Re: [tuning] Digest Number 2833

Hi Paul,

> > See
> http://tunesmithy.netfirms.com/fts_help/chord_progr_player.htm#ex_Cm6
>
> I think you got one of the chords wrong -- 1/1 6/5 3/2 5/3 should be
> 1/1 6/5 3/2 12/7 (which I called 1/(4:5:6:7) and 1/6:1/5:1/4:2/7)) --
> it's the minor tetrad of my paper.

Rightio. I'll fix it - yes makes sense. That one is Cjms6
So they are Cjms6 (same as Cu6m6), Csmj6 (same as Co6m6)
and Co5m6

>
> > Also, looking at your paper, I have had a few preliminary ideas
> about how
> > to add in the decatonic chords notation for 22 equal.
>
> Thanks for taking the time to look at it! And if you get a chance,
> try making up some chord progressions; you can pretty drag four
> sticks fractally through the decatonic sand and come up with nice
> harmonies.

Rightio. Maybe it would be good for a fractal tune or so I
wonder... Haven't explored them in 22-eq yet.

>
> > Idea is to allow the user to set a major mode, e.g.
> > Standard Pentachordal Major:
> > 0 2 4 7 9 11 13 16 18 20 (22)
> > and a minor mode, e.g.
> > Standard Pentachordal Minor:
> > 0 2 4 6 9 11 13 15 17 19 (22)
> >
> > But not really sure how to use those in the notation.
> > - sketched out a few ideas but they aren't entirely
> > satisfactory.
> >
> > ie. how to interpret, e.g. I9 and i9 (9 here = "seventh" of 12 eq)
> > when one wants to make a distinction between major and minor
> depending on the
> > numeral as upper or lower.
>
> What's the letter "I" here? Is it a Roman numeral? If so, you
> wouldn't even have the 9 on the symbol, if the chord you mean is 0-7-
> 13-18 in 22-equal.
>

I saw in the paper that you used I for the 0-7-13-18, but I
suppose I didn't understand why that was, because in
12-t "I" stands for the major triad without the seventh doesn't
it? So why does it have an added seventh in 22-eq?
How do you notate the triad without the seventh if you
use I for the seventh (ninth)?

> > Do you have any thoughts about what I9 and i9 should
> > be as scale degrees,
>
> Hmm . . . I'm not sure why you would want to use the symbol 9. I
> guess the 'default' is 1-4-7-9.
>
> > and ditto for the other upper and lower case
> > symbols in the Roman numeral notation?
>
> I'm visiting this point in your message from the future. Capital
> means major tetrad, lower case means minor tetrad, just like they
> mean major triad and minor triad in diatonic music, where the
> diminished triad is viio or iio and augmented is III+, so you could
> use + for augmented decatonic tetrads too.

Ah, I didn't know about the o for diminished. I'll add that in
- will need to do something to prevent confusion with the new
'o' for otonal.

Seems that if you leave out the o then vii is understood as
meaning viio as it is used like that e.g. here.
http://www.tonalityguide.com/xxnondom4.php
Can vii ever mean vii with a perfect fifth BTW? Or if you want
to notate that, do you do viiaug5 or something? Maybe
it is just never used...

Rightio, seems that the default in your decatonic notation is to use
roman numerals for tetrads. But why is that? Maybe I need
a check box somewhere so user can choose whether to
have the sevenths included in the roman numerals chord symbol.
Or something.

>
> > (and
> > their flats and sharps and augmented and diminished
> > chords)?
>
> Should work out alright . . .
>
> > Thing is that in 12 eq of course the I7 is always 7b
> > to make it a dominant seventh of the subdominant.
> > But what should one do here? I suppose rotate the
> > scale around so the 9 is 18. But what about e.g. I9sus2
> > - should the 2 there be chromatically altered too?
> > - I mean as 0 3 isntead of 0 2. Perhaps?
>
> How would a sus2 arise in the decatonic system? It wouldn't seem to,
> but . . . I'm afraid we may have to take this more slowly.
>

Well or a sus3, or an add3 (which would be 5 instead of 4
in the subdominant tuning). Not with any particular
harmonisation in mind, just that when you design a notation
system for a program, you have to assume user might
enter anything that is legal in the notation, and
sus2 or sus3 would surely have to be legal. So
then one needs to know how they should be tuned.
Then if the add2 or add3 occurs in the context of
a dominant seventh, does that mean that you think
of it as tuned to the subdominant at that point??
What if they occur outside that context. I know
it is kind of nit picking but if you are programming it
then you have to sort all this out, or at least think
about it and make some kind of reasonable default.

