Fw: [tuning] Re: Boethius modal system, chapter 15 of Book 4

Stupid yahoo messed up my table #@%$^&

> Hey there again!
>
> ----- Original Message -----
> From: "monz" <monz@tonalsoft.com>
> To: <tuning@yahoogroups.com>
> Sent: 16 Kas�m 2005 �ar�amba 23:23
> Subject: [tuning] Re: Boethius modal system, chapter 15 of Book 4
>
>
> > Hi Ozan and Hans,
> >
> >
> > --- In tuning@yahoogroups.com, <oyarman@o...> wrote:
> >
> >
> > [Ozan]
> > > I am suspecting whether he [Boethius] meant
> > > B C D E F G A b c d e f g a' b' instead?
> > > Boethius actually mentioned being in accord with the
> > > species of the consonance of the octave, and direct
> > > transposition is certainly not synonymous with his
> > > previous statement, modulation is.
> >
> >
> > Yes, upon further reflection, i think you're right.
> >
>
>
> Can you see my grin? :)))
>
>
> > In order to preserve the intervals of the octave-species,
> > and rotate the modes thru all forms without using any
> > flats or sharps in the nomenclature, the reference Hypodorian
> > mode must use either G or C as the reference pitch.
> > The example Ozan gaving using "natural pitches" was
> > based on C as the reference, but i think G is more
> > likely, as will become clear later.
> >
>
>
> Let's beg to differ on this, shall we?
>
>
> > This is interesting, because i've read some other analyses
> > of the modal system where the reference pitch was F.
> > In particular, i think i recall that Kathleen Schlesinger
> > based the whole modal system on Proslambanomenos as a low F.
> > But using G as the reference brings Boethius's system
> > exactly into agreement with the standard early medieval
> > gamut beginning on a low-G notated as the letter gamma.
> >
>
>
>
> If that be the case, the discovery belongs to Rauf Yekta. Please find his
> entry in French in the 1922 edition of the Lavignac Encyclopedia. There,
> under the article `Turquie`, not too far down, you will see that he
> explains:
>
>
..............Execution by Westerners..........Execution by Easterners

Proslambanomenos..............la..........................la
Hypate hypaton......................si..........................si
Parhypate hypaton................do (natural)..........do#
Lichanos hypaton...................re.........................re
Hypate meson........................mi........................mi
Parhypate meson...................fa (natural)..........fa#
Lichanos meson....................sol........................sol (natural)
Mese........................................la.........................la
Paramese...............................si..........................si
Trite diezeugmenon...............do (natural).........do#
Paranete diezeugmenon.......re.........................re
Nete diezeugmenon..............mi.........................mi
Trite hyperbolaion..................fa(natural)............fa#
Paranete hyperbolaion..........sol........................sol (natural)
Nete hyperbolaion..................la..........................la
>
>
> He then goes on to say that transposing the diatonic scale within the
octave
> over to Sol (G), we will find the Arezzian scale:
>
> G4 A B C D E F G5
>
> Whereby Yekta explains: rumor had it that Gui himself did not like the
minor
> scale La Si Do Re Mi Fa Sol La and added a Sol below and called it the
> hypoproslambanomenos which he notated with the letter Gamma. He says that
> this is the origin of the term "gamut" and also the origin of the faulty
> execution of Westerners. He comments that Alphonse Heegmann in his "Examen
> de la theorie musicale des Grecs" became almost aware of the situation
where
> he explicated that Guido made the A-proslambanomenos LA which he notated
> between the first and second lines of an F-cleffed staff. Equating
> proslambanomenos with LA, according to Yekta, is the single greatest
mistake
> made on this subject, because it was only necessary to equate
> proslambanomenos with SOL (G) for everything to fit together.
>
> But he then proceeds to ask himself: `why would Guido feel the need to add
a
> Gamma below if the existing Greek system was already major?`
>
> Perhaps, the answer lies with the faulty Hucbald interpretation of
Boethius.
>
> He also makes fun of the numerous mistakes that lead to this division
> between the East and the West, criticizes severely those accountable for
> this state of affairs and comments that even 5 volumes of the Lavignac
> encyclopedia would not suffice to review and analyze the entirety of the
> grave errors committed by those responsible. ROFL
>
>
> > This is fascinating, because while Boethius did use
> > Roman letters in his descriptions, they did not have
> > the same pitch-meaning as we use today, but rather were
> > simply labels for points along his arithmetic measurements.
