Scholars of Western chant usually rely on Guido of Arezzo, when they reduce the discussion of microtones to the question where to use b flat, they do even so, if the source is older than Guido's Micrologus. But what are the sources for earlier references?

One alternative is Aurelian's system of 15 modes which also mentions the Iastian and the Eolian mode. They both did not belong to the diatonic genus.

I always wondered, why there is so little attention to Aurelian's description of 15 modes which is not only a literal quotation of Aurelius Cassiodorus, but also a reference which might be an explanation for the author's name who is known today as "little Aurelius"? And why do they talk so much about Aurelian's 12 mode system, which was a superficial reference to the music therapy with twelve modes associated to the 4 elements and the zodiacal signs (by the way, it had nothing in common with Glarean's dodecachordon, but it was mentioned in the third book of Ptolemy's Harmonics)?

One reason might be that the "lesser perfect system" is not part of the "mainstream," in Byzantine terminology also known as the "triphonic system" (σύστημα κατὰ τριφωνίαν). Aurelian's Cassiodorus quotation proves, that it was known by Carolingians as well as the "tetraphonic system" (σύστημα κατὰ τετραφωνίαν) which was discussed as Dasia system by the author of Musica enchiriadis. In that case the "mainstream" is defined by Boethius' translation of Ptolemy, who excluded more or less the discussion of the lesser perfect system. Nevertheless, nobody explained so far the tropes of the synemmenon tetrachord in all its transpositions, despite it exists in the canonion of medieval Boethius manuscripts since the 9th century. The lesser perfect system was present in the Carolingian reception, not only in Aurelian's Cassiodorus quotation, but also as the tone system discussed in Martianus Capella's music treatise (the ninth volume of his Satyricon).

Aurelian's quotation of Cassiodorus is indeed an entirely diatonic mode system, but based on 5 chromatic pitch classes of the tetrachord:


Valenciennes, Bibliothèque municipale, ms. 148, fol. 67r-68r


Edition Lawrence Gushee (TML), I added in red colour an interpretation which fits to Cassiodorus' description of the intervals (TML):

"Quo autem ordine sonitus quindecim efficiant ac simphonias sex et tonos viii, hinc contemplare licebit cum inspexeris acute quantum singuli se superent, quousque altitudinem ultimi conscendant: ita ut singuli sese emitolio, id est medio tono, superent, quousque quintadecima primum octo tonis precedat.

Ypodorius tonus est omnium gravissime sonans [A—a], propter quod et inferior nuncupatur.

Ypoiastius autem ypodorium emitonio praecedit [B♭—♭].

Ypofrigius est ypoiastium emitonio, ypodorium tono praecedens [B—b].

Ypoeolius est ypophrigium emitonio [C—c], ypoiastium tono, ypodorium tono semis precedens.

Ypolidius est ypoeolium emitonio [C#—c#], ypophrigium tono, ypoiastium tono semis, ypodorium ditono precedens.

Dorius est ypolidium emitonio [D—d], ypoeolium tono, ypofrigium tono semis, ypoiastium ditono, ypodorium duobus semis tonis, (hoc est diatessaron [f.67v] symphonia).

Iastius est dorium emitonio [E♭—e♭], ypolidium tono, ypoeolium tono semis, ypophrigium ditono, ypoiastium duobus semis, (hoc est diatessaron symphonia), ypodorium tribus tonis precedens.

Phrigius est iastium emitonio [E—e], dorium tono, ypolidium tono semis, ypoeolium ditono, ypophrigium duobus semis tonis (hoc est diatessaron simphonia), ypoiastium tribus tonis, ypodorium tribus semis tonis (hoc est diapente simphonia) precedens.

Eolius phrigium emitonio [F—f], iastium tono, dorium tono semis, ypolidium duobus semis (hoc est diapente simphonia), ypodorium quattuor tonis precedens.

