Whittle it down?

I guess this is as good as any place, well actually I'll put this on the FB xenharmonic and micro theory pages as well. When I recognized that my 12 root of Phi (69.42419 cent interval ) was almost identical to 17 edo (70.58824 cent interval) I thought - what is the use? Is it really different? With that thought in mind I wonder if there could be value in whittling down the vast details of nuanced tunings into a smaller subset of tunings based on interval size - perhaps a Gaussian distribution classification around intervals with significant character differences. Of course I just injected a lot of subjective judgements into this suggestion. An obvious guide would be to use JI interval ratios or HE.

Bits and pieces of this very unoriginal thought I've seen discussed. I think what I would point out that probably these "class" have specific harmonic tendencies and could be treated with some common compositional practices if you don't mind a bit of a broad brush.

Perhaps I am alone in the observation that too often things get bogged down in the details - not that exploring is bad - but if we are to make headway into xenharmonic practice beyond imitation of 12 equal I think some generalizations are warranted.

After that I'll wait for someone to tell me I missed this discussion a year or two ago.

Thanks,

chris

--- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>
> I guess this is as good as any place, well actually I'll put this on the FB xenharmonic and micro theory pages as well. When I recognized that my 12 root of Phi (69.42419 cent interval ) was almost identical to 17 edo (70.58824 cent interval) I thought - what is the use? Is it really different? With that thought in mind I wonder if there could be value in whittling down the vast details of nuanced tunings into a smaller subset of tunings based on interval size - perhaps a Gaussian distribution classification around intervals with significant character differences. Of course I just injected a lot of subjective judgements into this suggestion. An obvious guide would be to use JI interval ratios or HE.
>
> Bits and pieces of this very unoriginal thought I've seen discussed. I think what I would point out that probably these "class" have specific harmonic tendencies and could be treated with some common compositional practices if you don't mind a bit of a broad brush.
>
> Perhaps I am alone in the observation that too often things get bogged down in the details - not that exploring is bad - but if we are to make headway into xenharmonic practice beyond imitation of 12 equal I think some generalizations are warranted.
>
> After that I'll wait for someone to tell me I missed this discussion a year or two ago.

This is sort of the whole point of using abstract temperaments rather than specific tunings. The different versions of the diatonic scale in 31edo or 50edo or 1/4-comma meantone or golden meantone or LucyTuning will sound indistinguishable to practically any listener, so we just call them all meantone diatonic. They're all characterized by the vanishing of 81/80, not by anything to do with phi or pi or whatever.

For your example of 12th-root-of-phi tuning, if you're using it in such a way that 17 generators is equivalent to an octave, then you could say it's equivalent to 17edo with compressed octaves. If you're not making that identification, or you're actually using the small step that's left over after 17 generators, then you're using some hitherto unnamed temperament, probably one found here: http://x31eq.com/cgi-bin/rt.cgi?ets=17+18&limit=13 . Which particular one depends on which intervals of the scale you're using to create which kinds of harmony.

Keenan

Hi Keenan - I was thinking in terms of Phi replacing the octave when I
wrote these: http://micro.soonlabel.com/12th-root-phi/ but now I question
is there any real difference besides what my thinking was?
There are many ways to think of 12 equal - so I'd assume there are many ways
to think of 17 equal (no doubt more).

Ok, so then perhaps classes of commas do make the most sense in the type of
classifications I'm talking about. The next question is then : do we have a
way of finding a reasonable approximation to the optimum tuning with respect
to every comma?

Thanks,

Chris

On Wed, Sep 7, 2011 at 9:48 PM, Keenan Pepper <keenanpepper@...>wrote:

> **
>
>
> --- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>
>
> This is sort of the whole point of using abstract temperaments rather than
> specific tunings. The different versions of the diatonic scale in 31edo or
> 50edo or 1/4-comma meantone or golden meantone or LucyTuning will sound
> indistinguishable to practically any listener, so we just call them all
> meantone diatonic. They're all characterized by the vanishing of 81/80, not
> by anything to do with phi or pi or whatever.
>
> For your example of 12th-root-of-phi tuning, if you're using it in such a
> way that 17 generators is equivalent to an octave, then you could say it's
> equivalent to 17edo with compressed octaves. If you're not making that
> identification, or you're actually using the small step that's left over
> after 17 generators, then you're using some hitherto unnamed temperament,
> probably one found here:
> http://x31eq.com/cgi-bin/rt.cgi?ets=17+18&limit=13 . Which particular one
> depends on which intervals of the scale you're using to create which kinds
> of harmony.
>
> Keenan
>
>
>

Hi Keenan - I was thinking in terms of Phi replacing the octave when I
wrote these: http://micro.soonlabel.com/12th-root-phi/ but now I question
is there any real difference besides what my thinking was?
There are many ways to think of 12 equal - so I'd assume there are many ways
to think of 17 equal (no doubt more).

