Re: [tuning] Diatonic?

> Interesting about the ancient Greek usage. What distinguishes the
diatonic
> from the Chromatic for them? It may be that the word "diatonic" takes on
a
> different meaning for the Middle Ages.
>
> Johnny Reinhard
>

The standard reference is Chalmers, _The Divisions of the Tetrachord_ (Frog
Peak). Chalmer's catalog uses a characteristic interval size of 250 cents
to distinguish chromatic from diatonic tetrachords. Classical theory did
not define a borderline between the genera in these terms, but it is clear
that a diatonic tetrachord was composed of two tones and a semitone and that
the principal sizes of tones used were 8/7, 9/8, and 10/9. The medieval
European reduction to one tetrachordal genus, the diatonic, in one tuning,
the ditone (Pythagorean) must have occurred through a confluence of factors:
encounters with musics outside of the Hellenistic traditions, Platonism,
trinitarianism etc.. On the other hand, in the Islamicate world, intervallic
variety remained relatively unimpoverished: although the enharmonic was
apparently lost forever, the development of new techniques for rotating and
permutating tetrachords contributed, in part, to the enduring presence of
these tunings.

Daniel Wolf

Johnny Reinhard wrote,

>Daniel has well pointed out the ancient Greek sense of diatonic. Nicola
>Vicentino wrote of the difference between the Renaissance and the
post-Roman
>(Boethius) versions. Vicentino wrote in 1555:

>Vicentino wrote in 1555:

>"The difference between our practice and the one discussed by Boethius is
>this: Ancient musicians used the genera individually in their practice and
>consequently the minor semitone with two sesquioctaval whole tones were
>satisfactory for the genera. But in our times, both the sound of practical

>music and the tuning of instruments are unlike those of ancient musicians,
>for we use the genera and the species together and with more consonances
than
>they had--namely, thirds and sixths. To be able to have more consonances
as
>well as to make many steps, we do not find it inconvenient to blunt a fifth

>and enlarge a fourth, as I said. This blunting, as you will learn in the
>proper place (book V, chapter 5), does not shock the sense of hearing
because
>the quantity removed is so tiny in itself and because these particles are
>distributed here and there wherever they are needed. Practitioners of this

>tuning describe such fifths and fourths as tempered." (Vicentino, p. 45 of

>Maria Rika Maniates translation)

Vicentino here proves to be my hero once again by stating, as I often do,
that the optimal fixed tuning for the diatonic scale with respect to 3-limit
harmony is Pythagorean tuning, while the optimal fixed tuning for the
diatonic scale with respect to 5-limit harmony is a meantone tuning.

>As sensible as the above seems to me, the translator wrote in a coupled
>footnote:

>Footnote #48: "The gist of this paragraph suggests that Vicentino here, as
>elsewhere, put together an inaccurate and rather haphazard conflation of
>propositions and opinions culled from the "Musica theorica" by Fogliano, an

>organist and choirmaster who served the Este family in Modena. Fogliano's
>text, then, may explain the anomalies in Vicentino's arguments."

>Does this dark shadow on her subject make sense to anyone?

Perhaps the translator was taking issue with the description of "ancient"
(pre-medieval?) practice? Otherwise, I might surmise that the translator
simply failed to understand Vicentino's reasoning -- how does the translator
react to the section in question (book V, chapter 5)?