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<font face="Calibri">The initial question, unless I am mistaken,
concerned the use of numerals for the bass notes – more
specifically as supporting harmonies. Numbering the degrees of the
scale is a somewhat different matter, but quite interesting
nevertheless.<br>
<br>
What is interesting here is to see when the numbering (letters of
the alphabet also may count as numbers) was made to cycle at the
octave.<br>
– Greek instrumental notation at times made use of the first seven
letters of the alphabet, repeating the same letters turned around
for the second (and possibly the third) octave.<br>
– Boethius and others made use of alphabets without limitation,
i.e. without cycling at any interval.<br>
– Between Hucbald and the pseudo Odo of Cluny, the notation often
was tetrachordal, i.e. made use of only four numbers, or letters,
or names; this is the origin of hexachordal solmisation.<br>
– Odo, <i>c</i>1100, apparently was the first medieval author to
suggest the notation with seven letters, cycling at the octave,
which is still in use today, and which for a long time was in use
in parallel with the tetrachordal/hexachordal naming of the
degrees.<br>
<br>
Ramos de Pareja is among those who proposed a solmisation system
covering the octave, in eight syllables instead of seven, <i>psal-li-tur
per vo-ces is-tas</i> ("one sings with these syllables"), with <i>tas</i>
denoting the same note as <i>psal</i>, but one octave higher (the
vowel <i>a</i> was intended to convey some idea of their
identity). Mersenne, I think, similarly proposed (among many other
systems) <i>ut re mi fa sol la si dut</i>, where <i>dut</i>
denoted that it was the high octave.<br>
Ramos started from F because that was the normal lower limit
of organ keyboards by the end of the 15th century, and the normal
extension of the musical system, one degree lower than the
original Gamma of Odo. However, he numbers the degrees in various
ways, once at least I think in the order of the cycle of fiths:
1=F, 2=C, 3=G, 4=D, etc.<br>
<br>
The numbering of the degrees of the rule of the octave is similar
to numbering any scale degree; it obviously concerns the bass,
though – but not yet the fundamental bass, it does not consider
inversions. The use of Roman numerals to denote the roots of the
chords originates with Georg Joseph Vogler, was popularized by
Gottfried Weber and became a characteristic Viennese technique
with Simon Sechter.<b></b><br>
<br>
Nicolas Meeùs<br>
Université Paris-Sorbonne (emeritus)<br>
<br>
<br>
</font>
<div class="moz-cite-prefix">Le 16/05/2014 23:16, Marcel de Velde a
écrit :<br>
</div>
<blockquote cite="mid:53768045.9080302@justintonation.com"
type="cite">
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<br>
<div class="moz-cite-prefix">Yes, where to draw the line?<br>
I have a copy of Bartolomeo Ramis de Pareia - Musica Practica
here from 1482.<br>
While he uses a letter system and ut, re, mi fa, sol, la and
even a finger bone system to lay out the tones etc. he will also
refer to "the third tone" of the scale, or the seventh tone,
eight tone (referring to the octave), 14th tone etc. throughout
the book. And later in his book he has a diagram of 22 positions
where the 1 begins on F.<br>
1 F, 2, G, 3 A, 4 B, 5 c, 6 d, 7 e, 8 f, 9 g, etc where certain
tones can be raised or lowered. <br>
I don't have any older books, but it seems likely that these
kinds of things have been done before that. Boethius or one of
the old Greeks? Ramis himself also refers to several old books
and tells of how the older theorists held numbers in special
regard and linking them to the order of the planets and various
other things.<br>
<br>
Marcel de Velde<br>
Zwolle, Netherlands<br>
<a moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:marcel@justintonation.com">marcel@justintonation.com</a><br>
<br>
<br>
</div>
<blockquote
cite="mid:CAPNT_sLyhACOtw3NCe=o4NapK15PEWLPYUOH9nn8KeHqdePf6A@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>
<div>
<div>
<div>
<div>
<div>
<div>Dear Nick et al., <br>
<br>
</div>
Perhaps this is addressing a broader question than
Nick originally asked, but if we are concerned
about the earliest uses of numerical notation to
describe the seven notes of the scale (and not
necessarily with attached "functional" meaning or
specifically having to do with rule of the octave
harmonizations), then there are earlier uses than
the 18th century.<br>
<br>
</div>
The first extensive system that I'm aware of where
any note of the scale could be "1" is in Athanasius
Kircher's "Musurgia universalis" (1650), where
Kircher uses the numbers 1-8 (where 8 and 1 are
basically interchangable) to number the notes of the
scale in any mode. He provides tables for his
12-mode system showing how to convert between the
numbers and notes (including common accidentals in
each mode). (See volume II, p. 51.) The
accidentals don't make a lot of sense in some of the
modes -- I won't bother to try to explain what I
think he was doing -- but the basic idea of
numbering scale degrees as 1-8 is clearly present.