> > First thought anyway is:
> > I9 = 1 4 7 9 (11) tuned to the subdominant key = 0 7 13 18
>
> I'd just call it I, not I9.

> > Im9 = 1 4 7 9 (11) in the minor mode = 0 6 13 17 (22)
>
> Yes!
>
> > where I suppose the m and M symbols should be thought of as
> > affecting the entire chord - immediately after the note name
> > the effect goes forwards and backwards and if used later in
> > the chord then it goes forwards only to affect notes that follow.
> > So the seventh in Im9 is 17 and in I9 is 18.
> >
> > So ImM9 = 0 6 13 18 (22)
> > and IMm9 = 0 7 13 17 (22)
>
> Those chords are defined in my paper, so again, you can drop the 9
> from the designation.

Can do. Could do them also as iM and Im in the mixed notation chord
then you need to do the triads as i(9) I suppose and I(9) where
you don't need to specify the m or M as it is to be omitted
anyway. It is quite neat if you want to use mainly tetrads.
But if your chord progression has many triads then all those
(9)s would get clumsy. Maybe that is it as I expect you probably
use lots of seventh chords when you play in this system,
and relatively few plain triads.

>
> > And Isus2 possibly as tuned to the subdominant too
> > = 1 2 4 7 9 (11) = 0 3 7 13 18 (22)
>
> Now I'm really confused. Diatonically speaking, Isus2 and Isus4
> chords have the same number of notes as I chords. And why would
> you "tune to the subdominant"?

Sorry, did a Iadd2 there.

Thing is that in 12-t the seventh on the root of a chord
is played as a b, e.g. Bb for the I7 in C major, so it is tuned
to the key of the subdominant of the root of the chord, so
it seems. I think of it that way because it would often
be used in the progression I7 IV, and of course originally
V7 I where the V7 there is tuned to the major scale for the
I chord.

Only got the one note that differs in tuning between the
tonic and the subdominant in 12-t. and that is the one
used for the seventh in thedominant seventh. I suppose you could
think of it instead as the minor seventh, but why
should one think of it that way for a piece in the
major key, rather than as a note from the subdominant key?
Or is there some other interpretation? Quite possibly
I'm way off track, don't hesitate to say if I am!

> > Can do I and i for major and minor and the sequence
> > of triads in the Pentachordal Major is then
> > I II III iv V VI VII viii ix x (XI)
>
> Should be tetrads,
>
> I II+ III+ iv VMm VI VII viii ix xmM
>
> > and then for the dominant "seventh" (i.e. ninth) chords it is
> > I9 II9aug7 III9aug7 iv9 Vm9 VI9 VII9 viii9 ix9 xM9
>
> See above. If you want no 9 you can use the no9 symbol.

Rightio, can do. As III(9) perhaps? That's how I do it
at present in the chord progression player. But why
- and is this something special about the decatonic
system if it is based on tetrads rather than triads
in the roman numeral notation, and if so when generalising
12-t to any number of notes per octave how do you decide
which tunings are tetrad based and which are triads
based?

>
> > But that is a bit hard to remember. So would do
> > a "keep to mode" option and perhaps use an '%' for that,
> > so in 12-eq %I is I and %II is ii etc
>
> nice

Great. Glad you like it.
>
> > so here with this example, %II9 will mean II9aug7 and %V9 will mean
> Vm9 etc
> > which will save the newbie user from the need to remember
> > which chords are which, and indeed be easier to type for everyone.
>
> Well, as you can in the table on page 11 on my paper, this is the way
> I did it, though I used I II III IV V VI VIII IX and X to mean the
> tetrads occuring as 1-4-7-9, in each of the eight given modes.

Yes I know. The thing is that I am thinking of it as a generalisation
from the 12-t system that will work with any number of notes per
octave.

