Galliard's major and minor tones

It is useful to know about the Galliard translation ... very useful
indeed. Those nice big fold-out tables easily disprove the supposition
that any meantone system was a standard model of scales for
non-keyboard musicians. They have major and minor t o n e s !

Actually, my university library website has access to an online
version. I have uploaded a few pages here:
/tuning/files/sphaerenklang/Galliard-Tosi/

The relevant passages of original text go more or less as I expected.

Galliard also supplies copious footnotes, particularly on the matter
of the Appoggiatura. He seems to have thought that Tosi had not given
a particularly clear explanation (p.32), and to have fallen into
'perplexity' (p.36) in trying to explain the reason why the
appoggiatura has not full liberty to proceed by any semitone whatsoever.

Galliard's footnotes give a clear explanation of the difference
between 'major' and 'minor' semitones: the former are between notes of
different letter names (ie A and B) and occupying a line and a space;
the latter are between notes of the same name (ie C and C#) and
occupying the same line or space. Galliard does not say anything about
the melodic size of the semitones: the distinction is quite
independent of how they are tuned. (He did not give any footnote to
the previous assertion that they are composed of 5 and 4, or 4 and 3,
commas.)

In the footnotes and some additional illustrations, Galliard refers to
'major and minor tones' - for example his scale of C major has a major
tone at C-D and a minor at D-E; his scale of D Dorian has a major tone
at D-E and a minor tone at F-G (Fig.1).

Now, from whatever source Galliard got his theory, its content cannot
be anything other than a JI scale with 9:8 and 10:9 tones!

Isn't it strange that, if Tosi had meant to refer to or describe a
particular meantone tempered scale, even his translator should be
completely unaware of this, and instead take a JI model of the scale
as his reference?

As we know, it is likely that early 18th century England was heavily
populated by meantone-tuned keyboard instruments in which there were
no major or minor tones. But Gaillard encounters no 'cognitive
dissonance' whatever in quoting a theory in which the tones are
distinct, and take different positions in the scale depending on the
key of the music (cf. Cavallo's violinists)... in fact, a thoroughly
adaptive and just type of scale.

