Wikipedia "tina" page

Hello all,

I posted here several times over the last few weeks
advocating the use of the "tina" (one degree of 8539-edo)
as an interval measurement, and encouraging its use
as a replacement for cents.

A tina is approximately 1/7-cent, thus 8539-edo gives
resolution about 7 times greater than cents. In addition,
it gives very accurate approximations to a very wide
variety of musical intervals, including all JI
tonality-diamonds thru the 37-limit.

I created a Wikipedia page for the tina a few weeks ago:

http://en.wikipedia.org/wiki/Tina_(music)

basically just copying the page that already existed
for "cent" and changing what was necessary to change,
with a few additional comments.

Upon looking at the page just now, i see that it has
been tagged for possible deletion because of a
Conflict Of Interest, in that the only citation provided
is to my own Tonalsoft Encyclopedia webpage about the tina.

Well, according to the Wikipedia guidelines this *is* a
borderline case of COI, but unfortunately, there is no
other reference available. And i think the use of the
tina really should be encouraged.

So i'm asking folks here to please contribute to the
Talk: Tina (music) page in hopes that the Tina page
will not be deleted. Thanks.

http://en.wikipedia.org/wiki/Talk:Tina_(music)

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> So i'm asking folks here to please contribute to the
> Talk: Tina (music) page in hopes that the Tina page
> will not be deleted.

Why? Why do we need to have a page about something that no one uses,
and probably no one ever will? (and by no one, I mean by more than one
or two people) Monz, *after* something is like this is adopted by a
sizable number of practitioners and theorists, *then* it won't look
like just some vanity page.

Seems like an attempt to immortalize his daughter, Allah bless her.

Oz.

----- Original Message -----
From: "Jon Szanto" <jszanto@cox.net>
To: <tuning@yahoogroups.com>
Sent: 15 May�s 2007 Sal� 18:09
Subject: [tuning] Re: Wikipedia "tina" page

> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> > So i'm asking folks here to please contribute to the
> > Talk: Tina (music) page in hopes that the Tina page
> > will not be deleted.
>
> Why? Why do we need to have a page about something that no one uses,
> and probably no one ever will? (and by no one, I mean by more than one
> or two people) Monz, *after* something is like this is adopted by a
> sizable number of practitioners and theorists, *then* it won't look
> like just some vanity page.
>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Seems like an attempt to immortalize his daughter, Allah bless her.

Well, Oz, I'm all for blessings on the sweet young thing, but then
again her name isn't "Tina". On the talk page, Monz says the following:

"But I created the Wikipedia page in a deliberate attempt to encourage
use of the Tina as a replacement for the common Cent measurement."

Ahem. Is that what anyone thinks the purpose of an encyclopedia is?
Monz, you aren't using it to document and solidify the definition of
an accepted usage, you are using it to promote an agenda. At least be
honest about it.

I'm not saying this to snipe at you in particular, or this particular
case. I just think that activities like this devalue any weight one
could give to efforts like Wikipedia.

> Well, according to the Wikipedia guidelines this *is* a
> borderline case of COI, but unfortunately, there is no
> other reference available. And i think the use of the
> tina really should be encouraged.

This is exactly the kind of thing that you should
NOT put on wikipedia, Joseph Monzo.

-Carl

I tend to agree with Jon.
Tina seems like a particularly "silly" unit of measurement of intervals for it perpetuates the significance of integer frequency ratios.
I appreciate that these intervals are the "source" of beating, yet for anyone making tuned music other than JI extensions they are irrelevant.
It would seem more appropriate to base your units on computer clock rates, binary, octal or radians to connect them with geometry.
In the meantime, I shall continue to use cents, since the concept is easily understood by all musicians, and uses a radix of ten
which every developing child learns as soon as they count beyond their fingers and thumbs.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 15 May 2007, at 16:09, Jon Szanto wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> > So i'm asking folks here to please contribute to the
> > Talk: Tina (music) page in hopes that the Tina page
> > will not be deleted.
>
> Why? Why do we need to have a page about something that no one uses,
> and probably no one ever will? (and by no one, I mean by more than one
> or two people) Monz, *after* something is like this is adopted by a
> sizable number of practitioners and theorists, *then* it won't look
> like just some vanity page.
>
>
>

