Octatonic temperament

Since the Pavane experiment drew my attention to 64-ET, I thought it would
be a good idea to supplement my Porcupine Temperament page with a new page
that gives some basic information about octatonic temperament (or at least,
what little I know about it, which isn't very much yet).

http://www.io.com/~hmiller/music/temp-octatonic.html

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
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--- In tuning@y..., Herman Miller <hmiller@I...> wrote:

> Since the Pavane experiment drew my attention to 64-ET, I thought
it would
> be a good idea to supplement my Porcupine Temperament page with a
new page
> that gives some basic information about octatonic temperament (or
at least,
> what little I know about it, which isn't very much yet).
>
> http://www.io.com/~hmiller/music/temp-octatonic.html

cool!

i thought we had established a consensus to call this 'diminished'
rather than 'octatonic'. do you have a differing view?

where did 225:224 come in? it doesn't really seem to be suggested by
the scale itself. gene just got finished explaining how different 7-
limit views of this scale absorb 126:125 and 50:49 -- perhaps you're
seeing it a different way?

gene, what 7-limit linear temperaments did you come up with with a
1/4-octave period, and what are their 'badness' measures?

i don't see 28 as 'marginal' -- it's at least as good as 12 for the
way i see it . . .

also, i'd include 16-equal here as well.

and the 'wolf' fifth and 'high minor third' rather seem like a
residue of 12-equal thinking -- since they don't occur as intervals
in the 8-tone scale, why be so concerned with them? if the pavane
suggested them, that may simply be a sign that ravel was really
thinking 12-equal . . .

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> http://www.io.com/~hmiller/music/temp-octatonic.html

This is good.

It might be better to say "a generator of around 93 cents".

I'm not sure "octatonic" is a good name for the temperament. There
must be other temperaments whose basic scale has 8 notes. Isn't this
what folks are calling the "diminished" temperament on tuning-math?

On Thu, 07 Mar 2002 02:48:14 -0000, "paulerlich" <paul@stretch-music.com>
wrote:

>i thought we had established a consensus to call this 'diminished'
>rather than 'octatonic'. do you have a differing view?

I was just going by Joe Monzo's chart. It's not easy keeping track of all
the discussions. (I also missed the 16-ET, since it's off the chart. Thanks
for mentioning it.)

>where did 225:224 come in? it doesn't really seem to be suggested by
>the scale itself. gene just got finished explaining how different 7-
>limit views of this scale absorb 126:125 and 50:49 -- perhaps you're
>seeing it a different way?

What I want is a category that specifically includes the 40, 52, and
64-ET's, which are roughly similar and form a nice little group by
themselves. 126:125 (or 50:49) covers 12, 16, and 28, but doesn't work with
these three.

>gene, what 7-limit linear temperaments did you come up with with a
>1/4-octave period, and what are their 'badness' measures?
>
>i don't see 28 as 'marginal' -- it's at least as good as 12 for the
>way i see it . . .
>
>also, i'd include 16-equal here as well.
>
>and the 'wolf' fifth and 'high minor third' rather seem like a
>residue of 12-equal thinking -- since they don't occur as intervals
>in the 8-tone scale, why be so concerned with them? if the pavane
>suggested them, that may simply be a sign that ravel was really
>thinking 12-equal . . .

I guess I need a name for this system that doesn't imply there's _only_
eight notes in the tuning. And "diminished" does suggest the 1/4-octave
framework of the scale, so it's a better name than "octatonic".

Certainly one possible use for these notes is as a kind of crude substitute
for meantone. But one of the things I'm hoping to do with this page is put
a positive spin on "inconsistency". The Pavane retuning might not be the
best illustration of this feature, but before doing the experiment, I
wouldn't have even considered 64-ET as a useful tuning. (I don't even have
a 64-ET example on the Canon page.)

Check out the updated page at:
http://www.io.com/~hmiller/music/temp-diminished.html

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> I'm not sure "octatonic" is a good name for the temperament. There
> must be other temperaments whose basic scale has 8 notes. Isn't this
> what folks are calling the "diminished" temperament on tuning-math?

Right, and there's always my suggestion of "igor".

