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Message: 11100 - Contents - Hide Contents

Date: Fri, 25 Jun 2004 00:04:48

Subject: Re: The tertiaseptal family

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...>
wrote:



> If we do a search for {2,5,7}-commas of size less than 50 cents and
> epimericity less than 0.6, the complete list seems to be 128/125,
> 50/49, 3136/3125, 2100875/2097152; all of which except for the last
> are quite familiar.



A similar search on {2,3,7}-commas gives the following list of commas
less than 50 cents in size with epimericity less than 0.6:

49/48, 64/63, 65536/64827, 1029/1024, 118098/117649

I'll take a look at these.
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Message: 11102 - Contents - Hide Contents

Date: Fri, 25 Jun 2004 00:47:07

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:


> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
> 


>> Fine. Anyone have a problem with this? Only a few days left.
> 


> Yipe! Don't we get to see your draft before you submit it?



Sure . . . the window might be quite small, though.
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Message: 11103 - Contents - Hide Contents

Date: Fri, 25 Jun 2004 04:10:21

Subject: Re: Paul's nifty fifty

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:


> Paul Erlich wrote:


>>> How about "armadillo" in place of "kleismic", and "pangolin" in 
>> 
>> place
>> 
>>> of "nonkleismic"?
>> 
>> 


>> Fine. Anyone have a problem with this? Only a few days left.
> 


> If 5-limit kleismic is "hanson", what about "keenan" for what we've
been 
> calling 7-limit kleismic, <<6, 5, 3, -6, -12, -7]]? (Larry Hanson's 
> paper implies a "catakleismic" 7-limit mapping, <<6, 5, 22, -6, 18, 
> 37]]: see http://www.anaphoria.com/hanson.PDF - Type Ok * [with cont.]  (Wayb.), fig. 12, which implies a 
> mapping of [0, 6, 5, 22], while on the other hand Dave Keenan's page at 
> 11 note chain-of-minor-thirds scale * [with cont.]  (Wayb.) implies 
> a [0, 6, 5, 3] mapping.)



Thanks for this! I've been promoting "hanson" as the new name for
catakleismic. I think "keenan" makes sense, though admittedly it isn't
as cute a name as armadillo. Given Dave's views on naming things,
someone had better ask him if he'd allow it first if Paul likes it
enough for the paper.
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Message: 11104 - Contents - Hide Contents

Date: Fri, 25 Jun 2004 04:42:42

Subject: Names for important high-complexity temperaments

From: Gene Ward Smith

While we are on the subject of names, a less urgent question which now
would nevertheless be a good time to bring up is what people think of
the names I've hung on some important temperaments over Paul's cutoff.

<<22 -5 3 -59 -57 21|| tertiaseptal

<<16 2 5 -34 -37 6|| hemiwuerschmidt

<<2 25 13 35 15 -40|| hemififths

<<5 13 -17 9 -41 -76|| amity

<<40 22 21 -58 -79 -13|| tritonic?

<<4 -32 -15 -60 -35 55|| sesquiquartififths?

The name "tritonic" I'm suggesting since 7/5 is a poptimal generator
(though not, as one might have guessed, because it is minimax.)
Sesquiqartififths is not a very elegant name, but (3/2)^(1/4) is a
poptimal generator for this temperament. Sesquiquarschismic or
something of that sort might be another approach. Or we could be to go
the zoo and pick an animal.
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Message: 11106 - Contents - Hide Contents

Date: Fri, 25 Jun 2004 16:10:56

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
wrote:


> Paul Erlich wrote:


>>> How about "armadillo" in place of "kleismic", and "pangolin" in 
>> 
>> place
>> 
>>> of "nonkleismic"?
>> 
>> 


>> Fine. Anyone have a problem with this? Only a few days left.
> 


> If 5-limit kleismic is "hanson", what about "keenan" for what we've 
been 
> calling 7-limit kleismic, <<6, 5, 3, -6, -12, -7]]?



I'll ask Dave.



>(Larry Hanson's 
> paper implies a "catakleismic" 7-limit mapping, <<6, 5, 22, -6, 18, 
> 37]]: see http://www.anaphoria.com/hanson.PDF - Type Ok * [with cont.]  (Wayb.), fig. 12, which 
implies a 
> mapping of [0, 6, 5, 22],



Thanks for pointing this out . . . but the paper indicates that this 
was Wilson's idea, not Hanson's. I'm not going to worry about this 
right now.



