7-limit JI: need a guide (for newbies)

I will admit I know little about 7-limit JI beyond using it to
emulate/approximate 5-limit JI-type chords. And I get the strong
impression that trying to think of 7-limit JI in 5-limit JI terms is
far from optimal in the same way using 3-limit terms for 5-limit JI is.

******************************
So, just as a starter's guide, what are some good 7-limit JI chords
and what's a good way of defining how consonant a 7-limit JI chord is
(beside just memorizing them)?

And, in your opinion, what are some of the best examples of 7-limit
JI far as compositions I can listen to (used in a way where it's NOT
trying to emulate 5-limit intervals/chords)?
-------------------------------------------

I also think...7-limit JI may be a great thing for myself and others
to benchmark new scales we create against. It seems to me 7-limit,
when used well, can provide near 5-limit consonance with more possible
chords and flexibility...thus providing more of a challenge to new
non-JI systems.

***********************************
I will also agree 7-limit is fairly "futuristic" as virtually all
the tuning systems I have seen are diatonic and seem to be based on
emulating 5-limit JI intervals.
So before I partly write-off 7-limit JI as a "slightly more flexible
version of 5-limit" I would like to see what it can do.

-Michael

Dear Michael,

On Feb 23, 2009, at 10:46 PM, djtrancendance wrote:
> So, just as a starter's guide, what are some good 7-limit JI chords

Below is a list of common 7-limit chords which I like particularly. Most names are from Scale, a few are my own.

* Triads

6 7 9 subminor
5/5 6/5 7/5 harmonic diminished
7/7 7/6 7/5 "utonal" diminished

* Tetrads

4 5 6 7 harmonic 7th
6 7 9 10 subminor 6th
1/3 1/4 1/5 1/7 subharmonic 6th, Vogel's Tristan Chord
12 14 18 21 subminor 7th

5 7 15 35 15-limit ASS 2
12 15 21 28 Hendrix Chord (Erlich)
16 21 24 28 Pepper's Square

Best
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Torsten,

    These are very nice chords!  I still wonder why so many people seem to think 7-limit is so much more dissonant or impractical than 5-limit...because I honestly can't hear it much.
------------------------------
    Trying to maintain as many of those chords as possible I tried to write my own 7-limit JI scale:

4/4 9/8 5/4 21/16 6/4 7/5 7/4 15/8
OR 
1 1.125 1.25 1.3125 1.5 1.575 1.75 1.875

   I am betting someone has already created that scale...any ideas who has and/or where I can find info on it?

-Michael

--- On Mon, 2/23/09, Torsten Anders <torsten.anders@...> wrote:

From: Torsten Anders <torsten.anders@plymouth.ac.uk>
Subject: Re: [tuning] 7-limit JI: need a guide (for newbies)
To: "tuning@yahoogroups.com" <tuning@yahoogroups.com>
Date: Monday, February 23, 2009, 3:35 PM

Dear Michael,

On Feb 23, 2009, at 10:46 PM, djtrancendance wrote:

> So, just as a starter's guide, what are some good 7-limit JI chords

Below is a list of common 7-limit chords which I like particularly.

Most names are from Scale, a few are my own.

* Triads

6 7 9 subminor

5/5 6/5 7/5 harmonic diminished

7/7 7/6 7/5 "utonal" diminished

* Tetrads

4 5 6 7 harmonic 7th

6 7 9 10 subminor 6th

1/3 1/4 1/5 1/7 subharmonic 6th, Vogel's Tristan Chord

12 14 18 21 subminor 7th

5 7 15 35 15-limit ASS 2

12 15 21 28 Hendrix Chord (Erlich)

16 21 24 28 Pepper's Square

Best

Torsten

--

Torsten Anders

Interdisciplinary Centre for Computer Music Research

University of Plymouth

Office: +44-1752-586219

Private: +44-1752-558917

http://strasheela. sourceforge. net

http://www.torsten- anders.de

>
> These are very nice chords! I still wonder why so many people seem to
> think 7-limit is so much more dissonant or impractical than
> 5-limit...because I honestly can't hear it much.

I don't think there's anybody saying 7-limit chords are dissonant.
1/1 5/4 3/2 7/4 is way more consonant than 1/1 5/4 3/2 16/9
Yet in my opinion is atleast common practice music it's 1/1 5/4 3/2 16/9 you
want for for instance the dominant 7th chord.

> ------------------------------
> Trying to maintain as many of those chords as possible I tried to write
> my own 7-limit JI scale:
>
> 4/4 9/8 5/4 21/16 6/4 7/5 7/4 15/8
> OR
> 1 1.125 1.25 1.3125 1.5 1.575 1.75 1.875
>
> I am betting someone has already created that scale...any ideas who has
> and/or where I can find info on it?

Try analyse - compare scale in scala after downloading the scale archive
from the scala webpage and setting this as the directory in scala.
btw 7/5 comes before 3/2

Marcel

--I don't think there's anybody saying 7-limit chords are dissonant.
Perhaps I misinterpreted, when you said 7-limit was "wrong" in previous e-mails, I took "wrong" to mean "less listenable".

--Yet in my opinion is atleast common practice music it's 1/1 5/4 3/2 --16/9 you want for for instance the dominant 7th chord.
    Right, but that's like saying X is not equal to Y or NEW is not nearly equal to OLD.
   Simply put, they are fundamentally different...and so it figures that music made for one is not perfectly convertible to the other and you can't "round" the notes of a 5-limit song to 7-limit and have them work as well.

  Thus, my guess is, in using 7-limit, it is best to start making new songs for it from scratch, rather than re-tuning 5-limit ones to fit it.
*************
  Mind my bringing up the "ethical issue" but...why does it seem so many people are set on making any new tuning or scale system fit 5-limit JI?

  Is it really that much of a crime to have a scale system with new chords that forces the composer to learn new theory rather than translate old notes/intervals into near-equivalents (and aren't new chords and theory part of what makes alternative tunings fun in the first place)?

-Try analyse - compare scale in scala after downloading the scale
-archive -from the scala webpage and setting this as the directory in
-scala.
   I will...and I assume that will compare the scale against the entire SCALA library.

-btw 7/5 comes before 3/2

Ugh, my bad, I incorrectly converted that interval, it should be

4/4 9/8 5/4 21/16 7/5 6/4(AKA 3/2) 7/4 15/8

and 7/5 = 1.4 not 1.575 (I must have taken 7/5 * 9/8 instead to get 1.575 before)