Score and audio files for fifthtone piece (c. 1600?)

Hello, everyone, and in response to some recent threads, I would say that
part of our present and future might involve creatively using "off the
shelf" tools for notating and playing music in a range of tuning systems.
Of course, many systems do require new approaches -- but sometimes there
is a not impossible meeting of the old and new.

An intriguing keyboard piece possibly from around 1600 appears in a
Portuguese manuscript (Coimbra Ms. Mus. 48) with symbols which Hoyle
Carpenter has persuasive interpreted as marks raising a note by a meantone
diesis or fifthtone of the kind described and embraced by Nicola Vicentino
(1555, 1561) and Fabio Colonna (1618). Here are some audio and score
files, the later in PostScript, PDF, and abc notation formats:

<http://www.bestii.com/~mschulter/Coimbra48.mp3>
<http://www.bestii.com/~mschulter/Coimbra48.ogg>
<http://www.bestii.com/~mschulter/Coimbra48.ps>
<http://www.bestii.com/~mschulter/Coimbra48.pdf>
<http://www.bestii.com/~mschulter/Coimbra48.abc>
<http://www.bestii.com/~mschulter/Coimbra48.mid>

In 1/4-comma meantone tuning, which I find very likely, a fifthtone is
often equal to the enharmonic diesis of 128:125 or about 41.06 cents --
with some smaller fifthtones equal to about 34.99 cents, these two
slightly unequal fifthtones making up a chromatic semitone of about 76.05
cents. In a mathematically precise 31-EDO, first described by Lemme Rossi
(1666) and Christian Huygens (e.g. 1691), each diesis or fifthtone is
equal to precisely 1/31 octave, or about 38.71 cents.

A problem, then and now, is how to notate these small fifthtone steps.
Both Vicentino and the anonymous composer or scribe in the Coimbra
manuscript use a symbol that raises a note by a fifthtone or diesis: a dot
above the note for Vicentino, and a sign something like a small "x" for
the Coimbra notator (and also interestingly, as Carpenter remarks, in a
discussion by Thomas Morley in 1597 about the enharmonic diesis). Colonna
has a kind of "half-sharp" sign for the diesis somewhat related to Coimbra
(and Morley).

In ASCII notation, Vicentino's dot (or the Coimbra "x") can be represented
easily as an asterisk (*). Thus the whole tone C-D can be divided into
five fifthtone steps in a complete 31-tone meantone: C-C*-C#-Db-Db*-D
(Vicentino-style), or C-C*-C#-C#*-Db*-D (one solution in Coimbra style).
The main difference is that Vicentino prefers to write C#-Db, and the
Coimbra manuscript to write C#-C#*, essentially equivalent notations for
C# and the note a fifthtone or diesis higher.

In seeking to make a score for the Coimbra fifthtone piece using abcm2ps,
a Linux utility available in many variations for a range of platforms, I
resolved the problem of representing fifthtone steps by using a staccato
mark as Vicentino's dot showing that a note is raised by a fifthtone --
with the distinction that Vicentino places the dot above the note, while
here it might go either above or below. Apart from this minor distinction,
and my use of the Coimbra style of spelling (e.g. C#* rather than Db),
abcm2ps can thus realize Vicentino's notation, applicable either to a
31-note cycle (or subset) of 1/4-comma meantone, or to a precise 31-EDO.

Another solution, by the way, would be to use double flats and sharps, as
I've seen done in some modern transcriptions: thus C-Dbb-C#-Db-Cx-D -- the
"x" here meaning a double sharp rather than the Coimbra fifthtone symbol.
In a style where the staccato dot might be in demand for its usual
meaning, this could be the best solution. I'm indebted to a member of this
group for an offline conversation pointing out to me this amenability of
31-note meantone (1/4-comma or 31-EDO) to conventional notation.

Let me add, as you can hear, that this is a very beautiful piece. While
Carpenter suggests a date around the third quarter of the 16th century,
the same general epoch as Vicentino's publications, the style of
dissonance treatment suggests to me something more around 1600, the epoch
of Colonna. In fact, one of Colonna's idioms for which he gives a musical
example, a "sliding of the voice" in fifthtones, occurs in this piece --
sometimes with fifthtone shifts producing fifths or fourths altered by a
diesis. Vicentino generally prefers that simultaneous fifths or fourths
remain perfect, although he states that any dissonance might be justified
in order aptly to express a text: here such altered intervals appear as
part of a colorful instrumental style.

