Musica clarissimi viri Hermanni

[1. Introductio]

In consideranda monochordi positione ea prima speculatio occurrit, quod omnis eius integritas quadruplo, id est bis diapason comprehenditur: quorum utrumque sesquialteri ac sesquitercii id est diapente et diatesseron collatione perficitur. Quare autem non ultra quadruplum extendatur, vel infra sesquitercium coartetur, haec est ratio: quod cum diapente et diatesseron unum diapason perficiant, diapason autem V tonis et duobus semitoniis, diapente vero tribus tonis et semitonio, diatesseron duobus tonis constet et semitonio, diapason autem duplicetur, non erunt deinceps consonantiae quae extensiores sint quadruplo aut contractiores || sesquitercio. Solus qui has coniungat tonus sesquialteri videlicet ac sesquitercii differentia restat. Ergo in utroque diapason VII sunt voces omnino inter se diversae; nam nulla earum cum alia perfecte concordat, nisi cum sua octava. Diapason superius, || quia gravibus modulatur vocibus, apte literis insignitur maioribus; posterius vero causa acuminis eisdem quidem literis, sed acutis notatur formulis. Ubi intuendum non alias atque alias denuo nasci; sed semel natas more VII septimanae dierum || iterum repeti sive innovari. Quare autem non amplius quam VII diversae sint; non debet mirum videri; eodem usque enim in definiendis rebus diversitas, quousque diversae desinant videri requiritur. Ut enim ex multis pauca dicamus, sicut grammatica ad VIII isagoge ad V praedicamenta ad X varietates rediguntur, || itemque aliae atque aliae in aliis; ita in monochordo elementaria quadrupli comprehensio rata proportionum dimensione VII diversarum vocum capax, octavo semper in

The Musica of the Very Illustrious Man Hermann.

Introduction

In surveying the disposition of the monochord, the observation first presents itself that its whole correctness is expressed in the quadruplum, that is, in two diapasons, each of which is produced by the union of a sesquialtera and a sesquitertia, that is, a diapente and a diatessaron. The disposition may not be extended beyond the quadruplum or compressed within the sesquitertia for this reason: Since a diapente and a diatessaron produce one diapason, while a diapason comprises five tones and two semitones, a diapente three tones and a semitone, and a diatessaron two tones and a semitone, and since furthermore the diapason is duplicated, there will be no further consonances that are more extended than the quadruplum or more compact than the sesquitertia. The single tone that joins these [intervals] remains as their difference, namely of the sesquialtera and the sesquitertia.