If Tosi was really referring to a commonly known and used sixth-comma
meantone model of intonation, why then is Galliard referring to a
completely different and in many ways contradictory model?

~~~T~~~

All well said, and those are important points.

As for why Galliard screwed up by gratuitously explaining a scale
system of naturals that is at odds with the source he's translating,
who knows. (If Tosi really had understood, or taken as important,
any system that has differently sized Ut-Re vs Re-Mi, or Fa-Sol vs
Sol-La, as shown in Galliard's plate 1, wouldn't he have found some
way to say so? But no, Tosi's pedagogical focus for melodic scale
intonation was only on semitones, not any distinction between two
differently-sized *tones* that a student or teacher should take pains
to understand, hear, or perform.)

It's perhaps important that we keep some chronology in mind here.
Tosi wasn't around anymore to offer an opinion about the translation
or explication of his work.

1723 Tosi's Italian original is published, with Tosi aged 68 or 69,
as an essay of the wisdom from his long career as teacher. And his
book is written to teachers, not directly to students; it's about how
to *teach* the musical principles important to fine musicianship.

1732 Tosi dies, aged 87 or 88.

1742 Galliard and his publisher Wilcox issue their English
translation, and it goes into at least a 1743 second edition as well.

1757 Agricola does a published German translation.

1774 there is a French translation.

1967 Galliard's English version is republished in London.

=====

Translators and reviewers screwing up by incorrectly amplifying the
source they're reporting upon, or inserting their own competing
premises into it, consciously/deliberately or not? It happens.

The most recent example of this that I've seen is the review of Ross
Duffin's book that is published in the current issue of _Early
Music_. The reviewer, who really should know better and who
shouldn't use straw-man arguments against the piece he's reviewing,
mistakenly attributes to (and affirms/congratulates!) Duffin and his
book something that Duffin not only didn't say, but which is also
technically wrong about the 55-division system and its reason for
being. The reviewer asserts that the 55-division has two different
types of tones, of 9 commas and 8 commas, which are somehow supposed
to correspond to (or approximate) the 9:8 and 10:9 tones making up a
5:4 in just intonation. And that's poppycock, for several reasons:

- The 8-comma "tone" in the 55-division is not even a musical tone at
all, for use in any tonal music, but rather it would be a doubly-
augmented unison (such as stepping directly from Ab to A#).

- The 9-comma tone in the 55-division is not some approximation of
*either* the 9:8 or 10:9. It's its own thing. It's an all-purpose
tone, of uniform size for all occasions. It happens to split an 18-
comma major 3rd exactly down the middle, but that doesn't have
anything to do with a 5:4 interval either.

- If things are being made up about the existence of some 8-comma
tone (and blamed upon Duffin, which is silly!), shouldn't things also
be made up about a 10-comma tone? An example would be G# to Bb, 10
commas. That's not a tone. It's a diminished minor 3rd. Unlike the
8-comma chimera, this one might actually come up (albeit rarely) in
18th century music, but the context isn't diatonic motion in any
normal scale. It's something like a Neapolitan cadence into A minor:
D-D-F-Bb, E-B-E-G#, A-C-E-A. Top voice takes a 10-comma step down
from Bb to G#, and then a five-comma step up to A. But again, this
has nothing to do with a 9:8, 10:9, or 5:4 interval, none of which
exist (or are even approximated) in the 55-division system.

Well, here's what that paragraph says in the review, in all its
splendor mis-representing Duffin's book, and mis-representing the 55-
division, along with a patronizing tone against Duffin (both in this
paragraph, and even more so elsewhere in the review):

"Although Duffin presents an interesting and useful selection of
historical evidence, I find his attitude to the historical material
is insufficiently critical and that this lack of discrimination
undermines even his main conclusion and advice to musicians. His
main claim rests on an already historical misinterpretation of the
division of the octave into 55 equal parts, an equal temperament of
55 steps (55-ET: Duffin calls it 'extended meantone', because of
certain resemblances to a variant of standard meantone temperament).
The older music theory defined a chromatic semitone as comprising
four 'commas' and the (larger) diatonic semitone as comprising five.
The octave, containing seven diatonic semitones and five chromatic
ones, must then consist of 55 commas, and Duffin correctly points out
that two different whole tones result: a major whole tone (ratio 9:8)
comprising nine 'commas', and a minor whole tone (10:9) consisting of
eight such commas. Both whole tones together form the pure major
3rd, 5:4, so crucial for harmony." (_Early Music_ August 2007, p453,
left column)

Make up something that directly DISAGREES with the model being
presented, congratulate the book's author on something he DIDN'T say
about the model, mis-represent the model itself as having an aim
incompatible with itself, and then accuse the book's author of being
insufficiently critical with the material? S t r a w - m a n !

Brad Lehman

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> It is useful to know about the Galliard translation ... very useful
> indeed. Those nice big fold-out tables easily disprove the
supposition
> that any meantone system was a standard model of scales for
> non-keyboard musicians. They have major and minor t o n e s !
>
> Actually, my university library website has access to an online
> version. I have uploaded a few pages here:
>
/tuning/files/sphaerenklang/Gallia
rd-Tosi/
>
> The relevant passages of original text go more or less as I
expected.
>
> Galliard also supplies copious footnotes, particularly on the matter
> of the Appoggiatura. He seems to have thought that Tosi had not
given
> a particularly clear explanation (p.32), and to have fallen into
> 'perplexity' (p.36) in trying to explain the reason why the
> appoggiatura has not full liberty to proceed by any semitone
whatsoever.
>
> Galliard's footnotes give a clear explanation of the difference
> between 'major' and 'minor' semitones: the former are between notes
of
> different letter names (ie A and B) and occupying a line and a
space;
> the latter are between notes of the same name (ie C and C#) and
> occupying the same line or space. Galliard does not say anything
about
> the melodic size of the semitones: the distinction is quite
> independent of how they are tuned. (He did not give any footnote to
> the previous assertion that they are composed of 5 and 4, or 4 and
3,
> commas.)
>
> In the footnotes and some additional illustrations, Galliard refers
to
> 'major and minor tones' - for example his scale of C major has a
major
> tone at C-D and a minor at D-E; his scale of D Dorian has a major
tone
> at D-E and a minor tone at F-G (Fig.1).
>
> Now, from whatever source Galliard got his theory, its content
cannot
> be anything other than a JI scale with 9:8 and 10:9 tones!
>
> Isn't it strange that, if Tosi had meant to refer to or describe a
> particular meantone tempered scale, even his translator should be
> completely unaware of this, and instead take a JI model of the scale
> as his reference?
>
> As we know, it is likely that early 18th century England was heavily
> populated by meantone-tuned keyboard instruments in which there were
> no major or minor tones. But Gaillard encounters no 'cognitive
> dissonance' whatever in quoting a theory in which the tones are
> distinct, and take different positions in the scale depending on the
> key of the music (cf. Cavallo's violinists)... in fact, a thoroughly
> adaptive and just type of scale.
>
> If Tosi was really referring to a commonly known and used sixth-
comma
> meantone model of intonation, why then is Galliard referring to a
> completely different and in many ways contradictory model?
>
> ~~~T~~~
>