Bass, Midrange, and Treble? What?

[BlueWizard]

This is more of a general information post, sort of an F-Y-I.

In another group the discussion of crossover frequencies came up, and that led to a discussion of exactly what is bass, which in turn lead to a discussion of what is bass, midrange, and treble. What frequency is bass, and what frequency is it not.

Since we used these terms all the time, we would assume they are pretty clearly defined. But, not so. You would have been surprised at how differently various people defined the frequency ranges.

I think in the end, there is no precise definition; they are more just concepts we use.

So, let's consider some models -

- Human Voice is generally regarded to be in the range of 80hz to 880hz. Now certainly singers can probably go higher or lower, but in general, the stated range is something of the accepted range.

So, do we consider human voice to be midrange?

- Music in general. The standard piano goes from 28hz to 3951hz. I think we can safely say that the extreme notes on each end of the piano are out of the Midrange.

Now there are certain large Pipe Organs and Synthesizers that have response outside this range, but rarely are those ultra deep and ultra high note used.

- Audible Frequency Spectrum. The audible range covers 10 octaves, and that allows us to divide up the spectrum with ease.

.....20hz
1.) 40hz
2.) 80hz
3.) 160hz
4.) 320hz
5.) 640hz
6.) 1,280hz
7.) 2,560hz
8.) 5,120hz
9.) 10,240hz
10.) 20,480hz

As a suggestion, let's assume

20hz - 80hz = ........ Low Bass
80hz - 320hz = ...... Hi Bass, also referred to as Midbass.
320hz - 1280hz = ... Midrange
1280hz - 5120hz = .. High Midrange/Low Treble
5120hz - 20840hz = . High Treble


Finally, what does it sound like? At what frequency, does a low note stop sounding low? Using the very basic Sony 5" speakers on my computer, in my subjective opinion, tone stop sounding bassy around 315hz.

The tones I have available on my computer are upto and including 200hz, 250hz, 315hz, and 400hz. While not really low, a 200hz tone does have some bassy undertones, 250hz, while sounding less like bass, still have some bassy weight and depth to it, but it is becoming more subtle. At 315hz, I can hear a very definite shift away from bass, and at 400hz, there is no way I would consider that remotely bassy.

So, using the Octaves listed above, 320hz seem a pretty good shift between bass and midrange.

Next, where does a mid-tone stop sounding like a mid-tone and start sounding like a high-tone? Again, this is subjective, and a test performed within the limits of my ancient hearing and my so-so speakers.

However, this is an altogether more difficult test. It seems clear when a bass tone no longer sounds bassy. I can, in my mind, clearly define and understand bass, but what is midrange? That's not so clear. So, again, I went on pure subjective impression alone.

Clearly there is a shift between 2000hz and 2500hz, but I'm not sure it is enough to push it over the line. At 4000hz and above, there is a definite shift, that would allow me to say we have crossed the threshold into High Frequency.

Above 5000hz at the modest volume I'm listening at, my high frequency hearing doesn't fade completely, but it starts to falter. Again, these tone are played at modest volumes. If I crank it up, I an certainly hear well above this range. And, even at this modest volume, I still heard well above this range, just compromised slightly.

But, in the 4000hz to 5000hz range, I clearly hear a change in the characteristic of the tone, that lets me confidently push it up into the next catagory; mid to high.

Just as 320hz represented the border between Bass and Mid, I would say that 3200hz stands on the border between Mid and high. Again, 4000hz has clearly crossed the line into high.

This second threshold at about 3200hz, is near the middle of the Hi-Mid/Low-Treble range, and again seems somewhat consistent with my division of the octaves.

If by chance, you would like to conduct your own test, to see if your perceptions are consistent with mine, here is a link to source of several sets of test tone. I used the 1/3 octave test tones which provide 31 tones between 20hz and 20,000hz.

http://www.avforums.com/forums/speakers/925527-audio-test-tones-several-sources.html


Now, one last point, while it is possible to hear up to 20,000hz, if the tone is loud enough and you are young enough, there actually aren't any fundamental musical notes up that high.

