The Geometry of Sound: A Guide to Horn Profiles

If you’ve spent any time in the high-efficiency speaker world, you know the horn is more than just a funnel. It is the acoustic transmission line that bridges the gap between a vibrating diaphragm and the air in your room.

Actually from personal experience, it's also more beautiful to listen to horn equipped speakers, although they are more bulky to live with. People not into HiFi definitely get drawn to them faster as they seem more "capable".

But not all horns are created equal. In fact, the curve of that wall changes everything. It dictates whether you get the dynamic snap of a live concert or the nasal "honk" of a subway announcement.

Today, we’re diving deep into the most legendary horn profiles. We’ll look at the history, the listening impressions, and yes, the math behind the magic.

Horn Type	Notable Brands	Iconic Model(s)	Key Distinction
Exponential	Klipsch, Altec Lansing	Klipschorn, Altec 511B	The "classic" high-efficiency theater sound.
Tractrix	Avantgarde Acoustic, Edgarhorn	Trio G3, Titan	Very natural midrange; popular in high-end DIY.
Le Cléac’h (JMLC)	Azurahorn, Auto-Tech	JMLC-200, Azura 160	Extreme smoothness; looks like a blooming flower.
Oblate Spheroid	GedLee, JBL (modern)	GedLee Summa, JBL M2	Modern "Master Reference" sound; no "horn" coloration.
Multi-Cellular	Altec, Western Electric	Altec 1505B, WE 22A	Distinctive "honeycomb" look; sprays sound evenly.
Smith / Sectoral	JBL	JBL 2397 (Wooden "Crate")	Wide horizontal dispersion with a very thin profile.
Folded / Snail	Western Electric	WE 15A, WE 16A	Massive 10+ foot paths folded into a wooden shell.
Manta Ray	Altec Lansing	MR94, MRII 594	"Fishtail" look; first true Constant Directivity horn.
Acoustic Lens	JBL	JBL 4343 ("Beehive" lens)	Uses slanted plates to "refract" sound outward.
Sato Horn	Hornsolutions, Sato	The "Big Sato"	A Japanese cult classic; 180° fold for "meaty" mids.
Synergy Horn	Danley Sound Labs	SH50, SH46, SH96	Multiple drivers (L/M/H) all firing into ONE horn.
Kugelwellen	Klangfilm, Oris	Oris 150, Klangfilm 302	German "Spherical Wave" math; very deep, round bells.
Eames Quadreflex	Stephens Tru-Sonic	Model E-1, E-4	The only "High-Art" designer horn (designed by the Eames).

1. The Classic: Exponential & Hyperbolic

The Efficiency Kings

For most of the 20th century, if you saw a horn, it was likely Exponential. Invented by Arthur Gordon Webster in 1919, this design changed the world of audio. Its primary goal was simple: Impedance Matching. It takes the high-pressure air at the driver and efficiently transforms it into low-pressure air at the mouth.

The Sound:

These are the punchiest horns. They make small amplifiers sound massive. However, they are infamous for "beaming"—as the frequency goes up, the sound narrows into a laser beam, leaving anyone outside the sweet spot in the dark. They can also suffer from "horn coloration"—that notorious shouted-through-cupped-hands effect.

The Math Bit: The area S expands exponentially over distance x:

Bernie’s Verdict:

Pros: Incredible dynamics; maximum efficiency.

Cons: High-frequency beaming; can sound colored ("honky").

 

2. The Natural: Tractrix & Kugelwellen

The Audiophile Darlings

In the late 1920s, Paul Voigt realized that sound waves aren't flat pistons—they are expanding bubbles (spheres). He developed the Tractrix profile to mimic this natural expansion. Unlike the Exponential horn, the Tractrix flares wider and faster, ideally terminating at a 90-degree angle to the axis.

The Sound:

Tractrix horns are beloved in the Hi-Fi community (think Avantgarde or Klipsch Heritage) because they sound "open." The wide mouth reduces reflections traveling back down the throat, cleaning up the midrange. They don't have the sheer bass loading of an exponential horn, but the clarity is often superior.

The Math Bit:

The curve is based on the Tractrix equation, where the length of the tangent from the curve to the axis remains constant.

