a strange phenomenon

I am observing a very strange phenomenon with this chord:

225:280:336

It is composed of 56:45 x 75:56, and is the simplest 7-limit JI major chord. Surprisingly, it sounds almost as consonant as 4:5:6.

It also makes a pretty decent Rast, more so than 4:5:6.

Oz.

Why is this strange?
     225/280 almost exactly equals 4/5
and 280/336 almost exactly equals 5/6

   So they are virtually the same chord...makes sense why they would have virtually the same level of consonance...right?

--- On Sat, 12/20/08, Ozan Yarman <ozanyarman@...> wrote:

From: Ozan Yarman <ozanyarman@...>
Subject: [tuning] a strange phenomenon
To: "Tuning List" <tuning@yahoogroups.com>
Date: Saturday, December 20, 2008, 5:24 PM

I am observing a very strange phenomenon with this chord:

225:280:336

It is composed of 56:45 x 75:56, and is the simplest 7-limit JI major

chord. Surprisingly, it sounds almost as consonant as 4:5:6.

It also makes a pretty decent Rast, more so than 4:5:6.

Oz.

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usually when someone says they are having a strange phenomenon to a chord, i take it they are hearing something. Maybe running to the calculator is the answer. but one should not always be so sure.
My centaur tuning http://anaphoria.com/centaur.html on B i there is a major triad of 56/45 and 112/75. i would cherish this chord for its uniqueness. close to a common chord but it says something different. for those who have a taste for the subtle.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

The relative frequency of 280:225 is 1.244444_, equalling 379 cents. It is not almost exactly equal to 5:4, whose relative frequency is 1.25, equalling 386 cents. There is a 7 cent difference, which is distinguishable. Whereas, 336:280 is no other than 6:5, with a relative frequency of 1.2, equalling 316 cents. 4:5:6 and 225:280:336 are not, in terms of beats, the same chord. The major third and the fifth do not coincide with harmonics, they are much flatter. Nevertheless, the beats sound very pleasant.

Could there be a parallel between this chord and Lucy-tuning, I wonder?

Oz.

On Dec 21, 2008, at 5:28 AM, Michael Sheiman wrote:

> Why is this strange?
> 225/280 almost exactly equals 4/5
> and 280/336 almost exactly equals 5/6
>
> So they are virtually the same chord...makes sense why they would > have virtually the same level of consonance...right?
>
>
>
> --- On Sat, 12/20/08, Ozan Yarman <ozanyarman@...> wrote:
>
> From: Ozan Yarman <ozanyarman@...>
> Subject: [tuning] a strange phenomenon
> To: "Tuning List" <tuning@yahoogroups.com>
> Date: Saturday, December 20, 2008, 5:24 PM
>
> I am observing a very strange phenomenon with this chord:
>
> 225:280:336
>
> It is composed of 56:45 x 75:56, and is the simplest 7-limit JI major
> chord. Surprisingly, it sounds almost as consonant as 4:5:6.
>
> It also makes a pretty decent Rast, more so than 4:5:6.
>
> Oz.
>
>

Dear Marcel, I am positive I am not confusing 7:4 with 225:128. I like the chord 225:280:336 as a better substitute to 4:5:6 for maqam Rast. Both 5/4 and 3/2 are tempered by the same amount: -7.7115 cents. The relative beat ratio between M3 and 5th equals 1.666667_ or 5/3.

I have been working to get a decent 7-limit Rast scale by the way, and I arrived at:

0: 1/1 0.000 unison, perfect prime
1: 28/25 196.198 middle second
2: 56/45 378.602
3: 75/56 505.757
4: 112/75 694.243
5: 3136/1875 890.442
6: 6272/3375 1072.846
7: 2/1 1200.000 octave

Oz.

On Dec 21, 2008, at 5:24 AM, Marcel de Velde wrote:

> I hope you realise the following:
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 35/32 155.140 septimal neutral second
> 2: 21/16 470.781 narrow fourth
> 3: 225/128 976.537 augmented sixth
> 4: 2/1 1200.000 octave
> |
> 0: 1/1 0.000 unison, perfect prime
> 1: 35/32 155.140 septimal neutral second
> 2: 21/16 470.781 narrow fourth
> 3: 7/4 968.826 harmonic seventh
> 4: 2/1 1200.000 octave
> and you're not confusing 225/128 with 224/128 which makes the chord > 4:5:6?
>
>
> On Sun, Dec 21, 2008 at 2:24 AM, Ozan Yarman <ozanyarman@...> > wrote:
> I am observing a very strange phenomenon with this chord:
>
> 225:280:336
>
> It is composed of 56:45 x 75:56, and is the simplest 7-limit JI major
> chord. Surprisingly, it sounds almost as consonant as 4:5:6.
>
> It also makes a pretty decent Rast, more so than 4:5:6.
>
> Oz.
>
>
>

--close to a common chord but it says something different. for
--those who have a taste for the subtle.

   Ah, ok.  So maybe those couple of cents off really DO change the chord's "character" in this case despite that, technically, it comes across as basically the same chord.
  I have seen this before a few times, where a few cents does not change the technical consonance of the chord but does change the character in such a way a listener may actually prefer the "second" chord by a huge margin because it is more "mood consonant".

