Blackwood[15] with brats of -1

Blackwood has a comma of 256/243, which does not involve 5, and the
least squares/minimax tuning splits the difference in the error of the
720 cent sharp fifth between the major and minor thirds, leading to a
generator of 84.664 cents. A generator which instead gives brats of -1
is 82.837 cents. This is closer to the 15-edo step of 80 cents, and
Blackwood[15] using this generator could be regarded as a sort of
circulating 15. Two-thirds of the major triads in close root position
are of the brat -1 variety, and the other one-third have minor thirds
which are 1.315 cents flat. The 7-limit implications are unaffected by
all this, because the period of 240 cents is what would be used as an 8/7.

Adventurous types such as Herman might want to try out Blackwood with
synchronized beating which I give below.

! blackbeat15.scl
Blackwood[15] with brats of -1
! generator g is unique real root of 9g^5+20g^4+80g^3-128 = 0
15
!
82.836732
157.163268
240.000000
322.836732
397.163268
480.000000
562.836732
637.163268
720.000000
802.836732
877.163268
960.000000
1042.836732
1117.163268
1200.000000

Gene Ward Smith wrote:

> Adventurous types such as Herman might want to try out Blackwood with
> synchronized beating which I give below.

Well, the Mizarian Porcupine Overture should be a good test, since it wasn't written for any specific temperament (porcupine temperament hadn't yet been named, and only the last bit is in porcupine temperament anyway). I put together an Absynth 3 arrangement (with Edirol VSC percussion), since it's got too many voices for Scala to do a good job with it, and I could use the practice creating Absynth voices anyway.

http://home.comcast.net/~teamouse/porcupine-absynth-blackwood.mp3

Compare with 15-ET:

http://home.comcast.net/~teamouse/porcupine-absynth.mp3

I think the Blackbeat15 scale works pretty well in comparison.

> ! blackbeat15.scl
> Blackwood[15] with brats of -1
> ! generator g is unique real root of 9g^5+20g^4+80g^3-128 = 0
> 15
> !
> 82.836732
> 157.163268
> 240.000000
> 322.836732
> 397.163268
> 480.000000
> 562.836732
> 637.163268
> 720.000000
> 802.836732
> 877.163268
> 960.000000
> 1042.836732
> 1117.163268
> 1200.000000

>Well, the Mizarian Porcupine Overture should be a good test, since it
>wasn't written for any specific temperament (porcupine temperament
>hadn't yet been named, and only the last bit is in porcupine temperament
>anyway). I put together an Absynth 3 arrangement (with Edirol VSC
>percussion), since it's got too many voices for Scala to do a good job
>with it, and I could use the practice creating Absynth voices anyway.
>
>http://home.comcast.net/~teamouse/porcupine-absynth-blackwood.mp3
>
>Compare with 15-ET:
>
>http://home.comcast.net/~teamouse/porcupine-absynth.mp3

Aaron Johnson and I are listening to this in Chicago at the moment.
Without consulting with him...

Is this the full-length version?
It sounds great. The sounds have much more depth than in previous
versions (as I'd expect).
The sheer variety of timbres used is a bit wearing and tends to
emphasize the episodic nature of the overture in a way I don't like.
Some of the timbres are a little too 'vague' for my taste, such
as the warbly one that states the first theme starting at 0:19.
It's hard to compare the tunings given the differences in timbre.

-Carl

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

> I think the Blackbeat15 scale works pretty well in comparison.

Wow. I think it definately is a keeper. The 15-et version has the
problem 15-et always has with me, which is that it simply sounds
seriously out of tune. The Blackbeat version somehow manages to sound
more in tune than in actually is, as if the ear is being convinced
that maybe it's right that way.

> It's also 1:30am California time.

It was 1:30 Chicago time, 11:30 California time.
Apparently Chicago time is more relevant to me at
this point in the trip *cough*.

-Carl

>> http://home.comcast.net/~teamouse/porcupine-absynth-blackwood.mp3
>>
>>Compare with 15-ET:
>>
>> http://home.comcast.net/~teamouse/porcupine-absynth.mp3
>
>Aaron Johnson and I are listening to this in Chicago at the moment.
>Without consulting with him...
>
>Is this the full-length version?
>It sounds great. The sounds have much more depth than in previous
>versions (as I'd expect).
>The sheer variety of timbres used is a bit wearing and tends to
>emphasize the episodic nature of the overture in a way I don't like.
>Some of the timbres are a little too 'vague' for my taste, such
>as the warbly one that states the first theme starting at 0:19.
>It's hard to compare the tunings given the differences in timbre.

