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<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 class="moz-txt-link-abbreviated" href="mailto:marcel@justintonation.com">marcel@justintonation.com</a><br>
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<div>Dear Nick et al., <br>
<br>
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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>
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<div><br>
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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>
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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>
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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>
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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>
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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>
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<div>All best,<br>
</div>
<div>-John<br>
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<div>---<br>
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<div>John McKay<br>
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<div>Assistant Professor<br>
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<div>University of South Carolina School of Music<br>
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<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>
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.8ex;border-left:1px #ccc solid;padding-left:1ex">
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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>
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<div><font face="Arial Regular"><span
style="line-height:115%;font-family:"Times
New Roman","serif";font-size:12pt"></span></font><br>
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-- <br>
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<div>John Z. McKay, Ph.D.<br>
</div>
Assistant Professor of Music Theory<br>
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University of South Carolina School of Music<br>
</div>
813 Assembly Street<br>
</div>
Columbia, SC 29208<br>
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<a moz-do-not-send="true" href="mailto:jmckay@mozart.sc.edu"
target="_blank">jmckay@mozart.sc.edu</a><br>
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