Topic: A pretty weird but definitely interesting scale

1 scales

Thread (6 messages)

From: Petr Pařízek (2008-03-02)
Subject: A pretty weird but definitely interesting scale

Hi everyone.

I would be very curious if someone had mentioned this before -- at least I 
haven't found nor a single word about it. Similarly to the way BP has a 
period of 3/1 and approximates 1:3:5:7:9, this is a 4/1-periodic linear 
temperament and approximates 1:4:7:10:13:16 so there's some kind of 
"triharmony" in it -- or whatever I could call it. It has two interval 
sizes, one being about 158 cents and another one being quite close to the 
usual 12-EDO semitone. The generator is ~357.076254 cents, which is the 9th 
root of 32/5.
I think this could be a similarly interesting possibility as BP is. 
Unfortunately, so far I've not found a way to easily set up the tuning in 
the XG format but I hope I'll think of a solution soon because, personally, 
I can't wait to make a new piece in it. The scale has 20 tones and looks 
like this:

! triharmon.scl
!
The triharmonic scale
 20
!
 99.53378
 257.54248
 357.07625
 456.61003
 614.61873
 714.15251
 8/5
 971.69498
 1071.22876
 1170.76254
 1328.77124
 1428.30502
 5/2
 1685.84749
 1785.38127
 1943.38997
 2042.92375
 2142.45752
 2300.46622
 4/1

Petr

From: iranief (2008-03-02)
Subject: Re: A pretty weird but definitely interesting scale

I was reading about the "47-step, non-octave scale within the framework of the double 
octave" by Heinz Bohlen http://members.aol.com/bpsite/pythagorean.html
and I see some similarities with yours.

--- In tuning@yahoogroups.com, Petr Pařízek  wrote:
>
> Hi everyone.
> 
> I would be very curious if someone had mentioned this before --

From: Kraig Grady (2008-03-02)
Subject: Re: [tuning] Re: A pretty weird but definitely interesting scale

if you really look at the 12th as an interval of equivalence BP can look 
like this type of diamonds
http://anaphoria.com/images/BPdiamond.gif
http://anaphoria.com/images/BPdia2.gif

iranief wrote:
>
> I was reading about the "47-step, non-octave scale within the 
> framework of the double
> octave" by Heinz Bohlen http://members.aol.com/bpsite/pythagorean.html 
> 
> and I see some similarities with yours.
>
> --- In tuning@yahoogroups.com , Petr 
> Pa\u0159ízek  wrote:
> >
> > Hi everyone.
> >
> > I would be very curious if someone had mentioned this before --
>
>  

-- 
Kraig Grady
North American Embassy of Anaphoria Island 
The Wandering Medicine Show
KXLU  88.9 FM Wed 8-9 pm Los Angeles

From: Herman Miller (2008-03-03)
Subject: Re: [tuning] Re: A pretty weird but definitely interesting scale

iranief wrote:
> I was reading about the "47-step, non-octave scale within the framework of the double 
> octave" by Heinz Bohlen http://members.aol.com/bpsite/pythagorean.html
> and I see some similarities with yours.
> 
> --- In tuning@yahoogroups.com, Petr Pa\u0159ízek  wrote:
>> Hi everyone.
>>
>> I would be very curious if someone had mentioned this before -- 

They do seem to be related. The harmonic resources are similar. The 
triharmonic scale can be extended to 47 notes with 27 large steps of 
58.47 cents and 20 small steps of 41.06 cents, compared with the 51.06 
cent steps of the equally tempered non-octave scale and the varying 
sizes of the intervals in the just scale on the Bohlen-Pierce site.

From: Petr Parízek (2008-03-03)
Subject: Re: [tuning] Re: A pretty weird but definitely interesting scale

> They do seem to be related. The harmonic resources are similar. The
> triharmonic scale can be extended to 47 notes with 27 large steps of
> 58.47 cents and 20 small steps of 41.06 cents, compared with the 51.06
> cent steps of the equally tempered non-octave scale and the varying
> sizes of the intervals in the just scale on the Bohlen-Pierce site.

And there's yet another possibility which lies somewhere in-between: If you 
take the 20 tone set and fill the larger steps with the smaller ones, you 
get a 27 tone scale, which is something neither the webpage nor I have 
mentioned. Still, 47 seems to me to be quite a lot of notes.

Petr

From: Herman Miller (2008-03-04)
Subject: Re: [tuning] Re: A pretty weird but definitely interesting scale

Petr Par\ufffdzek wrote:
>> They do seem to be related. The harmonic resources are similar. The
>> triharmonic scale can be extended to 47 notes with 27 large steps of
>> 58.47 cents and 20 small steps of 41.06 cents, compared with the 51.06
>> cent steps of the equally tempered non-octave scale and the varying
>> sizes of the intervals in the just scale on the Bohlen-Pierce site.
> 
> And there's yet another possibility which lies somewhere in-between: If you 
> take the 20 tone set and fill the larger steps with the smaller ones, you 
> get a 27 tone scale, which is something neither the webpage nor I have 
> mentioned. Still, 47 seems to me to be quite a lot of notes.

For a 2-octave scale it's not bad (less than 24 notes per octave), but 
still, a generalized keyboard with at least a 7x7 array of keys would be 
  useful to have (a 14x8 array for 4 octaves).

The 4:7:10:13 chord would fit nicely under the fingers with a 
generalized keyboard mapping of 357.076254 cents across and 99.533778 
cents down to the right. Put your fingers on X-G-U-K or C-H-I-L to get 
an idea. That won't be much help until generalized keyboards are more 
common, but maybe someday...