Yahoo Tuning Groups Ultimate Backup tuning How do you guys tune iim7-V7-I in JI?

I've posted about other frustrating comma pumps before, but this one
has me at my wit's end. This might be the most common chord
progression in all of music and it's also the most annoying to deal
with in JI.

Some things that seem to not work (let's assume we're in C):
- Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
This makes the C in the iim7 a comma sharp of the finishing I, which
sounds awful.
- Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
This makes the D in the iim7 a comma flat of the D in the V7, which
destroys the voice leading and also sounds awful.
- Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
This sounds completely out of place if your goal is to have beatless
"just" voicings, and since ii-V's are so common in almost everything,
it almost sounds like the piece isn't in JI at all. On the other hand,
this one avoids weird comma shifts.

Is there some miraculous fourth option that I haven't thought about?
It boggles my mind that such a natural and intuitive and "clean"
sounding chord progression would be so theoretically "dirty"
underneath the surface.

Sincerely,
A traJIcally lost soul

🔗Klaus Schmirler <KSchmir@...>

Mike Battaglia schrieb:
> I've posted about other frustrating comma pumps before, but this one
> has me at my wit's end. This might be the most common chord
> progression in all of music and it's also the most annoying to deal
> with in JI.
> > Some things that seem to not work (let's assume we're in C):
> - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
> This makes the C in the iim7 a comma sharp of the finishing I, which
> sounds awful.
> - Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
> This makes the D in the iim7 a comma flat of the D in the V7, which
> destroys the voice leading and also sounds awful.
> - Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
> This sounds completely out of place if your goal is to have beatless
> "just" voicings, and since ii-V's are so common in almost everything,
> it almost sounds like the piece isn't in JI at all. On the other hand,
> this one avoids weird comma shifts.
> > Is there some miraculous fourth option that I haven't thought about?

- The Bruckner/Sechter way, where the d is 32/27 below F and the a (40/27) is treated as a dissonance.

klaus

🔗Marcel de Velde <m.develde@...>

Hi Mike,

I've posted about other frustrating comma pumps before, but this one
> has me at my wit's end. This might be the most common chord
> progression in all of music and it's also the most annoying to deal
> with in JI.
>
> Some things that seem to not work (let's assume we're in C):
> - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
> This makes the C in the iim7 a comma sharp of the finishing I, which
> sounds awful.
> - Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
> This makes the D in the iim7 a comma flat of the D in the V7, which
> destroys the voice leading and also sounds awful.
> - Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
> This sounds completely out of place if your goal is to have beatless
> "just" voicings, and since ii-V's are so common in almost everything,
> it almost sounds like the piece isn't in JI at all. On the other hand,
> this one avoids weird comma shifts.
>
> Is there some miraculous fourth option that I haven't thought about?
> It boggles my mind that such a natural and intuitive and "clean"
> sounding chord progression would be so theoretically "dirty"
> underneath the surface.
>
> Sincerely,
> A traJIcally lost soul
>

Well I don't know if youre ready to accept this one, but here's what
tonal-ji sais about it (yes the 4th option)
If it's truly in the tonic of C then it's:
F (4/3) - A (5/3) - C (2/1) - D (9/4) iim7 (this is actually best seen as a
kind of IV sixth)
F (4/3) - G (3/2) - B (15/8) - D (9/4) V7
C (1/1) - G (3/2) - C (2/1) - E (5/2) I tonic major

Before you reject it please play it as I wrote it above.
It becomes more dissonant when you play the D an octave lower, but I hope
when you use it in a musical context your ear will hear it as correct, as my
ear does.