(For example, in many of the minor-ish modes, he
calls for flatting 6 and raising 7.)<br>
<br>
In any case, he uses this system in dozens of tables
to illustrate four-part composition. See, for
example: <a moz-do-not-send="true"
href="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FWFCRQUZK%2Fpageimg&mode=imagepath&pn=68"
target="_blank">http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FWFCRQUZK%2Fpageimg&mode=imagepath&pn=68</a><br>
</div>
<div><br>
</div>
However, Kircher is not the first to use this idea,
and I believe I've seen it in a few earlier Jesuit
treatises in particular. For example, Antoine
Parran's "Traité de la musique théorique et pratique"
(1639) has examples of his "Pratique de la Composition
par nombres Arithmetiques." He explains it thus:
"Pour signifier et exprimer en chaque partie, Vt, ré,
mi, fa, sol, la, nous mettons 1, 2, 3, 4, 5, 6: et
pour monter plus haut adjouterons 7 et puis 8. sera le
Diapason contre l'vnité" (p. 74).<br>
<br>
</div>
See the example from p. 77 in this image: <a
moz-do-not-send="true"
href="http://www.chmtl.indiana.edu/tfm/17th/PARTRA_24GF.gif"
target="_blank">http://www.chmtl.indiana.edu/tfm/17th/PARTRA_24GF.gif</a><br>
<br>
</div>
There may also be earlier sources than Parran. But from
his description, he may intend to limit this numerical
scheme to notes corresponding to hexachords beginning on
Ut, which would not allow it to be as movable as Kircher's
method (and thus perhaps is not yet as developed an idea
of "scale degree").<br>
<br>
</div>
Lastly, I would note that the earliest use of the numbers
1-8 for anything resembling this idea is probably in Spanish
tablature of the late 1500s and early 1600s (see description
and examples in Apel's notation book). However, I believe
this was basically an octave-repeating system where the
"white notes" were simply labeled 1-8, and other signs were
used for octave designations. So these weren't really
"scale degrees," but rather alternative designations for the
notes beginning on C. (But perhaps someone else knows more
about this -- I haven't really looked at these sources.)<br>
<br>
</div>
There may have been earlier applications of Roman numerals
describing the scale, but this is the first one I know of
which employs Arabic figures.<br>
<div><br>
</div>
<div>All best,<br>
</div>
<div>-John<br>
<br>
</div>
<div>---<br>
</div>
<div>John McKay<br>
</div>
<div>Assistant Professor<br>
</div>
<div>University of South Carolina School of Music<br>
</div>
<div>
<div>
<div>
<div>
<div>
<div><br>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote">On Thu, May 15, 2014 at 10:11 AM, <a
moz-do-not-send="true" href="mailto:nick@baragwanath.com">nick@baragwanath.com</a>
<span dir="ltr"><<a moz-do-not-send="true"
href="mailto:nick@baragwanath.com" target="_blank">nick@baragwanath.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr">
<div dir="ltr" style="font-family:'Calibri','Segoe
UI','Meiryo','Microsoft YaHei UI','Microsoft JhengHei
UI','Malgun Gothic','sans-serif';font-size:12pt">
<div><font face="Arial">Dear List,</font></div>
<div><br>
</div>
<div><font face="Arial"><font face="Arial">does anyone
know who was the first theorist to number the
scale (especially in the bass) from 1 to 7? </font></font></div>
<div><br>
</div>
<div><font face="Arial"><font face="Arial">This is a
mainstay of partimento rules, as in ‘add a 3rd
and a 5th to the FIRST</font><em><font
face="Arial"> </font></em><font face="Arial">of
the scale, add a 3rd and a 6th to the SECOND</font><font
face="Arial"> of the scale, etc.’ It
remains fundamental to modern approaches to
tonality. </font></font></div>
<div><br>
</div>
<div><font face="Arial Regular"><font face="Arial">Although
a seven-note scale is implicit in the modal
system, in counting intervals in counterpoint,
and in the French seven-note solfa system, I
have not been able to find any occurrences
earlier than about 1750. Numbered scales
are commonly found in late 18th-century sources,
such as </font><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">Fenaroli (1775), Paisiello
(1782), Azopardi (1786), and of course Vogler.
But neither A. Scarlatti nor Durante numbered
the notes of the scale. They used a Guidonian
system which is incompatible with the notion
of seven scale degrees. </font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"></span></font><br>
</div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">Could scale degrees be a late
18th-century invention? </font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">Private responses are welcome. </font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"></span></font><br>
</div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">Nick Baragwanath</font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">Associate Professor in Music</font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">University of Nottingham</font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">University Park,</font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><font
face="Arial">Nottingham, NG7 2RD, UK</font></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"><a
moz-do-not-send="true"
href="mailto:nicholas.baragwanath@nottingham.ac.uk"
target="_blank"><font face="Arial">nicholas.baragwanath@nottingham.ac.uk</font></a></span></font></div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"></span></font><br>
</div>
<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New
Roman","serif";font-size:12pt"></span></font><br>
</div>
<div><br>
</div>
<div><br>
</div>
</div>
</div>
</blockquote>
</div>
<br>
<br clear="all">
<br>
-- <br>
<div dir="ltr">
<div>
<div>
<div>
<div>
<div>John Z. McKay, Ph.D.<br>
</div>
Assistant Professor of Music Theory<br>
</div>
University of South Carolina School of Music<br>
</div>
813 Assembly Street<br>
</div>
Columbia, SC 29208<br>
</div>
<a moz-do-not-send="true" href="mailto:jmckay@mozart.sc.edu"
target="_blank">jmckay@mozart.sc.edu</a><br>
</div>
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