[Smt-talk] Scale degrees

[John Z McKay]

Dear Nick et al.,

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.

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.)

In any case, he uses this system in dozens of tables to illustrate
four-part composition.  See, for example:
http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=%2Fpermanent%2Flibrary%2FWFCRQUZK%2Fpageimg&mode=imagepath&pn=68

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).

See the example from p. 77 in this image:
http://www.chmtl.indiana.edu/tfm/17th/PARTRA_24GF.gif

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").

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.)

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.

All best,
-John

---
John McKay
Assistant Professor
University of South Carolina School of Music



On Thu, May 15, 2014 at 10:11 AM, nick at baragwanath.com <nick at baragwanath.com
> wrote:

>  Dear List,
>
>  does anyone know who was the first theorist to number the scale
> (especially in the bass) from 1 to 7?
>
>  This is a mainstay of partimento rules, as in ‘add a 3rd and a 5th to
> the FIRST of the scale, add a 3rd and a 6th to the SECOND of the scale,
> etc.’  It remains fundamental to modern approaches to tonality.
>
>  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 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.
>
>  Could scale degrees be a late 18th-century invention?
> Private responses are welcome.
>
>  Nick Baragwanath
> Associate Professor in Music
> University of Nottingham
> University Park,
> Nottingham, NG7 2RD, UK
> nicholas.baragwanath at nottingham.ac.uk
>
>
>
>
>


-- 
John Z. McKay, Ph.D.
Assistant Professor of Music Theory
University of South Carolina School of Music
813 Assembly Street
Columbia, SC  29208
jmckay at mozart.sc.edu
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