The Three Octave Rule

[Deang]

True or False?

"In theory, to achieve maximum efficiency, horn dimension should be 1 wave-length long and 1 wave-length in mouth circumference at the lowest frequency. At 3 octaves higher the wavelengths are 1/10 of horn size and too small for the horn to direct them. These small wave-lengths bounce around inside the horn chaotically. It is essential to rescale a smaller horn for the next 3 octaves. Long horns are for low frequencies. Short horns are for high frequencies. Saxophones Trumpets French horns Tubas Etc obey this rule. There is no such thing in physics as long-throw or short-throw horns. These irresponsible marketing terms loosely refer to horn directivity."

PK apparently followed this "rule".

Some cool stuff out here, I just don't know how solid the information is.

Compression drivers:

http://education.lenardaudio.com/en/07_horns_2.html

One of the things I've been curious about for years is " The Half Octave Rule". At the old LDSG Site, I read that for a compression driver to load properly, the transition (cross-over point) needs to be at least a half octave above the Fc or cut-off of the horn. Here again, PK followed this "rule". The K-400 is a 260Hz horn which is crossed at 400Hz.

We always see a lot of amplitude plots here along with the occasional polars, but not much in the way of distortion tests that show us how well these 2" drivers are loading in these aftermarket horns. Reports are generally positive, so one can only assume that everything is fine - but I do get the occasional call or email, usually from someone who listens fairly loud - that makes me think something is amiss in this area.

How can a horn that's been truncated, and has a Fc less than 100 cycles below the crossover point, be loading the driver correctly?

This is for my education, and to prevent me from disseminating false information to people.

I'm clearly missing something.

[derrickdj1]

That was an interesting read.  I don't have anything to offer but, I'll follow this thread for the education.

[Schu]

True or False?

At 3 octaves higher the wavelengths are 1/10 of horn size and too small for the horn to direct them.

 

isn't it 1/3(.33 or 25%) the size and not 1/10(.10 or 10%)?

Edited September 9, 2014 by Schu

[Chris A]

True or False?

"In theory, to achieve maximum efficiency, horn dimension should be 1 wave-length long and 1 wave-length in mouth circumference at the lowest frequency. At 3 octaves higher the wavelengths are 1/10 of horn size and too small for the horn to direct them. These small wave-lengths bounce around inside the horn chaotically. It is essential to rescale a smaller horn for the next 3 octaves. Long horns are for low frequencies. Short horns are for high frequencies. Saxophones Trumpets French horns Tubas Etc obey this rule. There is no such thing in physics as long-throw or short-throw horns. These irresponsible marketing terms loosely refer to horn directivity."...

 

One of the things I've been curious about for years is " The Half Octave Rule". At the old LDSG Site, I read that for a compression driver to load properly, the transition (cross-over point) needs to be at least a half octave above the Fc or cut-off of the horn. Here again, PK followed this "rule". The K-400 is a 260Hz horn which is crossed at 400Hz.

We always see a lot of amplitude plots here along with the occasional polars, but not much in the way of distortion tests that show us how well these 2" drivers are loading in these aftermarket horns. Reports are generally positive, so one can only assume that everything is fine - but I do get the occasional call or email, usually from someone who listens fairly loud - that makes me think something is amiss in this area.

How can a horn that's been truncated, and has a Fc less than 100 cycles below the crossover point, be loading the driver correctly?...This is for my education, and to prevent me from disseminating false information to people...I'm clearly missing something.

I'm pretty sure that I don't have your answers, but just some observations:

