I like this scale

Friends,

Here you have information regarding the twelve tone "toctaved" scale, equal tempered.

& = Toctave = 2.00678255512 = 1205.861...cents. Equal tone interval = &^(1/12) = 1.05976204110

C ---- 1 ------------------- = 0 cents

C# -- 1.05976204110 = 100.488... = &^(1/12) ------ C#^3 = Eb

D -- 1.12309558375 = 200.976... = &^(1/6) ------- D^3 = F#

Eb -- 1.19021406818 = 301.465... = &^(!/4) --------- Eb^3 = A

E --- 1.26134369025 = 401.953... = &^(1/3) -------- E^3 = &

F --- 1.33672416369 = 502.442... = &^(5/12) ------- [(F^3)/&] = E

F# -- 1.41660952811 = 602.93.... = &^(1/2) --------- [(F#^3)/&] = F#

G --- 1.50126900495 = 703.419... = &^(7/12) -------- (G^3)/& = A

Ab -- 1.59098790491 = 803.907... = &^(2/3) --------- (Ab^3)/& = &

A ---- 1.68606858948 = 904.395... = &^(3/4) --------- (A^3)/&^2 = Eb

Bb -- 1.78683148981 = 1004.884...= &^(5/6) --------- [(Bb^3)/&^2] = F#

B ---- 1.89361618675 = 1105.372...= &^(11/12) ----- [(B^3)/&^2] = A

& ---- 2.00678255512 = 1205.861...= & ---------------- (F#)^2

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

FIFTHS

C*G = G

C#*G = Ab

D*G = A

Eb*G = Bb

E*G = B

F*G = &

[(F#*G)/&] = C#

[(G*G)/&] = D

[(Ab*G)/&] = Eb

[(A*G)/&] = E

[(Bb*G)/&] = F

[(B*G)/&] = F#

MAJOR THIRDS

C maj. 3rd = E

C# maj. 3rd = E

D maj. 3rd = E

Eb maj. 3rd = E

E maj. 3rd = E

F maj. 3rd = E

F# maj. 3rd = E

G maj. 3rd = E

Ab maj. 3rd = E

A maj. 3rd = E

Bb maj. 3rd = E

B maj. 3rd = E

-------------------------------

Mario

August, 22
----- 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