Topic: 12 note 686/675 comma pump scale in 46et

1 scales

Thread (13 messages)

From: genewardsmith (2011-05-21)
Subject: 12 note 686/675 comma pump scale in 46et

This is just the union of the notes of a 686/675 comma pump. Quite a lot of 7-limit harmony, plus higher limit besides (it is in 46 equal tuning, after all.) If you find twelve notes convenient and irregularity doesn't worry you overmuch, it could be of interest.


! plum.scl
686/675 comma pump scale in 46et
12
!
130.43478
260.86957
391.30435
443.47826
521.73913
573.91304
704.34783
834.78261
965.21739
1069.56522
1095.65217
1200.00000

From: Mike Battaglia (2011-05-21)
Subject: Re: [tuning] 12 note 686/675 comma pump scale in 46et

On Fri, May 20, 2011 at 9:57 PM, genewardsmith
<genewardsmith@...> wrote:
>
> This is just the union of the notes of a 686/675 comma pump. Quite a lot of 7-limit harmony, plus higher limit besides (it is in 46 equal tuning, after all.) If you find twelve notes convenient and irregularity doesn't worry you overmuch, it could be of interest.

This is related to an idea I'd brought up earlier - that comma pumps
are really (part of) what determines tonality, and that by building a
scale around a comma pump instead of the scale's MOS's we might start
getting lots and lots of tonal scales. I have always had some
lingering doubt, however, that the MOS's would end up being the ones
with the most comma pumps. But in the case of codimension 2
temperaments this isn't a problem because there are an infinite amount
of commas being tempered out, and so there's probably a way to do it.

So in this case, I ask - might there be some MOS lurking nearby? Or,
might this be the MODMOS of some rank-2 temperament, or perhaps might
there be a MODMOS lurking nearby? If so, then that might be an
exceptional find.

Still holding out for the ability to just autogenerate "tonal comma
pump" scales for regular temperaments... here's to hoping I have
enough time to work on that or anything else sometime.

-Mike

From: genewardsmith (2011-05-21)
Subject: Re: 12 note 686/675 comma pump scale in 46et

--- In [email protected], Mike Battaglia <battaglia01@...> wrote:

> So in this case, I ask - might there be some MOS lurking nearby?

The most obvious candidate is the 5\46 generator I just mentioned. If this hasn't been named already it needs a name.

> Still holding out for the ability to just autogenerate "tonal comma
> pump" scales for regular temperaments... here's to hoping I have
> enough time to work on that or anything else sometime.

Not sure what a tonal comma pump scale is.

From: Mike Battaglia (2011-05-21)
Subject: Re: [tuning] Re: 12 note 686/675 comma pump scale in 46et

On Fri, May 20, 2011 at 10:26 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > So in this case, I ask - might there be some MOS lurking nearby?
>
> The most obvious candidate is the 5\46 generator I just mentioned. If this hasn't been named already it needs a name.

It doesn't look like it does too good for 6:7:9 and 10:13:15,
otherwise I'd suggest it as this mythical "Pandora" temperament I have
a spot for on the 91/90 page.

> > Still holding out for the ability to just autogenerate "tonal comma
> > pump" scales for regular temperaments... here's to hoping I have
> > enough time to work on that or anything else sometime.
>
> Not sure what a tonal comma pump scale is.

It was the thing that I wrote all that stuff about in all those
paragraphs that you cut out in your reply.

-Mike

From: Carl Lumma (2011-05-21)
Subject: Re: 12 note 686/675 comma pump scale in 46et

--- In [email protected], Mike Battaglia <battaglia01@...> wrote:

> > Not sure what a tonal comma pump scale is.
> 
> It was the thing that I wrote all that stuff about in all those
> paragraphs that you cut out in your reply.