Marcel

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, Klaus Schmirler <KSchmir@...> wrote:
>
> *** Michael asked:
> > Is there some miraculous fourth option that I haven't thought about?
> *** Klaus replied:
> - The Bruckner/Sechter way, where the d is 32/27 below F and the a
> (40/27) is treated as a dissonance.
>
in deed,
Sechter & and his pupil Bruckner both considered
within the common usual hepatonic C-major JI scale

C 1/1
D 9/8
E 5/4
F 4/3
G 3/2
A 5/3
B 15/8
c 2/1

in that even the the crude 5th inbetween D-A
is treated as an dissonant interval,
due to it is off downwards of an SC=81/80 against pure 3/2

1200Cents * ln( 40 / 27 ) / ln(2) = ~ 680.5 Cents

Reference
http://books.google.de/books/download/Die_Grunds__tze_der_musikalischen_Kompos.pdf?id=96gQAAAAYAAJ&output=pdf&sig=ACfU3U2_Lh0z63X3Wycrz7sQWg_3G0a7YQ

Analogous Paul Hindemith preferred on his viola in
"The craft of musical composition"
that 40/27 "wrong" 5-th located in G-major inbetween A and E.
Reference:
http://www.unitus.org/FULL/HindCMCpp54-131,+trist.pdf

Attend there his pitches absolute in Hz and theirs relative ratios
256 c' 1/1
288 d' 9/8
320 e' 5/4
341~f' 4/3 exactly 341+1/3
384 g' 3/2
432 a' 27/16 instead of 5/3 as in the Sechter/Bruckner case
480 B 15/8
512 c 2/1

bye
A.S.

🔗Carl Lumma <carl@...>

Different tunings of these chords are suited to different
voicings. Moreover, listening to short chord progressions in
isolation doesn't tell much about how they'll serve in a piece
of music. If the progression is used in passing, the tuning
might not matter at all. If the melody has previously been
making use of comma shifts, then perhaps you'll want them. If
you just want the 'diatonic' style, meantone-based adaptive JI
would probably be best. If you want 7-limit harmony and no
shifts, it can be rooted in pajara instead, e.g. D = '8/7' and
the 64/63 between the final two Gs vanishes.

-Carl

--- Mike Battaglia <battaglia01@...> wrote:
>
> I've posted about other frustrating comma pumps before, but this
> one has me at my wit's end. This might be the most common chord
> progression in all of music and it's also the most annoying to
> deal with in JI.
>
> Some things that seem to not work (let's assume we're in C):
> - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
> This makes the C in the iim7 a comma sharp of the finishing I,
> which sounds awful.
> - Rooting the D on 10/9 and building up 6/5's and 5/4's from
> there. This makes the D in the iim7 a comma flat of the D in the
> V7, which destroys the voice leading and also sounds awful.
> - Rooting the D on 9/8 and building up 32/27's and 81/64's from
> there.
> This sounds completely out of place if your goal is to have
> beatless "just" voicings, and since ii-V's are so common in almost
> everything, it almost sounds like the piece isn't in JI at all.
> On the other hand, this one avoids weird comma shifts.
>
> Is there some miraculous fourth option that I haven't thought
> about? It boggles my mind that such a natural and intuitive and
> clean" sounding chord progression would be so theoretically
> "dirty" underneath the surface.
>
> Sincerely,
> A traJIcally lost soul
>

🔗Mike Battaglia <battaglia01@...>

On 11/23/09, Carl Lumma <carl@...> wrote:
> Different tunings of these chords are suited to different
> voicings. Moreover, listening to short chord progressions in
> isolation doesn't tell much about how they'll serve in a piece
> of music. If the progression is used in passing, the tuning
> might not matter at all.

OK, so let's take a tune like Autumn Leaves:

| Cm7 | F7 | Bb | Eb | Am7 | D7 | Gm | Gm |
| Cm7 | F7 | Bb | Eb | Am7 | D7 | Gm | Gm |
| Am7 | D7 | Gm | Gm | Cm7 | F7 | Bb | Bb |
| Am7 | D7 | Fm | Bb7 | Eb | D7 | Gm | Gm |

That's kind of a simplified version of it, but almost the entire song
can be viewed as a series of ii-V's... just like every other piece of
music from this time period. Not to mention that as a jazz pianist I'd
be throwing in extra ii-V's for harmonic color if I feel like it.

> If the melody has previously been
> making use of comma shifts, then perhaps you'll want them. If
> you just want the 'diatonic' style, meantone-based adaptive JI
> would probably be best. If you want 7-limit harmony and no
> shifts, it can be rooted in pajara instead, e.g. D = '8/7' and
> the 64/63 between the final two Gs vanishes.

