Re: [tuning] What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal Temperament??

Hmm.......
    A minor second is most dissonant so far as the amount of beating, obviously, since it is closest to the root note and vibrates most against it.

    But the real question seems to be...which interval is farthest from it's pure form IE the perfect JI equivalent.  For example ET has the 5th at about 0.498 instead of the perfect 5th at 0.5.

   I am not sure what all the "perfect" intervals are, but, simply put, the tone with the greatest fractional difference between their perfect ET and JI equivalents (IE .5/.498 = apx. 1.004 "dissonance disadvantage rating").  So if anyone has a list of what all the perfect JI intervals are I (or anyone else) could easily figure this out.

--- On Wed, 1/21/09, Chris Vaisvil <chrisvaisvil@...> wrote:

From: Chris Vaisvil <chrisvaisvil@...>
Subject: Re: [tuning] What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal Temperament??
To: tuning@yahoogroups.com
Date: Wednesday, January 21, 2009, 2:20 PM

A minor 2nd.... maybe.

I don't know if the concept of dissonant, and especially out of tune, applies anymore, especially in this particular group of composers/listeners .

All intervals are equally useful, just in different ways. Western music harmony evolved to hide dissonance, especially the 7th. In our age this interval is accepted without special treatment. Harmony often is just color.

A more proper question would be most "tense" and again minor 2nd...

Chris

On Wed, Jan 21, 2009 at 11:48 AM, micro_piano <frankw802@yahoo. com> wrote:

Hi all!!

This question may SEEM very basic, but I'd like to see what everyone

ACTUALLY believes is the most "out-of tune" sounding (or "dissonant")

interval in Equal Temperament.

There are obviously both opinions that are going to be involved here

as well as facts.

Obviously, certain people are going to hear different intervals

differently. That is where the "opinions" come in.

But what about the facts, meaning the mathematical "certainties" that

answer the question for us, but where are our aural senses (and thus

our individual "opinions") answer the question quite differently.

I'd just like to know, once and for all, what each one of you think is

the most "out-of-tune" sounding (or "dissonant") interval in the Equal

Temperament system...

Thanks for your answers in advance,

Frank Wilson, Ph.D (Musicology)

--Well, 17/16 and 19/16 is pretty much right there in 12-tet. So you can
---definitely get at some upper-overtone stuff by messing around with
--those intervals, at least.

>>and require some accuracy (+-5 cents, maybe?) to be

This again seems to play into my theory...that
A) fractions with a maximum factor of around 16 or less have fairly good consonance.
B) but...getting too far off, as with the 3rd and 6th, which are 12+ cents off pure, can cause problems.  So all intervals must be within under 5 or so cents of about a limit 16 or less "pure" interval.

     Here is a question: what fixed scales do you all know off meet both of the above conditions AND has 7 notes per octave (where the octave is 2/1 IE not stretched)?
*******************************************************************************************************

    It amazes me I have not heard of such a scale...even fixed (diatonic) 7-note JI scales seem to have a problem with, for example, getting a fairly (IE within 5 cents) pure sounding 3rd starting from notes other than the root and/or getting a pure 4th using the same method.
__________________________________________________

   It seems the harmonic series IE
        1 *7/6 *8/7 *9/8 *10/9 * 11/10 *12/11 *13/12 *14/13(octave)
   barely meets this criteria as it tops out at 14/13 for exactly 7 notes per octave...
But even it has problems because the pattern does not stay with 16 limit as you go up further (IE the next octave at 26/13)...or down further (about 7/3), which has about 4 notes per octave instead of 7. 
   So the harmonic series does not seem to satisfy the criteria either across more than 1 octave.

Any ideas?

--- On Thu, 1/22/09, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal Temperament??
To: tuning@yahoogroups.com
Date: Thursday, January 22, 2009, 9:02 AM

On Thu, Jan 22, 2009 at 9:59 AM, caleb morgan <calebmrgn@yahoo. com> wrote:

>

> I've come to the opinion that 12-tet is only capable of suggesting 5-limit

> chains.

> So, you can almost guide the ear to hear 7-ratios, but not quite.

> 11-ratios and 13-ratios are just non-existent in 12-tet.

> they are more subtle, and require some accuracy (+-5 cents, maybe?) to be

> heard as themselves.

Well, 17/16 and 19/16 is pretty much right there in 12-tet. So you can

definitely get at some upper-overtone stuff by messing around with

those intervals, at least.

> C-G-E-F#-B-D#

> a cool chord, B triad over C.

> D# is definitely #2 (or #9) and the scale is C Lydian #3, or E harmonic

> minor.

> caleb

>

You mean #2? :)

Good to see someone else is up on modal theory on these forums :)

-Mike