Jon Szanto wrote:

>--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
>>Seems like an attempt to immortalize his daughter, Allah bless her.
>> >>
>
>Well, Oz, I'm all for blessings on the sweet young thing, but then
>again her name isn't "Tina". On the talk page, Monz says the following:
>
>"But I created the Wikipedia page in a deliberate attempt to encourage
>use of the Tina as a replacement for the common Cent measurement."
>
>Ahem. Is that what anyone thinks the purpose of an encyclopedia is?
>Monz, you aren't using it to document and solidify the definition of
>an accepted usage, you are using it to promote an agenda. At least be
>honest about it.
>

More of the same. I always wondered about this crap.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

Well, OK then, i guess the tuning community has spoken.

So much for me trying to promote something useful.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, David Beardsley <db@...> wrote:
>
> Jon Szanto wrote:
>
> >--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> >
> >>Seems like an attempt to immortalize his daughter, Allah bless her.
> >>
> >>
> >
> >Well, Oz, I'm all for blessings on the sweet young thing, but then
> >again her name isn't "Tina". On the talk page, Monz says the following:
> >
> >"But I created the Wikipedia page in a deliberate attempt to encourage
> >use of the Tina as a replacement for the common Cent measurement."
> >
> >Ahem. Is that what anyone thinks the purpose of an encyclopedia is?
> >Monz, you aren't using it to document and solidify the definition of
> >an accepted usage, you are using it to promote an agenda. At least be
> >honest about it.
> >
>
> More of the same. I always wondered about this crap.
>
> --
> * David Beardsley
> * microtonal guitar
> * http://biink.com/db
>

Hi Oz,

Huh?

This has nothing at all to do with my daughter.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Seems like an attempt to immortalize his daughter, Allah bless her.
>
> Oz.
>
> ----- Original Message -----
> From: "Jon Szanto" <jszanto@...>
> To: <tuning@yahoogroups.com>
> Sent: 15 Mayýs 2007 Salý 18:09
> Subject: [tuning] Re: Wikipedia "tina" page
>
>
> > --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > > So i'm asking folks here to please contribute to the
> > > Talk: Tina (music) page in hopes that the Tina page
> > > will not be deleted.
> >
> > Why? Why do we need to have a page about something that no one uses,
> > and probably no one ever will? (and by no one, I mean by more than one
> > or two people) Monz, *after* something is like this is adopted by a
> > sizable number of practitioners and theorists, *then* it won't look
> > like just some vanity page.
> >
> >
> >
>

Monz,

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> Well, OK then, i guess the tuning community has spoken.

No, just 3 or 4.

> So much for me trying to promote something useful.

Just so that *my* point is clear: I'm perfectly happy with you
promoting it, and I wish you well. I just don't think Wikipedia should
be used in that manner, as that is definitely not it's purpose.
Promote tina the way you would any other concept, and if and when it
becomes established, *then* you could consider putting it in an
encyclopedic framework.

Wikipedia is not a marketing tool, but a source of information. Weak,
but a source.

Best,
Jon

My two cents (no pun intended):

I personally don't see a need for all these new units and terminology unless they fill a vacuum--i.e. they neatly or succinctly convey something not before possible. I can say that often, some terminology around here has muddied the water and made things *harder* to understand, and in a way that I feel adds to the sense that the term is merely a self-promotional gimmick. The biggest example: after reading what a 'monzo' was---I thought---that's it? Why not just call it a 'prime distance' or something that would make it easy to grok right away? I love Gene, for example, but don't want to get a headache trying to be a PhD math professor to read his site and try to understand what he's getting at. This is not to de-value his or Joe's or anyone's work, which is very valuable, but a plea to make things *in plaine and easie English* where possible.