--- On Sun, 12/21/08, Kraig Grady <kraiggrady@anaphoria.com> wrote:

From: Kraig Grady <kraiggrady@...>
Subject: [tuning] Re: a strange phenomenon
To: tuning@yahoogroups.com
Date: Sunday, December 21, 2008, 12:49 AM

usually when someone says they are having a strange phenomenon to a

chord, i take it they are hearing something. Maybe running to the

calculator is the answer. but one should not always be so sure.

My centaur tuning http://anaphoria. com/centaur. html on B i there is a

major triad of 56/45 and 112/75. i would cherish this chord for its

uniqueness. close to a common chord but it says something different. for

those who have a taste for the subtle.

--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

Mesotonal Music from:

_'''''''_ ^North/Western Hemisphere:

North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:

Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

---Nevertheless, the beats sound very pleasant.---Could there be a parallel between this chord and Lucy-tuning, I wonder?
I would not be surprised.
In fact,
A) Charles Lucy made a point on here earlier...that most harmonic music does in fact beat...and that seems to imply that in many good chords, beating can (and perhaps even should) exist
B) Carl pointed out to me that the harmonic series (even at close ratios like 19/18 between notes) sounds good despite the beating because it "beats harmonically".  Perhaps said above chord also beats somewhat harmonically?
C) I have found in my own latest tuning (which is comprised of re-arranged intervals of the harmonic scale)...that taking away some of the intervals that cause the beating actually greatly weakens the emotional impact of the scale.

    One thing to me seems clear...there is a somewhat unexplored theoretical "hole" that exists in 5-limit JI...in determining how to strategically include beats in a scale (beside just the harmonic series) to make something pleasant and harmonic.  And Lucy-tuning, higher limit JI, the harmonic series itself...may help us explain just how to take advantage of "harmonic beating" to create beautiful new scales.

-Michael
--- On Sun, 12/21/08, Ozan Yarman <ozanyarman@...> wrote:

From: Ozan Yarman <ozanyarman@...>
Subject: Re: [tuning] a strange phenomenon
To: tuning@yahoogroups.com
Date: Sunday, December 21, 2008, 8:52 AM

The relative frequency of 280:225 is 1.244444_, equalling 379 cents. It is not almost exactly equal to 5:4, whose relative frequency is 1.25, equalling 386 cents. There is a 7 cent difference, which is distinguishable. Whereas, 336:280 is no other than 6:5, with a relative frequency of 1.2, equalling 316 cents. 4:5:6 and 225:280:336 are not, in terms of beats, the same chord. The major third and the fifth do not coincide with harmonics, they are much flatter. Nevertheless, the beats sound very pleasant.
Could there be a parallel between this chord and Lucy-tuning, I wonder?
Oz.
On Dec 21, 2008, at 5:28 AM, Michael Sheiman wrote:
Why is this strange?
     225/280 almost exactly equals 4/5
and 280/336 almost exactly equals 5/6

   So they are virtually the same chord...makes sense why they would have virtually the same level of consonance.. .right?

--- On Sat, 12/20/08, Ozan Yarman <ozanyarman@ozanyarm an.com> wrote:

From: Ozan Yarman <ozanyarman@ozanyarm an.com>
Subject: [tuning] a strange phenomenon
To: "Tuning List" <tuning@yahoogroups. com>
Date: Saturday, December 20, 2008, 5:24 PM

I am observing a very strange phenomenon with this chord:

225:280:336

It is composed of 56:45 x 75:56, and is the simplest 7-limit JI major 
chord. Surprisingly, it sounds almost as consonant as 4:5:6.

It also makes a pretty decent Rast, more so than 4:5:6.

Oz.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
> My centaur tuning http://anaphoria.com/centaur.html
> there is a major triad of 56/45 and 112/75. i would cherish this
> chord for its uniqueness. close to a common chord but it says
> something different. for those who have a taste for the subtle.

In case you didn't notice it, this is the very chord
Ozan is talking about. -Carl

2008/12/22 Ozan Yarman <ozanyarman@...>:
> The relative frequency of 280:225 is 1.244444_, equalling 379 cents. It is
> not almost exactly equal to 5:4, whose relative frequency is 1.25, equalling
> 386 cents. There is a 7 cent difference, which is distinguishable. Whereas,
> 336:280 is no other than 6:5, with a relative frequency of 1.2, equalling
> 316 cents. 4:5:6 and 225:280:336 are not, in terms of beats, the same chord.
> The major third and the fifth do not coincide with harmonics, they are much
> flatter. Nevertheless, the beats sound very pleasant.

> Could there be a parallel between this chord and Lucy-tuning, I wonder?

Could be. But it's also remarkably close to 19 note equal
temperament, you know. The minor third is exact in the chord and
nearly so in the temperament. The major third about 0.35 cents away.

Graham

This is what i had thought and recognized it first by his "description".

In case you didn't notice it, this is the very chord
Ozan is talking about. -Carl
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',