Hey, that pajara idea sounds pretty neat. I'll check that out, thanks
for the reply.

-Mike

🔗Danny Wier <dawiertx@...>

--- On Mon, 11/23/09, Mike Battaglia <battaglia01@...> wrote:

> From: Mike Battaglia <battaglia01@...>
> Subject: [tuning] How do you guys tune iim7-V7-I in JI?
> To: tuning@yahoogroups.com
> Date: Monday, November 23, 2009, 2:59 AM
> I've posted about other frustrating
> comma pumps before, but this one
> has me at my wit's end. This might be the most common
> chord
> progression in all of music and it's also the most annoying
> to deal
> with in JI.
>
> Some things that seem to not work (let's assume we're in
> C):
> - Rooting the D on 9/8 and building up 6/5's and 5/4's from
> there.
> This makes the C in the iim7 a comma sharp of the finishing
> I, which
> sounds awful.
> - Rooting the D on 10/9 and building up 6/5's and 5/4's
> from there.
> This makes the D in the iim7 a comma flat of the D in the
> V7, which
> destroys the voice leading and also sounds awful.
> - Rooting the D on 9/8 and building up 32/27's and 81/64's
> from there.
> This sounds completely out of place if your goal is to have
> beatless
> "just" voicings, and since ii-V's are so common in almost
> everything,
> it almost sounds like the piece isn't in JI at all. On the
> other hand,
> this one avoids weird comma shifts.

You've already gotten some good answers, but I thought of something a bit unorthodox: using the 19-limit minor triad. It's similar in sound to the Pythagorean minor, and could be a form of adaptive JI, with the second shifting by the 513/512 comma (3.378 cents) between the first and second chords:

ii7 = 64/57 4/3 32/19 2/1
V7 = 9/8 4/3 3/2 15/8
I7 = 1/1 5/3 3/2 15/8

~D. ¶¦¬{> http://dannywier.ucoz.com

🔗Mike Battaglia <battaglia01@...>

> You've already gotten some good answers, but I thought of something a bit unorthodox: using the 19-limit minor triad. It's similar in sound to the Pythagorean minor, and could be a form of adaptive JI, with the second shifting by the 513/512 comma (3.378 cents) between the first and second chords:
>
> ii7 = 64/57 4/3 32/19 2/1
> V7 = 9/8 4/3 3/2 15/8
> I7 = 1/1 5/3 3/2 15/8

That is a good idea and it's what I've been doing for the moment.
Actually, to be precise, I've been treating the 7th interval over the
V7 as being ideally placed at the 1003 cent metastable interval... And
then I put the minor seventh in the ii7 a fifth above that.

Since I usually work in 72-equal, this is effectively the same thing
for me as working with the Pythagorean intervals, as is it the same as
working with 19-limit intervals as you suggest... those 3 types of
intervals are made to be equivalent, I'm not sure what the exact comma
tempered out is.

Of course, in 72-equal, it's also the same thing as working in regular
old 12-tet >:| I was hoping there'd be some way to get away from that,
but maybe that's why ii7-V7-I7 sounds so fluid in 12-equal, anyway.

> ~D. ¶¦¬{> http://dannywier.ucoz.com
>

🔗Danny Wier <dawiertx@...>

--- On Mon, 11/23/09, Mike Battaglia <battaglia01@...> wrote:

> From: Mike Battaglia <battaglia01@...>
> Subject: Re: [tuning] How do you guys tune iim7-V7-I in JI?
> To: tuning@yahoogroups.com
> Date: Monday, November 23, 2009, 3:59 PM
> > You've already gotten some good
> answers, but I thought of something a bit unorthodox: using
> the 19-limit minor triad. It's similar in sound to the
> Pythagorean minor, and could be a form of adaptive JI, with
> the second shifting by the 513/512 comma (3.378 cents)
> between the first and second chords:
> >
> > ii7 = 64/57 4/3 32/19 2/1
> > V7 = 9/8 4/3 3/2 15/8
> > I7 = 1/1 5/3 3/2 15/8
>
> That is a good idea and it's what I've been doing for the
> moment.
> Actually, to be precise, I've been treating the 7th
> interval over the
> V7 as being ideally placed at the 1003 cent metastable
> interval... And
> then I put the minor seventh in the ii7 a fifth above
> that.