You mean a Fokker block?  -Carl

From: Mike Battaglia (2011-05-21)
Subject: Re: [tuning] Re: 12 note 686/675 comma pump scale in 46et

On Sat, May 21, 2011 at 2:32 PM, Carl Lumma <carl@...> wrote:
>
> > > Not sure what a tonal comma pump scale is.
> >
> > It was the thing that I wrote all that stuff about in all those
> > paragraphs that you cut out in your reply.
>
> You mean a Fokker block? -Carl

No - read here

I wrote:
> This is related to an idea I'd brought up earlier - that comma pumps
> are really (part of) what determines tonality, and that by building a
> scale around a comma pump instead of the scale's MOS's we might start
> getting lots and lots of tonal scales. I have always had some
> lingering doubt, however, that the MOS's would end up being the ones
> with the most comma pumps. But in the case of codimension 2
> temperaments this isn't a problem because there are an infinite amount
> of commas being tempered out, and so there's probably a way to do it.

-Mike

From: Carl Lumma (2011-05-21)
Subject: Re: 12 note 686/675 comma pump scale in 46et

--- In [email protected], Mike Battaglia <battaglia01@...> wrote:

> > You mean a Fokker block? -Carl
> 
> No - read here

That's exactly what I read that made me say so!
What are you describing, if not Fokker blocks?

-Carl

From: Mike Battaglia (2011-05-21)
Subject: Re: [tuning] Re: 12 note 686/675 comma pump scale in 46et

On Sat, May 21, 2011 at 3:20 PM, Carl Lumma <carl@...> wrote:
>
> > > You mean a Fokker block? -Carl
> >
> > No - read here
>
> That's exactly what I read that made me say so!
> What are you describing, if not Fokker blocks?

It very well may be the case that the MOS scales of a temperament are
the ones that will have the most comma pumps - for rank 2, codimension
one temperaments. What about for 11-limit Orwell, which is codimension
4? There are an infinite number of commas that Orwell tempers out. You
could pick one, and then design some MODMOS around that specific comma
pump. You could still have two consecutive 7/6's in the scale
equalling 11/8, and three equalling 8/5, so it would still be Orwell
harmony. However, the "minimal comma pump" for Orwell will change
depending on exactly what Orwell comma it is that you're looking for.

-Mike

From: Carl Lumma (2011-05-21)
Subject: Re: 12 note 686/675 comma pump scale in 46et

--- In [email protected], Mike Battaglia <battaglia01@...> wrote:

> > That's exactly what I read that made me say so!
> > What are you describing, if not Fokker blocks?
> 
> It very well may be the case that the MOS scales of a
> temperament are the ones that will have the most comma
> pumps - for rank 2, codimension one temperaments.

I said Fokker blocks, not tempered MOS.

> However, the "minimal comma pump" for Orwell will change
> depending on exactly what Orwell comma it is that you're
> looking for.

Likewise, the Fokker block will change.  It seems to me the
only difference is that you can specify a pump without
specifying enough commas to close a block.  Still the pump
will tend to be within the block if you've chosen a short
pump route and synergistic commas to close the block.
The block may be bigger than the pump scale, but in such
cases it will always be in the interest of melodic evenness.
The block may be smaller, but in such cases there will be a
block tone you can substitute, and this substitution will
be perfect when the block is tempered.

-Carl

From: Herman Miller (2011-05-22)
Subject: Re: [tuning] Re: 12 note 686/675 comma pump scale in 46et

On 5/20/2011 10:26 PM, genewardsmith wrote:
>
> --- In [email protected], Mike Battaglia<battaglia01@...>
> wrote:
>
>> So in this case, I ask - might there be some MOS lurking nearby?
>
> The most obvious candidate is the 5\46 generator I just mentioned. If
> this hasn't been named already it needs a name.

Looks like "twothirdtonic".

From: genewardsmith (2011-05-22)
Subject: Re: 12 note 686/675 comma pump scale in 46et

--- In [email protected], Herman Miller <hmiller@...> wrote:
>
> On 5/20/2011 10:26 PM, genewardsmith wrote:
> >
> > --- In [email protected], Mike Battaglia<battaglia01@>
> > wrote:
> >
> >> So in this case, I ask - might there be some MOS lurking nearby?
> >
> > The most obvious candidate is the 5\46 generator I just mentioned. If
> > this hasn't been named already it needs a name.
> 
> Looks like "twothirdtonic".

Thanks!

