Quarter Tone Composition Software
Most mainstream music composition software have full or partial support for quarter tone notation, though some may require plugins for quarter tone playback.
MuseScore
MuseScore is one of the leading free music notation software packages. It has full support for quarter tone accidental notation and support for quarter tone playback via plugins which are not bundled with the software. It does not playback quarter tones by default and will ignore quarter tone accidentals entirely during playback. However, multiple free plugins are available that will automatically adjust pitches to match their quarter tone accidentals.
Musescore is available at musescore.org.
Dorico
Dorico, by Steinberg, is a paid music notation software package. You can input quarter tone accidentals by selecting 24-EDO as the Tonality System under the key signature interface. Dorico natively supports quarter tone playback without any need to install or run plugins.
Dorico is available at steinberg.net.
Sibelius
Sibelius, by Avid, is a paid music notation software package. It exposes quarter tone accidentals through the accidentals tab of its keypad interface. However, it does not playback quarter tones by default and will ignore quarter tone accidentals entirely during playback. To playback the quarter tones correctly, you’ll need to highlight the phrase, or entire piece, that uses quarter tone accidentals, navigate to Plugins, and select the Quarter-tone playback plugin. The plugin will adjust the pitches of the quarter tones behind the scenes and will need to be invoked each time a change is made to the phrase. This plugin is included with Sibelius out-of-the-box.
Sibelius is available at avid.com.