| Name | Nationality | Period | Tunes |
|---|
| Hanby, Benjamin R. |  | 1833–1867 | 2 |
| Handel, George Frideric |  | 1685–1759 | 101 |
| Handy, William C. | | 1873–1958 | 1 |
| Harington, Henry |  | 1727–1816 | 2 |
| Harrington, Jeffrey Michael | | 1955— | 2 |
| Harris, Charles Kassel | | 1867–1930 | 1 |
| Harris, Margaret Jenkins | | 1865–1919 | 1 |
| Hatton, John | | 1710–1793 | 1 |
| Hayashi, Hiromori |  | ? | 1 |
| Haydn, Franz Joseph |  | 1732–1809 | 5 |
| Haydn, Michael | | 1737–1806 | 1 |
| Hayes, Philip | | 1738–1797 | 1 |
| Hays, William Shakespeare | | 1837–1907 | 1 |
| Hemans, Felicia | | 1793–1835 | 1 |
| Hemmenway, James | | 1792–1859 | 1 |
| Henry VIII of England | | 1491–1547 | 1 |
| Hensel, Fanny | | 1805–1847 | 1 |
| Herbert, Victor | | 1859–1924 | 2 |
| Hering, Karl Friedrich August | | 1819–1889 | 1 |
| Hérold, Ferdinand |  | 1791–1833 | 1 |
| Hewitt, John Hill | | 1801–1890 | 1 |
| Hicks, Laurence Henry | | 1912–1997 | 1 |
| Hill, Mildred J. | | 1859–1916 | 1 |
| Hime, B. | | ? | 2 |
| Hodson, George Alexander | | ?–1863 | 2 |
| Hoffman, Elisha Albright | | 1839–1929 | 1 |
| Hoffstetter, Roman | | 1742–1815 | 1 |
| Holst, Gustav | | 1874–1934 | 2 |
| Holst, Matthias von | | 1767–1854 | 12 |
| Honegger, Arthur |  | 1892–1955 | 1 |
| Hook, James | | 1746–1827 | 3 |
| Hopkins, John Henry, Jr. | | 1820–1891 | 1 |
| Horn, Charles Edward | | 1786–1849 | 4 |
| Hotteterre, Jacques | | 1674–1763 | 1 |
| Hughes, John | | 1873–1932 | 1 |
| Hugues, Luigi |  | 1836–1913 | 176 |
| Hugues, William Carter | | ? | 1 |
| Hullah, John Pyke | | 1812–1884 | 1 |
| Hummel, Johann Nepomuk | | 1778–1837 | 2 |
| Humperdinck, Engelbert | | 1854–1921 | 1 |