I forgot to mention: of the 5-limit solutions, I'd go with Hindemith's: ii7 = 9/8 4/3 27/16 3/2.

And how do you get 1003 cents, exactly? I know 25/14 is about 1004...

> Since I usually work in 72-equal, this is effectively the
> same thing
> for me as working with the Pythagorean intervals, as is it
> the same as
> working with 19-limit intervals as you suggest... those 3
> types of
> intervals are made to be equivalent, I'm not sure what the
> exact comma
> tempered out is.

I had 72-edo in mind too. And if you mean the comma between 32/27 and 19/16, it's Boethius' comma, 513/512.

~D.

🔗Mike Battaglia <battaglia01@...>

> I forgot to mention: of the 5-limit solutions, I'd go with Hindemith's: ii7 = 9/8 4/3 27/16 3/2.

Yeah, everyone's suggested that so far... Seems like an interesting
option, but it might not work for sections with a slower harmonic
rhythm. Sometimes a composer will hang onto the ii7 chord for a long
time before switching to the V7 chord, and to have the ii7 chord be
completely dissonant by itself would kind of give away the punchline,
so to speak.

> And how do you get 1003 cents, exactly? I know 25/14 is about 1004...

It's actually 1002 cents, or 1001.612 more precisely. I was
remembering it wrong. It's the metastable interval between 9/5 and
16/9, which is the same thing as the metastable interval between 7/4
and 9/5, which is the same thing as the metastable interval between
7/4 and 2/1.

More info can be found on it at: http://dkeenan.com/Music/NobleMediant.txt

The general idea is that it's a useful and quick approximation to get
"maximally dissonant" intervals, and hence intervals that are not
stable and want to resolve.

> I had 72-edo in mind too. And if you mean the comma between 32/27 and 19/16, it's Boethius' comma, 513/512.

Eh, I didn't feel like crunching the numbers, but it would actually be
a triad of commas tempered out:
- Boethius' ridiculously tiny 3.4 cent comma,
- The irrational interval between 32/27 and 299.657 cents (a perfect
fifth down from the 1002 cent metastable 7th), which turns out to be
5.522 cents,
- The irrational interval between 19/16 and 299.657 cents, which
turns out to be 2.144 cents.

These are pretty small numbers :D
Although would the irrational intervals still be called "commas" in
any sense, since they aren't rational? Working with metastable
intervals brings stuff like this out into the open.

-Mike

🔗Marcel de Velde <m.develde@...>

>
> I forgot to mention: of the 5-limit solutions, I'd go with Hindemith's: ii7
> = 9/8 4/3 27/16 3/2.
>

That should be 9/8 4/3 27/16 2/1, I assume? Not 3/2?

Then even if you see 81/64 / 128/81 as a better option than the 40/27 /
27/20 (I personally don't).
It doesn't really solve much as one could very easily turn the iim7 chord
into a IV chord which should clearly be 4/3 5/3 2/1, not 4/3 27/16 2/1.
The 27/16 will also give problems when going to the parralel A minor, etc
etc.
Using 27/16 instead of 5/3 will unavoidably get you into big trouble in most
real music uses.

Marcel

🔗duckfeetbilly <billygard@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I've posted about other frustrating comma pumps before, but this one
> has me at my wit's end. This might be the most common chord
> progression in all of music and it's also the most annoying to deal
> with in JI.
>
> Some things that seem to not work (let's assume we're in C):
> - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
> This makes the C in the iim7 a comma sharp of the finishing I, which
> sounds awful.
> - Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
> This makes the D in the iim7 a comma flat of the D in the V7, which
> destroys the voice leading and also sounds awful.
> - Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
> This sounds completely out of place if your goal is to have beatless
> "just" voicings, and since ii-V's are so common in almost everything,
> it almost sounds like the piece isn't in JI at all. On the other hand,
> this one avoids weird comma shifts.
>

This is something that I have found to be the most curious of the JI dilemmas, especially considering it is a simple chord set as well as one natural sounding to the ear.