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

> gene, what 7-limit linear temperaments did you come up with with a
> 1/4-octave period, and what are their 'badness' measures?

Here are some possibilities with a fifth as a possible generator--did you want the more high-octane ones as well?

wedgie [4, 4, 4, -2, 5, -3]

map [[0, -1, -1, -1], [4, 7, 10, 12]]

generators 214.3017930 300

badness 153.0959406 rms 19.13699259 g 2.828427124

wedgie [4, 4, 0, -11, 11, 3]

map [[0, 1, 1, 0], [4, 5, 8, 11]]

generators 359.7214038 300

badness 434.6652556 rms 40.74986774 g 3.265986323

wedgie [4, -8, -20, -24, 43, -22]

map [[0, -1, 2, 5], [4, 8, 6, 3]]

generators 494.2457155 300

badness 497.3644500 rms 2.220377008 g 14.96662955

wedgie [4, 4, -8, -30, 24, -3]

map [[0, -1, -1, 2], [4, 8, 11, 8]]

generators 491.5638496 300

badness 867.7149306 rms 13.55804579 g 8.

wedgie [4, 4, 16, 26, -14, 3]

map [[0, -1, -1, -4], [4, 8, 11, 18]]

generators 508.0077325 300

badness 878.5571441 rms 9.151636916 g 9.797958972

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:

> But one of the things I'm hoping to do with this page is put
> a positive spin on "inconsistency".

i'd put it this way: 64-equal supports several different reasonable
mappings of 7-limit ji to linear temperaments. it even supports
pajara!

i think it's better to have a name for each consistent mapping first,
and then later, if one wishes, one may identify instances where
different mappings coexist in a single tuning system (or even a
single piece of music). even in the 5-limit, what you're doing with
the minor third would seem to necessitate this step.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > gene, what 7-limit linear temperaments did you come up with with
a
> > 1/4-octave period, and what are their 'badness' measures?
>
> Here are some possibilities with a fifth as a possible generator--
>did you want the more high-octane ones as well?

i think we want to stick to the ones with the mappings and commas
herman indicated, or those in that range of complexity.

> map [[0, -1, -1, -1], [4, 7, 10, 12]]
>
> generators 214.3017930 300
>
> badness 153.0959406 rms 19.13699259 g 2.828427124

this looks like the {648:625, 126:125} one, right? is the TM-reduced
basis {50:49, 36:35}?

> map [[0, -1, -1, 2], [4, 8, 11, 8]]
>
> generators 491.5638496 300
>
> badness 867.7149306 rms 13.55804579 g 8.

is this {648:625, 225:224}?

what about herman's other minor third mapping?

is this a discussion for tuning-math?

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:

> this looks like the {648:625, 126:125} one, right? is the TM-reduced
> basis {50:49, 36:35}?

That's the one.

> is this {648:625, 225:224}?

Right.

> is this a discussion for tuning-math?

I thought you wanted it here for some reason, but I'll move it there. I need to go administer some midterms.

On Thu, 07 Mar 2002 12:26:39 -0000, "paulerlich" <paul@stretch-music.com>
wrote:

>--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
>
>> But one of the things I'm hoping to do with this page is put
>> a positive spin on "inconsistency".
>
>i'd put it this way: 64-equal supports several different reasonable
>mappings of 7-limit ji to linear temperaments. it even supports
>pajara!
>
>i think it's better to have a name for each consistent mapping first,
>and then later, if one wishes, one may identify instances where
>different mappings coexist in a single tuning system (or even a
>single piece of music). even in the 5-limit, what you're doing with
>the minor third would seem to necessitate this step.

That makes sense. 64-ET could have cross references to other pages
(kleismic, meantone, pajara). 52-ET could link to a different set of
temperaments (porcupine appears to be one of them). That's probably the
best way to deal with the inconsistent temperaments.

