Wilhelm von Hofmann, in his 1866 systemic nomenclature, proposed the name "quartane", and the modern name was introduced to English from German around 1874...

the tertian Feaver: foure the quartane. In like manner four grains of the seed of Turnisole being drunk, cures the quartane, but three the tertian. In like...

Principal 4' Flute 4' Flautina 2' Sesquialtera (12.17) 2 2/3', 2 ranks Quartane (12.15) (formerly 12th & 15th) 2 2/3', 2 ranks Mixture (19.22.26.29) 1...

Stopt Diapason 8 Principal 4 Harmonic Flute 4 Fifteenth 2 Tierce 1 3/5 Quartane II Mixture IV Trumpet 8 Clarion 4 Swell to Great Choir to Great Transept...