Topic: Hobbit scales

2 scales

Thread (7 messages)

From: genewardsmith (2010-09-26)
Subject: Hobbit scales

Over on tuning-math I've introduced hobbit scales. These generalize MOS scales to higher rank regular temperaments in the sense that hobbit scales in rank two are MOS. I'm not quite sure how to proceed with making these available; they aren't as easy to compute or understand as MOS, but they seem to have nice properties. Perhaps an archive of scales.

Below I give two examples of hobbit scales, one a 15-note scale for thrush temperament, and the other a 41-note scale for (17 limit) jove temperament. Both are strictly proper.

! thrush15.scl
Thrush[15] hobbit 7&9 limit minimax tuning
15
!
79.86894
159.73788
231.17409
311.04303
390.91197
498.04500
577.91394
622.08606
701.95500
809.08803
888.95697
968.82591
1040.26212
1120.13106
1200.00000
!
! Scale in fractional monzo format
! Commas 126/125, 176/175 
! |-7/3 1/3 0 2/3 0> 
! |-14/3 2/3 0 4/3 0> 
! |3 0 0 -1 0> 
! |2/3 1/3 0 -1/3 0> 
! |-5/3 2/3 0 1/3 0> 
! |2 -1 0 0 0> 
! |-1/3 -2/3 0 2/3 0> 
! |4/3 2/3 0 -2/3 0> 
! |-1 1 0 0 0> 
! |8/3 -2/3 0 -1/3 0>
! |1/3 -1/3 0 1/3 0> 
! |-2 0 0 1 0> 
! |17/3 -2/3 0 -4/3 0> 
! |10/3 -1/3 0 -2/3 0> 
! |1 0 0 0 0>

! jove41.scl
Jove[41] 17-limit hobbit in 243et
! commas 243/242, 441/440, 364/363, 595/594
41
!
34.56790
64.19753
83.95062
118.51852
148.14815
182.71605
202.46914
232.09877
266.66667
286.41975
316.04938
350.61728
380.24691
414.81481
434.56790
469.13580
498.76543
533.33333
553.08642
582.71605
617.28395
646.91358
666.66667
701.23457
730.86420
765.43210
785.18519
819.75309
849.38272
883.95062
913.58025
933.33333
967.90123
997.53086
1017.28395
1051.85185
1081.48148
1116.04938
1135.80247
1165.43210
1200.00000

From: Chris Vaisvil (2010-09-26)
Subject: Re: [tuning] Hobbit scales

Thanks for making these two scala files available.

Re: I'm not quite sure how to proceed with making these available

You can certainly use not only music to post an  archive - or simply a
post a thread with the scala information like you did in this post.
(or I can put your scala archive at micro.soonlabel.com under a folder
called "hobbit tunings" or some such).

Chris

On Sun, Sep 26, 2010 at 3:26 AM, genewardsmith
<genewardsmith@...t> wrote:
>
>
>
> Over on tuning-math I've introduced hobbit scales. These generalize MOS scales to higher rank regular temperaments in the sense that hobbit scales in rank two are MOS. I'm not quite sure how to proceed with making these available; they aren't as easy to compute or understand as MOS, but they seem to have nice properties. Perhaps an archive of scales.
>
> Below I give two examples of hobbit scales, one a 15-note scale for thrush temperament, and the other a 41-note scale for (17 limit) jove temperament. Both are strictly proper.
>

From: Herman Miller (2010-09-26)
Subject: Re: [tuning] Hobbit scales

genewardsmith wrote:
> Over on tuning-math I've introduced hobbit scales. These generalize MOS scales to higher rank regular temperaments in the sense that hobbit scales in rank two are MOS. I'm not quite sure how to proceed with making these available; they aren't as easy to compute or understand as MOS, but they seem to have nice properties. Perhaps an archive of scales.
> 
> Below I give two examples of hobbit scales, one a 15-note scale for thrush temperament, and the other a 41-note scale for (17 limit) jove temperament. Both are strictly proper.
> 
> ! thrush15.scl
> Thrush[15] hobbit 7&9 limit minimax tuning
> 15
> !
> 79.86894
> 159.73788
> 231.17409
> 311.04303
> 390.91197
> 498.04500
> 577.91394
> 622.08606
> 701.95500
> 809.08803
> 888.95697
> 968.82591
> 1040.26212
> 1120.13106
> 1200.00000

Could you give an example or two for each of these of which JI intervals 
these are approximations of? Obviously 701.955 is 3/2, and 390.91197 is 
a good approximation of 5/4. But it's not clear how some of the others 
(e.g. 159.73788, 1040.26212) fit in. Something like this:

79.86894 25/24
159.73788
231.17409 8/7
311.04303 6/5 25/21
390.91197 5/4
498.04500 4/3
577.91394 7/5 25/18
622.08606 10/7 36/25
701.95500 3/2
809.08803 8/5
888.95697 5/3
968.82591 7/4
1040.26212
1120.13106 40/21 48/25
1200.00000 2/1

but with more examples (particularly any 11-limit approximations).