I suppose one could argue that if I can't clearly understand what is being said, I have no right to say it's not new or necessary. True enough, but at least not in the case of 'monzos'.....there may be others, I suspect.

Also, usage should be organically developed rather than aggressively promoted. So I think the Wikipedia editorial bunch are really being responsible.

I don't mean to offend anyone, or hurt anyone's feelings, I just wanted to point out what I think many around here might consider a somewhat elitist procedure. So forgive me, please.

On a side note---I've always wondered why cents should be used when we could measure intervals in log base 2 (octaves). Why multiply by 1200 and give a special priority to 12-edo? (by the way, I like 'edo' better than 'tet'---I think it makes it *easier* to understand instantly to newbies)

Best,
Aaron.

monz wrote:
> Well, OK then, i guess the tuning community has spoken.
>
> So much for me trying to promote something useful.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
> --- In tuning@yahoogroups.com, David Beardsley <db@...> wrote:
> >> Jon Szanto wrote:
>>
>> >>> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
>>> >>>
>>> >>>> Seems like an attempt to immortalize his daughter, Allah bless her.
>>>> >>>>
>>>> >>> Well, Oz, I'm all for blessings on the sweet young thing, but then
>>> again her name isn't "Tina". On the talk page, Monz says the following:
>>>
>>> "But I created the Wikipedia page in a deliberate attempt to encourage
>>> use of the Tina as a replacement for the common Cent measurement."
>>>
>>> Ahem. Is that what anyone thinks the purpose of an encyclopedia is?
>>> Monz, you aren't using it to document and solidify the definition of
>>> an accepted usage, you are using it to promote an agenda. At least be
>>> honest about it.
>>>
>>> >> More of the same. I always wondered about this crap.
>>
>> -- >> * David Beardsley
>> * microtonal guitar
>> * http://biink.com/db
>>
>> >
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
>
>
>
>
>

[ Attachment content not displayed ]

Hi Aaron,

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
>
> My two cents (no pun intended):
>
> I personally don't see a need for all these new units
> and terminology unless they fill a vacuum--i.e. they neatly
> or succinctly convey something not before possible. I can
> say that often, some terminology around here has muddied
> the water and made things *harder* to understand, and in
> a way that I feel adds to the sense that the term is
> merely a self-promotional gimmick. The biggest example:
> after reading what a 'monzo' was---I thought---that's it?
> Why not just call it a 'prime distance' or something that
> would make it easy to grok right away?

The only really accurate way of describing a "monzo"
is to call it a "prime-factor-exponent vector". Gene's
whole purpose in giving it the short name (that i
obviously like) was that he didn't want to have to
keep typing that much longer term over and over again.

He named it after me because as far as he (and i) could
tell, i was the first person who proposed using the
prime-factor-exponent vector as a way of notating
musical intervals and/or pitches.

As for the whole debate about new terminology, that's
*exactly* the reason why i created the Encyclopedia
in the first place! I struggled for a long time doing
research on tuning terms that i didn't know, and wanted
to put it all into one online home would make it so much
easier for others in the same predicament.

If you're online and reading about a "tina", what's
so difficult about looking it up in either my Encyclopedia
or in Wikipedia? (assuming that the Wikipedia editors
allow the page to remain) ... in fact it would be a
lot more accessible in Wikipedia than in my own Encyclopedia,
which is precisely why i put it there.

There's always going to be a debate about new jargon,
and in fact i created an entire Yahoo group explicitly
for the purpose of debating tuning jargon. If others
can't see the value of using "tina" over "cents" or
any other logarithmic measurement, then that's too bad,
because the tina is clearly superior to any other integer
measurement, for a lot of reasons.

