[Excellence]

Every graph I see is segmented so that the x axis of the response has 3 main sections, low mid and high, and have no idea why the would compress uncompress the x axis 3 times. Why aren't frequency response graphs linear?


It seems that doing this on the x axis (frequency axis) would mask dips and peaks in the compressed areas and amplify them in the uncompressed areas.


HELP!

 

[Michael Grant]

I'm not sure what you're talking about. Are you sure you're not just referring to the fact that the x axis is logarithmic? That's an entirely sensible thing to do, given that's exactly the way we hear frequencies.

 

[Alimentall]

Or are you wondering why they often measure the drivers individually, then sum the response?

 

[Excellence]

 http://forum.ecoustics.com/bbs/messa...79/131062.html


Take a look at the familiar response graphs used in the early illustrations. You see how the columns distance from each other compress, and rarify, and compress and rarify again? I'd be highly suspect if the nicely spaced and dead on evenly numbered frequency response lines that have been used to change the way we perceive the data. Would the graphs tell us more imformation if the x axis weren't squished as it is? If the squishing they've done is good, how did they decide to squish it this way? Are there other examples of cyclical squishing of x axises in.

 

[Alimentall]

Could you put that in English, please? What are you trying to say/ask?

 

[TheMadMilkman]

1. Space issues.


2. Importance of certain frequency ranges.

 

[anupmc]

Dr.Grant is spot on... perhaps this will help:

Introduction to Logarithmic scales as commonly used in acoustic measurement

 

[Alimentall]

Huh. I feel almost silly for not understanding the question. I thought there was something more complex at work.


You mean "why is 50-100Hz the same as 500Hz-1000Hz" with is the same as 5000Hz-10,000H, IOW 50=500=5000?" Because everything is based on musical notes and every octave above is twice as "wide" as the octave below it (but doesn't contain more musical information). For instance you have A 440 and the A note above is 880 and the A note below is 220. So if you made a linear graph, it would inflate the importance of the upper notes (by several orders of magnitude) while the "compressed" graph gives equal weight to each musical octave.


Notice also that everything pertaining to crossovers is in octaves. So, the way it's illustrated now will show a nice visually even roll off on both sides crossover point. If you didn't, it would look very uneven - a 24dB/octave roll off on either side of 800Hz at ~96dB would show that it takes ~750 cycles to roll off completely at one end and 12,000Hz to roll off at the other side and that would graph evenly at all, especially since those 750 are, in fact musically equal to the 12,000Hz on the other side of the crossover. So, on a FR graph, the 750Hz and 12,000Hz on either side of the crossover appear to be the same because, to our ears and to everything in music and speaker design, they are the same.

 

[Terry Montlick]

For subwoofer range frequencies (10-100 Hz or so), the graphs are usually linear in frequency. This is not only a convenient way of seeing frequency response over a limited range, but more direct to compute.


When any modern RTA or other frequency analyzer is measuring a frequency response, it is doing so via a technique called the FFT (Fast Fourier Transform). This is a modern (last half century) method for computing frequency response from time-domain info. With any Fourier transform, you get frequencies which are linearly spaced. The FFT is taken over a "windowed" piece of time signal, which has a certain duration. The relationship between frequency resolution and time window length is simple:


frequency resolution in Hz = 1/time window size in seconds


So a 1 second time window yields a frequency resolution of 1 Hz. It is very easy to display this on a linear frequency graph, with no distortion of the FFT-gleaned information.


When logarithmic frequency graphs are used, more processing is typically required. Otherwise, with the fixed frequency resolution of the FFT, you will get much more relative resolution at the "compressed" high frequencies than at the low ones. This extra processing generally involves combining multiple resolution FFTs, and/or doing smoothing which uses varying numbers of frequency samples.


Regards,

Terry


PS: Sorry if this post is overly technical. I try to simplify things as much as possible without lossing the truth along the way. I think understanding the "why" is useful in demystifying any complicated subject. - T

 

[Morbius]

Quote:

Originally Posted by Michael Grant I'm not sure what you're talking about. Are you sure you're not just referring to the fact that the x axis is logarithmic? That's an entirely sensible thing to do, given that's exactly the way we hear frequencies.

Very understandable question - and Michael has the correct answer.


The notes of the musical scale in a "tempered tuning" are a geometric

progression in their frequencies - each semi-tone, i.e "half-step" of C to C#,

for example means the frequency is multiplied by the twelfth root of 2.

[There are 12 half-steps per octave, and an octave is the doubling of the

frequency.]


A geometric progression becomes linear if plotted on a logarithmic scale.

If you want each octave to have the same "step size" on the x-axis; then

you can see quite naturally that a logarithmic scale in base 2 would do that.

[Replacing the numbers of the geometric progression; 1, 2, 4, 8, 16, 32...

by their base 2 logarithms yields; 0, 1, 2, 3, 4, 5...]


Well a logarithmic scale in base 10 differs from a logarithmic scale base 2

by a constant divisor - namely the base 10 logarithm of 2.


So a base 10 logarithmic scale works equally as well as a base 2 logarithmic

scale.

 

[ChrisWiggles]

Quote:

The notes of the musical scale in a "tempered tuning" are a geometric progression in their frequencies

Not sure what tuning has to do with freq resp. graphs, but you mean "equally tempered" tuning, as ALL tunes are tempered by mathematic necessity. The choice to temper equally or otherwise is a subjective one made by the tuner, or whoever wants something tuned.