> while on the other hand Dave Keenan's page at 
> 11 note chain-of-minor-thirds scale * [with cont.]  (Wayb.) 
implies 
> a [0, 6, 5, 3] mapping.)
> 
> Admittedly, "nonkleismic" isn't a very good name, especially for 
> something that extends to a (theoretically) good 11-limit and even 
a 
> reasonably good 13-limit version.
> 
> <<10, 9, 7, 25, -9, -17, 5, -9, 27, 46]]
> <<10, 9, 7, 25, -5, -9, -17, 5, -45, -9, 27, -45, 46, -40, -110]]
> 
> So something like that deserves a pretty unique and memorable name, 
and 
> a pangolin is a pretty unique and memorable sort of animal.



Well, it's related to an armadillo, so it might be nice to use the 
two names for related temperaments. Let's see . . .
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Message: 11107 - Contents - Hide Contents

Date: Fri, 25 Jun 2004 16:48:58

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:



> [6, 10, 3, 2, -12, -21] minorsemi?



I suggest "nautilus" for this one -- look at the floragram:

Yahoo groups: /tuning-math/files/Paul/nautilus... * [with cont.] 

Unfortunately I still have some bugs in some of my floragrams (maybe 
they're trying to make honey), so it looks like it'll be good old 
horagrams for the paper.
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Message: 11108 - Contents - Hide Contents

Date: Fri, 25 Jun 2004 17:40:40

Subject: Re: Paul's nifty fifty

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:


> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
> wrote:
> 


>> [6, 10, 3, 2, -12, -21] minorsemi?
> 


> I suggest "nautilus" for this one -- look at the floragram:

Neat!




________________________________________________________________________
________________________________________________________________________



------------------------------------------------------------------------


Yahoo! Groups Links

<*> To visit your group on the web, go to:
     Yahoo groups: /tuning-math/ * [with cont.] 

<*> To unsubscribe from this group, send an email to:
     tuning-math-unsubscribe@xxxxxxxxxxx.xxx

<*> Your use of Yahoo! Groups is subject to:
     Yahoo! Terms of Service * [with cont.]  (Wayb.)
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Message: 11110 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 19:56:12

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
wrote:


> Paul Erlich wrote:


>> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" 
<gwsmith@s...> 
>> wrote:
>> 
>> 


>>> [1, -8, -14, -15, -25, -10] septischismic?
>> 
>> 


>> Continuing on our kick of naming after people, I might call this 
>> Garibaldi, since Eduardo Sabat-Garibaldi gave names to 5120/5103 
>> ("Beta 5") and 33554432/33480783 ("Beta 2") in his study which 
>> yielded the 1/9-schisma, pure-octave version of this temperament. 
>> 4000/3969, though, may have escaped his attention (at least 
Manuel 
>> doesn't list any other "Beta"s, or any name for 4000/3969 at all).
>> 
> 


> That also fits the trend of animal names, since a garibaldi is a 
kind of 
> fish (Hypsypops rubicundus). But is anything wrong with 
plain "schismic" 
> for this one?



That doesn't tell you it's 7-limit, for one thing. For 
another, "schismic" is plain to us, but we've been talking to each 
other, and practically only to each other, for years.
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Message: 11111 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 19:58:37

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
wrote:


> Paul Erlich wrote:


>> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
>> wrote:
>> 


>>> a pangolin is a pretty unique and memorable sort of animal.
>> 
>> 


>> Well, it's related to an armadillo, so it might be nice to use 
the 
>> two names for related temperaments. Let's see . . .
> 


> Similar, but not closely related (armadillos are related to 
sloths). 
> Still, it would be nice to use the name "armadillo" for something. 
It 
> would be even better if there was something related to the number 9 
in 
> the temperament, since one of the more common kinds of armadillo is 
a 
> nine-banded armadillo.



It would be awesome if Gene permitted the word "ennealimmal" to morph 
into the similar sounding word "armadillo".
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Message: 11112 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 20:02:26

Subject: Re: Paul's nifty fifty

From: Paul Erlich

You know I disagree with virtually all of this -- I'd love to see 
your set of systematic names for these 50 temperaments, and then I 
might eat my words.