> From: Herman Miller <hmiller@IO.COM>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, March 06, 2002 8:26 PM
> Subject: Re: [tuning] Re: Octatonic temperament
>
>
> On Thu, 07 Mar 2002 02:48:14 -0000, "paulerlich" <paul@stretch-music.com>
> wrote:
>
> > i thought we had established a consensus to call this 'diminished'
> > rather than 'octatonic'. do you have a differing view?
>
> I was just going by Joe Monzo's chart. It's not easy keeping track of all
> the discussions. (I also missed the 16-ET, since it's off the chart.
Thanks
> for mentioning it.)

thanks for pointing this out again ... it finally impelled
me to fix that chart:
http://www.ixpres.com/interval/dict/eqtemp.htm

> Certainly one possible use for these notes is as a kind of crude
substitute
> for meantone. But one of the things I'm hoping to do with this page is put
> a positive spin on "inconsistency". The Pavane retuning might not be the
> best illustration of this feature, but before doing the experiment, I
> wouldn't have even considered 64-ET as a useful tuning. (I don't even have
> a 64-ET example on the Canon page.)

and i'll mention again that my favorite retuning of the
_Pavane_ was also 64edo! i love it.

-monz

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> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, March 06, 2002 11:50 PM
> Subject: Re: [tuning] Re: Octatonic temperament
>
>
> > From: Herman Miller <hmiller@IO.COM>
> > To: <tuning@yahoogroups.com>
> > Sent: Wednesday, March 06, 2002 8:26 PM
> > Subject: Re: [tuning] Re: Octatonic temperament
> >
> >
> > On Thu, 07 Mar 2002 02:48:14 -0000, "paulerlich"
<paul@stretch-music.com>
> > wrote:
> >
> > > i thought we had established a consensus to call this 'diminished'
> > > rather than 'octatonic'. do you have a differing view?
> >
> > I was just going by Joe Monzo's chart. It's not easy keeping
> > track of all the discussions. (I also missed the 16-ET, since
> > it's off the chart. Thanks for mentioning it.)
>
>
> thanks for pointing this out again ... it finally impelled
> me to fix that chart:
> http://www.ixpres.com/interval/dict/eqtemp.htm

well ... i meant that i had added the names "augmented" (diesic)
and "diminished" (octatonic) ... not that i had added 16edo.

i'm just mentioning this now before paul barks that i didn't
add 16edo yet, because upon rereading my post now, i can see
that coming next...

(... i still love you, paul)

-monz

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Paul:
> > > i thought we had established a consensus to call this 'diminished'
> > > rather than 'octatonic'. do you have a differing view?

Herman:
> > I was just going by Joe Monzo's chart. It's not easy keeping track of
> > all
> > the discussions. (I also missed the 16-ET, since it's off the chart.
> Thanks
> > for mentioning it.)

Monz:
> thanks for pointing this out again ... it finally impelled
> me to fix that chart:
> http://www.ixpres.com/interval/dict/eqtemp.htm

Is this agreed then? I'll have to update my catalog to reflect the
consensus. Will Herman's URL stay the same?

Graham

On Sat, 9 Mar 2002 10:13 +0000 (GMT Standard Time), graham@microtonal.co.uk
wrote:

>Is this agreed then? I'll have to update my catalog to reflect the
>consensus. Will Herman's URL stay the same?

Now that I've moved it to
http://www.io.com/~hmiller/music/temp-diminished.html
it will.

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> > From: Herman Miller <hmiller@I...>
> > To: <tuning@y...>
> > Sent: Wednesday, March 06, 2002 8:26 PM
> > Subject: Re: [tuning] Re: Octatonic temperament
> >
> >
> > On Thu, 07 Mar 2002 02:48:14 -0000, "paulerlich"
<paul@s...>
> > wrote:
> >
> > > i thought we had established a consensus to call this
'diminished'
> > > rather than 'octatonic'. do you have a differing view?
> >
> > I was just going by Joe Monzo's chart. It's not easy keeping
track of all
> > the discussions. (I also missed the 16-ET, since it's off the
chart.
> Thanks
> > for mentioning it.)
>
>
> thanks for pointing this out again ... it finally impelled
> me to fix that chart:
> http://www.ixpres.com/interval/dict/eqtemp.htm

hate to repeat myself, but your claim that 12-equal is "just barely"
diesic (augmented) is like claiming 31-equal is "just barely"
meantone -- hope you'll correct this and also mention
diminished (octatonic) under 12-equal.

