Why is treble all over the place?

[Selbi]

For the sake of this post I measured my headphones using amateur experience and tools. It's far from what proper measurement devices would yield, but it's still close enough to the frequency response curve from InnerFidelity.
 
That reminded me of a question I had for a long time now. Why is there so much jitter around treble regions? At 4 kHz, the frequency response is just a wild roller coaster. This goes for all headphones, even HD 800S and STAX suffer from this. I was expecting a completely, quite literally, "flat" response line (not curve) for such pricey headphones.
 
I'm so bad at sound science that I don't even know how to word this question properly. Hence why I didn't find anything on Google when looking for what I typed here.
 
Please also note that I'm not trying to be ignorant here. I just really don't know what science lays behind this stuff.

 

[MindsMirror]

I believe it is related to the wavelength of those frequencies relative to the size of your ears and headphones. Human hearing is known to be most sensitive around the 4KHz region. The wavelength of 4KHz sound is around 8.5cm, which is on a similar scale to the size of the features in your ear. I'm no expert on the acoustics of human ears, and I don't think it's as simple as 8.5cm ear = 4KHz resonance, but hopefully you get where I'm going. The complex shape of your ears and also the parts in a headphone which are similar in size to the wavelength of those frequencies are what cause the uneven response there. It's easier to create a flat response at lower frequencies where the wavelength is long compared to the size of the parts of your ear or headphone, where they won't interact as much.

 

[pfzar]

 

[castleofargh]

 there are several reasons why trebles can look like a saw made by some crazy person while the low and medium frequencies can in comparison look more even:
part of it is just how it will be because high frequencies have such a small wave length that they can interact with almost anything in the headphone and the measurement tube, fake ear, whatever it is they use. while a low freq with a wave length of a meter or more is less likely to bother with the small stuff ^_^. if it can pass a concrete wall and make some "BOOM BOOM" sounds for the neighbors, it's not a fake ear  and a mic that will impress the sub frequencies

. 
 
and part of the mess in the trebles also comes from doing the measurements. for a few reasons, treble measurements are unreliable. I really have no idea how to start detailing some of the reasons without talking dirty science and I'm guessing that's not what you're after.
but I guess the conclusion would be that it's normal.  
 
if you care for the the grey measurements superimposed on innerfidelity's graphs. they show yet another problem with measurements. each grey line is a measurement with the headphone at a slightly different position on the dummy head. and as you can see sometimes a small movement can have several db impact at some frequencies. the low frequencies are in fact very stable and what we see changing is the quality of the seal around the ears. bad seal will roll off the bass more on the measurement, as simple as that.
the midrange is pretty stable overall, some little influence from the fake ear, or for very small drivers, you can move them away from the direct path to the mic, but that's about it, mostly stable. but the trebles aren't that lucky. again because they have short wavelength so they tend to interact with the headphone, the ear, and really anything in the area.
 
 

  I believe it is related to the wavelength of those frequencies relative to the size of your ears and headphones. Human hearing is known to be most sensitive around the 4KHz region. The wavelength of 4KHz sound is around 8.5cm, which is on a similar scale to the size of the features in your ear. I'm no expert on the acoustics of human ears, and I don't think it's as simple as 8.5cm ear = 4KHz resonance, but hopefully you get where I'm going. The complex shape of your ears and also the parts in a headphone which are similar in size to the wavelength of those frequencies are what cause the uneven response there. It's easier to create a flat response at lower frequencies where the wavelength is long compared to the size of the parts of your ear or headphone, where they won't interact as much.

I have no idea how it goes for the outer ear or if there is a simplified model we can use for the average ear? I only know the little trick for the resonant frequency inside the ear canal. use the simplified concept that the ear canal is a nice straight sealed cylinder where the resonance will occur for the ear canal length being 1/4th of the wavelength. 

 

[watchnerd]

  Why is there so much jitter around treble regions? 
 

 
Jitter is not the right term to use here.
 
Jitter has a very specific technical meaning and refers to time domain distortion during digital conversion.
 
You may be referring to comb filtering.

 

[Roseval]

 
You may be referring to comb filtering.

Maybe ringing as well?

 

[watchnerd]

  Maybe ringing as well?

 
Maybe.  Hard to say without seeing a graph or hearing it.
 
But it's definitely not jitter.

 

[Joe Bloggs]

 
Why is there so much jitter around treble regions? 

Jitter is not the right term to use here.

Jitter has a very specific technical meaning and refers to time domain distortion during digital conversion.

You may be referring to comb filtering.

I believe the technical term is "a roller coaster ride". That, or "like the NASDAQ on a bad day"?

 

[gregorio]

In addition to the mentioned fact that shorter wavelengths (higher freqs) are adversely affected by smaller and smaller details/materials, even by air molecules themselves at very high freqs, we also should consider the sensitivity of human hearing mechanism to discriminate higher freqs. For example, the standard (equal temperament) music scale is based on human perception. The frequency spectrum in music is divided into numerous semi-tones ("steps"), which are all perceived as being equal. For example, a semi-tone above middle "C" (C#4) sounds the same interval as a semi-tone above the "C" an octave higher (C#5), or indeed the same interval as a semi-tone above a "C" of any octave. This however is a trick of our perception, the relationship between the equal pitches we hear is not linear with actual frequency.
 
