| Hilprecht, Uwe | Uwe Hilprecht | Composer | 1983 - 1989 | 2 | |
| Hoskin, Steve | Steve Hoskin | Composer | 2012 | 1 | |
| Horner, James | James Horner | Composer | 1987 | 1 | |
| Hamelin, Clode | Clode Hamelin | Composer | 1991 | 1 | |
| Holiday, Billie | Billie Holiday | Composer | 1988 | 1 | |
| Hayashi, Hikaru | Hikaru Hayashi | Composer | 1991 | 1 | |
| Halldórsson, Sigurður | Sigurður Halldórsson | Composer | 1993 | 1 | |
| Haselbek, Willi | Willi Haselbek | Composer | 1993 - 2001 | 2 | |
| Hertel, Piotr | Piotr Hertel | Composer | 1994 | 1 | |
| Hall, George | George Hall | Composer | 1890 - 1962 | 2 | |
| Holtsch, Alexandra | Alexandra Holtsch | Composer | 2002 - 2009 | 5 | |
| Holloway, Theo | Theo Holloway | Composer | 2014 | 36 | |
| Hashagen, Klaus | Klaus Hashagen | Composer | 1966 | 1 | |
| Hilliger, Olaf | Olaf Hilliger | Composer | 2003 | 3 | |
| Heitzeg, Steve | Steve Heitzeg | Composer | 2003 | 1 | |
| Horáček, Martin | Martin Horáček | Composer | 2007 - 2008 | 3 | |
| Hofmann, Tobias | Tobias Hofmann | Composer | 2004 | 1 | |
| Hotvedt, Sindre | Sindre Hotvedt | Composer | 2015 - 2017 | 38 | |
| Hashimoto, Ichiko | Ichiko Hashimoto | Composer | 1989 - 1990 | 2 | |
| Hope, Peter | Peter Hope | Composer | 2006 | 1 | |
| Harvey, PJ | PJ Harvey | Composer | 2009 | 1 | |
| Henz, Hartmut | Hartmut Henz | Composer | 1955 | 1 | |
| Harnett, Daniel | Daniel Harnett | Composer | 2010 | 1 | |
| Heimüller, Jürgen | Jürgen Heimüller | Composer | 2009 | 11 | |
| Hübner, Markus | Markus Hübner | Composer | 2015 | 1 | |
| Hamza, Andreas | Andreas Hamza | Composer | 2011 | 1 | |
| Harris, Ted | Ted Harris | Composer | 1961 | 1 | |
| Heuser, Kurt | Kurt Heuser | Composer | 1961 | 1 | |
| Haune, Kjell-Ole | Kjell-Ole Haune | Composer | 2011 | 1 | |
| Holloway, Robin | Robin Holloway | Composer | 2013 | 1 | |
| Haugaard, Harald | Harald Haugaard | Composer | 2013 | 1 | |
| Haslauer, Gernot | Gernot Haslauer | Composer | 2013 | 1 | |
| Hall, Pauline | Pauline Hall | Composer | 1950 - 1958 | 3 | |
| Hansson, Carl-Erik | Carl-Erik Hansson | Composer | 1957 | 1 | |
| Hiller Jr., Lejaren A. | Lejaren A. Hiller Jr. | Composer | 1956 | 1 | |
| Hagar, Don | Don Hagar | Composer | 1998 | 1 | |
| Holter, Iver | Iver Holter | Composer | 1938 | 1 | |
| Hess, Lindell | Lindell Hess | Composer | 1948 | 1 | |
| Hristić, Zoran | Zoran Hristić | Composer | 2000 | 1 | |
| Haentjes, Werner | Werner Haentjes | Composer | 1976 | 1 | |
| Hoge, John | John Hoge | Composer | 1993 | 1 | |
| Henry Cow | Henry Cow | Composer | 2018 | 1 | |
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