Boy, for a group of people who embrace new tunings
enthusiastically, there sure is a strong conservative
bent to most mindsets around here.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Thanks, mikal. You seem to see where i'm coming from.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "mikal haley" <chipsterthehipster@...>
wrote:
>
> hemi demi semi quasi quavers.
>
> as someone who barely reads music i understand
> the value of musical literacy, and letting it evolve.
>
> once upon a time in chamber music, for example
> there were no RESTS. notation will go on evolving
> according to the needs of musicians...it just will.
>
> you have to watch the snippy divide and conquer stuff
> on groups...there are people spoiling for arguments,
> mad about what they are learning.
>
> i think anything thoughtful to add some 'cool' to music is
> okay. it's not hurting anyone who doesn't wanna use it.
>
> on the other hand
> lots of hate for wikipedia lately. don't know why?
>
> free music,
>
> mikal

Greetings,

It seems to me that someone has come up with an idea, prepared a justification of, suggested its usage and so offers it for the public. I can't consider this an exercise in vanity, unless the process of suggesting a new idea follows a different course such as:

Oh that's not true.
Well, it's true but useless.
Oh, well, it's true, but I knew it all along.

From the author Idries Shah.

All best wishes,

Gordon Rumson

On 15-May-07, at 11:37 AM, David Beardsley wrote:

> Jon Szanto wrote:
>
>> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>>
>>
>>> Seems like an attempt to immortalize his daughter, Allah bless her.
>>>
>>>
>>
>> Well, Oz, I'm all for blessings on the sweet young thing, but then
>> again her name isn't "Tina". On the talk page, Monz says the >> following:
>>
>> "But I created the Wikipedia page in a deliberate attempt to >> encourage
>> use of the Tina as a replacement for the common Cent measurement."
>>
>> Ahem. Is that what anyone thinks the purpose of an encyclopedia is?
>> Monz, you aren't using it to document and solidify the definition of
>> an accepted usage, you are using it to promote an agenda. At least be
>> honest about it.
>>
>

My mistake apparently. but then, your attitude is even less understandable,
given the fact, that other replacements for cent have been proposed -
especially by Gene. Why should tina take precedence without any solid
consensus in this community? For all I know, various suggestions by others
were much more promising compared to tina. I do not object to your desire to
put it up in your page, but to insist that people support you so that it
does not get deleted from wikipedia is going a bit too far.

Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 15 May�s 2007 Sal� 21:22
Subject: [tuning] Re: Wikipedia "tina" page

Hi Oz,

Huh?

This has nothing at all to do with my daughter.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Monz,

Point(s) taken. I see where you are coming from, and I hope you didn't take offense to where *i* was coming from.

I'm trying not to be or come off as conservative, because I'm not. What I'm still convinced of is the need for many off these concepts of a more advanced nature to be intuitively re-explained in a visual or more linguistic way, so that the advanced symbols and terminology don't turn the larger community, or even worse, the general
public, off.

And I also still think that Wikipedia should be much more about what is really established, not what is spanking new.

Hope your little one is doing well!

-A.

monz wrote:
> Hi Aaron,
>
>
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <aaron@...> wrote:
> >> My two cents (no pun intended):
>>
>> I personally don't see a need for all these new units
>> and terminology unless they fill a vacuum--i.e. they neatly
>> or succinctly convey something not before possible. I can
>> say that often, some terminology around here has muddied
>> the water and made things *harder* to understand, and in
>> a way that I feel adds to the sense that the term is >> merely a self-promotional gimmick. The biggest example:
>> after reading what a 'monzo' was---I thought---that's it?
>> Why not just call it a 'prime distance' or something that
>> would make it easy to grok right away?
>> >
>
> The only really accurate way of describing a "monzo"
> is to call it a "prime-factor-exponent vector". Gene's
> whole purpose in giving it the short name (that i > obviously like) was that he didn't want to have to
> keep typing that much longer term over and over again.
>
> He named it after me because as far as he (and i) could
> tell, i was the first person who proposed using the
> prime-factor-exponent vector as a way of notating
> musical intervals and/or pitches.
>
>
> As for the whole debate about new terminology, that's
> *exactly* the reason why i created the Encyclopedia
> in the first place! I struggled for a long time doing
> research on tuning terms that i didn't know, and wanted
> to put it all into one online home would make it so much
> easier for others in the same predicament.
>
> If you're online and reading about a "tina", what's
> so difficult about looking it up in either my Encyclopedia
> or in Wikipedia? (assuming that the Wikipedia editors
> allow the page to remain) ... in fact it would be a
> lot more accessible in Wikipedia than in my own Encyclopedia,
> which is precisely why i put it there.
>
>
> There's always going to be a debate about new jargon,
> and in fact i created an entire Yahoo group explicitly
> for the purpose of debating tuning jargon. If others
> can't see the value of using "tina" over "cents" or
> any other logarithmic measurement, then that's too bad,
> because the tina is clearly superior to any other integer
> measurement, for a lot of reasons.
>
> Boy, for a group of people who embrace new tunings
> enthusiastically, there sure is a strong conservative
> bent to most mindsets around here.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
> >
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
>
>
>
>
>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> He named it after me because as far as he (and i) could
> tell, i was the first person who proposed using the
> prime-factor-exponent vector as a way of notating
> musical intervals and/or pitches.