hi paul,

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 12:50 PM
> Subject: [tuning] Re: Octatonic temperament
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > [me, monz]
> > thanks for pointing this out again ... it finally impelled
> > me to fix that chart:
> > http://www.ixpres.com/interval/dict/eqtemp.htm
>
> hate to repeat myself, but your claim that 12-equal is "just barely"
> diesic (augmented) is like claiming 31-equal is "just barely"
> meantone -- hope you'll correct this and also mention
> diminished (octatonic) under 12-equal.

i've had to cut back on my internet addiction a bit,
but i never got a full understanding of your contention
over the "barely diesic" issue. i think we should discuss
it off-list ... i'll try to catch you with an IM when
i have time.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
> hi paul,
>
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Sunday, March 10, 2002 12:50 PM
> > Subject: [tuning] Re: Octatonic temperament
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > [me, monz]
> > > thanks for pointing this out again ... it finally impelled
> > > me to fix that chart:
> > > http://www.ixpres.com/interval/dict/eqtemp.htm
> >
> > hate to repeat myself, but your claim that 12-equal is "just
barely"
> > diesic (augmented) is like claiming 31-equal is "just barely"
> > meantone -- hope you'll correct this and also mention
> > diminished (octatonic) under 12-equal.
>
>
>
> i've had to cut back on my internet addiction a bit,
> but i never got a full understanding of your contention
> over the "barely diesic" issue. i think we should discuss
> it off-list ... i'll try to catch you with an IM when
> i have time.

or e-mail me.

think about it -- by your logic, 31-equal would be 'just barely'
meantone. this is patent nonsense. think about it!

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_35256.html#35440

> i've had to cut back on my internet addiction a bit,
> but i never got a full understanding of your contention
> over the "barely diesic" issue. i think we should discuss
> it off-list ... i'll try to catch you with an IM when
> i have time.
>

****Why is some of this, specifially, *tuning* stuff going off list?
Some of us are trying to understand these pages, too! :)

(With varying degrees of success, admittedly... :) )

jp

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> > I was just going by Joe Monzo's chart. It's not easy keeping
track of all
> > the discussions. (I also missed the 16-ET, since it's off the
chart.
> Thanks
> > for mentioning it.)
>
>
> thanks for pointing this out again ... it finally impelled
> me to fix that chart:
> http://www.ixpres.com/interval/dict/eqtemp.htm

hmm . . . 16 is still off the chart . . . oh well.

i notice that some new weirdness has crept into this page,
monz.

a bunch of the entries in the table had a '<' before the date,
indicating "before". for example,

<1875 Captain J. Herschel (cited by Bosanquet)

means "before 1875".

but you've now followed all of these entries with ">", depriving
them of the "before" meaning and making them look like
parenthetical remarks.

perhaps the word "before" would have been clearer?

cheers,
paul

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, March 10, 2002 12:48 PM
> Subject: [tuning] monz' et page
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > thanks for pointing this out again ... it finally impelled
> > me to fix that chart:
> > http://www.ixpres.com/interval/dict/eqtemp.htm
>
> hmm . . . 16 is still off the chart . . . oh well.
>
> i notice that some new weirdness has crept into this page,
> monz.
>
> a bunch of the entries in the table had a '<' before the date,
> indicating "before". for example,
>
> <1875 Captain J. Herschel (cited by Bosanquet)
>
> means "before 1875".
>
> but you've now followed all of these entries with ">", depriving
> them of the "before" meaning and making them look like
> parenthetical remarks.
>
> perhaps the word "before" would have been clearer?

i noticed a post about this before and didn't acknowledge it,
sorry.

hmmm ... i suspect that the browser is just reading my HTML
code incorrectly, because < and > are used to tag HTML commands.
this points out the necessity of always using the < and
> codes instead of the actual symbols, in a webpage.
i'll have to go do surgery on that one.

i think i agree with you: the word "before" is clearer.
i hope to get around to this in the next couple of days,
if not... "friendly reminder" down the road.

-monz

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