From: genewardsmith (2010-09-26)
Subject: Re: Hobbit scales

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> (or I can put your scala archive at micro.soonlabel.com under a folder
> called "hobbit tunings" or some such).

A directory called "hobbits" or "hobbit scales" would be nice.

From: Chris Vaisvil (2010-09-26)
Subject: Re: [tuning] Re: Hobbit scales

Ok,

Email me the archive or scala files - or whatever format you wish and I'll
put it up there.

For the time being I will put the two scala files you posted into there.

Chris

On Sun, Sep 26, 2010 at 3:20 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
>
> > (or I can put your scala archive at micro.soonlabel.com under a folder
> > called "hobbit tunings" or some such).
>
> A directory called "hobbits" or "hobbit scales" would be nice.
>
>  
>

From: Chris Vaisvil (2010-09-26)
Subject: Re: [tuning] Re: Hobbit scales

Hi Gene,

here is the folder with what I have so far.

http://micro.soonlabel.com/hobbit_scales/

Chris

On Sun, Sep 26, 2010 at 3:20 PM, genewardsmith
<genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > (or I can put your scala archive at micro.soonlabel.com under a folder
> > called "hobbit tunings" or some such).
>
> A directory called "hobbits" or "hobbit scales" would be nice.

From: genewardsmith (2010-09-26)
Subject: Re: Hobbit scales

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> but with more examples (particularly any 11-limit approximations).

That sounds kind of awkward, but the idea of giving at least one representative coset element which maps to the scale element under the temperament mapping strikes me as a terrific idea. Given that, all the others can be found by multiplying by commas. I think I'll always attach these to hobbit scales so as to precisely define them independently of the tuning choice. By an abuse of terminology I'm calling that a "transversal" but I doubt any angry group theorists will give me a bad time about it.

! thrush15.scl
Thrush[15] hobbit 7&9 limit minimax tuning
15
!
79.86894
159.73788
231.17409
311.04303
390.91197
498.04500
577.91394
622.08606
701.95500
809.08803
888.95697
968.82591
1040.26212
1120.13106
1200.00000
!
! Commas 126/125, 176/175 
! ! prethrush15.scl
! Thrush[15] transversal
! 15
! !
! 21/20
! 11/10
! 8/7
! 6/5
! 5/4
! 4/3
! 7/5
! 10/7
! 3/2
! 8/5
! 5/3
! 7/4
! 20/11
! 21/11
! 2/1

! jove41.scl
Jove[41] 17-limit hobbit in 243et
! commas 243/242, 441/440, 364/363, 595/594
41
!
34.56790
64.19753
83.95062
118.51852
148.14815
182.71605
202.46914
232.09877
266.66667
286.41975
316.04938
350.61728
380.24691
414.81481
434.56790
469.13580
498.76543
533.33333
553.08642
582.71605
617.28395
646.91358
666.66667
701.23457
730.86420
765.43210
785.18519
819.75309
849.38272
883.95062
913.58025
933.33333
967.90123
997.53086
1017.28395
1051.85185
1081.48148
1116.04938
1135.80247
1165.43210
1200.00000
!
! ! prejove41.scl
! Jove[41] transversal
! 41
! !
! 45/44
! 21/20
! 28/27
! 15/14
! 12/11
! 9/8
! 10/9
! 8/7
! 33/28
! 7/6
! 6/5
! 11/9
! 56/45
! 9/7
! 14/11
! 21/16
! 4/3
! 11/8
! 15/11
! 7/5
! 10/7
! 22/15
! 16/11
! 3/2
! 32/21
! 11/7
! 14/9
! 45/28
! 18/11
! 5/3
! 12/7
! 56/33
! 7/4
! 9/5
! 16/9
! 11/6
! 28/15
! 27/14
! 21/11
! 49/25
! 2/1