> > The descriptions of the ancient Greeks were later labeled
> > with Roman letters using A as the name for Mese, and it
> > was Hucbald who shifted the whole system down a tone to G,
> > which brings his system in line with Boethius. Hmm...
> >
>
>
> Are you sure it was Hucbald? Yekta says it was done in Guido's time.
>
>
> > Since Boethius only gives a detailed explanation of
> > the first four modes in this chapter, and just dismisses
> > the rest of his explanation with "similarly for the rest",
> > it's impossible to know whether the reference pitch is
> > G or C, because both labels work for the first four modes.
> > I'd have to study the other chapters to see if this can
> > be resolved.
> >
>
>
> Please confer to my other reply for a detailed interpretation by myself.
>
>
> > In fact this is a very intriguing topic, because the
> > _music enchiriadis_ and _scholia enchiriadis_ treatises,
> > which i think date from the early 800's, use the unique
> > daseain notation to specify where the semitone should
> > be placed, and it too leaves unresolved the question
> > of whether we would label the reference pitch as G or C.
> > Similiarly, the next really influential theorist after
> > Boethius was Guido d'Arezzo, and he too used a similar
> > procedure.
> >
>
>
> He notated HYPOproslambanomenos with GAMMA according to Yekta. I know not
if
> this is true. What sayest thou?
>
>
> > The later "fasola" system also simplifies modal rotation
> > to using a reference tetrachord containing two tones and
> > one semitone, and this became the basis of American
> > "shape-note" notation which results in just-intonation
> > singing.
> >
> >
>
>
> Shape note?
>
>
> > So anyway, here are some relevant sections from Boethius
> > again, with the Latin and English together, and my revised
> > illustrative scales using both C and G as reference pitches.
> > I append numbers to the letters here, to bring the
> > illustrations into conformity with the standard MIDI
> > pitch nomenclature where C4 = middle-C and each
> > new octave numbering begins on C ascending.
> >
> >
>
> Ach! You should have used octave designator numbers just once per octave!
> Look at that clutter...
>
>
> > >> [Latin]
> > >> EX diapason igitur speciebus consonantiae existunt. qui
> > >> appellantur modi. quos eosdem tropos uel tonos nominant.
> > >>
> > >> [English - Bower]
> > >> From the species of the consonance of the diapason
> > >> arise what are called "modes". They are also called
> > >> "tropes" or "tones".
> >
> >
> > >> Has igitur constitutiones [[constitutiones]] si quis
> > >> totas faciat acutiores. uel in graues totas remittat:
> > >> secundum supradictas diapason consonantiae species
> > >> efficiet modos septem. quorum nomina sunt haec.
> > >> Hypodorius. hypofrigius. hypolidius. dorius. phygius
> > >> [phrygius corr. supra lin]. lidius. mixolidius.
> > >>
> > >> If these entire systems were made higher or lower in
> > >> accordance with the species of the consonance of the
> > >> diapason discussed above, this would bring about seven
> > >> modes, which are named Hypodorian, Hypophrygian,
> > >> Hypolydian, Dorian, Phrygian, Lydian, and Mixolydian.
> >
> >
> >
> > >> Horum uero sic ordo procedit.
> > >>
> > >> The arrangement of the modes proceeds in the following
> > >> manner.
> >
> >
> > >> Sit in diatonico genere uocum ordo dispositus a
> > >> proslambanomenon in netenhyperboleon. atque hic
> > >> sit hypodorius modus.
> > >>
> > >> Set out the succession of pitches in the diatonic genus
> > >> from the proslambanomenos to the nete hyperboleon. Let
> > >> this be the Hypodorian mode
> >
> > [G2 A2 B2 C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4] or
> > [C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5]
> >
>
>
> G according to Yekta
> C according to Oz.
>
>
> >
> > >> Si quis igitur proslambanomenon in acumen intendit
> > >> [intendat corr. supra lin.] tono hypatenque hypaton
> > >> eodem tono attenuet. caeterasque omnes tono faciat
> > >> acutiores: acutior totus ordo proueniat quam fuit
> > >> prius quam toni susciperet intensionem. Erit igitur
> > >> tota constitutio acutior effecta hypofrigius modus.
