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

Just a brief aside here that might be of interest... Back when I was
looking at Enrique Ubieta's bimodal "triad," the "triads" I ended up
liking best -- in a closed position, and on a purely by ear basis --
were the ones where the two thirds were spaced something like a 54/49
apart, and the "triad" was something like a 1/1 7/6 9/7 3/2 (i.e., a
6:7:9 and a 1/(9:7:6) combined). And I briefly played around with an
0, 2, 3, 5, 6, 8, 9, 11, 13, 14, 9-tone scale in 14-tET (14-tET does
not distinguish between the 12/7 and the 7/4, and in fact it sort of
splits the difference):

14/9.--------,7/6.--------,7/4.
`. , `. , `.
`4/3,--------`1/1,--------,3/2.--------,9/8.
`. , `. , `.
`12/7,--------`9/7,--------27/14

However, I'm almost certain that some empirically derived 'optimal'
closed position bimodal triadic voicing was not the sort of thing that
Ubieta had in mind, as he wrote, "the essence of the harmonic
discipline of Bimodalism lies in the simultaneous blending of major
and minor modes in triads with the same fundamental root," and this
sounds to me as though he is perhaps seeing his bimodal "triad" as
something akin to a 16:19:20:24 identity:

5/4
/ \
19/16 \
/ \
/ \
/ \
/ \
/ \
1/1-------------3/2

where both thirds would be a harmonic series overtone, therefore
accomplishing the "simultaneous blending of major and minor modes in
triads with the same fundamental root." Though he also wrote,
"consequently, both remote tonalities and modulation concepts are
senseless in Bimodalism, as it is intrinsically a chain of 12
equivalent and harmonically linked chords, forming, in fact, a true
unitonality," and here I'm inclined to see this as something more
along the lines of a 4:5:6 overtonal, and a 1/(6:5:4) undertonal
symmetry (i.e., "unitonality"):

5/4
/ \
/ \
/ \
1/1-----3/2
\ /
\ /
\ /
6/5

Though I found this closed position "bimodal" triad to sound much
better in 12-tET than it does in 5-limit JI.

Dan Stearns

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:

"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)

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?

Johnny Reinhard?