Music-theoretical writings from the 13th to the 15th centuries maintained a basic distinction between two types of major sixth, customarily labeled hexachordum and deductio (or proprietas). The term hexachordum, more frequently called tonus (or semitonus) cum diapente, designated the interval of a major of minor sixth, frequently expressed by pitch letters only (such as G-e and A-F) and discussed independently of Guidonian solmization. On the other hand, proprietas and deductio indicated a ““virtual segment”” (the set of six syllables ut-la) that could be employed for the purpose of sight singing. Neither set challenged the conceptual primacy of the seven claves, expressed by the letters A-G. Hexachordum was routinely described as a portion of the octave, and the late-medieval notion of proprietas still reflected the principle of octave duplication, which had regulated musical practice since pre-Guidonian times. The ““two-tier”” model of diatonic space encountered in medieval music theory, based on the superimposition of Guido's six syllables onto the seven pitch letters, came to an end in the late 15th century, when authors such as Ramos de Pareja and Franchino Gafori began describing the Guidonian deductio——which they called hexachordum——as the primary mode of organization of the gamut that had superseded the Greek tetrachordum.
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