> > >>
> > >> If one were to raise the proslambanomenos by one tone,
> > >> and further raise the hypate hypaton by the same tone,
> > >> thereby making the whole disposition higher by a tone,
> > >> then the entire succession would turn out higher than it
> > >> was before it was raised by a tone. Thus this whole system,
> > >> having been made higher, forms the Hypophrygian mode.
> >
> > [A2 B2 C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4] or
> > [D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 D5]
> >
>
>
> Ditto.
>
>
> > The first version of this would be the "normal" system of
> > labeling, with "A" for proslambanomenos and mese.
> >
> >
> > >> [-f.87r-] Quod si in hypophrigio toni rursus intensionem
> > >> uoces acceperint. hypolidii modulatio nascitur.
> > >>
> > >> Now if the pitches of the Hypophrygian mode were similarly
> > >> raised by a tone, the collection of pitches for the
> > >> Hypolydian mode would be born.
> >
> > [B2 C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4] or
> > [E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 D5 E5]
> >
> >
>
>
> Ditto.
>
>
> > >> At si hypolidium quis semitonio intendat: dorium faciet.
> > >>
> > >> If someone raised the Hypolydian by a semitone,
> > >> he would make the Dorian
> >
> > [C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5] or
> > [F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 D5 E5 F5]
> >
> >
>
> Ditto.
>
>
> > >> Et in aliis quidem similis est in acumen intensionemque
> > >> processus;
> > >>
> > >> The progression to higher pitch is similar in the
> > >> other modes.
> >
> > So the whole system looks like this:
> >
>
>
> Hypodorian
>
> [C3 D E F G A B c4 d e f g a b c'5]
>
> or
>
> [G3 A B C D E F g4 a b c d e f g'5]
>
>
>
> Hypophrygian
>
> [D3 E F G A B C d4 e f g a b c' d'5]
>
> or
>
> [A3 B C D E F g a4 b c d e f g' a'5]
>
>
>
> Hypolydian
>
> [E3 F G A B C d e4 f g a b c' d' e'5]
>
> or
>
> [B3 C D E F g a b4 c d e f g' a' b'5]
>
>
>
> Dorian
>
> [F3 G A B C d e f4 g a b c' d' e' f'5]
>
> or
>
> [C4 D E F g a b c5 d e f g' a' b' c'6]
>
>
>
> Phrygian
>
> [G3 A B C d e f g4 a b c' d' e' f' g'5]
>
> or
>
> [D4 E F g a b c d5 e f g' a' b' c' d'6]
>
>
>
> Lydian
>
> [A3 B C d e f g a4 b c' d' e' f' g' a'5]
>
> or
>
> [E4 F g a b c d e5 f g' a' b' c' d' e'6]
>
>
>
> Mixolydian
>
> [B3 C d e f g a b4 c' d' e' f' g' a' b'5]
>
> or
>
> [F4 g a b c d e f5 g' a' b' c' d' e' f'6]
>
>
>
> > I have serious doubts if the Mixolydian mode was
> > really meant to illustrate the octave-species of
> > natural notes based on B, considering that the
> > tonic 5th is diminished instead of perfect, and
> > also considering the duplicity of B's which arose
> > later when Roman letters were applied to the system.
> >
>
>
> Why? Mixo means part Greek, part barbaric. Literally Mixolydian would mean
> `Barbaric Lydian`. What better mode to ascribe the tonic diminished fifth?
> Besides, your dissonant fifth lies with Hypolydian. Why should that be
more
> preferable? And look... here are your pitches:
>
>
> >
> > Thus, my current interpretation of Boethius's modal
> > system equates it to modern pitch notation as follows:
> >
> > G2 A2 B2 C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 hypodorian
> > A2 B2 C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 hypophrygian
> > B2 C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 hypolydian
> > C3 D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 dorian
> > D3 E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 D5 phrygian
> > E3 F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 D5 E5 lydian
> > F3 G3 A3 B3 C4 D4 E4 F4 G4 A4 B4 C5 D5 E5 F5 mixolydian
> >
> >
>
>
> G2 is just too low a pitch for Proslambanomenos, impossible for even
tenors
> to sing, while my C3 is just right.
>
> SNIPPED the rest.
>
> Cordially,
> Ozan
>