tuning of chords

Dear all,

This is my first post to this mailing list. I have a question and I hope somebody can help me.

I am looking for a reference (article or book) in which I can find something about the (just) tuning of chords. If for example 5-limit just intonation is considered, most people agree (I think) that a major triad should be tuned as 1-5/4-3/2. But if then a dominant seventh chord is considered it is not so obvious if this should be tuned as 1-5/4-3/2-9/5 or as 1-5/4-3/2-16/9 or even something else, right? And in more complicated chords the ambiguity seems even greater.

My question is now, is there ever written something about his? Can one say that there is no unambiguous theory about the tuning of chords?
Thanks for your help.

Kind regards,
Aline Honingh

--- In tuning@yahoogroups.com, Aline Honingh <ahoningh@s...> wrote:

> I am looking for a reference (article or book) in which I can find
> something about the (just) tuning of chords. If for example 5-limit
just
> intonation is considered, most people agree (I think) that a major
triad
> should be tuned as 1-5/4-3/2. But if then a dominant seventh chord is
> considered it is not so obvious if this should be tuned as
1-5/4-3/2-9/5
> or as 1-5/4-3/2-16/9 or even something else, right? And in more
> complicated chords the ambiguity seems even greater.

One answer is to tune to whatever sounds right. All three seventh
chords are the same in 12-equal, and so the question does not arise.
Since (9/5)/(16/9) = 81/80, we would not worry about the difference
between 9/5 and 16/9 in meantone; in other tuning systems, there is a
difference, and it might depend on whether you want a subdominant note
in the V7 chord, which one could claim is required for a true dominant
seventh. In meantone, of course, you *also* have the choice of
C-E-G-A# as a tuning, the German sixth, which is an approximate
1-4/3-3/2-7/4 and it is a very nice chord indeed. It gets used
relatively rarely in "common practice", I think, only because in the
meantone era people were usually restricted to twelve notes on fixed
intonation instruments. Needless to say, the question of whether to
use E## or Gbb for an 11/8 doesn't even arise. In 31-et, they are in
fact the same note.

My own practice is to use 1-5/4-3/2-7/4 a heck of a lot, but then I'm
not usually messing about with tonic-dominant.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> One answer is to tune to whatever sounds right.

Let me expand on that:

(1) Use 1-5/4-3/2-7/4 if you want the most harmonious, blended chord.

(2) Use 1-5/4-3/2-9/5 for a fairly harmonious 5-limit chord; it has
a 9/5 from 1, and a 6/5 from 3/2.

(3) Use 1-5/4-3/2-16/9 if it is a V7 chord and it is important for the
subdominant to be a chord element.

Aline Honingh wrote:

> I am looking for a reference (article or book) in which I can find
> something about the (just) tuning of chords.

If there's not one, there jolly well should be. One of us might need to write one. Just so happens I'm experimenting with how chords could be voiced in JI or 53-tone Pythagorean, using oud as my test instrument.

And welcome to the list!

> If for example 5-limit just
> intonation is considered, most people agree (I think) that a major triad
> should be tuned as 1-5/4-3/2. But if then a dominant seventh chord is
> considered it is not so obvious if this should be tuned as 1-5/4-3/2-9/5
> or as 1-5/4-3/2-16/9 or even something else, right? And in more
> complicated chords the ambiguity seems even greater.

As Gene said in another reply, there are three ways to play a seventh chord. This is my own opinion of when to use those three chords:

1/1 5/4 3/2 7/4 (0 17 31 43 in 53-tone): the non-resolving natural seventh, the kind of chord barbershop quartets can end a tune on. An example would be the "and many more" coda on "Happy Birthday", consisting of the pitches 3/2 5/3 3/2 7/4. Very important in jazz and blues, and if you add 7/3 (65), you get that famous chord from Jimi Hendrix's "Purple Rain".

1/1 5/4 3/2 16/9 (0 17 31 44) will most likely will resolve to a major on the fourth, 4/3 5/3 2/1 (22 39 53), since 16/9 is a perfect fourth higher than 4/3.

1/1 5/4 3/2 9/5 (0 17 31 45): This one would have to be connected with the minor third, 6/5. This could be the middle chord in the progression I-VI7-ii.

