Boethius-Hucbald connection (was:The C-Fb-G major triad: Pythag-Just tuning)

Yesterday, I wrote:

> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, December 03, 2001 4:04 PM
> Subject: Re: [tuning] : The C-Fb-G major triad: Pythag-Just tuning.2
>
>
> In my unpublished paper "An Examination of a Possible 5-Limit System
> of Boethius" (1997), the conclusion of which appears in my book
> _JustMusic: A New Harmony_, I examine the Greek-letter notation
> used by Boethius to describe the modes.
>
> ...
>
> 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.
>
> ...
>
> REFERENCES
> ----------
>
> ...
>
> Bower, Calvin M. (ed., trans.). 1989.
> _Boethius: "Fundamentals of Music"_.
> Music Theory Translation Series, ed. Claude Palisca.
> Yale University press, new Haven & London.
> ISBN: 0-300-03943-3
> L.o.C.#: MT5.5.B613
>
>
> Boethius, Anicius Manlius Severinus. c. 505.
> in Friedlein, Godofredus (ed.). 1867.
> _Boethii De institutione musica libri quinque_.
> B. G. Teubner, Leipzig.
> http://www.music.indiana.edu/tml/6th-8th/BOEMUS4_TEXT.html
>
>
> Hucbald of St. Amand. c. 880.
> _De harmonica institutione_.
> E. de Coussemaker (ed.), Durand, Paris, 1866-1876.
> http://www.music.indiana.edu/tml/9th-11th/HUCHAR_TEXT.html
>
>
> Warren Babb (trans.). 1978.
> _Hucbald, Guido, and John on music : three medieval treatises_.
> Edited, with introductions, by Claude V. Palisca;
> index of chants by Alejandro Enrique Planchart.
> New Haven : Yale University Press.
> (Music Theory Translation Series, 3)
> ISBN: 0300020406
> L.o.C.#: ML170 .H82

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
http://www.music.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
http://www.music.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
<http://www.music.indiana.edu/tml/9th-11th/HUCHAR_06GF.gif>,
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.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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