Actually I named it after you because you were an enthusiastic
proponent of the idea. And originally, I just used the name privately
in documenting my Maple programs.

> The only really accurate way of describing a "monzo"
> is to call it a "prime-factor-exponent vector". Gene's
> whole purpose in giving it the short name (that i
> obviously like) was that he didn't want to have to
> keep typing that much longer term over and over again.

On Graham's website, I saw something called "ratiospace". IIRC, if was just
the same thing. And, as far as I understood his words, the idea had already
been promoted by Fokker and others. In case I'm right, then I agree that the
name "ratiospace" contains a small bit of explanation in it. When I first
read about monzos, I thought I'm missing something like a brand new way of
describing JI intervals. Then, when I realized it was the same as what I
knew was being called ratiopsace, I began to doubt if I actually didn't
misunderstand the concept of ratiospace. But until now, I think I didn't.
That doesn't mean anything else than the fact that I can't see any
difference between ratiospace and monzo.

One more thing. When I first started to use EDs in my calculations, I was
pretty unsure if someone else hadn't already come with the same concept
earlier by chance. I asked a few people and they said they didn't think
anyone had. Convinced enough, I started to use the ED concept explicitely
applying this name to the unit. One of the people I spoke to was Manuel who
eventually added EDs to Scala (you can try it with "Set attribute epiden").
Did I call them parizeks? Or perhaps petrs? No, I just called them EDs (i.e.
epimoric denominators) as their value is equal to the denominator in case of
epimoric intervals, no matter if they rise or fall -- a major third upwards
is 5/4 and its ED is 4, a major third downwards is 4/5 and its ED is -5
since 4/5 is the same as (-4)/(-5). And, obviously, then you can convert
virtually any interval size to ED, even an irrational one. You only can't
express a unison's ED as you would have to use 1/0 then.

Petr

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> My mistake apparently.

Yes. It just happened because i wrote my "tina" page
the day before my daughter was born, and someone suggested
it was a good name for a baby girl. But we named her "Lelani".

> but then, your attitude is even less understandable,
> given the fact, that other replacements for cent have
> been proposed - especially by Gene. Why should tina
> take precedence without any solid consensus in this
> community?

Gene *did* suggest 8539-edo publicly just before i did.
And George Secor and Dave Keenan were using it privately
before that. This is all stated on both my webpage and
on the Wikipedia page.

> For all I know, various suggestions by others were
> much more promising compared to tina.

Wrong.

The reason i'm such a strong advocate of the tina
is *because* it is so good for use as an integer
logarithmic measurement for JI ratios, and for some
other types of musical intervals too.

> I do not object to your desire to put it up in your
> page, but to insist that people support you so that
> it does not get deleted from wikipedia is going a
> bit too far.

I didn't insist, i merely asked.

