The Greek-letter notation described by Boethius c.500 seems to indicate that the Greeks (or Graeco-Romans) recognized the near-similarity of notes separated by a skhisma. Hucbald, in the early 900s, reorganized the entire pitch system in an attempt to reconcile the current Frankish practice with the ancient Greek theory.
> Boethius's actual theoretical tuning of the diatonic genus supposedly
> would have been entirely Pythagorean (3-limit), but as Nicomachus
> wrote, c. 100 AD:
>
> >> [Barker 1989, p. 265]
> >>
> >> ... [the _synemmenon_ tetrachord] begins with its own _trite_
> >> a semitone away from _mese_, then, after a tone, has a _paranete_
> >> peculiar to itself, then, after another tone, has the _nete
> >> synemmene_, which is in all respects of the same tension and sound
> >> as _paranete diezeugmenon_.
>
> And this distinction is indicated in Boethius's Greek-letter notation.
>
> Much later (c. 900 AD), Hucbald directly contradicted this:
>
> >> [Babb 1978, p 33]
> >>
> >> ... the _paranete synemmenon_ is the same in sound as _trite
> diezeugmenon_.
>
> which shows that the basic diatonic tuning had changed by his time.
I simply copied this info from my notes, but upon writing this yesterday, that reference to Hucbald seemed a bit anomalous. So I re-read Hucbald, and decided to comment further on why I made reference to his book. I see thus that one reason why this paper has never been published is because I left a lot unsaid about the connection between Boethius and Hucbald.
First, it should be noted that the Hucbald text located at www.chtml.indiana.edu/tml/9th-11th/HUCHAR_TEXT.html and from which I'm quoting, is actually not from the Coussemaker edition in my reference-list, but rather from the following:
Gerbert, Martin (ed.). 1784.
_Scriptores ecclesiastici de musica sacra potissimum_ (3 vols.)
St. Blaise: Typis San-Blasianis
reprint: Hildesheim: Olms, 1963, p. 1:103-25.
Note that the TML also provides an additional text of Hucbald's treatise from yet another edition:
Migne, J. P. (ed.)
_Patrologia cursus completus, series latina (221 vols.)
Paris: Garnier, 1844-1904, p. 132:905-29
www.chtml.indiana.edu/tml/9th-11th/HUCHARM_TEXT.html
For the section under discussion here, the Migne version does not differ in any significant way from that of Gerbert.
Hucbald was attempting a drastic simplification of the letter notation given by Boethius (which Hucbald says gives a total of 288 different notes), in hopes of adapting it to the current practice of his time.
In the last section of his treatise, Hucbald adapts the Greek-letter notation used by Boethius as follows:
>> [Hucbald, in Gerbert 1784, p. 117-118]
>>
>> Sunt igitur notae quidem chordarum plurimae antiquitatis
>> usui habitae, quae a Boetio per singulos octo modos binae
>> singulis chordis appositae, in CCLXXXVIII. tenduntur: eaedem
>> quoque graecis quibusdam litteris rectis, quibusdam varie
>> immutatis expressae, plurimum paginae videntur spatium
>> occupare. Unde praesenti eas tantum, quae sunt Lydii modi
>> assumimus, quasdam supernas, quasdam subteriacentes. Et has
>> prout strictius fieri potuit decursatas, quae scilicet brevius
>> atque succinctius possunt affigi, easque usui praesentium
>> putamus sufficere.
>>
>> [GSI:118; text: Nete hyperbolaeon itaque habet I iota extensum
>> sic, Paranete hyperbolaeon [Pi] graecum extensum, Trite hyperbolaeon
>> Y simplex, Nete diezeugmenon N contractum, Paranete diezeugmenon
>> [Omega] quadratum, Trite diezeugmenon E simplex, Paramese [Pi]
>> graecum iacens, Nete synemmenon eadem, quae paranete diezeugmenon,
>> Paranete synemmenon eadem, quae trite diezeugmenon, Trite synemmenon
>> [Theta] graecum, Mese I simplex, Lichanosmeson M simplex,
>> Parypatemeson P [ro supra lin.] graecum simplex, Hypatemeson
>> C sigma graecum simplex, Lichanos hypaton F digamma simplex,
>> Parypate hypaton B beta simplex. Hypate hypaton [Gamma] gamma
>> simplex, Proslambanomenos [signum] dasian rectum, A, B, C, D, E,
>> F, G, V, [Pi], Y, N, O, E, [Theta], I, M, P, C, F, B, [Gamma]]
The TML webpage has a link at the end of this text to www.chtml.indiana.edu/tml/9th-11th/HUCHAR_TEXT.html, which is the illustration which goes with Hucbald's text. It shows a list of modified Greek letters, which is a subset of those used by Boethius, and what are apparently supposed to be Roman-letter equivalents. The illustration also shows explicitly the equation of _paranete synemmenon_ with _trite diezeugmenon_ and of _nete synemmenon_ with _paranete diezeugmenon_, which I mentioned in my post.
