Topic: Minerva[12]

1 scales

File Description Notes Period (¢)
minvera12 Minvera[12] (99/98&176/175) 11-limit hobbit, POTE tuning 12 1200.0

Thread (7 messages)

From: genewardsmith (2011-01-13)
Subject: Minerva[12]

The usual good scale stuff for hobbits: strictly proper, low mean variety. Tuning the transversal in orwell gives a related 12-note orwell scale.

! minvera12.scl
Minvera[12] (99/98&176/175) 11-limit hobbit, POTE tuning
12
!
113.18260
226.36520
273.37552
386.55812
499.74073
587.07667
700.25927
813.44188
926.62448
973.63480
1086.81740
1200.00000
!
!! preminerva12.scl
! Minerva[12] 5-limit transversal
! 12
!!
! 16/15
! 256/225
! 75/64
! 5/4
! 4/3
! 45/32
! 3/2
! 8/5
! 128/75
! 225/128
! 15/8
! 2/1
From: Michael (2011-01-13)
Subject: Re: [tuning] Minerva[12]

Gene>"The usual good scale stuff for hobbits: strictly proper, low mean 
variety."


    It also seems a pattern within these tunings...that the fifths from  the 
first 6 or so notes are perfect...but the others are skewed.  My first 
(recurring) question for all of these is what do the fifths look like (all 
possible fifths within a 2 octave span)?  Not that impure fifths are bad...it's 
just the I find by ear limited areas around 3/2 and/or 22/15 and 11/7 actually 
work well in the 5th-low 6th range.


     There looks to be (about) a nice 22/16 diminished fifth between 8/5 and 
75/64...and between 128/75 and 5/4....and a couple of perhaps overly stretched 
5ths around 1.517.


    The stretched fifths are about the most "evil" thing I can find in this 
scale...it actually looks GREAT to me at first glance!  Plus it has somewhat 
constant intervals (minus those revolving around the 22/15)...looks no worse 
than my Dimension^2 scale in a whole lot of ways to be honest...and maybe better 
in others. :-)   Gene...what are, in your opinion, the worst dyads in this 
scale?  I can't the anything really bad in here so far....

Overall...looks generally excellent to me...  




________________________________
From: genewardsmith <genewardsmith@...>
To: tuning@yahoogroups.com
Sent: Thu, January 13, 2011 1:19:35 AM
Subject: [tuning] Minerva[12]

  
The usual good scale stuff for hobbits: strictly proper, low mean variety. 
Tuning the transversal in orwell gives a related 12-note orwell scale.

! minvera12.scl
Minvera[12] (99/98&176/175) 11-limit hobbit, POTE tuning
12
!
113.18260
226.36520
273.37552
386.55812
499.74073
587.07667
700.25927
813.44188
926.62448
973.63480
1086.81740
1200.00000
!
!! preminerva12.scl
! Minerva[12] 5-limit transversal
! 12
!!
! 16/15
! 256/225
! 75/64
! 5/4
! 4/3
! 45/32
! 3/2
! 8/5
! 128/75
! 225/128
! 15/8
! 2/1
From: Michael (2011-01-13)
Subject: Re: [tuning] Minerva[12]

Though Minerva scale looked almost downright "perfect" at first glance 
(perfect being relative)...there seem to be some sour fourths lurking around 
21/16 and sour sixths lurking around 28/17, an ugly 7th around 20/11, and a "low 
6th/ high fifth" around 17/11.  Still, quite good on the average.
From: Mike Battaglia (2011-01-13)
Subject: Re: [tuning] Minerva[12]

On Thu, Jan 13, 2011 at 11:31 AM, Michael <djtrancendance@...> wrote:
>
>     It also seems a pattern within these tunings...that the fifths from the first 6 or so notes are perfect...but the others are skewed.  My first (recurring) question for all of these is what do the fifths look like (all possible fifths within a 2 octave span)?  Not that impure fifths are bad...it's just the I find by ear limited areas around 3/2 and/or 22/15 and 11/7 actually work well in the 5th-low 6th range.

Michael, I have a question for you. Why are you always so concerned
with the dyadic relationships in a scale? Why not look at the
constituent triads for a change?

-Mike
From: genewardsmith (2011-01-13)
Subject: Re: Minerva[12]

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

>     It also seems a pattern within these tunings...that the fifths from  the 
> first 6 or so notes are perfect...but the others are skewed.

There are seven fifths in a row, which not everyone will like. For the rest, I think you are counting approximate 22/15s and 32/21s as fifths. The actual fifths are well-supplied with triads: three major, three minor, three subminor, three supermajor and it's all topped off with a 1-11/9-3/2 neutral triad and a 1-27/22-3/2 neutral triad.

 Gene...what are, in your opinion, the worst dyads in this 
> scale?  

The 47 cent quarter-tones I suppose.
From: Michael (2011-01-13)
Subject: Re: [tuning] Minerva[12]

MikeB>"Michael, I have a question for you. Why are you always so concerned with 
the dyadic relationships in a scale? Why not look at the constituent triads for 
a change?"


     In the past I've found if I try to optimize the triads (at least to fairly 
low-limit), I end up severely limiting the number of chords possible...and I 
honestly can't think of a way to test high-limit accuracy well (too many triads 
possible...especially considering I find things like the occasional 10:11:12 and 
18:22:27 to be fairly "legal"). 


    Usually the first test I do is to see where the fifths are...1-2 bad fifths 
per 12 notes are somewhat expected...but anything more usually seems a good 
indicator of a sour scale. After looking at those I bother to test 3rds and 
4ths...then I start looking for triads (in Scala).  


    And if I see a triad is off by more than a certain amount (usually the cut 
is around 8-9 cents)...I try to de-align the dyads a bit to accommodate to it.  
Got any ideas to get a quick triadic "rating" on a scale...without looking at 
hundreds of triads in Scala and comparing their errors one by one? :-D
From: Mike Battaglia (2011-01-14)
Subject: Re: [tuning] Minerva[12]

On Thu, Jan 13, 2011 at 3:19 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"Michael, I have a question for you. Why are you always so concerned with the dyadic relationships in a scale? Why not look at the constituent triads for a change?"
>
>
>      In the past I've found if I try to optimize the triads (at least to fairly low-limit), I end up severely limiting the number of chords possible...and I honestly can't think of a way to test high-limit accuracy well (too many triads possible...especially considering I find things like the occasional 10:11:12 and 18:22:27 to be fairly "legal").
>
>     Usually the first test I do is to see where the fifths are...1-2 bad fifths per 12 notes are somewhat expected...but anything more usually seems a good indicator of a sour scale. After looking at those I bother to test 3rds and 4ths...then I start looking for triads (in Scala).
>
>     And if I see a triad is off by more than a certain amount (usually the cut is around 8-9 cents)...I try to de-align the dyads a bit to accommodate to it.  Got any ideas to get a quick triadic "rating" on a scale...without looking at hundreds of triads in Scala and comparing their errors one by one? :-D

No ideas. Brain hurts. Some day I'll finish the harmonic entropy
filterbank transform and that'll do it. I'm drowning in unfinished
tuning stuff.

-Mike