Re: Microtonal chord progression player (was Digest Number 2833)

Hi Paul,

Sorry about the digest subject heading btw. everyone.

> Not really 22-eq . . . but anyway it's a whole different system,
> where the tetrads are the basic consonances. The "triad" isn't even 1-
> 3-5 anymore?

Okay. I hadn't understood that. I've only just done a fast first
read through of the paper so far to get started thinking about
the notation you use in it. Need to read it again more slowly again.

> > How do you notate the triad without the seventh if you
> > use I for the seventh (ninth)?

> Ino9.

Okay fine.

> > Can vii ever mean vii with a perfect fifth BTW? Or if you want
> > to notate that, do you do viiaug5

> You wouldn't, but there are actually two conflicing conventional
> methods of roman numeral analysis -- the 'popular' and
> the 'classical'. You're actually mixing the two, in that roman
> numerals are usually 'classical', but the rest of your symbols
> aren't. In classical terminology, I7 in the key of C major is C-E-G-
> B, it's not C-E-G-Bb. And so on. So classically, you'd say vii#5 or
> viix5 or viiN5 (with a natural sign instead of the letter "N"),
> depending on the key, if you wanted vii with a perfect fifth. In
> popular terminology, roman numerals are not used, but in the key of C
> major, this chord would simply be called Bm.

Right. Okay, that's clear now, thanks, hadn't understood that.
I'll fix that for the player so that it understands the roman numerals
in the classical sense for seventh chords.

... - except, searching, I see that the roman numerals are often
used in this mixed sense, maybe that is where I got it.
e.g.
http://www.torvund.net/guitar/progressions/02-bluespro-1.asp

So probably I need to have to have a check box or radio button in the Gui
to allow user to decide whether to use classical roman numerals
notation or popular roman numberals.

In minor keys, presumably it is III in classical notation,
for the IIIb which I think you would use in the popular mixed notation.

Then I read somewhere just now that you use VI for the major triad
on the minor sixth, and VII for the major triad on the minor seventh,
but vio and viio can be used for the diminished triads on the major
sixth and sevenths in the minor scale (ascending mode).

Yes looking at my history folder, here:

http://www.jcjc.cc.ms.us/faculty/finearts/jbrown/MUS1223/Study_Material/Unit04_Harmonic_Progression/Unit04_Harmonic_Progresson.html

"
VI always refers to a triad built on a lowered sixth
viio always refers to a triad built on a raised sixth
VII always refers to a triad built on a lowered seventh
viio always refers to a triad built on a raised seventh.
"
So I suppose I should support those too for the minor
key roman numerals...

> > Sorry, did a Iadd2 there.

> OK, but why relate to the subdominant.

Okay - I understand that this doesn't apply to the classical notation.
But would apply to the popular notation. The C7 has a Bb because
it is a diatonic chord of F major, though it can also be used
as a chromatically altered chord in other keys.

Well this something of an aside really: I'll mark it off as such

..............aside......................

In the 12 t context, Csus2 for instance has two different
possible just intonation tunings anyway depending on whetehr one thinks
of the 2 as 9/8 or 10/9. I suppose 9/8 there is the more natural
choice as it gives harmonic ninths and means that nearly all the
notes are in the harmonic series, and all of them indeed if you
play a harmonic seventh for the 7.

So take for example 53-et, with the just major scale as:
(steps) 9 8 5 9 8 9 5

There you would tune C7 as
0 17 31 44 53

So far this makes no distinction in tuning between
a chromatically altered tonic and a subdominant tuning

However, if one did a C7add2, then you have the choice
of
(steps) 8 9 5+9 8+5
and
9 8 5+9 8+5

The first would tune it to the subdominant and the second
would tune it to the tonic.

The second one is the more restful one especially
if you also change the final 8+5 to 8+4 for the
7/4 approximation as then it is a harmonic series
chord to best approx in 53-eq. So I suppose that
is the tuning one would use if one thought of
the C7sus2 as a chromatically altered
chord in C major.

The second one would be a possible choice of
tuning for the dominant 7th of F major
As a just tuning it would be an approximation to
1/1 10/9 5/4 3/2 16/9

I suppose probably the popular system could
be extended to include either of those
as the desired tuning of C7add2 in 53
equal.

At present the chord player plays the nearest
to the 12-eq pitches for C7add2, so it will play
the second one 9 8 5+9 8+5

- or if one adds the tuning symbols to the chord
one could pick out the chords of course
using Cj7add2, or Ck7jadd2 for the 10/9 + 16/9 one
and Ch7add2 for the harmonic series one

..................end aside................

> Why? For example, there's no such think as sus7 in diatonic
> terminology, is there?

Whether or not, the chord progr. player will let one play
it if one uses it. I suppose I could get it to say that
the chord isn't recognised if user enters e.g. Isus7
as a symbol. Currently, it will just play it.