- The Piano ends at 3,951hz.
- Lead guitar encompasses 82hz to 1397hz, if we don't count stretching the guitar strings.
- Bass guitar encompasses 31hz to 440hz.
- All the standard orchestral instruments are somewhere within the frequency span of the piano.

So, while we can hear above 5,000hz, there is not much up there to hear. Just harmonic 'echoes' of lower frequencies. Though these harmonics are vitally important to giving an instrument its unique voice.

The first harmonic of the highest note (assumed 5,000hz) is 10,000hz, and the second harmonic of the fundamental is 20,000hz. The ultra-high notes aren't so much heard at a tone or note as perceived that the unique tone, timbre, and voice of specific instruments.

Back in the 'old days, when the science of acoustics and speaker design was in its infancy, it would not be uncommon to see top of the line Altec Lansing speakers with response from 60hz to 12,000hz, or possibly 14,000hz, that, despite the limited frequency response, sounded fantastic. Though, they were ultra efficient horn designs.

Also, keep in mind that when speaker design was in its infancy, so was amplifier design. They were limited to low powered, often noisy, tube amps at the time.

So, what does this all add up to? Well, nothing really.

But, I thought it might be worthwhile to get some idea of what we mean when we say bass, midrange, and treble, and to also point out the differences between available fundamental notes in music, and the range of human hearing.

So, this is just 'for your information'; accept it, reject it, take it or leave it, agree or disagree, or try to prove me wrong. I just though it presented an interesting perspective on the audible frequency range, and how that apply to speakers (primarily).

Steve/bluewizard

 

[deckingman]

Steve,

You might also be interested in this.

There's life above 20 kilohertz! A survey of musical instrument spectra to 102.4 kHz

And if you really want something to get your teeth into (or make you nod off depending on your mood ), there is some good stuff here.

Music and the Human Ear

Seems, that organs can go as low as about 16 Hz and many instruments produce harmonics way above 20kHz. Also, whilst we can't actually hear these notes, there is some evidence to suggest that we do respond to them. Fascinating stuff.

 

[Alan Mac]

The first harmonic of the highest note (assumed 5,000hz) is 10,000hz, and the second harmonic of the fundamental is 20,000hz.

Steve/bluewizard

Steve,


The first harmonic of 5,000 Hz is 5,000 Hz

The second harmonic of 5,000 Hz is 10,000 Hz

The third harmonic of 5,000 Hz is 15,000 Hz

The fourth harmonic of 5,000 Hz is 20,000 Hz



Musicians often use the term “overtones”

The first overtone of 5,000 Hz is 10,000 Hz

The second overtone of 5,000 Hz is 15,000 Hz

The third overtone of 5,000 Hz is 20,000 Hz


Alan

 

[BlueWizard]

Alan Mac is correct. I think I may have been confused with octaves.

The first harmonic is the frequency itself.

The first harmonic is the frequency, the second is the frequency times 2, third harmonic = F x 3, etc.... The first overtone is Fx2, the second overtone is Fx3, etc....

The only odd and unexpected thing I found in this analysis, is a certain symmetry. The bass/mid transition was 320hz, and the mid/high transition was 3200hz.

Typically, in speakers design, though not a hard and fast rule, they try to make the midrange cover three octaves. That doesn't quite coincide with the 320/3200hz. It would put the crossovers at 320hz and 2,560hz.

In a sense, the change to the smaller woofer tower design has altered the whole underlying concept of speakers design.

Back in the old days of large woofers in the 10", 12", and 15" range, the low to mid crossover what typically 500hz (rarely) or 800hz (more commonly) because that reflected the limited ability of large woofers to reach into the midrange. Three octaves up from 800hz is 6400hz. From a practice stand point that is a little too high, the horn midrange's would have no problem going that high. but not so easy for dome and cone midranges. So, the mid to high crossover is usually backed down into the 4khz to 5khz range.

But modern 5.25", 6.5", and 8" woofer are more able to each up into the midrange. So, we see very nice smooth sounding bookshelf, and even floorstanding, 2-way speakers dominating the market.

So what was once in the old 'big woofer' days, a bass, midrange, and treble setup, has given way to more of a low-bass, mid-bass, and tweeter setup.