1. Three octaves would be 1/(2 cubed) = 1/8th, not 1/10th wavelength - but you already knew that...
2. Maximum acoustic efficiency may be achieved at one wavelength in horn length, but every horn that I've seen is ~1/4 wavelength at "cutoff".  Try blowing into a tube with and without stopping the other end...then test the frequency on the piano/keyboard to see what frequency it resonates at.
3. The K-402 horn does pretty well from 250 Hz to something greater than 16 KHz, probably due to the breakpoint of the compression driver's snout to the expansion of the conical section of the horn.  Something other than a "three octave rule" exists.  If you ever heard Maynard Ferguson play in real life, you'd know that the "three octave rule" isn't a rule at all.  "It's more like a guideline"--for traditional exponential-profile horns (i.e., maximum efficiency horns)
4. There are "higher order modes" (HOMs) inside the horn (I can give you references to the theory and test measurements if you want it), but there is also something known as a "cut-on frequency" that keeps you from hearing most of them - they just don't exit the horn until you get to a fairly high frequency (i.e., "frying eggs").  However, these lower frequency HOM reflections back to the compression driver diaphragm and phase plug cause other issues - complex issues.  Constant Directivity (CD) horns that use diffraction slots (i.e., the ones that were developed by Keele and others) are HOM generators - and don't sound very good if used above defined high frequency cut-on points, and will generate their own high frequency harmonics due to HOM generation.
5. "Long throw horn" is an interesting idea - just like alien abductions and magic rocks.  But I have seen horns designed for narrow exit angles, like in microwave use.  At home for acoustic use, we typically like to have 90 degree coverage angles horizontally and perhaps 30-40 degree vertically, or perhaps a bit more depending on the height of your ceiling.
6. I'm not that familiar with the "half octave rule" - so I'll pass on that topic for now
7. Your observation on distortion measurements (especially modulation distortion measurements, but I'll settle for harmonic distortion...) is pretty much true for horns being used below their cutoff frequency.  For instance, you can see it in this data sheet below 2 KHz as the fundamental frequency drops off - and the second harmonic doesn't...but note that you're still probably doing a lot better than direct radiating drivers in terms of modulation distortion.  That's why the 31 Hz bass boost on the Jub bass bin works so well, because the alternatives to using the Jub bass bin below 40 Hz aren't usually nearly as good.
8. The "loading below Fc" topic is usually connected to discussions centering on the Webster horn equation, i.e., the "one-dimensional horn equation".  Once you release yourself from that constraint (Webster eqn.) then loading below Fc is something that is much easier to accept conceptually.  Understanding the exact physics of what's happening, however, is another story.

Chris

Edited September 9, 2014 by Chris A

[Don Richard]

These observations that you quoted seem to apply to exponential high frequency horns. Exponential high frequency horns are rarely used in new designs these days, supplanted by other horn profiles such as  tractrix, constant directivity, and conical profiles. However, even with the newer horns you still need some "breathing room" at both the lower and upper ends of the horns' frequency response range for proper crossover performance.

 

Many of the older horn loaded systems using exponential horns for the higher frequencies were 3 and 4 way designs for several reasons, including maximizing efficiency, getting sufficient SPL, lower distortion, and consistent polar response over a wide frequency range. You see more 2 way designs these days because of better horns and compression drivers along with the availability of more powerful and cheaper amplification equipment.

[ClaudeJ1]

These observations that you quoted seem to apply to exponential high frequency horns. Exponential high frequency horns are rarely used in new designs these days, supplanted by other horn profiles such as  tractrix, constant directivity, and conical profiles. However, even with the newer horns you still need some "breathing room" at both the lower and upper ends of the horns' frequency response range for proper crossover performance.

 

Many of the older horn loaded systems using exponential horns for the higher frequencies were 3 and 4 way designs for several reasons, including maximizing efficiency, getting sufficient SPL, lower distortion, and consistent polar response over a wide frequency range. You see more 2 way designs these days because of better horns and compression drivers along with the availability of more powerful and cheaper amplification equipment.

Yes, and even though the site is expansive in scope, there is no mention of Tom Danley's patented Unity Summation Aperture horns in a 2-step conical form that offer the benefits of 2 and 3-ways in a single, cohesive horn.

[ClaudeJ1]

Maximum acoustic efficiency may be achieved at one wavelength in horn length, but every horn that I've seen is ~1/4 wavelength at "cutoff".  Try blowing into a tube with and without stopping the other end...then test the frequency on the piano/keyboard to see what frequency it resonates at.