--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> 
wrote:


> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" 
<gwsmith@s...> 
> wrote:


>> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
> wrote:


>>> Paul Erlich wrote:


>>>>> How about "armadillo" in place of "kleismic", and "pangolin" 
> in 
>>>> 
>>>> place
>>>> 
>>>>> of "nonkleismic"?
>>>> 
>>>> 


>>>> Fine. Anyone have a problem with this? Only a few days left.
>>> 


>>> If 5-limit kleismic is "hanson", what about "keenan" for what 
> we've
>> been 


>>> calling 7-limit kleismic, <<6, 5, 3, -6, -12, -7]]? (Larry 
> Hanson's 


>>> paper implies a "catakleismic" 7-limit mapping, <<6, 5, 22, -6, 
> 18, 


>>> 37]]: see http://www.anaphoria.com/hanson.PDF - Type Ok * [with cont.]  (Wayb.), fig. 12, which 
> implies a 


>>> mapping of [0, 6, 5, 22], while on the other hand Dave Keenan's 
> page at 
>>> 11 note chain-of-minor-thirds scale * [with cont.]  (Wayb.) 
> implies 


>>> a [0, 6, 5, 3] mapping.)
>> 


>> Thanks for this! I've been promoting "hanson" as the new name for
>> catakleismic. I think "keenan" makes sense, though admittedly it 
> isn't


>> as cute a name as armadillo. Given Dave's views on naming things,
>> someone had better ask him if he'd allow it first if Paul likes it
>> enough for the paper.
> 


> Dear Herman, Gene and Paul E., 
> 
> Thanks for thinking of me here. And thanks especially Gene for 
> suggesting to ask me. 
> 
> I know you all think I'm a spoilsport with regard to the naming of 
> commas and temperaments, but I really don't think eponyms are much 
> better than the cryptic (or even meaningless) names that I also 
> object to. 
> 
> Sure these names are fun (mostly for those who get to make them 
up), 
> but they are of very little help to the person trying to break into 
> this stuff from scratch. They are of no educational assistance 
apart 
> from being _a_ name as opposed to no name, except in those few 
cases 
> where (a) there is a connection, albeit a cryptic one, between the 
> name and some memorable property of the temperament, and (b) this 
> connection is explained along with the giving of the name. "Orwell" 
> is the only one that comes to mind, with its generator near 19/84 
> ths of an octave. Although it probably isn't much help for younger 
> people who haven't heard of the book and it's author.
> 
> Some time ago, I was impressed by a note regarding eponyms in the 
> back of a well-regarded University-level textbook, 'Principles of 
> Anatomy and Physiology' by Tortora and Grabowski, now in its 10th 
> edition. I found this a very easy book to read and understand and I 
> have no background in the field, beyond high school biology and 
> chemistry.
> 
> I just found the same note on the web, so you can read it for 
> yourselves. It comes immediately after the heading "CHANGES IN 
> TERMINOLOGY" on this page:
> Addison-Wesley and Benjamin Cummings-Page Not ... * [with cont.]  (Wayb.)
> PRE,00.html
> 
> They instead named parts according to their properties, e.g. their 
> function or location or appearance etc. It just seems obvious to me 
> that from an educational point of view this is vastly superior.
> 
> So no. I'd prefer you didn't call it "keenan". But perhaps instead 
> of doing me that honour, you will do me the honour of considering 
my 
> wishes regarding how it ought to be named, particularly since that 
> didn't happen when I begged off "keenan's kleisma" for the same 
> reason. I'd prefer you left well-enough alone and continued to call 
> it 7-limit kleismic. The same goes for schismic. Has Graham breed 
> been consulted about renaming that?
> 
> These names have been in use for over a decade and they do relate 
to 
> a property of the temperament, namely the comma that vanishes. 
> 
> Admittedly this isn't my favourite property on which to base a new 
> name. I prefer to use the generator (and period if this is not a 
> whole octave, and relative complexity if there is more than one of 
> interest with the same interval approximated by its generator). By 
> this reckoning it is simply "minor thirds". But I have a preference 
> for "kleismic" because it is already well established.
> 
> If it needs to be distinguished from other 7-limit extensions of (5-
> limit) kleismic which, sadly, you also want to rename eponymically, 
> then one could use the adjective "simple" the first time it is 
> mentioned, or simply give the generator prime mapping.
> 
> -- Dave Keenan
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Message: 11113 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 00:57:10