From: Mike Battaglia (2011-05-22)
Subject: Re: [tuning] Re: 12 note 686/675 comma pump scale in 46et

On Sat, May 21, 2011 at 3:48 PM, Carl Lumma <carl@...> wrote:
>
> > It very well may be the case that the MOS scales of a
> > temperament are the ones that will have the most comma
> > pumps - for rank 2, codimension one temperaments.
>
> I said Fokker blocks, not tempered MOS.

?? I was talking about building scales around the comma pump for a
temperament. That means the scale has to be tempered. If you're
talking about untempered Fokker blocks, how will there be a pump?

> > However, the "minimal comma pump" for Orwell will change
> > depending on exactly what Orwell comma it is that you're
> > looking for.
>
> Likewise, the Fokker block will change.

How will it change? If we're talking about Orwell, there will be four
unison vectors and one chromatic vector. That gives us four base
commas to explore and then an infinite number of combinations. How
does me suggesting we look at pumping around one comma vs the other
change anything about the block?

> It seems to me the
> only difference is that you can specify a pump without
> specifying enough commas to close a block.

You can already do that with meantone, right? You can specify a pump
without having to close the block off at 7 or 12 notes or whatever.

> Still the pump
> will tend to be within the block if you've chosen a short
> pump route and synergistic commas to close the block.
> The block may be bigger than the pump scale, but in such
> cases it will always be in the interest of melodic evenness.

Or you could use a decent MODMOS to do the trick. Harmonic minor is a
case study for this - it contains a comma pump, but we don't need to
use the full 12-note scale - we can just use the 7-note MODMOS
harmonic minor subset of it. In fact, the whole point of harmonic
minor is to have the comma pump in it but alter notes to get the chord
qualities that we want, which would be a great approach to take to
something like Orwell[9] where the chord qualities often just suck. We
have two 6:7:9 chords a 7/6 away. I'm not sure how workable Orwell
specifically will be, but if you could figure out a way to get more
usable chords while retaining at least one comma pump, then that might
provide a better "tonal" foundation for the orwell system in general.

> The block may be smaller, but in such cases there will be a
> block tone you can substitute, and this substitution will
> be perfect when the block is tempered.

How are we picking the block? By itself, Orwell wouldn't denote a
block at all, I don't think, just a series of higher-dimensional
strips until you pick a chromatic vector.

-Mike

From: Carl Lumma (2011-05-22)
Subject: Re: 12 note 686/675 comma pump scale in 46et

--- Mike Battaglia <battaglia01@...> wrote:

> > I said Fokker blocks, not tempered MOS.
> 
> ?? I was talking about building scales around the comma pump
> for a temperament. That means the scale has to be tempered.
> If you're talking about untempered Fokker blocks, how will
> there be a pump?

Fine, temper it then.

> > Likewise, the Fokker block will change.
> 
> How will it change? If we're talking about Orwell, there will
> be four unison vectors and one chromatic vector. That gives
> us four base commas to explore and then an infinite number of
> combinations. How does me suggesting we look at pumping around
> one comma vs the other change anything about the block?

If we're talking about the 11-limit there are always
four commas to make a block.  The commatic/chromatic
distinction depends on the tuning.  If the tuning is
11-limit orwell, there are 3 commatic and one chromatic
commas.  Presumably you would choose the commas for
the block so that one of them is the comma you're
pumping.

> > It seems to me the
> > only difference is that you can specify a pump without
> > specifying enough commas to close a block.
> 
> You can already do that with meantone, right? You can specify
> a pump without having to close the block off at 7 or 12 notes
> or whatever.

Yes- in the 5-limit, 81/80 will give you a sheet not a block.

> > Still the pump
> > will tend to be within the block if you've chosen a short
> > pump route and synergistic commas to close the block.
> > The block may be bigger than the pump scale, but in such
> > cases it will always be in the interest of melodic evenness.
> 
> Or you could use a decent MODMOS to do the trick.

How does MODMOS construction lead to success?

> > The block may be smaller, but in such cases there will be a
> > block tone you can substitute, and this substitution will
> > be perfect when the block is tempered.
> 
> How are we picking the block? By itself, Orwell wouldn't
> denote a block at all, I don't think, just a series of
> higher-dimensional strips until you pick a chromatic vector.

Since orwell is a rank 2 temperament it always needs one
additional comma to make a block.

-Carl