It works ... But how is it called?

Hi there.

This is a method of 5-limit tempering which is totally different from
schismic or meantone tunings. I'm out of words. It just works. But is there
also a name for this kind of temperament?

! limx15.scl
!
Linear 5-limit temperament with minor third as generator
15
!
67.9700
181.0525
249.0225
316.9925
384.9625
4/3
566.0150
633.9850
3/2
815.0375
883.0075
950.9775
1018.9475
1132.0300
2/1

Petr

Hi petr

You have intervallic pattern of abaaabaaabaaaaba with :
a=67.97
b=113.082
11a+4b=1200
With 2 tetrachords as abaaab and baaaba which are enantiomorph of each other.

its rational version is :
0: 1/1 0.000 unison, perfect prime
1: 26/25 67.900
2: 10/9 182.404 minor whole tone
3: 15/13 247.741 tridecimal 5/4-tone
4: 6/5 315.641 minor third
5: 5/4 386.314 major third
6: 4/3 498.045 perfect fourth
7: 43/31 566.482
8: 49/34 632.696
9: 3/2 701.955 perfect fifth
10: 8/5 813.686 minor sixth
11: 5/3 884.359 major sixth, BP sixth
12: 45/26 949.696
13: 9/5 1017.596 just minor seventh, BP seventh
14: 25/13 1132.100
15: 2/1 1200.000 octave
|

1: 26/25 67.900
2: 125/117 114.503
3: 27/26 65.337 tridecimal comma
4: 26/25 67.900
5: 25/24 70.672 classic chromatic semitone, minor chroma
6: 16/15 111.731 minor diatonic semitone
7: 129/124 68.437
8: 1519/1462 66.214
9: 51/49 69.259
10: 16/15 111.731 minor diatonic semitone
11: 25/24 70.672 classic chromatic semitone, minor chroma
12: 27/26 65.337 tridecimal comma
13: 26/25 67.900
14: 125/117 114.503
15: 26/25 67.900

If we take (b) as (114.503+111.731)/2= 113.117 which has 0.035 cent with your (b) and (a) as (1200-(4*113.117))/11=67.957 with deviation of -0.0125 cent with your (a) then we will have :

0: 1/1 0.000 unison, perfect prime
1: 67.957 cents 67.957
2: 181.074 cents 181.074
3: 249.031 cents 249.031
4: 316.988 cents 316.988
5: 384.945 cents 384.945
6: 498.062 cents 498.062
7: 566.019 cents 566.019
8: 633.976 cents 633.976
9: 701.933 cents 701.933
10: 815.050 cents 815.050
11: 883.007 cents 883.007
12: 950.964 cents 950.964
13: 1018.921 cents 1018.921
14: 1132.038 cents 1132.038
15: 1200.000 cents 1200.000

With maximum and minimum difference of 0.022 cent and -0.025 cent with your scale.

Shaahin Mohaajeri

Tombak Player & Researcher , Microtonal Composer

My web site

My page in Harmonytalk

My tombak musics in Rhythmweb

My article in DrumDojo

My musics in Wikipedia, the free encyclopedia :

- A composition based on a folk melody of Shiraz region, in shur-dastgah by Mohajeri Shahin

- An experiment in Iranian homayun and chahargah modes by Mohajeri Shahin

-----Original Message-----
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Petr Pa??zek
Sent: Sunday, October 08, 2006 1:53 PM
To: Tuning List
Subject: [tuning] It works ... But how is it called?

Hi there.

This is a method of 5-limit tempering which is totally different from
schismic or meantone tunings. I'm out of words. It just works. But is there
also a name for this kind of temperament?

! limx15.scl
!
Linear 5-limit temperament with minor third as generator
15
!
67.9700
181.0525
249.0225
316.9925
384.9625
4/3
566.0150
633.9850
3/2
815.0375
883.0075
950.9775
1018.9475
1132.0300
2/1

Petr

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Hi Shaahin.

I'm surprised. How did you get your rational version? I also made one. But
it's completely different.

! ramx15.scl
!
Untempered version of the 5-limit minor third chain
15
!
25/24
10/9
125/108
6/5
5/4
4/3
25/18
36/25
3/2
8/5
5/3
216/125
9/5
48/25
2/1

Petr

this is the solution larry hanson did. based on a chain of 6/5 formings scales at 11,15,19, etc. ?
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Hi Kraig.

This sounds interesting. I've never heard of Hanson's scales. Where is it
documented? Where can I find more?
Thanks.

