Higher than a high C on a piano I imagine. Anyone?
In other words, what’s the highest note that a human can hear? It depends on the human.
Hearing thresholds of individuals, both canine and human are going to vary so much that it is probably of little use to attempt to relate them to musical pitch.
That said, middle c is in the vicinity of 256 Hz (a power of 2, making it nice for computer types to remember - the usual standard is that A above middle c is 440 Hz). You double frequency for each octave, so that gives us 4096 Hz for the high c on a piano. The fundamental frequencies of most musical instruments don’t extend much above this. Here’s a picture:
http://www.psbspeakers.com/frequenciesOfMusic.html
Pitches that extend much above 4000 will tend to lose their coloration, as you can no longer detect very many harmonics.
The top end for someone who has normal hearing is around 16-20,000 Hz. IIRC, dogs can generally hear into the 30 K’s. I don’t know if there is a standard frequency for “soundless” dog whistles, and what kind of tolerance there is.
What is the cutoff point for the top frequency that humans can hear? Dogs can hear as high as 50,000 hertz. But what’s the cutoff for humans?
It differs for different people. In general, the young can hear higher frequencies, and as people age they gradually lose the upper range of frequencies. (When I was a kid my dad had a stereo effects demonstration record. It included a gradually rising pitch way into the dog whistle range. I noticed that I could continue hearing the tone after my dad couldn’t hear it any more.)
Let’s arbitrarily assign a cutoff of 20,000 hertz. Some people can’t hear that high, some can hear higher.
Concert A above Middle C is the well-known 440 hertz.
Middle C is 262 hertz.
C’, an octave higher, is 524.
C’’ (the “High C” you asked about, the province of operatic sopranos) is only 1048.
C’’’ = 2096
C’’’’ = 4192
C’’’’’ = 8384. This is, I believe, the highest note on the piano. No other instrument (expect a synthesizer) can hit any note in this range.
C’’’’’’ = 16,768, one octave above the highest reach of the piano. Almost as high as the human ear can hear.
To find out what note 20,000 hertz would be, let’s divide it down. An octave below that would be 10,000. Then 5000, then 2500, then 1250, then 625, then 312.5. That is prit’near 311 hertz, which is the D# or E-flat above Middle C.
So the (admittedly arbitrary) answer to your question would be D#’’’’’’. Slightly more than six octaves above Middle C, four octaves above your High C.
Chronos is correct in pointing out that different people and different dogs are going to be able to hear different ranges. The range of human hearing is usually stated as 20-20,000 Hz, but that’s actually the extremes. A kid could probably hear a 20kHz tone, but a guy my age isn’t likely to, since the eardrum gets more rigid as you age.
Another point, though, is that the common (Western) musical notation and scale is not based off of the range of notes humans can hear. It was based on the range of the human voice, originally. So, I’m not sure if a tone that is just short of ultrasonic could really be assigned a note.
Lastly, if I were to try to extrapolate from A=440Hz up to 20kHz, I’d surely screw up the math. Since the harmonic scale is logarithmic, you can’t just use long division.
Obviously I wimped out too quickly, and I should have previewed to see the other answers that came in. Then I could have abandoned my post. Great work, people!
[slight hijack]
Technically, that’s not quite true. Although the fingerboard of a guitar can only get you to C’’’’, crafty harmonics trickery can get you notes 2 octaves higher.
[/slight hijack]
If you believe in equal temperament, you simply divide by the twelfth root of two for each half step. This may give you 262 Hz for middle c from the 440 Hz A above it, as Jomo Mojo suggests. Nonetheless, I have seen 256 Hz stated as the frequency of middle c, and 256 Hz tuning forks sold as “c”. That’s why I said the “vicinity of”. It’s a convenient number to remember. For this discussion, we needn’t quibble over a few Hz.
That said, I think the high c on the piano is the one in the 4000’s - that would be four octaves above middle c - a piano has a few notes over a 7 octave range (88 keys, 12 per octave). It’s also consistent with the picture in the link I published.
There is simply no definite cutoff frequency. As frequency increases your sensitivity decreases gradually so to make any sense of the question you would have to state a given intensity in dBs. Furthermore, hearing sensitivity varies with individuals, with age, etc. We lose hearing with age.
There’s actually a few different standards for musical scales. In the “scientific” scale, middle C is defined as exactly 256 Hz, whereas in the more commonly used scale for musicians (I forget what it’s called), the standard is A440.
By the way, a piccolo has the same high end range as a piano, but the lowest note on the keyboard is below a tuba’s continuous range (you can get lower by playing the fundamentals, but there’s notes missing in between).
Oh, I get it, by “High C on the piano” you meant c’’’’, all the way at the right end of the 88s. I’m used to thinking of “High C” as the note that only the prima sopranos like Beverly Sills can reach, which is c’’.
(Correction: I think I goofed by using uppercase for the notes above Middle C. Aren’t they supposed to be lowercase, and the uppercase notes are used for the lower range?)
As usual, Chronos, you’re quite right. This is a really nit-picky hijack, just for general edification since it’s something I happen to know a bit about.
Good tuba players don’t have the gap in their ranges that you refer to above. Five-valved horns (which many professional caliber tubas are) give you enough tubing to finger all the way down to the fundamental. Four valves give you enough that you only miss out on one or two notes. Three-valve tubas do better on the wall at Chili’s.
For those who may not be familiar with what he’s referring to, tubas are quite capable of playing their fundamental pitch in a useful capacity. That’s great, but the next “open note” is a full octave above that, and 3- and 4-valve horns simply don’t have enough tubing to “finger” all the way down from the 2nd harmonic to the fundamental. Adding a fifth valve solves that problem (as well as conveying some other benefits).
Sorry for the hijack…