minor sixth (semitone + fifth). ( — [Dissonances] are said median when two voices are joined so that they partly match the perfect, partly the imperfect. And they are of two species, namely tone and semitone plus fifth.") Perfect dissonance: semitone, tritone, major seventh (major third + fifth). (Here again, the perfect dissonances can only be deduced by elimination from this phrase: — These species of dissonances are seven: semitone, tritone, major third plus fifth; tone plus fifth, minor third plus fifth; tone and semitone plus fifth.") One example of imperfect consonances previously considered dissonances in Guillaume de Machaut's "Je ne cuit pas qu'onques": According to Margo Schulter: Stable: Purely blending: unisons and octaves Optimally blending: fourths and fifths Unstable: Relatively blending: minor and major thirds Relatively tense: major seconds, minor sevenths, and major sixths Strongly discordant: minor seconds, tritonus, and major sevenths, and often minor sixths It is worth noting that "perfect" and "imperfect" and the notion of being () must be taken in their contemporaneous Latin meanings (perfectum la, imperfectum la) to understand these terms, such that imperfect is "unfinished" or "incomplete" and thus an imperfect dissonance is "not quite manifestly dissonant" and perfect consonance is "done almost to the point of excess". Also, inversion of intervals (major second in some sense equivalent to minor seventh) and octave reduction (minor ninth in some sense equivalent to minor second) were yet unknown during the Middle Ages. Due to the different tuning systems compared to modern times, the minor seventh and major ninth were "harmonic consonances", meaning that they correctly reproduced the interval ratios of the harmonic series which softened a bad effect. They were also often filled in by pairs of perfect fourths and perfect fifths respectively, forming resonant (blending) units characteristic of the musics of the time, where "resonance" forms a complementary trine with the categories of consonance and dissonance. Conversely, the thirds and sixths were tempered severely from pure ratios, and in practice usually treated as dissonances in the sense that they had to resolve to form complete perfect cadences and stable sonorities. The salient differences from modern conception: parallel fourths and fifths were acceptable and necessary, open fourths and fifths inside octaves were the characteristic stable sonority in 3 or more voices, minor sevenths and major ninths were fully structural, tritones—as a deponent sort of fourth or fifth—were sometimes stacked with perfect fourths and fifths, thirds