Babb 1978, p. 8-9, explains how Boethius used a pair of Greek symbols (one each from the so-called "vocal" and "instrumental" notation as transmitted by Alypius), and shows how Hucbald selected one Greek letter from each pair given by Boethius.
One other thing i should note: most scholars believe that the _enchiriadis_ treatises were written in the later 900s, but i feel fairly strongly that they are at least a century older.
The only cogent argument against my early dating is that the daseian notation of _enchiriadis_ seems to be a simplification of the notation system presented by Hucbald, who lived 840-930, in his treatise _de harmonica institutione_. apparently this is an early work by him ... list member Margo Schulter cites it as c.880 in Hexachords, solmization, and musica ficta.
Some scholars believe that he also wrote the _enchiriadis_ treatises, later in life; see: Catholic Encyclopedia: Hucbald of St-Amand.
In fact, one or both of the _enchiriadis_ treatises were long attributed to Hucbald, but then he was discredited, which is how it stood when i did most of my research on this period in music theory. now apparently he's back in.
Medieval music-theory is an attempt to amalgamate ancient Greek theory with the practice current during the Frankish era (c.700-1000).
Basically, the Frankish theorists set up a system where their 4 main modes were the ones which today we would call:
1. D E F G A B C 2. E F G A B C D 3. F G A B C D E 4. G A B C D E F (but they were usually less than 7 tones)
There was an auxillary group of 4 modes which used the same notes but had the "finals" (D, E, F, G) in the middle of the tessitura instead of at the bottom.
They simply used the Greek words _protos_ (1st), _deuteros_ (2nd), _tritos_ (3rd), and _tetrardos_ (4th) to name them, and called the main group "authentic" and the secondary group "plagal".
During the early 900s, Hucbald rearranged the Greek PIS by:
The _synemmenon_ (conjunct) tetrachord, which involved what we would today call "Bb", was still used and so named. The process of "mutation" was invented (actually, reinvented, since the Greeks used it too.) for melodies which shifted between the _superiores_ and _synemmenon_ tetrachords.
During the next century, the use of the Greek letters was replaced with the first seven letters of the Roman alphabet A B C D E F G, with the two different kinds of B ("round" and "square") used to denote the disjunct and conjunct tetrachords, respectively, above the _finales_.
Yes. It was Hucbald who created the link between the Byzantine octoechos and the Boethian modes. BTW, Boethius based his description of the modal system on Ptolemy.
> > Hucbald reorganized the whole pitch structure so that
> > the finals of the 4 main modes agreed with the most
> > often used modes in the chant repertoire, and it was
> > easy for him to do that by simply moving the _hestotes_
> > (fixed bounding notes of each tetrachord) down by a
> > whole-tone.
>
>
> Can you provide a comparison chart here showing the shift?
The essential feature of Hucbald's change is that the ascending intervallic structure of each tetrachord became t-s-t as in the pitches D-E-F-G, which were the finals of the four main Frankish modes.
.............................................. Greek .. Hucbald . notation / nete hyperbolaion .............................. a' .. g ...... V | | paranete hyperbolaion .......................... g ... f ...... Π | | trite hyperbolaion ............................. f ... e ...... Y + nete diezeugmenon .............................. e ... d ...... N | | paranete diezeugmenon . / nete synemmenon ...... d ... c ...... Ω | ....................... | | trite diezeugmenon .... | ...................... c ... b ...... E | ....................... | paranete synemmenon .. c ... bb...... E \ paramese .............. | ...................... b ... a ...... = ......................... | trite synemmenon ..... bb .. a ...... Θ / mese ...................\ mese ................. a ... G ...... I | | lichanos meson ................................. G ... F ...... M | | parhypate meson ................................ F ... E ...... P + hypate meson ................................... E ... D ...... C | | lichanos hypaton ............................... D ... C ...... F | | parhypate hypaton .............................. C ... B ...... B \ hypate hypaton ................................. B ... A ...... Γ .. proslambanomenos ............................... A ... G'...... f
REFERENCES
Barker, Andrew (ed.). 1989.
Bower, Calvin M. (ed., trans.). 1989.
Boethius, Anicius Manlius Severinus. c. 505.
Hucbald of St. Amand. c. 880.
E. de Coussemaker (ed.), Durand, Paris, 1866-1876.
www.chtml.indiana.edu/tml/9th-11th/HUCHAR_TEXT.html
manuscript: Einsiedeln Stiftsbibliotek / Codex 169 (468), p. 113-128
manuscript: Cambridge MS Gg.5.35, fol. 263r-272v (images 535 to 554)
manuscript: Brussels KBR 10078-95 (fee charged for copies in any form)
Joe Monzo & Ozan Yarman. 2005.
Warren Babb (trans.). 1978.
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