[Smt-talk] Scale degrees

Fri May 16 14:16:53 PDT 2014

Yes, where to draw the line?
I have a copy of Bartolomeo Ramis de Pareia - Musica Practica here from 
1482.
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.
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.
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.

Marcel de Velde
Zwolle, Netherlands
marcel at justintonation.com

> 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 
> <mailto:nick at baragwanath.com> <nick at baragwanath.com 
> <mailto: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 SECONDof
>     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
>     <mailto: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 <mailto:jmckay at mozart.sc.edu>
>
>
> _______________________________________________
> Smt-talk mailing list
> Smt-talk at lists.societymusictheory.org
> http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.societymusictheory.org/pipermail/smt-talk-societymusictheory.org/attachments/20140516/e2e8dc66/attachment-0002.htm>