When I try to come up with a solution to this I base it on the idea that I am discovering the real arithmetic behind the ii-V-I that explains its musical quality, i.e. what is the ear hearing about it that has made it stand the test of time?

One of my ideas is that the particular minor 7th chord that appears in this progression could actually be tuned differently, as an 11th chord extension of the following dominant. The tuning I have in mind is the sub-minor 7th, or septimal-minor 7th. 12:14:18:21. As such, it really would share a fundamental with the following dominant. Using this math, you can use the following harmonics, relative to the tonic as the fundamental, to complete the whole chord progresssion:

36:42:54:63 -> 36:42:48:60 - > 32:40:48:64

Billy

🔗hpiinstruments <aaronhunt@...>

Great topic. This is one of my favorite flavors of ii7 V7 I.
Supertonic 7 with the small minor thirds sounds really dark
and leads perfectly to a septimal dominant 7, and that small
minor seventh sounds so perfect moving to a small major third.
I'm with duckfeetbilly on this one. But there are so many ways
to do it, and they all have unique affect. Like, I love the tortured
sound of comma shifting from a ii7 tuned with large minor
third and seventh into the septimal dominant. It pulls
everything down and just ... kills. It's all just awesome.
MUSIC IS AWESOME.

--- In tuning@yahoogroups.com, "duckfeetbilly" <billygard@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > I've posted about other frustrating comma pumps before, but this one
> > has me at my wit's end. This might be the most common chord
> > progression in all of music and it's also the most annoying to deal
> > with in JI.
> >
> > Some things that seem to not work (let's assume we're in C):
> > - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
> > This makes the C in the iim7 a comma sharp of the finishing I, which
> > sounds awful.
> > - Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
> > This makes the D in the iim7 a comma flat of the D in the V7, which
> > destroys the voice leading and also sounds awful.
> > - Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
> > This sounds completely out of place if your goal is to have beatless
> > "just" voicings, and since ii-V's are so common in almost everything,
> > it almost sounds like the piece isn't in JI at all. On the other hand,
> > this one avoids weird comma shifts.
> >
>
> This is something that I have found to be the most curious of the JI dilemmas, especially considering it is a simple chord set as well as one natural sounding to the ear.
>
> When I try to come up with a solution to this I base it on the idea that I am discovering the real arithmetic behind the ii-V-I that explains its musical quality, i.e. what is the ear hearing about it that has made it stand the test of time?
>
> One of my ideas is that the particular minor 7th chord that appears in this progression could actually be tuned differently, as an 11th chord extension of the following dominant. The tuning I have in mind is the sub-minor 7th, or septimal-minor 7th. 12:14:18:21. As such, it really would share a fundamental with the following dominant. Using this math, you can use the following harmonics, relative to the tonic as the fundamental, to complete the whole chord progresssion:
>
> 36:42:54:63 -> 36:42:48:60 - > 32:40:48:64
>
> Billy
>

🔗Mike Battaglia <battaglia01@...>

> Great topic. This is one of my favorite flavors of ii7 V7 I.
> Supertonic 7 with the small minor thirds sounds really dark
> and leads perfectly to a septimal dominant 7, and that small
> minor seventh sounds so perfect moving to a small major third.
> I'm with duckfeetbilly on this one. But there are so many ways
> to do it, and they all have unique affect. Like, I love the tortured
> sound of comma shifting from a ii7 tuned with large minor
> third and seventh into the septimal dominant. It pulls
> everything down and just ... kills. It's all just awesome.
> MUSIC IS AWESOME.

You're saying something like 10/9 4/3 5/3 2/1 -> 9/8 21/16 3/2 15/8 ->
1/1 5/4 3/2 2/1 for the second one?