Petr

--- In tuning@yahoogroups.com, Petr Par�zek <p.parizek@...> wrote:
>
> Hi Kraig.
>
> This sounds interesting. I've never heard of Hanson's scales. Where
is it
> documented? Where can I find more?
> Thanks.

This is simply an example of MOS for a linear temperament. The 5-limit
temperament tempering out the kleisma, 15625/15552 has in fact been
given the name "hanson" by Paul Erlich. The generator is around 317
cents, a slightly sharp minor third. There are MOS of size 11, 15, 19,
34, 53, 87, 140 etc.

Petr Par�zek wrote:
> Hi Kraig.
> > This sounds interesting. I've never heard of Hanson's scales. Where is it
> documented? Where can I find more?
> Thanks.

Larry Hanson's keyboard design is described here:

http://www.anaphoria.com/hanson.PDF

More detailed information about the chain of minor thirds scale (specifically an 11-note version of the scale, but with a brief mention of the 15-note scale) is on Dave Keenan's page:

http://dkeenan.com/Music/ChainOfMinor3rds.htm

Hi petr

You can use farey rational approximation of scala . I used its default parameters for order and prime.

Shaahin Mohaajeri

Tombak Player & Researcher , Microtonal Composer

My web site <http://240edo.tripod.com/>

My page in Harmonytalk <http://www.harmonytalk.com/id/908>

My tombak musics in Rhythmweb <http://www.rhythmweb.com/gdg>

My article in DrumDojo <http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>

My musics in Wikipedia, the free encyclopedia :

- A composition based on a folk melody of Shiraz region, in shur-dastgah by Mohajeri Shahin <http://www.xenharmony.org/mp3/shaahin/shur.mp3>

- An experiment in Iranian homayun and chahargah modes by Mohajeri Shahin <http://www.xenharmony.org/mp3/shaahin/homayun.mp3>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Petr Pa??zek
Sent: Sunday, October 08, 2006 5:24 PM
To: tuning@yahoogroups.com
Subject: Re: [tuning] It works ... But how is it called?

Hi Shaahin.

I'm surprised. How did you get your rational version? I also made one. But
it's completely different.

! ramx15.scl
!
Untempered version of the 5-limit minor third chain
15
!
25/24
10/9
125/108
6/5
5/4
4/3
25/18
36/25
3/2
8/5
5/3
216/125
9/5
48/25
2/1

Petr

here is another link to some more of hanson work and how the keyboard design works well for 72.
Calling this temperment "Hanson" predates the tuning list
http://anaphoria.com/starr.PDF
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

> Calling this temperment "Hanson" predates the tuning list
> http://anaphoria.com/starr.PDF

This system used to be called "kleismic" on this list, before we knew
about Hanson's contribution, for those of you using the search feature.

Paul E., Dave K., Gene, Graham, myself, and probably Herman Miller
have made substantial original contributions to the theory of this
system, none of which are evident in this pdf.

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> here is another link to some more of hanson work and how the keyboard
> design works well for 72.

72 works well as a tuning for two different versions of the 7-limit
kleismic family. One has octave equivalent wedgie <<6 5 22...
("catakleismic" = 53&72) and the other, much less complex but also
much more out of whack in the 7-limit, <<6 5 3 ... ("keemun" = 19&34.)
The difference is that in keemun, we take three 6/5's of 316 2/3
cents, 19 steps of 72, to be the 7/4. This gives a 7/4 of 950 cents,
which is quite flat. Otherwise we can use 58 steps of 72, 966 2/3
cents. This is about two cents flat.

It's also possible to use 72 with 59 steps as the 7/4, which tempers
out 50/49. If you want to do 50/49 planar and are much more concerned
to get good triads than good 7 harmonies, not a bad choice. More
on-topic, however, is to temper out both 50/49 and the kleisma. This
gives <<12 10 10 -12 -18 -5||, the 4&38 temperament, with a 6/5
generator and a half-octave period. This temperament does not seem to
have a name, but it appears to be usable, and 72 is a poptimal tuning
for it. Using all three versions of the 7/4 would certainly be
possible for the ambitious.

Larry Hanson came up with his tuning and keyboard design during WWII.
the article has been up since 2000
as has been the Horogram (#9) which labels this generator as Hanson

Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

> Larry Hanson came up with his tuning and keyboard design during WWII.
> the article has been up since 2000 as has been the Horogram (#9) which
> labels this generator as Hanson

Dave and I were posting here about this system in 1999, if not earlier.
As you can see by Gene's recent post, a lot has gone down since WWII.

-Carl

I am just aware of what Hanson did.
tempering out this small interval.
Just what else applies i have not seen
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles