 442
Chicago Symphony Orchestra 442
Houston Symphony Orchestra 442
Los Angeles Philharmonic Orchestra 442
Saint Louis Symphony Orchestra 442
I am curious how difficult this question is for most people given common understanding of octaves, chromatic scales, and human hearing.
The above references are about "concert pitch" or a tuning frequency for the A above middle C. Given that
1) the lowest note on a piano is an A
2) the highest note on a piano is a C (three halftones above an A)
3) pianos have 88 keys
4) assume a concert pitch of 440 cycles per second
Tell me the frequency range of a piano (bottom note and top not).
Approximations and roots are permitted in your answer. Please comment on your thought process.
Pittsburgh Symphony Orchestra 440
Vancouver Symphony Orchestra 440
Mexico City Philharmonic Orchestra 440
Baltimore Symphony Orchestra 440
Cleveland Orchestra 440
Seattle Symphony at Benaroya Hall 440
Detroit Symphony Orchestra 441
Philadelphia Orchestra 441
Boston Symphony Orchestra 442
Sao Paulo Symphony Orchestra 442
Chicago Symphony Orchestra 442
Houston Symphony Orchestra 442
Los Angeles Philharmonic Orchestra 442
Saint Louis Symphony Orchestra 442
I am curious how difficult this question is for most people given common understanding of octaves, chromatic scales, and human hearing.
The above references are about "concert pitch" or a tuning frequency for the A above middle C. Given that
1) the lowest note on a piano is an A
2) the highest note on a piano is a C (three halftones above an A)
3) pianos have 88 keys
4) assume a concert pitch of 440 cycles per second
Tell me the frequency range of a piano (bottom note and top not).
Approximations and roots are permitted in your answer. Please comment on your thought process.
April 22nd, 2015 at 9:16:35 AM
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Let's see how far I can get.
by common understanding of octaves, I assume you mean that we know that the
frequency of a note doubles each time you go up one octave.
by chromatic scales, I assume you mean that we know that there are 12 notes
in the chromatic scale - C, C#, D, D#, E, F, F#, G, G#, A, A#, B
88/12 = 7 full octaves staring on A with 4 keys, A, A#, B, C above that.
The "middle octave" with the "middle C" implies that there are 3 octaves above,
and 3 octaves below, the middle octave.
The way I'm counting the octaves, though, the A=440 note is in the 5th octive, not the 4th.
so I end up with this, with my octaves running from A to G#
keys 1-12 octave 1 A = 27.75
keys 13-24 octave 2 A = 55.5
keys 25-36 octave 3 A = 110
keys 37-48 octive 4 A = 220
keys 49-60 octave 5 A = 440
keys 61-72 octave 6 A = 880
keys 73-84 octave 7 A = 1760
keys 85-88 octive 8 A = 3520
I am going to use a little of my own musical knowledge here that isn't implied in the question,
and re-label my octaves to "standard", so the octaves start on C and go to B, so
middle c is called "C4" and tuning A=440 is "A4",
keys 1-3 octave 0 A = 27.75
keys 4-15 octave 1 A = 55.5
keys 16-27 octave 2 A = 110
keys 28-39 octive 3 A = 220
keys 40-51 octave 4 A = 440
keys 52-63 octave 5 A = 880
keys 64-75 octave 6 A = 1760
keys 76-87 octive 7 A = 3520
key 88 octive 8 C
At this point, I don't know how to do the math to calculate the frequencies of the rest of the notes.
I know that since the frequency doubles each octave, each note sounds evenly spaced within the octave,
that the distance in frequency from one note to the next gets larger as you go up.
I see you have a hint with roots, too.
That is as far as I can get.
by common understanding of octaves, I assume you mean that we know that the
frequency of a note doubles each time you go up one octave.
by chromatic scales, I assume you mean that we know that there are 12 notes
in the chromatic scale - C, C#, D, D#, E, F, F#, G, G#, A, A#, B
88/12 = 7 full octaves staring on A with 4 keys, A, A#, B, C above that.
The "middle octave" with the "middle C" implies that there are 3 octaves above,
and 3 octaves below, the middle octave.
The way I'm counting the octaves, though, the A=440 note is in the 5th octive, not the 4th.
so I end up with this, with my octaves running from A to G#
keys 1-12 octave 1 A = 27.75
keys 13-24 octave 2 A = 55.5
keys 25-36 octave 3 A = 110
keys 37-48 octive 4 A = 220
keys 49-60 octave 5 A = 440
keys 61-72 octave 6 A = 880
keys 73-84 octave 7 A = 1760
keys 85-88 octive 8 A = 3520
I am going to use a little of my own musical knowledge here that isn't implied in the question,
and re-label my octaves to "standard", so the octaves start on C and go to B, so
middle c is called "C4" and tuning A=440 is "A4",
keys 1-3 octave 0 A = 27.75
keys 4-15 octave 1 A = 55.5
keys 16-27 octave 2 A = 110
keys 28-39 octive 3 A = 220
keys 40-51 octave 4 A = 440
keys 52-63 octave 5 A = 880
keys 64-75 octave 6 A = 1760
keys 76-87 octive 7 A = 3520
key 88 octive 8 C
At this point, I don't know how to do the math to calculate the frequencies of the rest of the notes.
I know that since the frequency doubles each octave, each note sounds evenly spaced within the octave,
that the distance in frequency from one note to the next gets larger as you go up.
I see you have a hint with roots, too.
That is as far as I can get.
April 22nd, 2015 at 10:12:14 AM
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Ok, I have done some some ensemble singing, and my work as an engineer occasionally takes me into the realm of sound frequency analysis, so I'll try, and shame on me if I don't get close! :)
Well, the lowest note should be straightforward. 88 keys = 7 full octaves A-A (13 chromatic steps per octave, inclusive) plus an extra Bb, B, & C. The frequency ratio of an octave is 1:2. If the A above Middle C is 440 Hz, the A below should be 220 Hz. The last key on the low end is 3 octaves below that, which would be 1/2 ^ 3 * 220 = 27.5 Hz.
For the last key, let's first look at the highest A, which should be 3 octaves above the Concert Pitch A = 2 ^ 3 * 440 = 3520 Hz. Now the C above that would be a jump of a minor 3rd. I know that harmonies are low whole number ratios. For example, the ratio for a perfect 5th chord (e.g. A to E) is 2:3. I don't recall what a minor 3rd is, but I'll guess a major 3rd is 3:4, and maybe a minor 3rd is 4:5? Seems reasonable. That would put the last C at 1.25 * 3520 = 4400 Hz.
This would only be true if the piano was tuned specifically for the key of A. However, a piano is tuned to a justified or "just" scale. This allows the pianist to play in any key. What this means is that the frequencies of the notes are fudged a little so that the intervals are the same regardless of the key.
So, I'll have to use Paco's "Approximate" tag and put the frequency of the last key of the piano at approximately 4400 Hz. This would make the range of the piano approximately 27.5 Hz - 4400 Hz.
So, I'll have to use Paco's "Approximate" tag and put the frequency of the last key of the piano at approximately 4400 Hz. This would make the range of the piano approximately 27.5 Hz - 4400 Hz.
"Dealer has 'rock'... Pay 'paper!'"
April 22nd, 2015 at 11:19:40 AM
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Quote: Joeman, so I'll try, and shame on me if I don't get close! :)
Very close
Low A Frequency: You both got this one correct. As a test I didn't say how many octaves there were in a piano because I was curious who knew that 20-24 Hz was the lower limit of human hearing. It varies a little with age and sex. But you certainly could not go down an additional octave.
High A Frequency: You both got this one correct. Until about 1880 this was the top key of a standard 85 key piano. Steinway added 3 more notes, and that became the standard. A concert piano had about 30 tons of string tension so these extra notes are difficult. Bosendorfer has a 96 key grand piano but it costs about $175K and the extra keys are black.
For the very young, hearing frequency goes above 20 kHz, but that is the domain of snare drums and cymbals. The most sensitive human hearing is around 4000 Hz, which may explain the extra 3 keys.
High C Frequency: Both of you did a linear approximation for the intermediate keys: BASE*(1+n/12) where n=1,2,3,...12 .
BASE*2^(n/12) which would make the top key closer to 3520*2^(1/4)= 4200 Hz instead of 3520*(1+1/4)= 4400 Hz
I am assuming an equal temperament in tuning. The exercise was supposed to be in in logic, not musicianship. In real life piano tuning they don't tune to exactly equal temperments.
April 22nd, 2015 at 11:40:24 AM
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Quote: pacomartinI am assuming an equal temperament in tuning. The exercise was supposed to be in in logic, not musicianship. In real life piano tuning they don't tune to exactly equal temperments.
Oops, I meant to say "equal temperament" scale instead of "just" scale in my answer. I got them backwards. I thought pianos were tuned to an "equal temperament" scale (or close thereabouts) that would let the instrument be played in any key. Maybe just closer to "equal" than to "just?"
I looked it up. A minor 3rd interval ratio is 5:6, not 4:5 (which is a major 3rd). A perfect 4th ratio is 3:4. So, 3520 Hz * 1.2 = 4224 Hz. Even closer! :)
"Dealer has 'rock'... Pay 'paper!'"
April 22nd, 2015 at 11:55:11 AM
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Quote: pacomartinFor the very young, hearing frequency goes above 20 kHz, but that is the domain of snare drums and cymbals.
I remember in junior high or high school being taught that the extents of human hearing was 20 Hz - 20,000 Hz. In my late 20's, I took a seminar in sound measurement, and the teacher, who was an acoustician, said that for most adults, the 20 kHz limit is very optimistic. He had a sound generator and entoned a 20 kHz sound. Nobody in the class could detect it.
He also said that CRT TV's produced a brief 14 kHz sound when they are turned on. At the time, I typically set my TV to wake me up in the morning. I remember that I could hear that sound, as that is what would wake me, before the sound of the show could be heard. In the seminar, about half of the people recognized hearing that sound.
Since I don't own a CRT TV any more, I can't say if I can still detect 14 kHz.
"Dealer has 'rock'... Pay 'paper!'"
April 22nd, 2015 at 11:58:31 AM
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I have some interesting links which show the even temperment roots and compares them to the just temperment (?) ratios.
I'll post them in a while, I don't want to spoil the thread with real spoilers yet.
I'll post them in a while, I don't want to spoil the thread with real spoilers yet.
April 23rd, 2015 at 4:08:49 AM
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Quote: JoemanI remember in junior high or high school being taught that the extents of human hearing was 20 Hz - 20,000 Hz. In my late 20's, I took a seminar in sound measurement, and the teacher, who was an acoustician, said that for most adults, the 20 kHz limit is very optimistic.
It really is a round number and easy to remember for the species. Adults generally can't hear up to 20 kHz, and a lot depends on your exposure to headphones and other modern phenomena. Dogs can hear up to 60 kHz, but they can't hear pure tones below 40 HZ.
Human beings have the most sensitive hearing of any animal. Most people are shocked to hear that fact, but in reality at our optimal frequency of around 4 kHz if our ears were any more sensitive we would be overwhelmed by molecular noise. What is often called "sensitivity" in other animals like dogs, cats, horses, and bunny rabbits is the ability to hear higher frequencies.
Quote: JoemanHe also said that CRT TV's produced a brief 14 kHz sound when they are turned on. At the time, I typically set my TV to wake me up in the morning. I remember that I could hear that sound, as that is what would wake me, before the sound of the show could be heard. In the seminar, about half of the people recognized hearing that sound.
Since I don't own a CRT TV any more, I can't say if I can still detect 14 kHz.
The vibrations of the flyback transformer that is responsible for the horizontal deflection of the electron beam that creates the picture. There are 525 lines drawn on a television and the display refreshes at a frequency of 59.94Hz. BUT REMEMBER THAT IT'S INTERLACED. This means that the signal that causes the horizontal deflection has to sweep across the 525 lines of the screen 30 times per second 525*30 = 15.75kHz
Some adults can't hear the sound as they have lost much of their hearing capacity at high frequency. Other people get headaches from listening to CRT televisions.
April 23rd, 2015 at 5:19:34 AM
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Quote: pacomartinIt really is a round number and easy to remember for the species. Adults generally can't hear up to 20 kHz, and a lot depends on your exposure to headphones and other modern phenomena. Dogs can hear up to 60 kHz, but they can't hear pure tones below 40 HZ.
Human beings have the most sensitive hearing of any animal. Most people are shocked to hear that fact, but in reality at our optimal frequency of around 4 kHz if our ears were any more sensitive we would be overwhelmed by molecular noise. What is often called "sensitivity" in other animals like dogs, cats, horses, and bunny rabbits is the ability to hear higher frequencies.
The vibrations of the flyback transformer that is responsible for the horizontal deflection of the electron beam that creates the picture. There are 525 lines drawn on a television and the display refreshes at a frequency of 59.94Hz. BUT REMEMBER THAT IT'S INTERLACED. This means that the signal that causes the horizontal deflection has to sweep across the 525 lines of the screen 30 times per second 525*30 = 15.75kHz
Some adults can't hear the sound as they have lost much of their hearing capacity at high frequency. Other people get headaches from listening to CRT televisions.
Wow that's interesting stuff about CRT TV's my wife used to complain all the time about the "humming of the TV". She said she could hear it from another room. Complained it gave her headaches sometimes. I wonder if this is what she was hearing. I usually couldn't hear it. Of course with modern TV's the problem is now moot...or should I say mute. Little pun sorry.
April 23rd, 2015 at 5:40:26 AM
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Quote: pacomartinHuman beings have the most sensitive hearing of any animal. Most people are shocked to hear that fact
Certainly I am!
Frank, you have great creditability here and with me too, but just for the hell of it, do you have a source for that?
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