-Mike

> --- In tuning@yahoogroups.com, "duckfeetbilly" <billygard@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > I've posted about other frustrating comma pumps before, but this one
> > > has me at my wit's end. This might be the most common chord
> > > progression in all of music and it's also the most annoying to deal
> > > with in JI.
> > >
> > > Some things that seem to not work (let's assume we're in C):
> > > - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
> > > This makes the C in the iim7 a comma sharp of the finishing I, which
> > > sounds awful.
> > > - Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
> > > This makes the D in the iim7 a comma flat of the D in the V7, which
> > > destroys the voice leading and also sounds awful.
> > > - Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
> > > This sounds completely out of place if your goal is to have beatless
> > > "just" voicings, and since ii-V's are so common in almost everything,
> > > it almost sounds like the piece isn't in JI at all. On the other hand,
> > > this one avoids weird comma shifts.
> > >
> >
> > This is something that I have found to be the most curious of the JI dilemmas, especially considering it is a simple chord set as well as one natural sounding to the ear.
> >
> > When I try to come up with a solution to this I base it on the idea that I am discovering the real arithmetic behind the ii-V-I that explains its musical quality, i.e. what is the ear hearing about it that has made it stand the test of time?
> >
> > One of my ideas is that the particular minor 7th chord that appears in this progression could actually be tuned differently, as an 11th chord extension of the following dominant. The tuning I have in mind is the sub-minor 7th, or septimal-minor 7th. 12:14:18:21. As such, it really would share a fundamental with the following dominant. Using this math, you can use the following harmonics, relative to the tonic as the fundamental, to complete the whole chord progresssion:
> >
> > 36:42:54:63 -> 36:42:48:60 - > 32:40:48:64
> >
> > Billy
> >
>
>

🔗hpiinstruments <aaronhunt@...>

Well, to simplify, spelling local harmonic series
on roots 9/8, 3/2 and 1/1, I mean the chords:

ii7 on 9/8 = 10:12:15:18
V7 on 3/2 = 4:5:6:7:(9)
I on 1/1 = 8:10:12:(15)

In C it would be the third 6/5 from 9/8 of the ii
chord becoming the seventh 7/4 from 3/2 of
the dominant that is the comma shift motion I
find so appealing. You could use the root of ii
on 10/9 instead, but to me it doesn't sound
as good - just an opinion.

Start this video at about 1:10 for the a version
of the smoother septimal ii7 chord with added
harmonic series extensions:
<http://www.youtube.com/watch?v=b-YqbdQtmvI>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Great topic. This is one of my favorite flavors of ii7 V7 I.
> > Supertonic 7 with the small minor thirds sounds really dark
> > and leads perfectly to a septimal dominant 7, and that small
> > minor seventh sounds so perfect moving to a small major third.
> > I'm with duckfeetbilly on this one. But there are so many ways
> > to do it, and they all have unique affect. Like, I love the tortured
> > sound of comma shifting from a ii7 tuned with large minor
> > third and seventh into the septimal dominant. It pulls
> > everything down and just ... kills. It's all just awesome.
> > MUSIC IS AWESOME.
>
> You're saying something like 10/9 4/3 5/3 2/1 -> 9/8 21/16 3/2 15/8 ->
> 1/1 5/4 3/2 2/1 for the second one?
>
> -Mike
>
> > --- In tuning@yahoogroups.com, "duckfeetbilly" <billygard@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > > >
> > > > I've posted about other frustrating comma pumps before, but this one
> > > > has me at my wit's end. This might be the most common chord
> > > > progression in all of music and it's also the most annoying to deal
> > > > with in JI.
> > > >
> > > > Some things that seem to not work (let's assume we're in C):
> > > > - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
> > > > This makes the C in the iim7 a comma sharp of the finishing I, which
> > > > sounds awful.
> > > > - Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
> > > > This makes the D in the iim7 a comma flat of the D in the V7, which
> > > > destroys the voice leading and also sounds awful.
> > > > - Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
> > > > This sounds completely out of place if your goal is to have beatless
> > > > "just" voicings, and since ii-V's are so common in almost everything,
> > > > it almost sounds like the piece isn't in JI at all. On the other hand,
> > > > this one avoids weird comma shifts.
> > > >
> > >
> > > This is something that I have found to be the most curious of the JI dilemmas, especially considering it is a simple chord set as well as one natural sounding to the ear.
> > >
> > > When I try to come up with a solution to this I base it on the idea that I am discovering the real arithmetic behind the ii-V-I that explains its musical quality, i.e. what is the ear hearing about it that has made it stand the test of time?
> > >
> > > One of my ideas is that the particular minor 7th chord that appears in this progression could actually be tuned differently, as an 11th chord extension of the following dominant. The tuning I have in mind is the sub-minor 7th, or septimal-minor 7th. 12:14:18:21. As such, it really would share a fundamental with the following dominant. Using this math, you can use the following harmonics, relative to the tonic as the fundamental, to complete the whole chord progresssion:
> > >
> > > 36:42:54:63 -> 36:42:48:60 - > 32:40:48:64
> > >
> > > Billy
> > >
> >
> >
>