 

Pros: Low coloration; open and "airy" sound; less "honk."

Cons: Beams at high frequencies; shorter bass reach than exponential designs.

3. The Perfectionist: Le Cléac’h (JMLC)

The Modern Masterpiece

Developed by the late French audiophile Jean-Michel Le Cléac’h in the 2000s, this profile is the Holy Grail for many DIYers. Le Cléac’h realized that even the Tractrix had a flaw: the transition from the horn mouth to the room air wasn't perfectly smooth.

His solution? A profile that expands and then rolls back (often a full 180 degrees), looking like a blooming flower or a mushroom cap.

The Sound:

Liquid. Transparent. Because the wave launches into the room with virtually zero diffraction or reflection, the speaker "disappears." It is arguably the most neutral of the loading horns. The downside? They are physically huge and difficult to mount in a box.

The Math Bit: There is no single closed-form equation. The profile is calculated iteratively to ensure the wavefront is always a spherical cap orthogonal to the walls, usually based on a Hyperbolic expansion (T=1) applied to the wavefront surface area rather than the axis.

Bernie’s Verdict:

Pros: Zero "honk"; smoothest frequency response; stunning aesthetics.

Cons: Enormous physical size; difficult to manufacture.

4. The Scientist: Oblate Spheroid (OS)

The Pattern Controller

Enter Dr. Earl Geddes in 1989. He argued that we shouldn't be using horns for amplification anymore (watts are cheap now). We should use them for Directivity Control.

The Oblate Spheroid isn't a "horn" in the traditional sense; it's a Waveguide. It transitions from a curved throat to straight conical walls.

The Sound:

This is the sound of modern accuracy. The "sweet spot" is massive. The frequency response is consistent whether you sit on the couch or stand in the doorway. However, because it doesn't boost the highs on-axis like older horns, it requires a specific crossover (EQ) to sound right. Without EQ, it sounds dull; with EQ, it sounds perfect.

The Math Bit:

The profile creates a specific hyperbola to match angles:

Bernie’s Verdict:

Pros: Constant directivity (sounds the same everywhere); very low distortion.

Cons: Requires active EQ or complex crossovers; less "romantic" sound than Tractrix.

 

5. Multi-Cellular Horns (The "Honeycomb")

In the 1930s and 40s, engineers realized that one big horn would beam sound like a flashlight. To fix this, they built Multi-Cellular horns. These are essentially 8 to 15 small exponential horns (cells) bundled together into one mouth.

• Visual: Looks like a cluster of square tubes or a honeycomb.

• The "Trick": Each cell covers a specific small "zone," ensuring that high frequencies are sprayed evenly across a large theater balcony.

• Example: The Altec Lansing 1005 or 1505.

6. Smith Horns / Sectoral Horns (The "Slatted Box")

Invented by Bob Smith in the 1950s and popularized by JBL, these look more like wooden crates than horns.

• Visual: A shallow, rectangular wooden box with vertical wooden "vanes" or slats inside.

• The "Trick": The vanes force the sound to expand horizontally while keeping the vertical profile very thin. This creates a wide, "cinemascope" soundstage that doesn't bounce sound off the ceiling.

• Example: JBL 2397.

 

7. Folded / Snail Horns (The "Grandpa’s Ear")

Because low frequencies require massive horns (sometimes 10+ feet long), engineers had to find a way to fit them into theaters. They "folded" the horn path like a trombone or a snail shell.

• Visual: A giant, spiraling wooden structure.

• The "Trick": By curving the sound path, you can get 12 feet of "expansion" in a cabinet only 3 feet deep.

• Example: The legendary Western Electric 15A, which is often called the most beautiful-sounding horn ever built.

 

8. Manta Ray / Biradial Horns (The "Fishtail")

In the late 70s, Altec and JBL competed to create "Constant Directivity." These horns have very sharp, non-curved angles and a "fishtail" flare.

• Visual: A wide, flat mouth with a distinct "pinch" in the middle.

• The "Trick": They use a "diffraction slot" (a tiny vertical opening) to force the sound to spread out at a perfect 90-degree angle, regardless of the frequency.

• Example: Altec Manta Ray or JBL "Baby Butt" horns (like the JBL 4425).