Major thirds of 1,25

Brad and Mike:

I deduced a scale whose twelve major thirds are 1,25 but the number of perfect fifths diminished to four: C major, Mi major, Fa major and A major.
Do you think this scale is an important result?

Regards

Mario

Lima, October 01

On Wed, Oct 1, 2008 at 4:08 PM, Mario Pizarro <piagui@...> wrote:
> Brad and Mike:
>
> I deduced a scale whose twelve major thirds are 1,25 but the number of
> perfect fifths diminished to four: C major, Mi major, Fa major and A major.
> Do you think this scale is an important result?

No, it sounds awful. "Octaves" of 125/64 (1159 cents) might sound fine
in some gamelans, but for Western music they're just plain out of tune
(and badly).

Keenan

Mario wrote:

> I deduced a scale whose twelve major thirds are 1,25 but the number
> of perfect fifths diminished to four: C major, Mi major, Fa major
> and A major.
> Do you think this scale is an important result?

May I chime in ? Could you list the intervals? If I understand you correctly, there should be 12 major thirds of ~386.314 cents. If so, then the octaves probably aren't tuned just, is that right?

Petr

Petr,

Here are the tones and intervals in blue.

C --- 1 x (16/15)= 1,06666666
C # --- 1,06666... x Square root of(9/8)=1,06066017178
D --- 8/[5 (Square root of 2)]=1,13137085 x Square root of (9/8)=1,06066017178
Eb --- (6/5) = 1,2 x (25/24)= 1,04166666
E --- (5/4) = 1,25 x (16/15) = 1,06666666
F --- (4/3) x Square root of (9/8)=1,06066017178
F# --- Square root of 2 x Square root of (9/8)=1,06066017178
G --- (3/2)x (25/24)= 1,04166666
Ab --- (25/16) = 1,5625 x (16/15) = 1,06666666
A --- (5/3) = 1,666666....x Square root of (9/8)=1,06066017178
Bb --- 5/2(Square root of 2)x Square root of (9/8)=1,06066017178
B --- (15/8) = 1,875 x (16/15) = 1,06666666
2C --- 2

The octaves aren't tuned just.

Regards

Mario

Lima, October 01
----- Original Message -----
From: Petr Parízek
To: tuning@yahoogroups.com
Sent: Wednesday, October 01, 2008 3:26 PM
Subject: Re: [tuning] Major thirds of 1,25

Mario wrote:

> I deduced a scale whose twelve major thirds are 1,25 but the number
> of perfect fifths diminished to four: C major, Mi major, Fa major
> and A major.
> Do you think this scale is an important result?

May I chime in ? Could you list the intervals? If I understand you correctly, there should be 12 major thirds of ~386.314 cents. If so, then the octaves probably aren't tuned just, is that right?

Petr