 

 

I would dispute the "full wave" statement and say that 1/2 wave is conservative enough for a reasonably linear behavior. Besides, horns are inherently narrow band devices when used with a single driver without EQ and can only be made with "flat" frequency response on axis by allowing gradual narrowing of higher frequency dispersion in their shape (LeCleach horns being the most talked about in this regard).

[CECAA850]

If you ever heard Maynard Ferguson play in real life

 

Great point.  I've heard him on many occasions and was amazed each time.  Much more than 3 octaves going on there.

[Deang]

Great posts. Thanks guys.

[cradeldorf]

Not sure if this helps, But I figured it can't hurt.

http://www.fohonline.com/home/73-speaking-of-speakers/7250-understanding-horns.html

[beeker]

http://education.lenardaudio.com/en/07_horns_2.html

I love that link. Details of all different horns but that horizontal horn dispersion has always been an interest of mine. Jbl to cheap 80's speakers and others used that design. I'v never seen the detailed conclusion of these slots and direction of the noise produced out of them. Very interesting

[Chris A]

From the linked site...

 

 

"With 'no horn', the cone movement increases 4 times for each octave decrease.   With a horn the speaker cone movement is reduced to 2.   Efficiency increase is approx 4 times (+6dB).   In theory, power to the speaker can also be doubled (+3dB).   Total advantage is approx +10dB with increased directivity."

 

You get ~5x reduction in cone motion with horn loading for equal SPL output (not 2x), and an efficiency increase of 7x to 10x (not 4x). 

 

The total advantage between horn vs. direct-radiating (baffle) is between 15-20 dB in SPL (or alternatively, reduction in required input electrical power of 50x-100x) and a typical 20-25 dB reduction in modulation distortion--the most notable difference, IMHO. 

 

Harmonic distortion levels are lower for horn-loaded due to lower required input power/driver amplitudes required to generate the same SPL in-room. 

 

All this assumes the same driver used as a direct radiator vs. in a proper horn-loaded configuration, i.e., apples-apples.

 

Why someone would subdivide this advantage into separate smaller quantities--with the combined effect to obfuscate the perceived difference (but NOT hearing difference)--is beyond me.  

Edited September 11, 2014 by Chris A

[pzannucci]

What is the difference between the efficiency of a K-horn and a Cornwall?  Is there something wrong with the K-horn bass section if it only gains 7db efficiency over the vented Cornwall?

 

When talking horn loading, it is required to speak apples to apples along with frequency ranges while using the same driver.

 

From what I read in the old Olson book (many many years ago), the shorter the length, the less control.  1/4 wave length is minimum.  As you approach the Fc of the horn, your control is lost due to not being able to manage the resistance/reactance in the horn, just the frequency response gets very jagged.  If this is true, you definitely want to keep the crossover up away from the actual horn Fc for smoother response.

 

The nice part is today everything has correction built in via DSP.  This may not be a 100% cure though it does help us break a lot of rules we assumed correct in the pure analog world.

[ClaudeJ1]

From the linked site...

 

 

"With 'no horn', the cone movement increases 4 times for each octave decrease.   With a horn the speaker cone movement is reduced to 2.   Efficiency increase is approx 4 times (+6dB).   In theory, power to the speaker can also be doubled (+3dB).   Total advantage is approx +10dB with increased directivity."

 

You get ~5x reduction in cone motion with horn loading for equal SPL output (not 2x), and an efficiency increase of 7x to 10x (not 4x). 

 

The total advantage between horn vs. direct-radiating (vented) is between 15-20 dB in SPL (or alternatively, reduction in required input electrical power of 50x-100x) and a typical 20-25 dB reduction in modulation distortion--the most notable difference, IMHO. 

 

Harmonic distortion levels are lower for horn-loaded due to lower required input power/driver amplitudes required to generate the same SPL in-room. 

 

All this assumes the same driver used as a direct radiator vs. in a proper horn-loaded configuration, i.e., apples-apples.

 

Why someone would subdivide this advantage into separate smaller quantities--with the combined effect to obfuscate the perceived difference (but NOT hearing difference)--is beyond me.  