There are 12 (equal pitch) semi-tones in every octave, so if we were to take a musical note with a frequency of 24Hz, an octave above that would have a frequency of 48Hz and each semi-tone within that octave would therefore equal roughly 2Hz. But, if we take a musical note with a frequency of say 4,800Hz, an octave above that would be 9,600Hz and now each semi-tone within that octave roughly equals 400Hz. In other words, an interval of 2Hz in a very low bass octave sounds the same as an interval of 400Hz in a treble octave. Due to our perception we've lost a great deal of frequency resolution/discrimination! Therefore, we're relatively insensitive to that zigzag mess we see in the higher freq response, the ear in effect averages much/most of it out. As it does with the same sort of treble zigzag mess we see in all acoustic spaces.
 
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[Selbi]

  Therefore, we're relatively insensitive to that zigzag mess we see in the higher freq response, the ear in effect averages much/most of it out. As it does with the same sort of treble zigzag mess we see in all acoustic spaces.

 
So, do I understand it correctly that headphone designers just don't really bother to adjust those high frequencies because it wouldn't be worth the effort due to the way our ears automatically adjust to it?

 

[MindsMirror]

  In addition to the mentioned fact that shorter wavelengths (higher freqs) are adversely affected by smaller and smaller details/materials, even by air molecules themselves at very high freqs, we also should consider the sensitivity of human hearing mechanism to discriminate higher freqs. For example, the standard (equal temperament) music scale is based on human perception. The frequency spectrum in music is divided into numerous semi-tones ("steps"), which are all perceived as being equal. For example, a semi-tone above middle "C" (C#4) sounds the same interval as a semi-tone above the "C" an octave higher (C#5), or indeed the same interval as a semi-tone above a "C" of any octave. This however is a trick of our perception, the relationship between the equal pitches we hear is not linear with actual frequency.
 
There are 12 (equal pitch) semi-tones in every octave, so if we were to take a musical note with a frequency of 24Hz, an octave above that would have a frequency of 48Hz and each semi-tone within that octave would therefore equal roughly 2Hz. But, if we take a musical note with a frequency of say 4,800Hz, an octave above that would be 9,600Hz and now each semi-tone within that octave roughly equals 400Hz. In other words, an interval of 2Hz in a very low bass octave sounds the same as an interval of 400Hz in a treble octave. Due to our perception we've lost a great deal of frequency resolution/discrimination! Therefore, we're relatively insensitive to that zigzag mess we see in the higher freq response, the ear in effect averages much/most of it out. As it does with the same sort of treble zigzag mess we see in all acoustic spaces.
 
G

This is not related to the uneven treble response you see in headphone FR graphs or the way we perceive them. These graphs are plotted on a logarithmic scale which is the same way that humans perceive frequencies. A semitone interval at the low frequency end of the graph is the same width as a semitone at the high frequency end.

 

[gregorio]

  So, do I understand it correctly that headphone designers just don't really bother to adjust those high frequencies because it wouldn't be worth the effort due to the way our ears automatically adjust to it?

 
I wouldn't say that entirely. As others mentioned, the high freqs interact with virtually everything, so it would be impossible to remove all those amplitude swings in the treble anyway and then combine that fact with the ears' relative insensitivity to it and these two facts together mean that manufacturers target their resources where it makes more difference. I don't believe any manufacturers therefore just completely ignore/not bother at all with the treble, IME they certainly do but they are less bothered about getting as flat a response as lower down.
 

  [1] These graphs are plotted on a logarithmic scale which is the same way that humans perceive frequencies. [2] A semitone interval at the low frequency end of the graph is the same width as a semitone at the high frequency end.

 
1. No, the graphs mimic a similar scale but not how humans perceive frequencies.
 
2. Yes but I think you've missed my point. Take say D#2(77.8Hz) and F2(87.3Hz), a two semi-tone interval which covers about 10Hz. Then take D#9(9956Hz) and F9(11175Hz), a two semi-tone interval which covers over 1200Hz. Look at a headphone freq response curve and compare the freq response of the headphone between A. 75Hz-85Hz with it's response between B. 10kHz-11.2kHz, obviously we can only do this roughly due to the scale. Generally we'd expect to see that "A" is virtually flat or maybe a dB or two difference but that "B" is considerably greater, maybe 10dB or so and in some cases >30dB. If we transposed the differences we commonly see at "B" to freq range "A" (IE. The 75-85Hz range had an amplitude variation of 10dB or maybe even 30dB) the result would sound pretty shocking! The point I was trying to make, maybe not very clearly, is that human hearing effectively compresses amplitude variations at higher freqs, that the relatively small amplitude variations within a semitone/s in the lower octaves sound the same as the relatively high amplitude variations within a semitone/s in the high octaves. In this respect, while logarithmic graphs may loosely mimic the same scale, they're actually the opposite of how we perceive frequencies! Such scales result in the transitions between peaks and troughs appearing steeper and the density of peaks and trough appearing greater (the zigzag mess) but we don't perceive these numerous steep transitions, we perceive the opposite, relatively few peaks and troughs and without steep transitions, effectively more and more of an RMS average the higher the freqs.
 
Presumably the ear does this because: 1. In music (and most naturally occurring relevant sounds) the highest note (C8)/fundamental frequency is about 4kHz, above that it's just fairly wildly variable harmonics and 2. In any natural acoustic, such short wavelengths vary wildly in amplitude with only very small movements in the position of the ear/s, so the brain needs to smooth out these variations in order to still recognise something as the same sound when say turning our head. Very useful if, for example, we're trying to identify some dry leaf rustling sounds and recognise if we're being stalked by a sabre-toothed tiger!
 
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