Diatonic tonality in harmony or JI

Hello there.
> --- In tuning@yahoogroups.com, "frizzerius"
<lorenzo.frizzera@l...>
> wrote:
> > Ciao.
> >
> > If you consider diatonic modes and you rearrange them through a
> > circle of fifths you will have this list: lydian, ionian,
> > mixolidian, dorian, eolian, phrigian and locrian. Each passage
to a
> > new mode produces the lowering of a note so that, at the end,
you
> > will have lowered any note except the tonic. If you do the same
on
> > this last note you will reach again a lydian mode but an half
tone
> > below.
> >
> > Considering the structure of these modes you will find that
there
> is
> > a specularity in the structure between lydian and locrian,
ionian
> > and phrigian, mixolidian and eolian; and that dorian mode is
> > specular respect himself.

Well, this "specularity" is the first discovery many of us have come to
(including myself). But when you start inverting actual music, soon you get
to another important result. The tonic is no longer tonic because the only
degree that has still the same meaning is the third. The inversion makes the
tonic exchange the position with the dominant. So if you invert the ionian
mode, in fact, you get the hypoaeolian rather than phrigian. As an example I
could take a scale of C-D-E-F-G-A-B-C which is ionian. If I want to leave
the C unchanged, after inverting I get C-Bb-Ab-G-F-Eb-Db-C. Right, let's try
it with the major chord of C-E-G-C. Inverting this makes C-Ab-F-C, or
upwards, C-F-Ab-C. You see, it looks like phrigian but the centre is on F,
not on C, and that's just why I think that calling it "hypoaeolian" would be
rather in place here. This can be also explained well in the terms of just
intonation. Suppose you make a dorian mode on D so that the basic three
triads (d-minor, G-major, a-minor) are in tune. Just for clarity I will list
the scale here for you:
9/8
6/5
4/3
3/2
5/3
9/5
2/1
OK, let's invert this in the way of "2/factor". And what do we get?
10/9
6/5
4/3
3/2
5/3
16/9
2/1
What a strange result? So both C and E are a syntonic comma lower now and
the rest is unchanged. In this scale, the a-minor chord is out of tune. On
the other hand, the C-major chord, which was unusable in the previous scale,
is now maximally in tune. Does it mean we got a mixolydian mode? Yes, we
almost did. More precisely, we turned a dorian into a hypomixolydian.
Petr

Ciao Petr.

> Well, this "specularity" is the first discovery many of us have
come to
> (including myself). But when you start inverting actual music,
soon you get
> to another important result. The tonic is no longer tonic because
the only
> degree that has still the same meaning is the third. The inversion
makes the
> tonic exchange the position with the dominant. So if you invert
the ionian
> mode, in fact, you get the hypoaeolian rather than phrigian. As an
example I
> could take a scale of C-D-E-F-G-A-B-C which is ionian. If I want
to leave
> the C unchanged, after inverting I get C-Bb-Ab-G-F-Eb-Db-C. Right,
let's try
> it with the major chord of C-E-G-C. Inverting this makes C-Ab-F-C,
or
> upwards, C-F-Ab-C. You see, it looks like phrigian but the centre
is on F,
> not on C, and that's just why I think that calling
it "hypoaeolian" would be
> rather in place here. This can be also explained well in the terms
of just
> intonation. Suppose you make a dorian mode on D so that the basic
three
> triads (d-minor, G-major, a-minor) are in tune. Just for clarity I
will list
> the scale here for you:
> 9/8
> 6/5
> 4/3
> 3/2
> 5/3
> 9/5
> 2/1
> OK, let's invert this in the way of "2/factor". And what do we get?
> 10/9
> 6/5
> 4/3
> 3/2
> 5/3
> 16/9
> 2/1
> What a strange result? So both C and E are a syntonic comma lower
now and
> the rest is unchanged. In this scale, the a-minor chord is out of
tune. On
> the other hand, the C-major chord, which was unusable in the
previous scale,
> is now maximally in tune. Does it mean we got a mixolydian mode?
Yes, we
> almost did. More precisely, we turned a dorian into a
hypomixolydian.

What you observe it is absolutely true.
And this is related to the fact that these rearrangement of modes is
based on a circle of fifths. So has to be expected that, in just
intonation, there is a shift of tonal center of a descending fifth
(or an ascending fourth).

I think that this specularity is not interesting as a source for JI
tunings but to understand that there is a descending stability in
modes when you order in fifths. To me (these was the argument) the
minor triad is the next step respect major triad in this descending
stability scale. The next one is the diminished triad.
I was trying to show that a minor triad comes from a specularity
model which also produces a "flattening" process. This also confirm
that feeling regarding major triad as more rooted or the locrian
scale as less rooted. Infact during this process each mode change a
note (inserting a flat) and this note is the root respect the tonic
of the mode. So the mode looses gradually his "tonicity".
I think that the minor mode (I consider the official minor as
dorian) comes from this process.

Ciao

Lorenzo