The term 'coniuncta', referring to 'irregular' semitones or whole tones used in some Gregorian melodies which do not fit into the framework of the traditional Guidonian gamut, appears in theoretical sources as late as the second half of the fourteenth century, and then only sporadically; it comes to be employed on a wider scale during the next century, particularly during its final decades. Plain chant treatises representing the so-called Johannes Hollandrinus tradition, among them the treatises by Anonym XI and Laszlo Szalkai, analysed in detail by Albert Seay and Dolores Pesce, consitute a significant part of these sources. Apart from the treatises by Magister Szydlovita and Johannes Valendrinus, by now familiar from published editions, this group contains a number of anonymous texts, preserved in three manuscripts held at the 'Biblioteka Jagiellonska' in Krakow and manuscripts held at 'Biblioteka Uniwersytecka' and 'Biblioteka Ossolinskich' in Wroclaw. These texts are the source on which this article is based. In the fifteenth century the 'coniuncta' was not regarded as a problem relating exclusively to 'cantus planus'. In the plain chant treatises from the Johannes Hollandrinus tradition it was also related to vocal polyphony and instrumental music. One can thus suppose that the 'coniuncta' doctrine was intended to expand the traditional Guidonian gamut towards creating a unified standard system, applicable to 'cantus planus' as well as 'cantus mensuralis' and 'cantus organicus'. This kind of system might have been provided by the twelve-step octave.