I really can't believe that this thing has turned
into what looks like such a big flame-war. Sheesh,
i'm just trying to encourage people to use something
that really is useful.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > He named it after me because as far as he (and i) could
> > tell, i was the first person who proposed using the
> > prime-factor-exponent vector as a way of notating
> > musical intervals and/or pitches.
>
> Actually I named it after you because you were an
> enthusiastic proponent of the idea. And originally,
> I just used the name privately in documenting my
> Maple programs.

Thanks, i stand corrected.

BTW, i know that Fokker used the "monzo" idea in some
of his papers, but AFAIK he never went beyond 7-limit,
and he didn't propose it as an actual notation for
intervals, he only used it to help the reader visualize
the lattice position of intervals.

The concept is implicit in Euler's work, but he never
actually wrote out the vector.

Did anyone else ever use the idea for notation before me?

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > My mistake apparently.
>
>
> Yes. It just happened because i wrote my "tina" page
> the day before my daughter was born, and someone suggested
> it was a good name for a baby girl. But we named her "Lelani".

And *NO*, i'm not proposing "Lelani" as a term for
some tuning concept!

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:

> On Graham's website, I saw something called "ratiospace". IIRC, if
was just
> the same thing.

It seems to be that "ratiospace" suggests a vector space, so that, at
least, the coefficients are allowed to be rational numbers. If they
are confined to integers, would that still be a "ratiospace"?

> Did I call them parizeks? Or perhaps petrs? No, I just called them
EDs (i.e.
> epimoric denominators) as their value is equal to the denominator
in case of
> epimoric intervals, no matter if they rise or fall -- a major third
upwards
> is 5/4 and its ED is 4, a major third downwards is 4/5 and its ED
is -5
> since 4/5 is the same as (-4)/(-5). And, obviously, then you can
convert
> virtually any interval size to ED, even an irrational one. You only
can't
> express a unison's ED as you would have to use 1/0 then.

If q is any number other than 1, then 1/(q-1) is the corresponding
ED. Hence, any number other than 1 may be so converted. Moreover,
infinity is given an ED of zero.

What I don't get is what the heck the point of it is. Epimoric
intervals are now represented by integers, and every integer besides
1 and 0 represents an epimoric interval. Is this part of it?

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> Gene *did* suggest 8539-edo publicly just before i did.

Along with other stuff, of course.

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> Did anyone else ever use the idea for notation before me?

As with Fokker, I used it in a theoretical context. I also played with
matrix transformations using it, which I suppose you could call
notational though I wasn't thinking about notation per se.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 16 May�s 2007 �ar�amba 20:05
Subject: [tuning] Re: Wikipedia "tina" page

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > My mistake apparently.
>
>
> Yes. It just happened because i wrote my "tina" page
> the day before my daughter was born, and someone suggested
> it was a good name for a baby girl. But we named her "Lelani".
>
>

Nice name. And there is nothing wrong with tagging something musical by a
girl's name. In fact, Rauf Yekta named a perde by his friend Ali Rifat Bey's
daughter, "Nerime".

> > but then, your attitude is even less understandable,
> > given the fact, that other replacements for cent have
> > been proposed - especially by Gene. Why should tina
> > take precedence without any solid consensus in this
> > community?
>
>
> Gene *did* suggest 8539-edo publicly just before i did.
> And George Secor and Dave Keenan were using it privately
> before that. This is all stated on both my webpage and
> on the Wikipedia page.
>

Well, then it was one among many.

>
> > For all I know, various suggestions by others were
> > much more promising compared to tina.
>
>
> Wrong.
>
> The reason i'm such a strong advocate of the tina
> is *because* it is so good for use as an integer
> logarithmic measurement for JI ratios, and for some
> other types of musical intervals too.
>

These statements are not convincing. Demonstrate to us its superiority by
some examples first.

>
> > I do not object to your desire to put it up in your
> > page, but to insist that people support you so that
> > it does not get deleted from wikipedia is going a
> > bit too far.
>
>
> I didn't insist, i merely asked.
>

Uh, it seemed more than that at first.