> then you need to do the triads as i(9)

> I still think "no9" is better, since in standard 'popular'
> terminology you see "no3" and "no5" used

Okay fine, I didn't understand that it was a notation. Yes,
I can do that, and no risk of confusion with anything
else (won't get confused with the otonal symbol
because of the preceding 'n').

> Again, it's not a matter of generalizing 12, since conventional
> notation applies equally well to all meantone systems, but only if a
> diatonic basis is assumed -- even in 12. My paper hopefully explains
> how diatonic systems (in meantones) relate naturally to triads, while
> decatonic systems (in 22-equal and other decatonic tunings) relate
> naturally to tetrads.

Okay fine, I haven't read it in detail yet, so will find out
when I do.

> > The idea there is that the chord symbol gives the desired exact
pitch
> > which if the notation used was 22-eq would be 22-eq. But then if
user
> > is playing in a just 22 tone scale, each pitch in the chord gets
> > played as the nearest pitch in the current scale.

> Why 'nearest', necessarily? If there are 22 notes, wouldn't you want
> to use *all* of them, so have a one-to-one mapping from 22-equal to
> them? If the JI scale is a Constant Structure, this will at least
> never give you one 'consonant' chord quality when you're expecting
> another . . .

That makes sense, yes, if the scale has the same number of notes as the
notation system then I suppose normally you want to use them all...

Well, but not always. Suppose user has entered some kind of uneven mixed scale
maybe just a twelve tone scale with many extra intervals for different
flavours of third for instance, and the total number of notes
happens to be 22. Or a harmonic series fragment that
happens to have 22 notes...

If I allowed one to one correspondences with 22 note scales
then would need a way to find out which ones it can be used
for and which not.

Using the nearest pitch works pretty well for 12 eq. I suppose
if you use some strange scale like half comma meantone it mightn't
always find the intended pitch.

But as you increase the number of notes, the nearest pitch
method is probably more likely to get you to a "wrong note"
as the notes will move around more relative to the smaller step
size.

Probably the sort of thing that needs to be an option that
can be set by the user, in the interface or in the
chord progression.

I'll need to think it over. Because the notation will also work
with j.i. scales of more than 22 notes too. Maybe then there
will be lots of possible choices, and the nearest pitch
not the best one for a particular context. So maybe user
has to be able to decide on a just interpretation of
the chord symbols or something. Maybe this can be
left to later; I think it could get rather complex...

I'm thinking about using key signatures in the chord progression
with the roman numerals notation now BTW.

Major, or Minor, or to change key in the middle,

Emajor, or Bmajor or Dminor (all one word).

Robert

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
wrote:

> In minor keys, presumably it is III in classical notation,

Yes.

> for the IIIb which I think you would use in the popular mixed
>notation.

I doubt that, Robert.

> Okay - I understand that this doesn't apply to the classical
notation.
> But would apply to the popular notation. The C7 has a Bb because
> it is a diatonic chord of F major, though it can also be used
> as a chromatically altered chord in other keys.

OK, but that doesn't apply for decatonic music, where there
are "seventh chords" all over the scale!

> Well this something of an aside really: I'll mark it off as such
>
> ..............aside......................
>
> In the 12 t context, Csus2 for instance has two different
> possible just intonation tunings anyway depending on whetehr one
thinks
> of the 2 as 9/8 or 10/9. I suppose 9/8 there is the more natural
> choice as it gives harmonic ninths and means that nearly all the
> notes are in the harmonic series, and all of them indeed if you
> play a harmonic seventh for the 7.

I would say that the real key is the 4:3 vs. 27:20 in these chords.
The 4:3 is way more 'natural' than the the 27:20.

> So take for example 53-et, with the just major scale as:
> (steps) 9 8 5 9 8 9 5
>
> There you would tune C7 as
> 0 17 31 44 53

Diatonic harmony falls apart in 53-equal, or any other non-meantone.

> > > The idea there is that the chord symbol gives the desired exact
> pitch
> > > which if the notation used was 22-eq would be 22-eq. But then if
> user
> > > is playing in a just 22 tone scale, each pitch in the chord gets
> > > played as the nearest pitch in the current scale.
>
> > Why 'nearest', necessarily? If there are 22 notes, wouldn't you
want
> > to use *all* of them, so have a one-to-one mapping from 22-equal
to
> > them? If the JI scale is a Constant Structure, this will at least
> > never give you one 'consonant' chord quality when you're expecting
> > another . . .
>
> That makes sense, yes, if the scale has the same number of notes as
the
> notation system then I suppose normally you want to use them all...
>
> Well, but not always.

Right, it should be 'epimorphic' (in tuning-math terms) if you will
use them all.
>
> I'll need to think it over. Because the notation will also work
> with j.i. scales of more than 22 notes too. Maybe then there
> will be lots of possible choices, and the nearest pitch
> not the best one for a particular context. So maybe user
> has to be able to decide on a just interpretation of
> the chord symbols or something. Maybe this can be
> left to later; I think it could get rather complex...

Yeah, I think this should be handled mathematically, according to
mappings of the basic lattice intervals.

Keep up the good work!