Topic: From Mohajira to Slendro

1 scales

Thread (5 messages)

From: Jacques Dudon (2011-02-16)
Subject: From Mohajira to Slendro

This is a tuning that could fit among the "Ethno extras" series  
initiated by Margo.
I have always been intrigued by a very classic but singular Mohajira  
sequence, that goes :
[5  49  15  147  45  55  135]
or in ascending order :
[147  160  180  196  220  240  270  294]

because of the links it suggests with complementary 7th-limit harmonies.
As I mentionned it to John about his latest scale that contains a  
part of it, the secret of this interesting coïncidence between 7th  
and 11th limit lies in the 540/539 comma we find between 60/49 and 11/9.
In order to analyse it closer, I developped the "Dudon scale" of  
540/539, or the scale formed by the divisors of both 540 and 539 :
D(540/539) = [1  539-135  9  77  5  11  45  3  49  27  7  15]
and also of the 441/440 inside the scale as well :
D(441/440) = [1  9  147  5  21  11  3  49  55-441  7  63]
then the "summing Dudon scale" of both commas :
D(540/539,  441/440) = [1  539-135   9  147  77  5  21  11  45  3   
49  27  55-441  7  15  63]

This is how we can complete the original  [5  49  15  147  45  55   
135] Mohajira with 5 notes (or more of them if you wish), extending  
it to many slendros :

! mohajira-to-slendro.scl
!
 From Mohajira to Aeolian and Slendros
  12
!
  21/20
  9/8
  6/5
  49/40
  4/3
  7/5
  3/2
  8/5
  49/30
  9/5
  11/6
  2/1
! 12 notes selection among two "Dudon scales" :
! D(540/539) = [1  539-135  9  77  5  11  45  3  49  27  7  15]
! D(441/440) = [1  9  147  5  21  11  3  49  55-441  7  63]
! Mohajira scale on white keys : [15  135  147  5  45  49  55]

I have not counted how many slendros you have in here. The black keys  
have an ordinary "N" slendro ; the closest to Mohajira is a "M"  
slendro with E  F#  A  B  C# ;
a Jogyakarta type is E F# G# B C# ; a nice one is of the "SJ" type,  
in C# Eb F# G# B  that tempers 1029/1024 through the B (=55) of  
Mohajira.
There is also a full Aeolian scale in C minor.

Have fun !

Has anyone an idea of what temperaments the tempering of both 540/539  
and 441/440 would best refer to ? Miracle ?
- - - - - - -
Jacques

From: genewardsmith (2011-02-17)
Subject: Re: From Mohajira to Slendro

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:

> Has anyone an idea of what temperaments the tempering of both 540/539  
> and 441/440 would best refer to ? Miracle ?

Just by itself it's jove temperament, but the tuning of harry temperament is basically the same, but it's rank two instead of three. Harry also tempers out 4000/3993. It's also possible to temper out 65625/65536 instead, leading to the 11-limit version of tertiaseptal, or to do both, leading to 202et.

I posted your scale here on the Xenwiki, it seems like quite an interesting 12-note JI scale which some people find to be useful.

From: Jacques Dudon (2011-02-17)
Subject: Re: From Mohajira to Slendro

> Gene wrote :
> > Has anyone an idea of what temperaments the tempering of both  
> 540/539
> > and 441/440 would best refer to ? Miracle ?
>
> Just by itself it's jove temperament, but the tuning of harry  
> temperament is basically the same, but it's rank two instead of  
> three. Harry also tempers out 4000/3993. It's also possible to  
> temper out 65625/65536 instead, leading to the 11-limit version of  
> tertiaseptal, or to do both, leading to 202et.

Sorry, I still haven't catch what was a hobbit temperament, I must  
say the explanation page is too complex for me... I note that Jove 
[41] transversal indeed contains all of "Mohajira-to-slendro" ratios,  
except 8/5 represented by 48/25 instead, 225/224 higher, but I  
haven't checked possible transpositions (BTW it looks like there is  
an inversion in this transversal list, between 11/7 and 14/9). So  
what are Jove, or Harry's generators, or other relevant ones here ?
What about Miracle ? it has a perfect Mohajira and many correct 7th- 
limit tempered Slendros ; it also tempers 1029/1024, which is  
relevant in this scale with its [63 : 55 : 48 : 42 : 36] "SJ" type of  
slendro.

> I posted your scale here on the Xenwiki, it seems like quite an  
> interesting 12-note JI scale which some people find to be useful.

Thanks ! (I didn't know I had a whole citation in the JI page,  
agremented with links... it also reminds me I should try to write a  
few lines about the use of recurrent sequences for eq-b and -c  
temperaments and what you called "algebraic solutions"... any  
volunteer to correct my english ?)
- - - - - - -
Jacques

From: genewardsmith (2011-02-17)
Subject: Re: From Mohajira to Slendro

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:

> Thanks ! (I didn't know I had a whole citation in the JI page,  
> agremented with links... it also reminds me I should try to write a  
> few lines about the use of recurrent sequences for eq-b and -c  
> temperaments and what you called "algebraic solutions"... any  
> volunteer to correct my english ?)

Write the article and I'll correct your English.

From: genewardsmith (2011-02-17)
Subject: Re: From Mohajira to Slendro

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
So  
> what are Jove, or Harry's generators, or other relevant ones here ?

Here's Jove:

http://xenharmonic.wikispaces.com/Breed+family

Here's Harry and Tertiaseptal:

http://xenharmonic.wikispaces.com/Breedsmic+temperaments

Miracle I didn't mention because it involves a small reduction in tuning accuracy, but if we allow that other things crowd in as well.