Subject: HTT temperament

From: Gene Ward Smith

On Yahoo! Groups : MakeMicroMusic Messages * [with cont.]  (Wayb.)
George Secor wrote:

Gene, for your enlightenment: 29-HTT consists (except for one filler
tone) of 3 chains of fifths of ~703.5787c, or exactly (504/13)^
(1/9). The 3 chains of fifths contain tones 1/1, 5/4, and 7/4,
respectively, and the tones in each chain are taken to as many places
as are required to result in otonal ogdoads on roots Bb, F, C, G, D,
and A. This also gives very-near-just diatonic (5-limit) scales in 5
different keys.

Since the fifth is (504/13)^(1/9), we immediately have that

(504/13)/(3/2)^9 = 28672/28431

is a comma of the temperament, which must go up to the 13 limit at
least. It seems clear also that three of these slightly sharp fifths
are intended to represent 44/13, which means

(44/13)/(3/2)^3 = 352/351

is another comma of the system. It does not appear any more commas are
intended, since the 5/4 and 7/4 are introduced as independent
generators. This means that the HTT temperament is a two-comma
temperament in the 13-limit; the TM basis for which turns out to be
352/351 and 364/363. This is a spacial temperament, meaning one with
four generators, counting octaves. In this case we can take the
generators to be the approximation to 2,3,5,and 7, and the commas then
give us

11 ~ 896/81
13 ~ 28672/2187

Five is not a factor of the commas, so we can make this into a
no-fives system very easily. The reduction to the 11-limit is
896/891-spacial in the 11-limit, again of course a no-fives comma.
Aside from George's tuning, we have all the usual rms, minimax, TOP
etc. tunings if we want them. An interesting question is what 7-limit
JI scales would be good ones to temper using HTT; the question of high
dimensional temperaments has of course not been much explored.
Possibly looking at how near the TOP tunings are for various commas
would be useful in discovering pairings which make sense.
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Message: 11114 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 20:03:00

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
wrote:


> Herman Miller wrote:
> 


>> Paul Erlich wrote:
>> 


>>> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
>>> wrote:
>>> 
>>> 


>>>> a pangolin is a pretty unique and memorable sort of animal.
>>> 
>>> 


>>> Well, it's related to an armadillo, so it might be nice to use 
the 
>>> two names for related temperaments. Let's see . . .
>> 
>> 


>> Similar, but not closely related (armadillos are related to 
sloths). 
>> Still, it would be nice to use the name "armadillo" for 
something. It 
>> would be even better if there was something related to the number 
9 in 
>> the temperament, since one of the more common kinds of armadillo 
is a 
>> nine-banded armadillo.
> 


> I just realized that nonkleismic is a starling temperament 
(126/125). So 
> maybe a bird-related name would be better. Myna?



Sure, unless someone disagrees.
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Message: 11115 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 20:03:40

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Graham Breed <graham@m...> wrote:


> Dave Keenan wrote:
> 


>> it 7-limit kleismic. The same goes for schismic. Has Graham breed 
>> been consulted about renaming that?
> 


> i'm always here.  i've got a broken wrist so i don't post much.
> 
> 'schismic' has been around a long time as a 5-limit term, one 
speling or 
> another.  it's comes from the german, as used by and before 
helmholtz.
> 



Who used the temperament before Helmholtz, and how was it tuned?
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Message: 11116 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 20:05:13

Subject: Re: Paul's nifty fifty

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:



> This leaves kleismic free 
> to be a purely 7-limit name,



But then its name fails to uniquely identify it (many temperament 
have a vanishing kleisma).
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Message: 11117 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 22:37:28

Subject: Re: Paul's nifty fifty

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:


> You know I disagree with virtually all of this -- I'd love to see 
> your set of systematic names for these 50 temperaments, and then I 
> might eat my words.