On some small points my reading here varies from Carpenter: a "B#" in his
transcription at measure 27 (highest part) is here taken as B-natural
(my hunch, with the excuse that in more conventional 16th-century contexts
the sharp and natural symbols are sometimes interchangeable); at measure
39, Hoyle credibly suggests that the B-natural at the end of the bar in
the second to lowest voice might be only a placeholding symbol for the
following B* (postulating a convention that a note with a fifthtone
alteration must first be shown without such an alteration, e.g. B-B*).

Anyway, I'm pleased to present this keyboard piece in the
medieval/Renaissance Phrygian mode (E-E octave), noteworthy for its bold
beauty, with fifthtone steps only one aspect.

Peace and love,

Margo
mschulter@...

thanks for posting this , especially with score as i always like looking while listening.
The cadence sounds like a half cadence at the end even knowing it starts with a mode on e, a strange ending to your ear too? or do you think/know there is more that follows movement wise so a strongest cadence would not be desired

Margo Schulter wrote:

>
>An intriguing keyboard piece possibly from around 1600 appears in a
>Portuguese manuscript (Coimbra Ms. Mus. 48) with symbols which Hoyle
>Carpenter has persuasive interpreted as marks raising a note by a meantone
>diesis or fifthtone of the kind described and embraced by Nicola Vicentino
>(1555, 1561) and Fabio Colonna (1618). Here are some audio and score
>files, the later in PostScript, PDF, and abc notation formats:
>
><http://www.bestii.com/~mschulter/Coimbra48.mp3>
><http://www.bestii.com/~mschulter/Coimbra48.ogg>
><http://www.bestii.com/~mschulter/Coimbra48.ps>
><http://www.bestii.com/~mschulter/Coimbra48.pdf>
><http://www.bestii.com/~mschulter/Coimbra48.abc>
><http://www.bestii.com/~mschulter/Coimbra48.mid>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

> From: Kraig Grady <kraiggrady@...>
> Date: Wed Dec 7, 2005 1:31 am

> thanks for posting this , especially with score as i always like looking
> while listening.
> The cadence sounds like a half cadence at the end even knowing it
> starts with a mode on e, a strange ending to your ear too? or do you
> think/know there is more that follows movement wise so a strongest
> cadence would not be desired

Hello, there, Kraig, and this is a very interesting question: personally I
find this type of cadence in an E mode satisfyingly conclusive, but not
quite 30 years ago a skilled harpsichord teacher remarked when I played
this kind of close that he wanted it to be followed by A. I can say that I
routinely use it as a final cadence myself, and try to explain the musical
cues I tend to follow, some of them which might be rather specific to a
middle to late 16th-century style (or an early 17th-century style, since
this piece might be from the era right around 1600).

First of all, as your comments suggest, there _is_ a potential and
often creative ambiguity in the modal system, since A is the
"confinal" or alternative focus of lots of phrases and cadences in an
E mode (specifically the plagal form of the mode or Hypo-Phrygrian,
with a typical range of B-E-B, with the final or resting note E in the
middle of the octave range). At the same time, E is the confinal for
an A or Aeolian mode (more specifically the authentic form with an
octave built above the final, A-E-A).

Thus we have the question: is E pulling toward a final of A, or A toward a
final of E? In this piece, I'm satisfied with the latter answer. One cue
is the use of major or minor thirds above the bass in vertical sonorities,
the former more conclusive in Renaissance/Manneristic music evidently
starting sometime around 1520-1530 (e.g. Pietro Aaron).

Thus in a final cadence from E to A in the bass, we'd expect the
concluding A sonority to have a major third (at or close to 4:5:6 in
either JI or, as here, in meantone). I use C4 as middle C:

G#4 A4
E4 E4
B3 C#4
E3 A2

(By the way, note the near-ideal spacing from Zarlino's point of view,
who says that we should seek to follow the order of the "sonorous
numbers," with the major third ideally spaced as a 17th at 5:1, and
next most harmoniously as a 5:2 tenth rather than a 5:4 third.)

