Word pronunciation can be peculiar in the US military. However, if we look at it with logic, we can understand the the application of those possible peculiarities (See this article, Root Step and Command Pronunciation).
Page 16 of the Nov 2013 edition of AFMAN 36-2203 has an historic pictogram, Figure 2.2, that shows how the Air Force calls commands. After separating from the Army in 1947, we, the Air Force, eventually created our own drill and ceremonies manual, AFM 50-14, by taking several moves and techniques from the Marine Corps and the Army and created an “Air Force-ized” drill and ceremonies manual. “Harch” and “Harms” just happen to be two of those techniques from the Corps, which does not use the term anymore except at Marine Barracks Washington (note: the Marines at MBW are the only ones in the Marine Corps who are authorized to use Harch, Hace, and Harms). My research indicates that those terms were used Marine Corps- and maybe even military-wide and then changes began in the 1960s.
Having said all of that, the terms, “Harch” and “Harms” are not written anywhere except for in that image. All references to commands write out the whole words, “Forward, MARCH!” and “Present, ARMS!” So, why is this image in the manual? In paragraph 2.3.4 the Air Force defines the meaning of inflection as a necessary quality for calling commands, along with projection, distinctness, and snap. This is the only reference for Figure 2.2 as graphically portraying some commands as far as inflection goes, not pronunciation. This does not mean that Harch and Harms are the terms that must replace March and Arms, respectively. Again, the figure is historic. None of the writing in the manual describes command pronunciation except for counting cadence (“Hut, Toop, Threep, Fourp“).
This then creates an issue with the command for Attention. In the Air Force we say, “Tench-Hut!” For the other services, we say, “Ah-Ten-Shun!”. All by tradition. On an historic side note, all of the services used to use the term, “Ten-Hut!” as late as the 1960s. I’m glad we got away from that one, however, I was taught to use that term in AFJROTC starting my freshman year in 1979. But, you should not!
As a reference, Army Training Circular has a similar issue, nothing states how to exactly pronounce Attention, but the Figure 3-1 on page 3-5 shows the pronunciation but, again, it is in the section regarding the qualities of the command voice. So, even though there isn’t strict pronunciation guide in AFMAN 36-2203, we can, and probably should, still use the traditional pronunciations of Harch and Harms, but what about, Hace?
I cannot find “Hace” anywhere in the AFMAN. Not in Figure 2.2 or anywhere else. This indicates that it should not be used at all.
Why the “H”?
Projection, mainly. When I was in high school I was in AFJROTC and band. During marching band season, we went to the Arizona State Band Day, a marching band competition. On that Saturday, we finished very early so that all of the bands in competition that day could play on the football field of Sun Devil Stadium at the half time of the game. We formed up and played to the crowd on one side, executed a Rear March Face (from Attention, left foot forward, turn on the platforms of both feet 180-degrees to the right, bring the left along side the right), and played to the other side of the stadium. We executed the three-count turn around for a reason, to yell out the schools letters, “ASU!” However, just saying the letters can sound muddled from a distance. So, what do you do? You put an “H” in front of each letter for better projection and enunciation. The result was, “HAY, HESS, HOO!” This could be why the US military used/uses the Harch, (HACE,) and Harms.