I doubt it. You're too far gone. ;-)

And there's no time before your paper has to be in. I'm away for the 
next 3 days.
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Message: 11118 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 02:47:13

Subject: Re: Paul's nifty fifty

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:


> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> 
wrote:


>> Paul Erlich wrote:


>>>> How about "armadillo" in place of "kleismic", and "pangolin" 
in 
>>> 
>>> place
>>> 
>>>> of "nonkleismic"?
>>> 
>>> 


>>> Fine. Anyone have a problem with this? Only a few days left.
>> 


>> If 5-limit kleismic is "hanson", what about "keenan" for what 
we've
> been 


>> calling 7-limit kleismic, <<6, 5, 3, -6, -12, -7]]? (Larry 
Hanson's 
>> paper implies a "catakleismic" 7-limit mapping, <<6, 5, 22, -6, 
18, 
>> 37]]: see http://www.anaphoria.com/hanson.PDF - Type Ok * [with cont.]  (Wayb.), fig. 12, which 
implies a 
>> mapping of [0, 6, 5, 22], while on the other hand Dave Keenan's 
page at 
>> 11 note chain-of-minor-thirds scale * [with cont.]  (Wayb.) 
implies 
>> a [0, 6, 5, 3] mapping.)
> 


> Thanks for this! I've been promoting "hanson" as the new name for
> catakleismic. I think "keenan" makes sense, though admittedly it 
isn't
> as cute a name as armadillo. Given Dave's views on naming things,
> someone had better ask him if he'd allow it first if Paul likes it
> enough for the paper.



Dear Herman, Gene and Paul E., 

Thanks for thinking of me here. And thanks especially Gene for 
suggesting to ask me. 

I know you all think I'm a spoilsport with regard to the naming of 
commas and temperaments, but I really don't think eponyms are much 
better than the cryptic (or even meaningless) names that I also 
object to. 

Sure these names are fun (mostly for those who get to make them up), 
but they are of very little help to the person trying to break into 
this stuff from scratch. They are of no educational assistance apart 
from being _a_ name as opposed to no name, except in those few cases 
where (a) there is a connection, albeit a cryptic one, between the 
name and some memorable property of the temperament, and (b) this 
connection is explained along with the giving of the name. "Orwell" 
is the only one that comes to mind, with its generator near 19/84 
ths of an octave. Although it probably isn't much help for younger 
people who haven't heard of the book and it's author.

Some time ago, I was impressed by a note regarding eponyms in the 
back of a well-regarded University-level textbook, 'Principles of 
Anatomy and Physiology' by Tortora and Grabowski, now in its 10th 
edition. I found this a very easy book to read and understand and I 
have no background in the field, beyond high school biology and 
chemistry.

I just found the same note on the web, so you can read it for 
yourselves. It comes immediately after the heading "CHANGES IN 
TERMINOLOGY" on this page:
Addison-Wesley and Benjamin Cummings-Page Not ... * [with cont.]  (Wayb.)
PRE,00.html

They instead named parts according to their properties, e.g. their 
function or location or appearance etc. It just seems obvious to me 
that from an educational point of view this is vastly superior.

So no. I'd prefer you didn't call it "keenan". But perhaps instead 
of doing me that honour, you will do me the honour of considering my 
wishes regarding how it ought to be named, particularly since that 
didn't happen when I begged off "keenan's kleisma" for the same 
reason. I'd prefer you left well-enough alone and continued to call 
it 7-limit kleismic. The same goes for schismic. Has Graham breed 
been consulted about renaming that?

These names have been in use for over a decade and they do relate to 
a property of the temperament, namely the comma that vanishes. 

Admittedly this isn't my favourite property on which to base a new 
name. I prefer to use the generator (and period if this is not a 
whole octave, and relative complexity if there is more than one of 
interest with the same interval approximated by its generator). By 
this reckoning it is simply "minor thirds". But I have a preference 
for "kleismic" because it is already well established.

If it needs to be distinguished from other 7-limit extensions of (5-
limit) kleismic which, sadly, you also want to rename eponymically, 
then one could use the adjective "simple" the first time it is 
mentioned, or simply give the generator prime mapping.

-- Dave Keenan
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Message: 11119 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 22:42:33

Subject: Re: Paul's nifty fifty

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:


> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> 
> wrote:
> 


>> So no. I'd prefer you didn't call it "keenan". But perhaps 
instead 
>> of doing me that honour, you will do me the honour of 
considering 
> my 


>> wishes regarding how it ought to be named, particularly since 
that 
>> didn't happen when I begged off "keenan's kleisma" for the same 
>> reason. I'd prefer you left well-enough alone and continued to 
call 
>> it 7-limit kleismic. The same goes for schismic. Has Graham 
breed 
>> been consulted about renaming that?
> 


> The problem is that in both cases there is another 7-limit 
> temperament with a low badness figure which is much closer to the 
5-
> limit temperament in tuning, so the names are in a way deceptive.



