Re: A good result

Friends,

This Sunday I deserve to sleep well for I had very busy days fighting with a new scale. This time, playing or fighting with numbers I got a very good scale, members that don´t like much stretched scales will find uncommon features when taking a look at it. I mention here some of them:

--- If we call & to the new toctave, each of its 12 tones takes the form &^n, where n is a common fraction like 1/4, 2/3... similar to the 12 tet.

--- The tone frequencies gradually raise their magnitudes up to the toctave (1205 cents).

--- Equal tempered

--- Any tone (T) is exponentially linked with other one by the same 3 exponent.------ (T1)^3 = (T2)

--- Twelve equal fifths very close to 3/2.

--- Twelve equal major thirds.

--- Other properties to be found by the reader.

The first steps to derive the scale were done thanks to the information contained in a new short progression of 456 cells which is based on the original one that works with 624 elements.

This week I will send you all the data

Thanks

Mario

August, 21
----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Sunday, August 14, 2011 8:29 PM
Subject: Re: [tuning] Re: Xenwiki on Wikipedia

On Aug 14, 2011, at 8:00 AM, Graham Breed <gbreed@...> wrote:

"Keenan Pepper" <keenanpepper@...> wrote:

Why aren't you calling Mario a crackpot? He looks like a
crackpot to me.

Because it's worthwhile to maintain an air of civility when discussing academic subjects on mailing lists on the internet.

When you read Mario's work, you find it's playing with
numbers that have no foundation in anything observable.

The observation is that people prefer stretched octaves. When I listened to Mario's tuning, it sounded pleasantly bright, bright in the same way that I prefer stretched octaves. I haven't read Terhardt's work but if you say that the addition of harmonics causes a tone to drop in pitch, that would be perfectly in line with all this.

Do I think it so happens that the perfect chroma match point for all human beings is octave is 2/1 * 2 schismas and 1/8 of a Pythagorean comma? Of course not. Do I think this value is the "true octave?" No. But when people say "the octave is 2/1," and assume an unyielding view that states that this interval has its ultimate origin in mathematics, and that its perception is unclouded by auditory system nonlinearities and other intricacies of psychoacoustics, that's equally silly... Almost.

-Mike