> I really can't believe that this thing has turned
> into what looks like such a big flame-war. Sheesh,
> i'm just trying to encourage people to use something
> that really is useful.
>
>

Flame-wars are a specialty of the tuning list. Convince us "conservatives"
first, then we'll see what we can do.

Oz.

Gene wrote:

> It seems to be that "ratiospace" suggests a vector space, so that, at
> least, the coefficients are allowed to be rational numbers. If they
> are confined to integers, would that still be a "ratiospace"?

Well, how about something like PS then? I'm thinking of "prime space" now.

> What I don't get is what the heck the point of it is. Epimoric
> intervals are now represented by integers, and every integer besides
> 1 and 0 represents an epimoric interval. Is this part of it?

What do you mean by "besides 1 and 0"?
Yes, it undoubtedly is.
A) You can easily find out if one certain interval of a temperament, for
example, is close to an epimoric ratio or if it actually is an epimoric
interval.
B) You get a chance to imagine how low or how high the pitches was if the
frequency difference should be 1Hz.
C) You are not limited to rational intervals.

BTW: Some years ago, Monz said that perhaps John Chalmers could help me in
my quest for ED -- in case he's not following the list or just isn't here
for whatever reason, does someone else have any idea if something like ED
was documented somewhere ever before?
Thanks in advance.

Petr

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:

> These statements are not convincing. Demonstrate
> to us its superiority by some examples first.

The entire second quarter of my Encyclopedia page

http://tonalsoft.com/enc/t/tina.aspx

is taken up by a table showing how close the integer
tina values are to their floating-point counterparts,
for a wide variety of 31-limit JI intervals.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Petr,

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Gene wrote:
>
> > It seems to be that "ratiospace" suggests a vector space,
> > so that, at least, the coefficients are allowed to be
> > rational numbers. If they are confined to integers, would
> > that still be a "ratiospace"?
>
> Well, how about something like PS then? I'm thinking of
> "prime space" now.

You might want to read this:

http://tonalsoft.com/enc/p/prime-space.aspx

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Oz,

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
>
> > These statements are not convincing. Demonstrate
> > to us its superiority by some examples first.
>
>
> The entire second quarter of my Encyclopedia page
>
> http://tonalsoft.com/enc/t/tina.aspx
>
> is taken up by a table showing how close the integer
> tina values are to their floating-point counterparts,
> for a wide variety of 31-limit JI intervals.

If that's not convincing enough to you, then provide
me with a list of intervals you're interested in, and
i'll calculate and post the tina values for you.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Monz wrote:

> http://tonalsoft.com/enc/p/prime-space.aspx

If this is the case, then those are prime space coordinates, aren't they?

Petr

where is a list showing the level of the tina's inaccuracy?
both Wilson and Hanson preferred 12.276 which is divisible by 12
Once again they already found the Tina see
http://anaphoria.com/sieve.PDF
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

Hi Petr,

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Monz wrote:
>
> > http://tonalsoft.com/enc/p/prime-space.aspx
>
> If this is the case, then those are prime space coordinates,
> aren't they?

Yes. The exponents listed in a "monzo" are exactly that:
prime-space coordinates.

Note that according to Gene's definition of "monzo",
the coordinates must be integers, but i also allow
non-integer rational numbers and give it the name
"rational monzo".

For example, a meantone which uses a tempering which
is an exact rational part of the syntonic-comma
(such as 1/4-comma or 2/7-comma, for example) can
be plotted on the helical lattice as a spiral which
has a few points falling at regular intervals exactly
onto the tempered prime-space integer coordinates,
but has other points between those which have rational
coordinates, representing rational exponents of the
prime-factors.

I haven't yet created a good graphic of this, and
Tonescape can't do it yet. But you can get an idea
of what i'm talking about by looking at my "meantone"
Encyclopedia entry:

http://tonalsoft.com/enc/m/meantone.aspx

under the section titled "MEANTONE COINCIDENCES OF
JUST INTONATION INTERVAL CHAINS" and also looking at the
graphic titled "1/4-comma meantone rational implications".