It's also 1:30am California time. It does seem full-length, but
maybe the timbre-highlighted transitions made it seem shorter.
I didn't even see the 15-equal version with the same timbres.

The equal version has a much stronger finish at the top of the
first lead phrase at 0:03 for some reason. It sounds sharper;
maybe that does it. Some of the blackbeat15 version's chords sound
less sour -- the last three before the break at 0:19 for example.
Ditto the famous ending progression. There's something to be
said for the boldness of the equal version, though.

-Carl

Carl Lumma wrote:

> Aaron Johnson and I are listening to this in Chicago at the moment.
> Without consulting with him...
> > Is this the full-length version?

Yes.

> It sounds great. The sounds have much more depth than in previous
> versions (as I'd expect).

There's only so much you can do with a SoundFont, after all, even with all the time I spent on those sounds for the original version. I agree that some of the new sounds are a little bit rough, and the balance isn't quite right in some places.

> The sheer variety of timbres used is a bit wearing and tends to
> emphasize the episodic nature of the overture in a way I don't like.
> Some of the timbres are a little too 'vague' for my taste, such
> as the warbly one that states the first theme starting at 0:19.
> It's hard to compare the tunings given the differences in timbre.

I'll have to tone down some of the effects, it sounds like.

Herman Miller wrote:
> Carl Lumma wrote:
>>Some of the timbres are a little too 'vague' for my taste, such
>>as the warbly one that states the first theme starting at 0:19.
>>It's hard to compare the tunings given the differences in timbre.
> > > I'll have to tone down some of the effects, it sounds like.

I've made some changes to the timbres, which should be much better for tuning comparison. And as it turns out, some of the tracks had the polyphony set at 4 voices when they needed as many as 9 in some cases. I thought I'd set them all to 8, but apparently not.

http://home.comcast.net/~teamouse/porcupine-absynth-blackwood.mp3
http://home.comcast.net/~teamouse/porcupine-absynth.mp3

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

> I've made some changes to the timbres, which should be much better for
> tuning comparison.

My basic reaction is the same--15-et is pretty painful, but the
Blackwood version seems much better.

>> I think the Blackbeat15 scale works pretty well in comparison.
>
>Wow. I think it definately is a keeper. The 15-et version has the
>problem 15-et always has with me, which is that it simply sounds
>seriously out of tune. The Blackbeat version somehow manages to sound
>more in tune than in actually is, as if the ear is being convinced
>that maybe it's right that way.

I agree, but wonder if this has anything to do with beating. My
first guess would be that the piece happens to use some of the
better keys of blackbeat15.

-Carl

>>>Some of the timbres are a little too 'vague' for my taste, such
>>>as the warbly one that states the first theme starting at 0:19.
>>>It's hard to compare the tunings given the differences in timbre.
>>
>> I'll have to tone down some of the effects, it sounds like.
>
>I've made some changes to the timbres, which should be much better
>for tuning comparison.

Seems better.

>And as it turns out, some of the tracks had the
>polyphony set at 4 voices when they needed as many as 9 in some cases.
>I thought I'd set them all to 8, but apparently not.

The consonance difference between the two tunings seems less.
The biggest difference I notice is melodic -- the equal version
has more 'edge'.

> http://home.comcast.net/~teamouse/porcupine-absynth.mp3
> http://home.comcast.net/~teamouse/porcupine-absynth-blackwood.mp3

There's more dissonance at 0:50 than I remember. The orchestration
seems thinner there in the original soundfont version.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> The consonance difference between the two tunings seems less.
> The biggest difference I notice is melodic -- the equal version
> has more 'edge'.

It seems to me it has crossed over the edge into the downright
unpleasant. 15 is just too out of tune for me, I think, and the
regularity of it makes it all that much more grating.

Carl Lumma wrote:

> There's more dissonance at 0:50 than I remember. The orchestration
> seems thinner there in the original soundfont version.

The balance still isn't quite the same as the original version; I think the quillophone section still needs to be a little quieter. But now that you've brought this chord to my attention, I think it would sound better if I changed that one note.

>> There's more dissonance at 0:50 than I remember. The orchestration
>> seems thinner there in the original soundfont version.
>
>The balance still isn't quite the same as the original version; I think
>the quillophone section

:):):)

-Carl