For Harry Berv in A Creative Approach to the French Horn the concept of “leverage” was essential to a good slur.
In making a slur on the horn, the airflow must be even so that the lips will be in a constant state of vibration. Should the airstream become uneven, the lips will not vibrate correctly and the upper note will pop out.
Think in terms of leverage when slurring. When executing a wide interval slur, a slight thrust of air should be applied to the first note, and this will assist in making the upper note speak easily. The only note that is attacked in any slur is the initial one. The last note is never attacked; it should be tied to the initial note by a gracefully executed arch. A slur in either direction is difficult to perfect. Control of lip and air must be practiced slowly and intelligently in order to achieve proper results.
Berv does recommend that the tongue arch up slightly in the upper range and be in a lower position in the low register as an aid to slurs. He thinks of it in terms of the tongue “changing the size of the channel in the mouth.” He describes a coordination of the embouchure, tongue, and air column with the key action of the valves. He continues
The next step will clarify what I referred to at the beginning of this chapter concerning leverage. The Bb horn is now brought into use. With its shorter tubing, and in combination with the F horn, it helps greatly in producing a beautiful, even slur.
In the exercise that follows he demonstrates that slurs may be made more easily through fingering choices by “cutting in” the Bb horn.
As a composer Verne Reynolds in The Horn Handbook takes on with slurring the larger, musical topic of slurs as phrase markings—some notes certainly should be tongued within slurred passages.
Musicians agree that a slur is a curved line placed under or over a group of notes to indicate that those notes should be played smoothly. The tongue is used to begin the first note and may be used within the slur somewhat in the same way a violinist changes the direction of the bow, providing its use does not violate the spirit of smoothness. In other slurred phrases the tongue is not used again after the first note. Within the curved line may be dots, dashes, accents, and even sforzando and forte piano, all of which require the use of the tongue. The same curved line can indicate phrase length and possible breathing places. A slur could be called a phrase boundary when it encloses many notes. Within the boundary there can be several tongued notes added to adorn the phrase and to give it shape and definition. Seldom are these articulations used to separate the smaller units within the phrase. A composer occasionally, and intentionally one hopes, includes silence within the phrase boundary, thus offering the player an opportunity to employ the elegance of tapered release and non-accented reentry. A brass player cannot succeed without being able to connect notes without using the tongue, or without a complete assortment of tongue strokes to articulate notes within a legato phrase.
As to playing slurs, the key for Reynolds was “continuity of lip vibrations.” He notes that in for example a two-octave slur
…the embouchure must know how the second note sounds and feels while it is producing the first note. Fast wide slurs are difficult because the embouchure has little time to predict the feel of the second note while we are playing the first note. Yes, we can think while we play. Not to think is to shoot at an unheard and unfelt target. Here is another case in which thoughtful repetition produces results.