<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 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 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 href="mailto:nick@baragwanath.com">nick@baragwanath.com</a> <span dir="ltr"><<a href="mailto:nick@baragwanath.com" target="_blank">nick@baragwanath.com</a>></span> wrote:<br>
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<div><font face="Arial">Dear List,</font></div>
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<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?
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<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.
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<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.
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<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>
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<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 href="mailto:nicholas.baragwanath@nottingham.ac.uk" target="_blank"><font face="Arial">nicholas.baragwanath@nottingham.ac.uk</font></a></span></font></div>
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</blockquote></div><br><br clear="all"><br>-- <br><div dir="ltr"><div><div><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 href="mailto:jmckay@mozart.sc.edu" target="_blank">jmckay@mozart.sc.edu</a><br></div>
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