Ninths, elevenths, thirteenths, sixths, suspended chords... I'm a long way from figuring those out. But hopefully I'll put up a list of oud/fretless guitar chords in the Files section before too long. I use 53-tone as an easy reference, and go as far as 11-limit right now. One of my favorites is 1/1 11/9 3/2 11/6 (0 15 31 46) typically on E half-flat, a neutral seventh, which can also be found in the Arabic maqams Iraq, Rast, Husayni and Sikah.

__________________________________________

-3/2 5/3 3/2 7/4. Very important in jazz and blues, and if you add 7/3
(65), you
-get that famous chord from Jimi Hendrix's "Purple Rain".

Either you meant "Purple Haze" or there is an "Artist Formally Known As
Jimi Hendrix"

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Danny Wier wrote:

>1/1 5/4 3/2 7/4 (0 17 31 43 in 53-tone): the non-resolving natural seventh, >the kind of chord barbershop quartets can end a tune on. An example would be >the "and many more" coda on "Happy Birthday", consisting of the pitches 3/2 >5/3 3/2 7/4. Very important in jazz and blues, and if you add 7/3 (65), you >get that famous chord from Jimi Hendrix's "Purple Rain".
>
It's good to hear that you're in touch with your inner Jimi Hendrix.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

>> -3/2 5/3 3/2 7/4. Very important in jazz and blues, and if you add 7/3 >> (65), you
>> -get that famous chord from Jimi Hendrix's "Purple Rain".
>
> Either you meant "Purple Haze" or there is an "Artist Formally Known As > Jimi Hendrix"

Thanks, I did meant "Purple Haze". It was early in the morning when I posted that.

hi Aline,

--- In tuning@yahoogroups.com, Aline Honingh <ahoningh@s...> wrote:

> Dear all,
>
> This is my first post to this
> mailing list. I have a question
> and I hope somebody can help me.
>
> I am looking for a reference
> (article or book) in which I can
> find something about the (just)
> tuning of chords. If for example
> 5-limit just intonation is
> considered, most people agree
> (I think) that a major triad
> should be tuned as 1-5/4-3/2.
> But if then a dominant seventh
> chord is considered it is not so
> obvious if this should be tuned as
> 1-5/4-3/2-9/5 or as 1-5/4-3/2-16/9
> or even something else, right? And
> in more complicated chords the
> ambiguity seems even greater.
>
> My question is now, is there ever
> written something about his? Can
> one say that there is no unambiguous
> theory about the tuning of chords?
> Thanks for your help.

i have an entry on the "dominant-7th chord"
in the Tonalsoft Encyclopedia:

http://tonalsoft.com/enc/dominant-7th.htm

and also a webpage i wrote a few years ago
which explores various different tunings
of this chord and its resolutions, and
including MIDI audio files of the examples:

http://tonalsoft.com/td/monzo/i-iv-v7-i/i-iv-v-i.htm

-monz

Danny,

So, have we found a volunteer to write the book? :-)

Surely, the book should be written (if there is only
to be ONE book) by an author (or authors) who is a
practising musician with significant experience in the
subject.

Looks like we have a _qualified_ volunteer.

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Tue, 5 Apr 2005 07:54:33 -0500
From: "Danny Wier"
Subject: Re: tuning of chords

Aline Honingh wrote:

> I am looking for a reference (article or book) in which I can find
> something about the (just) tuning of chords.

If there's not one, there jolly well should be. One of us might need to
write one. Just so happens I'm experimenting ...

________________________________________________________________________
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Yahya Abdal-Aziz wrote in response to me:

> So, have we found a volunteer to write the book? :-)

I could help, but for this kind of thing I'd much rather it be a group project.

> Surely, the book should be written (if there is only
> to be ONE book) by an author (or authors) who is a
> practising musician with significant experience in the
> subject.

Aw, there are folks here with MUCH more experience in that field than me. And I'm more of a bassist than anything, so I should concentrate on writing something for microtonal bass.

Of course having a strong interest in this sort of field and a motivation to study and learn more is important, and I definitely have that.

~Danny~