Full 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: [email protected]
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 [email protected], 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