I do also have an option to define symbols particularly for
particular tunings that don't need to fit into that pattern,
which I will work on and it could be done that way

Indeed they could be done like that already in the player - just
set the scale to 22-eq and define each roman numeral
individually in the Extra Symbols list as a tetrad
with the appropriate list of degrees.

But that is less flexible. You can't make up new symbols
for instance and immediately use them - you have to
add each symbol you want to the list of extra symbols
complete with degrees etc before you can use it.
Also currently the extra symbols only define a pattern
of degrees so if you change to another scale with
a different number of notes to anoctave say, then all
your notes will shift about. This extra symbols section
is something I will work on later.

>
> > Anyway, if the tricky issues can get sorted out, this general idea
> > is immediately generalisable to scales with any number
> > of notes - you just need to set a "major" and "minor" mode and you
> can then
> > immediately use the notation,
>
> or maybe eight modes! :)

Ah the thing there is that yes you can have any number of modes
for the keyboard mapping, and easily switch between them.
But this is not yet integrated into the chord progression view - you
would have to change back and forth between that and the
retuning keyboard views - or else show an Arpeggio Window
and do it there. Anyway I'll deal with that.

At present the chord progression player doesn't take
account of the modes at all, but it should, I now realise.
It is just playing major chord progressions at present
I suppose. User should be able to set the mode to
minor or anything else, and then it should
move the chord up or down to the nearest note in the
mode. For minor should use it in the melodic minor form
with separate ascending and descending modes,
and VI and VII then refer to the major triads on the descending
mode, and vio and viio to the minor triads on the ascending
mode. Or, I suppose the generalisation there is to
look for a match for the chord in both the ascending and
descending modes, and choose the root of the chord in
one or the other depending on which gives the best match.

HOwever - that is for the tuning of the root. Interpretation
of the chord symbol is another matter - which intervals
to use between the successive notes in the chord.

To do that it needs a major mode in order to know how to
interpret the upper case roman numerals, and a minor mode to interpret
the lowercase roman numerals. Which _doesn't_ have to be
the same as the mode you are currently playing in.

So you could play in any mode, invent one too,
but still I or i would refer to chords tuned
to the reference major and minor modes that you have
set up for the chord symbols, with the root
tuned to the current mode, so e.g. III will be
a major triad (or tetrad) on the third degree
of the current mode whatever it is.

I think that is prob. how it has to be done.

>
> > leaving the user free to do something
> > totally unconventional there too if they so wish, no restriction on
> > what has to count as major or minor modes.
> >
> > So, that is the first thought that springs to mind for this.
> > What do you think?
>
> Cool stuff! You can try to, ultimately, support all the notations
> SCALA supports . . .

Yes, that is planned in fact. I've been discussing it with
Manuel. No way am I going to be able to code all that,
as it would be an immense duplication of programming
effort. But, who knows, maybe somehow I will be able
to call SCALA to get it to do the translations, running invisibly.
It seems that it can be done technically in piped mode, but there is a
question about whether the programs will be able to communicate through the
pipe quickly enough if FTS needs to know how to interpret
many note names in short succession. Will just have to try and see.

Probably FTS will keep a database of the users most recent note
name queries, maybe the most recent 1000 queries or some such,
and only ask SCALA about names that haven't been requested for
some time, come to think of it, so that
will probably be fast enough in nearly all situations.

>
> > One would also need a way of showing that the entire chord
> progression is
> > to be interpreted in 22 equal
>
> Or any such 'decatonic' tuning . . .

Yes that will be understood.
>
>
> > because that affects how all the
> > numbers are interpreted in the chords, e.g. 9 instead of 7 for
> the "seventh"
> > of twelve equal,
>
> Or any diatonic tuning, presumably . . .
>
> > and there maybe just prefix
> > the start of the progression with "eq22" to do that.
>
> Well, you would eventually be able to notate other scales that 22-
> equal supports (including, for example, 'Pythagorean/septimal'
> diatonic scales I mention in my paper that go 4 1 4 4 1 4 4 for the
> minor mode, etc), so it's really not 22-equal that needs to be
> specified . . .
>
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. Main thing there
I suppose is to say what the effect is of a b and # and + and -
etc in the notation system. That is something I'll go into
more in later programming, but at present you can already
use the 19, 31 and 72-et accidentals in the chord symbols
- for the name for the root. Can't yet use them for the modifiers
of the chord but no reason why not use them there too.