🔗hpiinstruments <aaronhunt@...>

There's a ii-V-i in minor at the bridge (about 1/3 way through)
on this MIDI file too, along with some other shifting extensions:
<http://www.h-pi.com/midi/Dream2.mid>

🔗Carl Lumma <carl@...>

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "duckfeetbilly" <billygard@...> wrote:

> The tuning I have in mind is the sub-minor 7th,
> or septimal-minor 7th. 12:14:18:21.
> As such, it really would share a fundamental
> with the following dominant. Using this math,
> you can use the following harmonics,
> relative to the tonic as the fundamental,
> to complete the whole chord progresssion:
>
> 36:42:54:63 -> 36:42:48:60 - > 32:40:48:64 = 8*(4:5:6:7:8)
>
Hi Billy, how about to extend that
to Hindemith's more resonant progession

iim9 -> V9 -> I9

20:24:30:35:45 -> 12:15:18:21:27 -> 4:5:6:7:9

within generalized 7-limit JI?

🔗Klaus Schmirler <KSchmir@...>

duckfeetbilly schrieb:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>> I've posted about other frustrating comma pumps before, but this one
>> has me at my wit's end. This might be the most common chord
>> progression in all of music and it's also the most annoying to deal
>> with in JI.
>>
>> Some things that seem to not work (let's assume we're in C):
>> - Rooting the D on 9/8 and building up 6/5's and 5/4's from there.
>> This makes the C in the iim7 a comma sharp of the finishing I, which
>> sounds awful.
>> - Rooting the D on 10/9 and building up 6/5's and 5/4's from there.
>> This makes the D in the iim7 a comma flat of the D in the V7, which
>> destroys the voice leading and also sounds awful.
>> - Rooting the D on 9/8 and building up 32/27's and 81/64's from there.
>> This sounds completely out of place if your goal is to have beatless
>> "just" voicings, and since ii-V's are so common in almost everything,
>> it almost sounds like the piece isn't in JI at all. On the other hand,
>> this one avoids weird comma shifts.
>>
> > This is something that I have found to be the most curious of the JI dilemmas, especially considering it is a simple chord set as well as one natural sounding to the ear.
> > When I try to come up with a solution to this I base it on the idea that I am discovering the real arithmetic behind the ii-V-I that explains its musical quality, i.e. what is the ear hearing about it that has made it stand the test of time?
> > One of my ideas is that the particular minor 7th chord that appears in this progression could actually be tuned differently, as an 11th chord extension of the following dominant. The tuning I have in mind is the sub-minor 7th, or septimal-minor 7th. 12:14:18:21. As such, it really would share a fundamental with the following dominant. Using this math, you can use the following harmonics, relative to the tonic as the fundamental, to complete the whole chord progresssion:
> > 36:42:54:63 -> 36:42:48:60 - > 32:40:48:64
> > Billy

Wow!

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Klaus Schmirler <KSchmir@...> wrote:

> > 36:42:54:63 -> 36:42:48:60 - > 32:40:48:64
> >
> > Billy
>
> Wow!

These are the same chords I suggested, except it starts
with D=9/8 instead of 8/7. That means here, the two Cs
are a 64/63 apart

C B C
A G G
F F E
D D C

vs. the final two Gs the way I had it

1/1 40/21 1/1
12/7 32/21 3/2
4/3 4/3 5/4
8/7 8/7 1/1

As mentioned, these two progressions are the same in
pajara, since 64/63 vanishes. One can use an adaptive
solution based on pajara if one desires just intonation.

-Carl