The Cincinnati Musical Center half dollar or Cincinnati Music Center half dollar is a commemorative 50-cent piece struck by the United States Bureau of the Mint in 1936. Produced with the stated purpose of commemorating the fiftieth anniversary of Cincinnati, Ohio, as a center of music, it was conceived by Thomas G. Melish, a coin enthusiast who controlled the group which was allowed to buy the entire issue from the government, and who resold the pieces at high prices.

Congress approved legislation for the coin on March 31, 1936, authorizing 15,000 pieces to be struck at the three mints then in operation. Melish had hired sculptor Constance Ortmayer to design the coin, but the Commission of Fine Arts refused to recommend the designs. Members objected to the depiction of Stephen Foster on the obverse, finding no connection between Foster, who died in 1864, and the supposed anniversary. Nevertheless, the designs were approved by the Bureau of the Mint, and 5,000 sets from the three mints were issued and sold to Melish's group, the only authorized purchaser.

Melish likely held back much of the issue for later resale, and with few pieces available, prices for the set spiked, rising to over five times the issue price. The value dropped somewhat when the boom in commemorative coins burst in late 1936, but quickly recovered and the coins are valuable today. Melish has been assailed by numismatic writers for greed.

Sparked by low-mintage issues which appreciated in value, the market for United States commemorative coins spiked in 1936. Until 1954, the entire mintage of such issues was sold by the government at face value to a group authorized by Congress, who then tried to sell the coins at a profit to the public. The new pieces then came on to the secondary market, and in early 1936 all earlier commemoratives sold at a premium to their issue prices. The apparent easy profits to be made by purchasing and holding commemoratives attracted many to the coin collecting hobby, where they sought to purchase the new issues. Among the pieces which had recently been struck and had appreciated in value was the 1935 Old Spanish Trail half dollar. This piece had been issued at the behest of L. W. Hoffecker, a Texas entrepreneur and coin dealer, who put aside a fifth of the 10,000 mintage for himself and sold them well into the 1940s, by which time he had served as president of the American Numismatic Association (ANA). Congress authorized an explosion of commemorative coins in 1936; no fewer than fifteen were issued for the first time. At the request of the groups authorized to purchase them, several coins minted in prior years were produced again, dated 1936, senior among them the Oregon Trail Memorial half dollar, first struck in 1926.

Thomas G. Melish, a coin collector and entrepreneur from Cincinnati, came up with an idea for a commemorative coin that he would control and from which he could profit. Melish was a prominent businessman who had inherited the Bromwell Wire Company. He formed the Cincinnati Musical Center Commemorative Coin Association, and secured the introduction of H.R. 10264 on January 31, 1936. This bill would have provided for 10,000 coins from the Philadelphia Mint, 2,000 coins from Denver, and 3,000 from the San Francisco Mint. Such a low mintage would have made the Denver coin a significant rarity, increasing Melish's profit. On February 17, the House Committee on Coinage, Weights and Measures recommended that it be amended to provide for a total of 15,000 coins without dictating at what mint or mints they should be struck. That committee, in its report accompanying the bill, noted that the piece was "in commemoration of the fiftieth (golden) anniversary of Cincinnati, Ohio, as a center of music, and its contribution of the annual May festival to the art of music for the past 50 years." Melish, through political influence, was able to retain the provision that they should be struck "at the mints", allowing coinage at all three mints. This marked the last time that a coinage bill would pass Congress in the 1930s with that phrasing—later issues were limited to a single mint.

The bill passed Congress, and was signed by President Franklin Roosevelt on March 31, 1936. The pieces were to honor "the 50th anniversary of Cincinnati, Ohio, as a center of music, and its contribution to the art of music for the past 50 years". Anthony Swiatek and Walter Breen, in their volume on commemorative coins, concluded that "pressure from the above-named Association on Congress induced passage of the Act".

Melish engaged Constance Ortmayer to design the coin. Ortmayer later remembered, "I was recommended by them, someone came through Cincinnati ... they were just looking for somebody so they recommended me". Ortmayer apparently prepared a design before the bill passed Congress, for Melish wrote to Assistant Director of the Mint Mary Margaret O'Reilly on April 4, 1936, that the original "lacked distinction and artistic merit" and that Ortmayer would redesign the coin. He wrote again on May 7, asking if Ortmayer's new design was satisfactory. The models were submitted to the Commission of Fine Arts, charged since 1921 with advising on coin design, though the government was not bound to follow its recommendations. On May 13, the chairman, Charles Moore, wrote to Mint Director Nellie Tayloe Ross, withholding approval.

Moore recited the stated purpose of the coin, to commemorate the 50th anniversary of Cincinnati as a center of music, then noted that the obverse depicted Stephen Foster, the composer and songwriter—who died in 1864, whereas Cincinnati was not notable as a center of music until at least 1873. "The Commission is at a loss to connect a fiftieth anniversary in 1936 with a movement that began in 1873." Foster did live in Cincinnati, Moore admitted, but only for a brief period while working as a bookkeeper, and his main contributions to American music came later, when he lived in Pittsburgh and in New York City. Further, the coin was to commemorate Cincinnati's contributions to the art of music, and Foster "was an American troubadour, but to music as an art he made no contribution". Moore felt that if anyone should be depicted, it should be Theodore Thomas, who conducted the Cincinnati May Festival from its beginning in 1873 and in 1878 became director of the Cincinnati College of Music. He stated that "Theodore Thomas was, artistically, the founder of Cincinnati as a musical center. His portrait should appear on any coin commemorative of Cincinnati 'as a center of music'".