Lidius aeolium emitonio [F#—f#], phrigium tono, iastium tono semis, dorium duobus tonis, ypolidium duobus semis tonis (hoc est diatessaron simphonia), [-76-] ypoeolium tribus tonis, ypofrigium tribus semis tonis (hoc est diapente simphonia), ypoiastium quattuor tonis, ypodorium quattuor semis precedens.

Hyperdorius est lidium emitonio [G—g], eolium tono, phrigium tono semis, iastium duobus tonis, dorium duobus semis (hoc est diatessaron simphonia), ypolidium tribus tonis, ypoeolium tribus semis tonis (hoc est diapente simphonia), ypophrigium quattuor, ypoiastium quattuor semis, ypodorium quinque.

Hyperiastus est ypodorium emitonio [a♭—aa♭], lidium tono, aeolium tono semis, phrigium duobus tonis, iastium duobus semis (hoc est diatessaron symphonia), dorium tribus tonis, ypolidium tribus semis tonis (hoc est diapente symphonia), ypoeolium quattuor tonis, ypophrigium quattuor semis, ypoiastium quinque tonis, ypodorium quinque semis. [f.68]

Hyperphrigius yperiastum emitonio [a—aa], yperdorium tono, lidium tono semis, eolium duobus, phrigium duobus semis (hoc est diatessaron simphonia), iastium tribus tonis, dorium tribus semis (hoc est diapente simphonia), ypolidium quattuor tonis, ypoeolium quattuor semis, ypophrigium quinque, ypoiastium quinque semis, ypodorium sex (hoc est diapason simphonia) precedens.

Hypereolius est yperfrigium emitonio [♭—♭♭], yperiastum tono, yperdorium tono semis, lidium duobus tonis, eolium duobus semis (hoc est diatessaron simphonia), phrigium tribus tonis, iastium tribus semis tonis (hoc est diapente simphonia), dorium quattuor tonis, ypolidium quattuor semis, ypoeolium quinque, ypophrigium quinque semis, ypoiastium sex tonis (hoc est simphonia diapason), ypodorium sex tonis semis.

Hyperlidius est novissimus et acutissimus omnium [b—bb], ypereolium emitonio, yperphrigium tono semis, yperiastum duobus tonis, lidium duobus semis (hoc est diatessaron simphonia), eolium tribus, phrigium tribus semis (hoc est diapente simphonia), iastium quattuor tonis, dorium quattuor, ypolidium quinque, ypereolium quinque semis tonis, yperphrigium sex tonis (hoc est diapason simphonia), ypoastium sex tonis semis, ypodorium septem tonis. Unde claret quoniam yperlidius tonis omnium acutissimus septem tonis precedit ypodorium, omnium gravissimum."

The odd result of this interpretation was, that Lydius was based on a kind of F sharp. Even if my interpretation was not right, it would mean in any case that the concept of the modern term "chromatic" existed since Cassiodorus, but the division of the tetrachord into 5 more or less equal intervalls was definitely not called "chromatic", because a division of the tetrachord by 5 intervals was not part of the concept genus. It was just possible by the fact, that the chromatic and enharmonic genus did establish other pitches, which could be only used within triphonia in order to become the frame of an own tetrachord. It seems that Martianus Capella had a closer understanding of Alypius in comparison to Cassiodorus' new interpretation.

The open question is, was the triphonic system relevant for Carolingian cantors when they did use b flat?


I am curious to read your answers.



  • Bernhard, M., 2003. „Die Rezeption der ‚Institutione musica‘ des Boethius im frühen Mittelalter“. In Boèce ou la chaîne des savoirs: Actes du colloque international de la Fondation Singer-Polignac, présidée par Edouard Bonnefous, Paris, 8-12 Juin 1999, ed. Alain Galonnier, 601–12. Leuven: Peeters Publishers. Google.
  • Haggh, B., 2001. Aurelian’s Library. In Cantus Planus: Papers read at the ninth meeting, Esztergom and Visegrád 1998. Budapest: Magyar Tudomanyos Akademia, pp. 271–300. CP.

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