Blackwood-ized Father temperament

This is another weird temperament, definitely something you have to
use specially crafted timbres for, even more so than Blackwood. If you
do use the right kind of timbre, it's beautiful. I'm also not sure
exactly how to map it, because it's not really a "temperament" in the
normal sense. There are probably a bunch of mappings that support
this, which is more like a concept, or maybe a temperament "paradigm,"
or who knows.

I said in my last message to the list that getting into Blackwood was
a transformative experience in my paradigm of how this all works, and
the first scale to really break me fully out of the "diatonic"
paradigm. Rather than mapping 5/4 to a bunch of fifths, you let the
fifths do their own thing, and then add in a second contorted chain of
fifths offset by 5/4. Then you get some kind of kaleidoscopic
symmetric diatonic scale, which is beautiful. And the puns are also
really beautiful.

So I sought to recreate this feel with father temperament, by taking
the really sharp fifths and then just sticking a 5/4 in there such
that the whole thing makes somewhat recognizable 4:5:6 triads. So I
guess the criteria here is that 256/243 end up reversed. I have set it
such that the fifths have a lower boundary of 5-equal and an upper
boundary of 8-equal, which is like the absolute maximum to hear them
as fifths at all, but I don't want 5/4 to equate to 4/3. 26-equal is a
good choice if you use the sharper mapping for the fifth. Play some
major triads around the circle of fifths and it works really well.

As for a mapping - I'm not sure how to do it. On one end you have
8-equal with the wide fifth mapping, which is about a maximum of
recognizability, and on the other hand you have 15-equal as the other
bound. Graham's temperament finder spits out porcupine for 8&15,
though, which ain't right. So I went with 8&10, which gives you a
temperament called "supersharp" that has 2/1 mapped to 2 periods;
sounds like we're headed in the right direction but I'm not sure
that's the only way to go, either. 8&25 gives you an interesting
unnamed scale. Still not sure what the obvious canonical version is
here.

-Mike

Try a generator around 469 cents. Map the 5 to +6 generators (octaves being equivalent). Maybe this would be 13&23? It's on the 5&8 continuum, just about in the middle.

But I really think once you get sharper than 720 cents/flatter than 480 cents, aiming for a 4:5:6 is a mistake...this is where I go for the 16:18:21's.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> This is another weird temperament, definitely something you have to
> use specially crafted timbres for, even more so than Blackwood. If you
> do use the right kind of timbre, it's beautiful. I'm also not sure
> exactly how to map it, because it's not really a "temperament" in the
> normal sense. There are probably a bunch of mappings that support
> this, which is more like a concept, or maybe a temperament "paradigm,"
> or who knows.
>
> I said in my last message to the list that getting into Blackwood was
> a transformative experience in my paradigm of how this all works, and
> the first scale to really break me fully out of the "diatonic"
> paradigm. Rather than mapping 5/4 to a bunch of fifths, you let the
> fifths do their own thing, and then add in a second contorted chain of
> fifths offset by 5/4. Then you get some kind of kaleidoscopic
> symmetric diatonic scale, which is beautiful. And the puns are also
> really beautiful.
>
> So I sought to recreate this feel with father temperament, by taking
> the really sharp fifths and then just sticking a 5/4 in there such
> that the whole thing makes somewhat recognizable 4:5:6 triads. So I
> guess the criteria here is that 256/243 end up reversed. I have set it
> such that the fifths have a lower boundary of 5-equal and an upper
> boundary of 8-equal, which is like the absolute maximum to hear them
> as fifths at all, but I don't want 5/4 to equate to 4/3. 26-equal is a
> good choice if you use the sharper mapping for the fifth. Play some
> major triads around the circle of fifths and it works really well.
>
> As for a mapping - I'm not sure how to do it. On one end you have
> 8-equal with the wide fifth mapping, which is about a maximum of
> recognizability, and on the other hand you have 15-equal as the other
> bound. Graham's temperament finder spits out porcupine for 8&15,
> though, which ain't right. So I went with 8&10, which gives you a
> temperament called "supersharp" that has 2/1 mapped to 2 periods;
> sounds like we're headed in the right direction but I'm not sure
> that's the only way to go, either. 8&25 gives you an interesting
> unnamed scale. Still not sure what the obvious canonical version is
> here.
>
> -Mike
>

On Thu, Feb 3, 2011 at 10:48 AM, cityoftheasleep
<igliashon@...> wrote:
>
> Try a generator around 469 cents. Map the 5 to +6 generators (octaves being equivalent). Maybe this would be 13&23? It's on the 5&8 continuum, just about in the middle.

13&23 screws it up, though, because the canonical mapping for 23 has
the 5 mapped differently. I don't know if there's a good way to
describe this one in terms of patent vals. Graham's temperament finder
pumps something totally different out for 13&23, has a 367 cent
generator.

This is another interesting take on this concept, though, because with
8-et, 6 generators ends up giving you 300 cents, whereas for 23 it
gives you 417 cents. Mapping 6/5 to +6 generators is really
interesting. It seems to be most appropriate to say that this is the
planar temperament where 256/243 is reversed and 8192/6561 is not.
Using Bosanquet's terminology, 8 and 23 map this to a 256/243
singly-negative temperament. I really don't know if there's a
canonical comma to be eliminated here.

> But I really think once you get sharper than 720 cents/flatter than 480 cents, aiming for a 4:5:6 is a mistake...this is where I go for the 16:18:21's.

Does the 23 version not sound like 4:5:6 to you anymore? Try it with
sines, I still hear it. Following the circle of fifths around the
scale really trips me out here.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Feb 3, 2011 at 10:48 AM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > Try a generator around 469 cents. Map the 5 to +6 generators (octaves being equivalent). Maybe this would be 13&23? It's on the 5&8 continuum, just about in the middle.
>
> 13&23 screws it up, though, because the canonical mapping for 23 has
> the 5 mapped differently. I don't know if there's a good way to
> describe this one in terms of patent vals.

I don't know what article this is quoting, but 5&18 seems to work. Tempers out 28/27 and 256/245, and if you don't like 23, you can try it in 64.

On Thu, Feb 3, 2011 at 1:05 PM, genewardsmith
<genewardsmith@...> wrote:
>
> I don't know what article this is quoting, but 5&18 seems to work. Tempers out 28/27 and 256/245, and if you don't like 23, you can try it in 64.

Yes! That's it, thanks. So 3 fifths gets you to 7/4; this works really well.

My first approach with this scale was to just play 4:5:6's, if you can
still call them that, all the way around the circle of fifths, and
observe the more and more exotic roots I was landing on. The MOS's
don't really throw much 5 in there, though, so I guess I was thinking
about this more like a simple 28/27 planar temperament, of which
eliminating 256/245 gives us this, and eliminating 16/15 gives us
father.

Another interesting, but related thing from this is that the 7:11:14
recurrence relation is right around here, which gives a nice pleasant
buzz. 7:14 is almost exactly 5\8, so a good way to do this is to start
with 8-tet and then add another 8-tet chain, blackwood style, offset
by ~11/7. Since there's no point pretending that this is perceived as
anything but out of tune 5-limit harmony, this then is the 5-limit
temperament eliminating 8192/6561.

Not sure I'll ever use these too much, but at least as of the present
moment they're tripping me out pretty good.

-Mike