So, like I said, call one "simple kleismic" and the other "complex 
kleismic", or even "simple-7 kleismic" and "complex-7 kleismic".

It doesn't make sense to have a completely unrelated name for the 
same temperament at a higher limit.
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Message: 11120 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 22:43:24

Subject: Some 7-limit temperaments supported by 152

From: Gene Ward Smith

The second on the list has a major third as generator, and the fourth
has a fifth. Both are worth noting. I give the 7 and 9 limit Graham
complexities, and the TOP error, in the second line.

Enneadecal
[19, 19, 57, -14, 37, 79] [[19, 30, 44, 53], [0, 1, 1, 3]]
57 57 .046052 {4375/4374, 703125/702464}

[23, -1, 13, -55, -44, 33] [[1, 9, 2, 7], [0, -23, 1, -13]]
24 47 .328389 {6144/6125, 16875/16807}

Amity
[5, 13, -17, 9, -41, -76] [[1, 3, 6, -2], [0, -5, -13, 17]]
30 30 .276106 {4375/4374, 5120/5103}

[1, 33, 27, 50, 40, -30] [[1, 2, 16, 14], [0, -1, -33, -27]]
33 33 .319505 {5120/5103, 16875/16807}

[28, 12, -4, -46, -85, -43] [[4, 8, 10, 11], [0, -7, -3, 1]]
32 60 .382797

[24, 32, 40, -5, -4, 3] [[8, 13, 19, 23], [0, -3, -4, -5]]
40 48 .269877

[33, 25, 131, -37, 115, 234] [[1, 17, 14, 64], [0, -33, -25, -131]]
131 131 .036482

[29, 45, 23, 4, -45, -73] [[1, -7, -11, -4], [0, 29, 45, 23]]
45 58 .348387

[47, 31, 53, -60, -48, 36] [[1, -8, -4, -8], [0, 47, 31, 53]]
53 94 .260647

[37, 5, 87, -78, 34, 188] [[1, 14, 4, 32], [0, -37, -5, -87]]
87 87 .108163

[41, -15, 43, -119, -47, 142] [[1, -3, 4, -2], [0, 41, -15, 43]]
58 97 .270148

[51, 11, 9, -101, -129, -10] [[1, 14, 5, 5], [0, -51, -11, -9]]
51 102 .375205

[33, 25, -21, -37, -126, -119] [[1, 17, 14, -7], [0, -33, -25, 21]]
54 87 .348077

[27, -21, -31, -96, -125, -13] [[1, 11, -5, -8], [0, -27, 21, 31]]
58 85 .324470

[57, 57, 19, -42, -130, -116] [[19, 29, 43, 53], [0, 3, 3, 1]]
57 114 .365107
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Message: 11121 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 22:47:26

Subject: Re: Paul's nifty fifty

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:



> So, like I said, call one "simple kleismic" and the other "complex 
> kleismic", or even "simple-7 kleismic" and "complex-7 kleismic".



So would "dominant sevenths" become "simple meantone" and (septimal)
meantone become "complex meantone"?



> It doesn't make sense to have a completely unrelated name for the 
> same temperament at a higher limit.



That's what I'm trying to avoid, by giving the name (as in the case of
meantone) to the one keeping the tuning, rather than the least complex
(which would be dominant sevenths in this case.)
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Message: 11122 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 10:11:53

Subject: Re: Paul's nifty fifty

From: Graham Breed

Dave Keenan wrote:



> it 7-limit kleismic. The same goes for schismic. Has Graham breed 
> been consulted about renaming that?



i'm always here.  i've got a broken wrist so i don't post much.

'schismic' has been around a long time as a 5-limit term, one speling or 
another.  it's comes from the german, as used by and before helmholtz.


                        graham
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Message: 11123 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 23:36:17

Subject: Some 11-limit temperaments supported by 152

From: Gene Ward Smith

Below I give the wedige, the mapping, a badness figure computed using
Graham complexity and TOP error, and then the complexity and error. 

<<23 -1 13 42 -55 -44 -13 33 101 73|| has a generator of a major
third, so we might call it voodoo, as a relative of magic, muggles,
and wizard. 

