The Buglers
The organizational tables of each Union regiment usually had two musicians to each company plus one or two principal musicians per regiment. Musicians made the musical calls that regulated activities in a unit.
An infantry regiment of ten companies would have places for twenty company musicians, drummers and fifers, as well as two principal musicians, often a drum major and a fife major.
A cavalry regiment with ten companies would have places for twenty company musicians, buglers or trumpeters, plus at least one principal musician, a chief bugler or chief trumpeter.
Each regiment also had a regimental band - a totally separate organization from the musicians - but most regimental bands were disbanded in 1862, leaving only the bands for brigades and larger units.
With tens of thousands of musicians in the Union army at any one time, the United States government probably spent the equivalent of hundreds of millions or billions of 2016 dollars on military music during the Civil War.
The vast investment in military music is interesting considering that the rank of musician had the highest concentration of teenage and pre-teen soldiers of any rank in the army. The average age of Union soldiers was twenty five, but one study claimed that the average age of drummers was eighteen.
Marlowe's Raid in The Horse Soldiers is based on the historical Grierson's Raid of 1863.
In real life the three regiments in Grierson's Brigade had about 1,700 men on the raid, an average of 566.66 men per regiment, below their full authorized strength. The three regiments had a total of 30 places for company buglers or trumpeters, though it is possible that fewer rode on the raid.
Two buglers are listed in the IMDB full credits of The Horse Soldiers.
Ron Hagerthy (born March 9, 1932) is listed as "Bugler" and is probably the bearded bugler seen in most of the movie. William Wellman Jr. (born January 20, 1937) is listed as "Bugler (uncredited)" and is probably the beardless bugler seen in the final battle scene.
Both buglers wear the chevrons of corporals on their sleaves, point downward as was usual in the 19th century instead of point upward as was usual in the 20th century.
In the modern US army there are relatively many corporal positions and promotion to corporal is relatively easy. But in the Civil War there were only four corporals per company and promotion to corporal was relatively much harder and rarer.
And as I wrote above, musician (often written as drummer, fifer, bugler, or trumpeter) was a separate rank or grade, not an assignment, in the Civil War and Indian Wars army. Being a bugler and a corporal at the same time was about as likely as being a private and a corporal at the same time, or being a corporal and a first sergeant at the same time.
However, principal musicians such as chief buglers often wore insignia similar to a sergeant major's. https://www.google.com/search?q=US+Civil+War+drum+major&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjrsZrr8c7NAhXHNSYKHTc3BIkQ_AUICCgB&biw=1280&bih=913#imgrc=_
Anyway, you can imagine what it might have been like if they tried to imply the presence of twenty or thirty buglers in the brigade. They could show the chief bugler of a regiment selecting which of his assembled buglers would be their orderly bugler at the brigade commander's headquarters that day. Colonel Marlowe could order the charge and his orderly buglers could start to blow the charge. Then then they could cut briefly to the commanders of the three regiments ordering their chief buglers to blow the charge, and then the sounds of the company buglers joining in the call could be heard.