[Smt-talk] Scale degrees
Nicolas Meeùs
nicolas.meeus at scarlet.be
Sun May 18 15:01:44 PDT 2014
The initial question, unless I am mistaken, concerned the use of
numerals for the bass notes -- more specifically as supporting
harmonies. Numbering the degrees of the scale is a somewhat different
matter, but quite interesting nevertheless.
What is interesting here is to see when the numbering (letters of the
alphabet also may count as numbers) was made to cycle at the octave.
-- Greek instrumental notation at times made use of the first seven
letters of the alphabet, repeating the same letters turned around for
the second (and possibly the third) octave.
-- Boethius and others made use of alphabets without limitation, i.e.
without cycling at any interval.
-- Between Hucbald and the pseudo Odo of Cluny, the notation often was
tetrachordal, i.e. made use of only four numbers, or letters, or names;
this is the origin of hexachordal solmisation.
-- Odo, /c/1100, apparently was the first medieval author to suggest the
notation with seven letters, cycling at the octave, which is still in
use today, and which for a long time was in use in parallel with the
tetrachordal/hexachordal naming of the degrees.
Ramos de Pareja is among those who proposed a solmisation system
covering the octave, in eight syllables instead of seven, /psal-li-tur
per vo-ces is-tas/ ("one sings with these syllables"), with /tas/
denoting the same note as /psal/, but one octave higher (the vowel /a/
was intended to convey some idea of their identity). Mersenne, I think,
similarly proposed (among many other systems) /ut re mi fa sol la si
dut/, where /dut/ denoted that it was the high octave.
Ramos started from F because that was the normal lower limit of
organ keyboards by the end of the 15th century, and the normal extension
of the musical system, one degree lower than the original Gamma of Odo.
However, he numbers the degrees in various ways, once at least I think
in the order of the cycle of fiths: 1=F, 2=C, 3=G, 4=D, etc.
The numbering of the degrees of the rule of the octave is similar to
numbering any scale degree; it obviously concerns the bass, though --
but not yet the fundamental bass, it does not consider inversions. The
use of Roman numerals to denote the roots of the chords originates with
Georg Joseph Vogler, was popularized by Gottfried Weber and became a
characteristic Viennese technique with Simon Sechter.**
Nicolas Meeùs
Université Paris-Sorbonne (emeritus)
Le 16/05/2014 23:16, Marcel de Velde a écrit :
>
> 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>
>>
>>
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