[Smt-talk] Scale degrees

[Ildar Khannanov]

Dear List,

in addition to very informative references to Western European treatises, it could be of interest to observe what Nikola Diletsky in his Idea Musikiiskoi Grammatiki (1679) used for scale steps. His book is a very peculiar mélange of theoretical approaches. For the scale steps he uses Guidonian solmizatioin notation (!) and the diagram of the hand, but his musical examples reveal tonal structure of emerging Russian homophonic-harmonic texture. The hexachordal notation of pitches is related in his system not to three types of hexachords, but to three clefs, used at the time. The notation of each pitch with Latin letter and two or three solfege syllables here means something entirely different from the Guidonian system. It is not very clearly expressed, but Diletsky implies that in aLaRe the la "goes down" and the re "goes up." This has lead Yuri Khoopov to an analogy with tonal-harmonic function, a kind of orientation and directionality within the
 modal framework. He called this one "modal functions of the scale steps."

Diletsky clearly defines major and minor key, major and minor triads (Ut, Mi, Sol and re, fa, la (!)), and provides a beautiful circular diagram of the circle of fifth, with the enumeration of each key with the  Arabic numbers, from 1-12. 


Later in his text he provides a kind of specie counterpoint concept of his own.

The origin of his concept is dual, Russian and Polish (perhaps, related to Catholic tradition in some way).

In all, a very interesting eclectic concept that defies traditional periodization.

Best wishes,

Ildar Khannanov
Peabody Institute, Johns Hopkins University
Solfeggio7 at yahoo.com
On Friday, May 16, 2014 4:02 PM, John Z McKay <jmckay at mozart.sc.edu> wrote:
  


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 FIRSTof 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 
>
> 
>
> 
>
> 
>
>   


-- 

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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