Will have to think it over.

> > This gives the flexibility to use this notation even with scales
> that
> > aren't themselves 22 equal, e.g. j.i. 22 tone scales or ones
> > with more or less notes because the chord symbols would actually
> pick
> > out exact pitches in 22eq, then use closest to those in the
> currently
> > selected scale.
>
> Just as conventional notation really only works out in meantone
> scales (without getting unexpected "wolves" and the like), decatonic
> notation would work out only in certain tuning systems.
>

Yes of course. That is up to user, needs to use it in an
appropriate system

> > I'll think it over a bit before doing it as it is the sort of thing
> > where you can probably find a neat way of doing it that makes the
> > coding much easier. Amount of code needed is probably rather modest,
> > only a few dozen or maybe at most a couple of hundred lines of so.
> > But it is a matter of deciding what one wants to achieve with it.
>
> Hopefully the above is a start. I'd love to go further!

Yes, thanks, it's brought up a number of issues already and it is a
great help. I will be interested to find out what you make of this
too.

Robert

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

> I saw in the paper that you used I for the 0-7-13-18, but I
> suppose I didn't understand why that was, because in
> 12-t

Well, it's not really 12-t we're talking about, it's Western
tonal/modal harmonic analysis so it applies equally well to all
meantones.

> "I" stands for the major triad without the seventh doesn't
> it?

Right, where the major triad is 1-3-5.

> So why does it have an added seventh in 22-eq?

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?

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

Ino9.

> Seems that if you leave out the o then vii is understood as
> meaning viio as it is used like that e.g. here.
> http://www.tonalityguide.com/xxnondom4.php
> 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.

> you have to assume user might
> enter anything that is legal in the notation, and
> sus2 or sus3 would surely have to be legal.

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

Furthermore, I don't see where relating sus chords to the subdominant
comes from.

> Can do. Could do them also as iM and Im in the mixed notation chord

Clever.

> 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

> Maybe that is it as I expect you probably
> use lots of seventh chords when you play in this system,
> and relatively few plain triads.

Yes. With tetrads, you can 'project' all the notes of the scale more
easily with just a few of them. With triads, it gets harder to keep
the whole scale together in the listener's mind.

> > > And Isus2 possibly as tuned to the subdominant too
> > > = 1 2 4 7 9 (11) = 0 3 7 13 18 (22)
> >
> > Now I'm really confused. Diatonically speaking, Isus2 and Isus4
> > chords have the same number of notes as I chords. And why would
> > you "tune to the subdominant"?
>
> Sorry, did a Iadd2 there.

OK, but why relate to the subdominant.

> Thing is that in 12-t the seventh on the root of a chord
> is played as a b, e.g. Bb for the I7 in C major, so it is tuned
> to the key of the subdominant of the root of the chord, so
> it seems. I think of it that way because it would often
> be used in the progression I7 IV, and of course originally
> V7 I where the V7 there is tuned to the major scale for the
> I chord.

Right, but *all* the chords are what you would call "seventh chords"
now! This isn't tonality as you know it.

> > > Can do I and i for major and minor and the sequence
> > > of triads in the Pentachordal Major is then
> > > I II III iv V VI VII viii ix x (XI)
> >
> > Should be tetrads,
> >
> > I II+ III+ iv VMm VI VII viii ix xmM
> >
> > > and then for the dominant "seventh" (i.e. ninth) chords it is
> > > I9 II9aug7 III9aug7 iv9 Vm9 VI9 VII9 viii9 ix9 xM9
> >
> > See above. If you want no 9 you can use the no9 symbol.
>
> Rightio, can do. As III(9) perhaps? That's how I do it
> at present in the chord progression player. But why
> - and is this something special about the decatonic
> system if it is based on tetrads rather than triads
> in the roman numeral notation, and if so when generalising
> 12-t to any number of notes per octave how do you decide
> which tunings are tetrad based and which are triads
> based?

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.

> and vio and viio to the minor triads on the ascending

diminished triads. But classical analysis assumes the "natural" minor
only, and explicitly indicates any alterations such as those you'd
find in the ascending mode. Popular analysis doesn't use roman
numerals, and just names the chord according to its construction
without regard for context.
>
> 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 . . .