The trade-off you make vs. direct radiation of the same driver is you limit the frequency response by effectively adding more legs to the filter. Horns are inherently narrow band devices and you do make compromises when you cram lots of EQ in them to reduce the number of horns in the system (2 way vs. 3-way). In either case, the best sound I ever got from a K-402 is when I crossed at 300 Hz. at low power (10-100 milliwatts range). That way my Quarter Pie woofer horns and their interaction with the room were dealt with separately with active filtering. I heard Jubes with Klipsch factory 2-way and 3-way. I preferred the 3-way because of the lower crossover point in the midrange gave me much more detail on female vocals, sax, guitar, piano, you name it.

[ClaudeJ1]

 

These observations that you quoted seem to apply to exponential high frequency horns. Exponential high frequency horns are rarely used in new designs these days, supplanted by other horn profiles such as  tractrix, constant directivity, and conical profiles. However, even with the newer horns you still need some "breathing room" at both the lower and upper ends of the horns' frequency response range for proper crossover performance.

 

Many of the older horn loaded systems using exponential horns for the higher frequencies were 3 and 4 way designs for several reasons, including maximizing efficiency, getting sufficient SPL, lower distortion, and consistent polar response over a wide frequency range. You see more 2 way designs these days because of better horns and compression drivers along with the availability of more powerful and cheaper amplification equipment.

Yes, and even though the site is expansive in scope, there is no mention of Tom Danley's patented Unity Summation Aperture horns in a 2-step conical form that offer the benefits of 2 and 3-ways in a single, cohesive horn.

 

As owner of the patented technology, I would say Tom Danley has added quite a few new chapters to the "book of horns" with his innovative designs. It will take some time for the world to absorb it, but his company is kicking butt in the stadium and church marketplace.

[CECAA850]

What is the difference between the efficiency of a K-horn and a Cornwall? Is there something wrong with the K-horn bass section if it only gains 7db efficiency over the vented Cornwall?

 

7dB is almost twice as loud with the same amount of power applied.

[ClaudeJ1]

 

What is the difference between the efficiency of a K-horn and a Cornwall? Is there something wrong with the K-horn bass section if it only gains 7db efficiency over the vented Cornwall?

 

7dB is almost twice as loud with the same amount of power applied.

 

Along with 1/10th the amount of IM distortion for the Khorn.

[DrWho]

Lots of talk about "theory", but nobody is actually pointing to any of the equations - nor stating the assumptions and what variables are being held constant when making generalized claims.

Acoustics Sound Fields and Transducers by Beranek and Mellow would be a great place to start. The acoustics text by Olsen is good too, but probably too deep in the math and he only covers exponential horns, and briefly at that.

John Post's thesis on tractrix horns is also very good and he even shows that tractrix is more efficient than exponential....

[Chris A]

What is the difference between the efficiency of a K-horn and a Cornwall?  Is there something wrong with the K-horn bass section if it only gains 7db efficiency over the vented Cornwall?

 

When talking horn loading, it is required to speak apples to apples along with frequency ranges while using the same driver.

 

From what I read in the old Olson book (many many years ago), the shorter the length, the less control.  1/4 wave length is minimum.  As you approach the Fc of the horn, your control is lost due to not being able to manage the resistance/reactance in the horn, just the frequency response gets very jagged.  If this is true, you definitely want to keep the crossover up away from the actual horn Fc for smoother response.

 

The nice part is today everything has correction built in via DSP.  This may not be a 100% cure though it does help us break a lot of rules we assumed correct in the pure analog world.

 

See enclosed excerpt from PWK/Bruce Edgar article...

Excerpts from A Visit to the Klipsch Kingdom - Bruce Edgar.pdf

[ClaudeJ1]

Lots of talk about "theory", but nobody is actually pointing to any of the equations - nor stating the assumptions and what variables are being held constant when making generalized claims.

Acoustics Sound Fields and Transducers by Beranek and Mellow would be a great place to start. The acoustics text by Olsen is good too, but probably too deep in the math and he only covers exponential horns, and briefly at that.

John Post's thesis on tractrix horns is also very good and he even shows that tractrix is more efficient than exponential....

I'm assuming you are referring to the original link?