<<1 33 27 -18 50 40 -32 -30 -156 -144|| has a generator of a fifth,
like meantone and schismic, with TM basis {540/539, 1375/1372,
5120/5103}. The poptimal range runs from about 0.01 to 0.67 cents
sharp. It can be gotten by wedging the standard vals for any two of
41, 111, or 152 together, and so can be taken to be 41&152, with the
41 note DE an obvious possibility. None of this gives me a strong clue
about a good name. Anyone want to take another trip to the zoo?



Octoid
[24, 32, 40, 24, -5, -4, -45, 3, -55, -71] [[8, 13, 19, 23, 28], [0,
-3, -4, -5, -3]]
171.094038 48 .269877

Voodoo
[23, -1, 13, 42, -55, -44, -13, 33, 101, 73] [[1, 9, 2, 7, 17], [0,
-23, 1, -13, -42]]
201.010324 47 .328389

[1, 33, 27, -18, 50, 40, -32, -30, -156, -144] [[1, 2, 16, 14, -4],
[0, -1, -33, -27, 18]]
224.092825 51 .319505

[25, 65, 67, 6, 45, 36, -77, -27, -211, -215] [[1, 8, 19, 20, 5], [0,
-25, -65, -67, -6]]
331.030402 67 .299509

[9, -7, -61, -10, -32, -122, -47, -122, 1, 183] [[1, 2, 2, 0, 3], [0,
-9, 7, 61, 10]]
365.559169 79 .251331

[3, -53, -71, -54, -91, -121, -96, -16, 58, 94] [[1, 2, -5, -7, -4],
[0, -3, 53, 71, 54]]
370.926981 77 .266157

[13, -27, 47, 70, -73, 38, 66, 185, 256, 34] [[1, 8, -11, 26, 38], [0,
-13, 27, -47, -70]]
490.345468 97 .239451

[15, 39, -51, 34, 27, -123, 2, -228, -56, 272] [[1, 8, 19, -19, 18],
[0, -15, -39, 51, -34]]
499.053026 90 .276106

Amity
[5, 13, -17, 62, 9, -41, 81, -76, 99, 233] [[1, 3, 6, -2, 21], [0, -5,
-13, 17, -62]]
500.754537 79 .344281

[47, 31, 53, 66, -60, -48, -58, 36, 46, 2] [[1, -8, -4, -8, -10], [0,
47, 31, 53, 66]]
506.523230 94 .260647

Enneadecal
[19, 19, 57, -38, -14, 37, -126, 79, -154, -304] [[19, 30, 44, 53,
66], [0, 1, 1, 3, -2]]
518.966378 95 .262382

[27, -21, -31, -30, -96, -125, -141, -13, 3, 23] [[1, 11, -5, -8, -7],
[0, -27, 21, 31, 30]]
533.178660 85 .324470

[8, -40, 64, 8, -82, 79, -15, 261, 157, -199] [[8, 13, 17, 25, 28],
[0, -1, 5, -8, -1]]
541.551816 104 .235460

[41, -15, 43, 22, -119, -47, -107, 142, 103, -87] [[1, -3, 4, -2, 1],
[0, 41, -15, 43, 22]]
553.207897 97 .270148

[17, -47, 3, -2, -114, -43, -62, 139, 158, -16] [[1, -3, 15, 2, 4],
[0, 17, -47, 3, -2]]
579.688915 81 .382284
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Message: 11124 - Contents - Hide Contents

Date: Sat, 26 Jun 2004 10:03:27

Subject: Re: Paul's nifty fifty

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> 
wrote:



> So no. I'd prefer you didn't call it "keenan". But perhaps instead 
> of doing me that honour, you will do me the honour of considering 
my 
> wishes regarding how it ought to be named, particularly since that 
> didn't happen when I begged off "keenan's kleisma" for the same 
> reason. I'd prefer you left well-enough alone and continued to call 
> it 7-limit kleismic. The same goes for schismic. Has Graham breed 
> been consulted about renaming that?



The problem is that in both cases there is another 7-limit 
temperament with a low badness figure which is much closer to the 5-
limit temperament in tuning, so the names are in a way deceptive.



> These names have been in use for over a decade and they do relate 
to 
> a property of the temperament, namely the comma that vanishes. 



The competing temperaments have the exact same 5-limit comma, and use 
same tuning rather than trying to change it.
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