Ok, so then perhaps classes of commas do make the most sense in the type of
classifications I'm talking about. The next question is then : do we have a
way of finding a reasonable approximation to the optimum tuning with respect
to every comma?

Thanks,

Chris

On Wed, Sep 7, 2011 at 9:48 PM, Keenan Pepper <keenanpepper@...>wrote:

> **
>
>
> --- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>
>
> This is sort of the whole point of using abstract temperaments rather than
> specific tunings. The different versions of the diatonic scale in 31edo or
> 50edo or 1/4-comma meantone or golden meantone or LucyTuning will sound
> indistinguishable to practically any listener, so we just call them all
> meantone diatonic. They're all characterized by the vanishing of 81/80, not
> by anything to do with phi or pi or whatever.
>
> For your example of 12th-root-of-phi tuning, if you're using it in such a
> way that 17 generators is equivalent to an octave, then you could say it's
> equivalent to 17edo with compressed octaves. If you're not making that
> identification, or you're actually using the small step that's left over
> after 17 generators, then you're using some hitherto unnamed temperament,
> probably one found here:
> http://x31eq.com/cgi-bin/rt.cgi?ets=17+18&limit=13 . Which particular one
> depends on which intervals of the scale you're using to create which kinds
> of harmony.
>
> Keenan
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> The next question is then : do we have a
> way of finding a reasonable approximation to the optimum tuning with respect
> to every comma?

You can find the optimal tunings for various definitions of optimal for any codimension 1 temperament.

I see your point Gene. The definition I am proposing is classification by xenharmonic function families. This seems to already exist for scale families (I think).

Chris
-----Original Message-----
From: "genewardsmith" <genewardsmith@...>
Sender: tuning@yahoogroups.com
Date: Thu, 08 Sep 2011 02:16:12
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: Whittle it down?

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> The next question is then : do we have a
> way of finding a reasonable approximation to the optimum tuning with respect
> to every comma?

You can find the optimal tunings for various definitions of optimal for any codimension 1 temperament.

Mike B. said that what I'm talking about is the regular mapping paradigm -
so I guess I'll read up on that and the angle Keenan talked about.

Thanks everyone!

Chris

On Wed, Sep 7, 2011 at 10:16 PM, genewardsmith
<genewardsmith@...>wrote:

> **
>
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > The next question is then : do we have a
> > way of finding a reasonable approximation to the optimum tuning with
> respect
> > to every comma?
>
> You can find the optimal tunings for various definitions of optimal for any
> codimension 1 temperament.
>
>
>

On Wed, Sep 7, 2011 at 10:33 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I see your point Gene. The definition I am proposing is classification by xenharmonic function families. This seems to already exist for scale families (I think).

What do you mean by function family?

-Mike

for example

in 12 you have functional harmony like I IV V being a cadence. In different
tuning this may be distorted or perhaps completely unavailable. On the other
hand the same other tuning may offer different progressions unavailable or
totally distorted in 12 equal.

So, my point is for example:

Harmonic progressions in 17 equal and 12th root of Phi probably have a lot
in common - they belong in the same general harmonic family. That is when
composing you can treat them in some similar ways and get a somewhat
consistent result.

As further example of this thinking - during the spring I was very lucky in
a weekly class in Urbana thanks organized by Jacob and Andrew. One of the
handouts showed the relationship between different tunings in terms of the
size of the "fifth" and position of diatonic / anti-diatonic steps. Here is
the handout: http://micro.soonlabel.com/various/Image0029.JPG

Chris

On Thu, Sep 8, 2011 at 5:12 PM, Mike Battaglia <battaglia01@gmail.com>wrote:

> **
>
>
> On Wed, Sep 7, 2011 at 10:33 PM, Chris Vaisvil <chrisvaisvil@...>
> wrote:
> >
> > I see your point Gene. The definition I am proposing is classification by
> xenharmonic function families. This seems to already exist for scale
> families (I think).
>
> What do you mean by function family?
>
> -Mike
>
>
>