By specifically isolating the low range into low-bass and mid-bass, we actually make speaker design easier, especially with small woofers. It allows us to have a low-bass specifically design for only a very limited range of low frequencies. Then the mid-bass, while it can't reach as low as necessary for single woofer design, can reach reasonably low, and more importantly can reach up into the new midrange with ease and clarity. Getting a tweeter to respond nicely in the range of, say, 2khz and up, is also not that hard. That is the low response of most dome tweeters.

So, now rather than seeing crossover of 800/5000, we see crossovers in the 300/2500 range. This allows the upper bass driver to cleanly and clearly span the range of true midrange sound.

If you look at twin woofer designs, you will notice a difference between the low-bass and mid-bass driver. Most notable is that the low-bass will have a flat or soft dome, whereas the mid-bass will have a hard bullet or missile shaped dome. That hard center dome helps improve the upper midrange response.

The next advantage of the multi-driver tower/floorstander design has to do with something called 'baffle step' and 'baffle step correction'. I'll try to give the most basic uncomplicated explanation of Baffle Step.

Baffle Step is a factor in speaker design related to the width of the front of the cabinet in the area of the woofer.

At frequencies of a wavelength less that the width of the cabinet, sound tends to radiate into a space of 180° or narrower. At a frequency of a wavelength greater than the width of the cabinet, sound tends to radiate into (more or less) 360° space.

Now, let's consider energy density. In one case we have a fixed amount of energy radiating on all directions, but since it is a fixed amount of energy, that means less energy radiating in any one direction. A given amount of sound is dispersed in all direction, meaning less sound density radiating forward toward the listener.

Again, assuming a fixed amount of sound, when the field narrows to 180° or less, all the sound is concentrated in a forward direction. That means the density of the sound moving forward is higher, more concentrated.

Below the Baffle Step that results in a slight drop in measurable output level. Above the Baffle Step that results in a relative rise in the output level.

Now purist, seeking perfectly flat response, simply can't live with this, even though the drop in sound is small, they have to fix it. In a system with only one woofer, all the can do is lower the response between the Baffle Step and the low to mid crossover.

However, it occurred to someone, that if they added a second woofer that only ran at and below the Baffle Step, everything would flatten out. This gave way to the 'halfway' design.

On occasion, you will hear of speakers referred to as 2.5-way or 3.5-way designs. That's what they are talking about, speakers that have a second woofer for 'baffle step correction'.

Below the Baffle Step, both speakers are playing; at and above the Baffle Step, the lower woofer is fading out and the upper woofer is carrying on. This creates a very flat clean response on the low end.

But notice this, the frequency location of the Baffle Step is related to the wavelength of the frequency and the width of the baffle; baffle meaning the front of the speaker cabinet.

Wide cabinet = low Baffle Step frequency; narrow cabinet = high baffle step frequency. So, there is an advantage to having narrow cabinets. And low and behold, what do we have with modern tower/floorstanding designs - narrow front baffles.

This lends itself perfectly to the multi-driver low-bass/mid-bass design. If the low-bass to mid-bass crossover just happens to coincide with the Baffle Step frequency, we kill two birds with one stone. Since the designer can control the width of the cabinet front, within the limits of the width of the woofer, he can control the location of the Baffle Step.

Look carefully at the design of a Diamond 9.6 which is a 3.5-way design.

Here is a photo of my Diamond 9.6 -

http://www.avforums.com/forums/atta...2142-speaker-colours-flesh-diy-diamond-sm.jpg

Those are 8" woofers, but the front of the cabinet is only 8.25" wide. Look carefully at the sides of the woofers, and note that they are 'truncated', the frames have been trimmed off at the side to allow for a narrower cabinet.

Also notice the difference in the center of the two woofers. The lower woofer has a large soft flat center, and the upper bass driver has a small hard bullet shaped dome.

The crossover between the low-bass and the mid-bass is at 150hz. Below that both woofers are playing. Above that only the upper mid-bass is playing.

The other speaker in the photo is of a standard box larger 12" woofer design with 800hz/5000hz crossovers.

So, despite missing the good old day of large woofers, the future days of multi-driver towers doesn't look that bad. In fact, it looks a very good future indeed.

Just a few random thoughts and a bit of information.

Steve/bluewizard