 

[Morbius]

Quote:

Originally Posted by ChrisWiggles Not sure what tuning has to do with freq resp. graphs, but you mean "equally tempered" tuning, as ALL tunes are tempered by mathematic necessity. The choice to temper equally or otherwise is a subjective one made by the tuner, or whoever wants something tuned.

Chris,


Musicians typically use the terms "tempered tuning" and "equally tempered tuning"

synonymously.


The notes of the musical scale don't have to have equal "temper".


For example, the musical interval of a "fifth", i.e. from a C to a G for example,

can be tuned to be a multiplication in frequency by 3/2. [ Musicians would call

this a "non-tempered tuning" or "natural tuning".]


One thing that makes a "tempered tuning" or "equally tempered tuning"

advantageous is that you can play songs in alternate keys because the

step sizes are uniform. In a "non-tempered" tuning, the step sizes are

not uniform, and if you write in the key of C; you essentially have to play

the work in C if you want to have it sound exactly the same.


Guitars, which I play; are usually made for "equally tempered tuning".

However, there are guitars that have been made for the non-equally

tempered tuning. You can recognize those guitars on sight because

the frets on the fretboard are not parallel to each other - they vary

in "tilt".


The adjustable frets of a Sitar allow them to be played in "untempered

tuning":

http://yellowbellmusic.com/instrumen...tion_sitar.php

 

[ChrisWiggles]

but that "non-tempered" tune is a misnomer, because it still is tempered. To make some intervals more mathematically "correct" you gotta make others worse, so you're just shifting things around as you know.

 

[Morbius]

Quote:

Originally Posted by ChrisWiggles but that "non-tempered" tune is a misnomer, because it still is tempered. To make some intervals more mathematically "correct" you gotta make others worse, so you're just shifting things around as you know.

Chris,


There's no "correct" size for the intervals. There are just different ways of tuning.


Many eastern musicians, like Indian sitar players consider the equally tempered

tuning to be the "incorrect" tuning. After all, "eqaully tempered tuning" is a

relatively recent invention:

http://www.jimloy.com/physics/scale.htm


Musically, there are arguments to be made on both sides - on one hand it is

nice to have a "fifth" be a 3/2 multiplication in frequency. The fifth is more

harmonically related to the root if it corresponds exactly to an integral number

of half-wavelengths.


However, it is also nice to be able to transpose to differing keys which is what

an equally tempered tuning gives you.


As to what terminology to use - "tempered", "untempered", whatever - I am

defaulting to how most musicians use the terms - it's their field after all.

 

[Dean Roddey]

I prefer ill tempered instruments.

 

[Morbius]

Quote:

Originally Posted by Dean Roddey I prefer ill tempered instruments.

Dean,


With plenty of "wolf notes". Wolves are pretty ill-tempered.

 

[Terry Montlick]

Quote:

Originally Posted by Dean Roddey I prefer ill tempered instruments.

Ah, bagpipes!


- Terry

 

[ChrisWiggles]

I meant as in mathematically, and thus sonically most pleasing, correct. I.e. each octave is exactly 2x hz, each interval is precise. This is impossible to do, or you end up with an octave too big, that's all I meant. You have to fudge somewhere and how you fudge it depends. Fudging it equally so that all intervals are a little bit "off" within the octave is the equally tempered way, and sort of the usual way to do it. A lot of things aren't like this though, for instance organs are made with different kinds of tunes, that you can map out. This will make certain chords sound better, and others worse. Equally tempered, all chords would sound decent, but still a little bit "off" from their mathematically "correct" harmonic ideal. We're stumbling together over different words is all.


But what do I know about tuning, I always wanted to be a drummer...

 

[Michael Grant]

Excellence, thanks for the illustration. That is exactly what I thought: you're looking at logarithmic scales. It would help if they put the numbers along the bottom of the x axis. If they were to do that, you would see that what you call "compress and rarify" really isn't that at all. Things keep on compressing the same throughout---but periodically they just draw the grid lines less frequently so they don't get too crowded.


So for example, when you see a frequency response chart for, say, 10Hz-10kHz, the grid lines are drawn at the following places:


10, 20, 30, 40, 50, 60, 70, 80, 90,

100, 200, 300, 400, 500, 600, 700, 800, 900,

1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000,

1000.


So what you see as "compress and rarify" is just the fact that they jump from drawing the lines every 10Hz to drawing them every 100Hz, and then again every 1000Hz.


The distance between two points on a logarithmic frequency axis is proportional to the ratio between the frequencies. For example, if you took a ruler and measured the distance on this graph between, say, 30Hz and 3000Hz, this distance would be the same as if you measured the distance between 50Hz and 5000Hz, because both have a ratio of 100.


Since our brain interprets frequencies in this fashion, this is a sensible way to draw frequency response charts. No matter where they are along the x-axis, features on the chart (dips, peaks, etc.) are represented in a proportion that corresponds to the way we hear them.

 

[Dean Roddey]

The even tempering, at least on the guitar and other stringed instruments, actually is kind of nice in a way, since that slight detuning can provide a 'thicker' sound. At least I always have though that the slightly 'off' tuning contributed in that way. Instead of exact multiple vibrations you get interesting fractional combinations of vibrations between the different notes.


Though that has to be taken in the context of the fact taht where you pick on the string also has a lot of effect, since you can pick exctly halfway between the fingered fret and bridge and get two long and sonorous nodes of vibration, or pick near the bridge and get a more complex set of different sized nodes. This is actually a good way to teach people about standing waves and how one can vibrate in many different combinations according to the relationship of the space to the wavelength, since you can literally see them if you look closely.