Anyway, the final cadence from A to E generally has the first third
above the bass minor, and the second major, lending more finality to
the E.

A4 G#4
E4 E4
C4 B3
A2 E3

In some ways, these two final cadences look almost "time-reversed"
versions of each other, but the minor third above A in the second
example is the notable asymmetry.

However, to say that I find this kind of E cadence satisfyingly final
doesn't mean that it couldn't -- and isn't -- often used as an
internal cadence in a piece on A; or vice versa, since the cadence on
A is very common in pieces concluding on E. There is a certain poised
balance: it could go either way.

Thank you for raising an intriguing musical issue, and your question
raises another issue: given E-A and A-E as co-equal options, what
clues in this piece or others might point toward one or the other
expectation? This is a neat invitation to consider the piece more
carefully, and others, in search of possible insights.

I'm leaving for Los Angeles in a few hours, but wanted first to post a
quick response. It's curious to recall after all these years that your
reaction is the same as that of another accomplished keyboardist -- and to
reflect that back then (c. 1977) I little idea what terms such as
"meantone" meant, although discerning harpsichordists knew better.

Peace and love,

Margo
mschulter@...

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@c...>
wrote:

> An intriguing keyboard piece possibly from around 1600 appears in a
> Portuguese manuscript (Coimbra Ms. Mus. 48) with symbols which Hoyle
> Carpenter has persuasive interpreted as marks raising a note by a
meantone
> diesis or fifthtone of the kind described and embraced by Nicola
Vicentino
> (1555, 1561) and Fabio Colonna (1618).

Would you mind my using this information in a Wikipedia article?
Someone needs to write one on 31 equal temperament, (and another on
1/4 comma meantone), and if no one else does I will.

Links to the Coimbra files would also be nice.

On Tue, 6 Dec 2005, Margo Schulter wrote:

> An intriguing keyboard piece possibly from around 1600 appears in a
> Portuguese manuscript (Coimbra Ms. Mus. 48) with symbols which Hoyle
> Carpenter has persuasive interpreted as marks raising a note by a meantone
> diesis or fifthtone of the kind described and embraced by Nicola Vicentino
> (1555, 1561) and Fabio Colonna (1618). Here are some audio and score
> files, the later in PostScript, PDF, and abc notation formats:

Hi Margo and thanks, this is very interesting. Three questions for you: where is the Hoyle Carpenter publication about the fifthtones? Where does Morley talk about the diesis notation (surely not in A Plaine and Easie Introduction...)? And, about the tuning: why are some of the G-D fifths noticeably more impure than other fifths?

Best wishes,

Jon Wild

--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@c...>
wrote:
In a mathematically precise 31-EDO, first described by Lemme Rossi
> (1666) and Christian Huygens (e.g. 1691), each diesis or fifthtone is
> equal to precisely 1/31 octave, or about 38.71 cents.

Would you object to my making a 31-et version for use as an example on

http://en.wikipedia.org/wiki/31_equal_temperament

Also, do you know where I can get Vicentino examples?

from his book
ancient music adapted to modern practice .
hasn't margo already made some samples of these?
otherwise i could scan and send, but not for a few days

Gene Ward Smith wrote:

>--- In MakeMicroMusic@yahoogroups.com, Margo Schulter <mschulter@c...>
>wrote:
>In a mathematically precise 31-EDO, first described by Lemme Rossi
> >
>>(1666) and Christian Huygens (e.g. 1691), each diesis or fifthtone is
>>equal to precisely 1/31 octave, or about 38.71 cents.
>> >>
>
>Would you object to my making a 31-et version for use as an example on >
>http://en.wikipedia.org/wiki/31_equal_temperament
>
>Also, do you know where I can get Vicentino examples?
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In MakeMicroMusic@yahoogroups.com, Kraig Grady <kraiggrady@a...>
wrote:
>
> from his book
> ancient music adapted to modern practice .
> hasn't margo already made some samples of these?
> otherwise i could scan and send, but not for a few days

I was asking Margo if I could change the 1/4-comma meantone example
she gave to 31-et, which isn't much of a change but which presumably
requires permission. But any other examples people can dig up would be
great.

Due to a recent addition to Scala, such changes should be easy.