As someone who has forgotten most of the harmony he ever learned, and never learned counterpoint at all, I very much like the idea that it might actually be useful to study counterpoint before brushing up my harmony. And I note that some eminent authorities have recommended bringing in counterpoint at a very early stage.
Sir Charles Stanford wrote in Musical Composition (1911):
"The first principle to be laid down is to study counterpoint first, and through counterpoint to master harmony. [Stanford's emphasis] It is not necessary to remind a student of musical history that this was the process by which were trained all the great masters from Palestrina down to Wagner and Brahms...
The second principle is that the study of counterpoint, if it is to be of real value, must be strict...
What is strict counterpoint? The best way of finding an answer to that highly important question is to investigate history and see what kind of strict counterpoint was the main study of the great masters of the past, whose works have best withstood the inroads of time. Let us take for our inquiry such names as Palestrina, Purcell, Bach, Handel, Haydn, Mozart, Beethoven, Wagner and Brahms. Every one of these masters was brought up upon what is called modal counterpoint [my emphasis], at once the most interesting and the most severe form of the study."
Stanford did not write a textbook; but in Counterpoint and Harmony (1937) Edward Bairstow, Master of Music at York Minster, expressly adopted this approach. Actually Bairstow says that Stanford had recommended studying counterpoint and harmony simultaneously, which isn't quite what he had said (at any rate in his book) and isn't quite what Bairstow offers. Part I is entitled "Strict Counterpoint and Contrapuntal Harmony", but the only harmony to be found in it is that of the 16th century. Even the modes are not dealt with until Section XI (page 184!), which comes after 4th species (though not 3rd), 4-part writing and suspensions. At the start of that section he remarks that "a knowledge of the modal harmony of the polyphonic period elucidates much in modern harmony and counterpoint that would otherwise be inexplicable."
I have hesitated to embark on the study of this book because other, equally eminent authorities have argued (a) that it is impossible to learn counterpoint at all without a good command of harmony, and/or (b) that if you are going to learn counterpoint you should start with the 18th century kind.
R. O. Morris, a professor at the Royal College of Music, took the latter view (at least) in his Introduction to Counterpoint (1944):
"Sixteenth-century music, with all its beauty, is apt to sound remote and strange to the beginner when he first makes its acquaintance. Its rhythm and its modality perplex him, while its harmony seems artificially restrained and austere until he has acquired the experience and understanding necessary for its appreciation. The other school, representing the contrapuntal practice not only of Bach and Handel, but also of the great Viennese composers from Haydn to Brahms, strikes a familiar note at once and brings him into immediate contact with a type of music that he already knows and loves."
But this assumes that the beginner will not already know and love the music of the 16th century, an assumption perhaps less well founded today than it was in 1944. I have known and loved Palestrina for over 50 years; I don't understand it, but then I don't really understand Bach either.
As ever, I'd be interested to hear where our experts stand in this debate.