The Harmony Company was founded in 1892 by Wilhelm Schultz, (a former employee of Lyon & Healy) In 1916, it was bought by Sears, Roebuck and Co., which wanted to corner the Ukulele market, (Sears had first included Ukuleles in its 1914 catalogue), and went on to become the largest producer of stringed instruments in the US, selling some 250,000 pieces in 1923 and 500,000 in 1930, including all kinds of Guitars, Banjos, and Mandolins. and was marketing not only Harmony branded instruments, but also using the Sears names like Supertone and Silvertone. Silvertone was registered by Sears in 1915, originally as their record label but by 1920 they were also branding radios with it. Supertone was another record label started by the Fletcher Record Company in 1924 but they soon collapsed and Sears took over the name to avoid any confusion. Unfortunately this plan failed as Fletcher never registered the name and another firm decided they would use it for records too, thus adding to the confusion. Sears, as well as law suits decided to strengthen their claim by branding other things, including Ukuleles as Supertone. By 1928 Sears had control of the branding but in 1931 they decided to drop it themselves and used Silvertone, the brand they had properly registered for Ukuleles and other things previously branded Supertone by them. 

In 1938 there was a management buy out of all the Harmony production facilities from Sears although Sears was still Harmony's biggest customer

In the late 1930s the firm bought the brand names from the bankrupt Oscar Schmidt Co.—La Scala, Stella, and Sovereign—plus over the years they used a variety of other Sears owned trade names, such as  Playtime, Monterey, Vogue, Valencia, Vagabond and Wings. There were also endorses like Johnny Marvin, and Roy Smeck, (I have also seen John Grey have Roy Smeck endorsed Banjoleles in the UK), plus there was also a lot of largely unbranded instruments sold through the Sears Roebuck catalogue and a lot of business with some of the big US distributors like P'IMCo. 

The company hit a post war peak in 1964-1965, selling 350,000 instruments, but low-end foreign competition led to the company’s demise 10 years later. Between 1945 and 1975, Harmony had mass produced about ten million guitars, but finally even though in 1954 they had taken over Regal, their biggest rival up to that point, (They sold the Regal name on, certainly for guitars, but probably for everything to Fender in the late 1950's), they were no longer competitive with the Far East. It should also be noted that some of the final Harmony products, particularly the lower end ones, were produced in the Far East rather than Chicago. 

Sears Roebuck continued on after the demise of Harmony and are still going today. For a while after the Harmony factory had gone they had Japanese or Taiwanese import Ukuleles branded Harmony and later just Sears Roebuck. From, certainly the 80's on, they no longer branded instruments and just sold other peoples in their catalogue.

In 2015 Samick acquired and reintroduced the Slvertone name, for use on electric guitars and Chinese made Ukuleles.

Harmony particularly liked the Standard Approved definitions of scale length because for the next 10 years they were inclined to put a label on all of their major brands of Ukulele, usually in the sound hole or on the back of the headstock, stating the instrument was "Standard Approved". This is also why it is hard to gauge the scale length of instruments from this period by name.

Other Harmony labels can help date the Ukulele too, I'm not sure of the exact date of change but as a general rule before WWII they had a Gold and Red decal label and after they had a Gold and Green one. Another after the war sign is the use of plastic fretboards. Harmony, I believe came up with this idea in the early 50's on the back of the rise of the plastic Ukulele, (which they to tried to cash in on, with their Modern Bali Range), or possibly remembering Globes experiments with the Tru-Fret range. This idea was copied by a number of other manufacturers at the time including Kay, Teisco Guyatone and MUSIMA The other thing that started at this time and was copied was the distinctive "Sharks Tooth" tuners, (Kay never copied these).

Another innovation they were proud of in the late 20's was an aeroplane shaped bridge they called the "Aero bridge" and claimed it protected Guitars against the soundboard sagging at the bridge? It was more likely just a gimmick though during the period of pioneering aviation along with their wings range of Ukuleles. It was also a feature on the Johnny Marvin Professional Tenors in the beginning or their production but it was phased out for a more normal bridge well before the end of production.