front radial horns have been used, for instance by Community in their SQ 90 high-frequency horn. JBL's diffraction or "Smith" horn was a variation on the radial design, using a very small vertical dimension at the mouth as a method of avoiding the mid-range horizontal beaming of radial horns that have a larger vertical dimension at the mouth. The diffraction horn has been popular in monitor designs and for near-field public address applications which benefit from its wide horizontal dispersion pattern. Counterintuitively, the narrow vertical dimension provided for an expansive vertical output pattern approaching 90° for frequencies of a wavelength equal to the narrow vertical dimension. A very small version of the diffraction horn was designed in 1991 into the JBL model 2405H Ultra-High Frequency Transducer, yielding a 90° x 35° output pattern at . Tractrix The tractrix horn is very similar in many respects to the exponential horn and has gained adherents among DIY horn enthusiasts, audiophile consumers, and some manufacturers. It uses a curve formula derived by assuming that a tangent to any point on the horn's inner curve will reach the central axis of the horn with a line segment of set length. At the mouth, the tangent line segment becomes perpendicular to the axis and describes the radius of the mouth. This horn concept was studied by Paul G.A.H. Voigt in the mid-1920s and patented in 1927. The size of the tractrix horn is generated by specifying the desired low frequency "cutoff" or limit which will determine the mouth diameter. Two incremental improvements over the exponential horn include slightly better support for low frequency extension and a somewhat broader high-frequency coverage pattern. Constant directivity In May 1975, to address problems of beamwidth changing at different frequencies, D. Broadus "Don" Keele, Jr. of Electro-Voice introduced a hybrid horn with an exponential expansion rate near the throat followed by a conical expansion section and ending with a rapidly flaring flange at the mouth. The flange at the mouth solved some remaining problems with lobing at higher frequencies. Don Keele specified in one version of his design a wider horizontal flare for pattern control appropriate to public address purposes. Keele's paper set forth the relationships between mouth size, frequency and coverage angle, providing a basis for many future developments of horn design. One problem found with constant directivity horns is that the horizontal coverage pattern cannot be narrowed without