My webpage "Ellis's Duodene and a 'best-fit' meantone"
also illustrates this idea further:

http://sonic-arts.org/monzo/meantone/lattices/PB-MT.htm

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Kraig,

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> where is a list showing the level of the tina's inaccuracy?

At the bottom of this post is a list, for all of the
31-limit JI intervals in the table in the second quarter
of my Encyclopedia webpage

http://tonalsoft.com/enc/t/tina.aspx

of the errors of the tina integer values from the
floating-point values -- multiply by 100 to get the
percentage error.

You'll see that out of the 148 intervals i listed,
only 9 have an error of around 30 percent or more
(here in order of decreasing error):

interval ......... tinas .. percent error

semicomma ........... 72 .. 41
nanisma .............. 1 .. 35
kleisma ............. 58 .. 31
23rd subharmonic .. 4068 .. 30
29th harmonic ..... 7326 .. 30
23rd harmonic ..... 4471 .. 30
29th subharmonic .. 1213 .. 30
mercator-comma ...... 26 .. 28
magic-comma ........ 211 .. 27

And of those, i'd say that the only really important
ones for most people will be the semicomma, kleisma,
and magic-comma.

All the rest of the JI intervals in my table (except one)
have an error of 17 percent or less.

That's a remarkably low level of error for an integer
logarithmic measurement unit.

0
0.04
0.01
0.17
0.08
0.12
0.02
-0.15
-0.11
0.05
0.03
-0.07
-0.13
-0.15
0.06
-0.04
-0.06
-0.09
-0.05
0.14
-0.3
-0.09
0.05
-0.05
0.09
-0.01
0.12
0
0
0.04
-0.03
0.01
-0.02
-0.12
0.02
0.05
-0.14
0.05
-0.14
0.06
0.1
-0.05
-0.1
0.04
-0.06
0.08
-0.02
-0.08
0.11
-0.01
0.03
-0.08
0
-0.03
0.01
0.04
0.01
-0.15
0.17
0.05
0.09
-0.14
-0.1
0.3
0.06
0.03
-0.07
0.07
-0.03
-0.06
-0.3
0.1
-0.09
-0.05
-0.17
0.15
0.06
-0.04
0.09
-0.01
0.13
0
0.16
0.08
-0.03
0.01
-0.15
-0.11
0.02
-0.08
-0.14
0.06
0.05
-0.1
-0.06
0.14
-0.09
0.05
-0.05
-0.05
0.08
-0.02
-0.08
0.12
-0.01
0.03
-0.04
0
-0.02
0.01
0.05
0.3
-0.14
0.05
0.09
-0.1
0.06
0.04
-0.06
0.15
0.07
-0.03
-0.05
-0.09
0.11
0.19
-0.12
-0.08
0.14
-0.04
-0.17
-0.01
0.12
0.27
-0.01
0.06
-0.04
-0.13
0.41
0.31
0.13
-0.07
0.28
-0.04
0.1
-0.08
-0.35
0

-monz
http://tonalsoft.com
Tonescape microtonal music software

Monz wrote:

> Yes. The exponents listed in a "monzo" are exactly that:
> prime-space coordinates.

I'm actually very glad to hear this as I was using just this name for them
in my calculation almost two years ago (having called it PSC) when I was
comparing various EDOs by layering multiples of rational intervals and
eventually finding schismatic or kleismatic shifts.

Petr

Ok then, let's see you approximate these:

126/125,100/99,80/81
64/63,3125/3072,55:54
128/125,36/35,33/32
729/704,28/27,27/26
25/24,117/112,22/21
20/19,256/243,135/128
17/16,16/15,2187/2048
15/14,14/13
27/25,13/12
88/81,12/11,35/32
11/10,54/49
65536/59049,10/9
28/25,9/8
9/8,26/23
256/225,8/7
144/125
37/32,81/70,125/108
7/6
33/28,13/11,32/27
32/27,25/21,81/68
6/5,19683/16384
63/52,40/33,17/14
39/32,11/9,27/22
16/13,100/81,21/17
31/25,41/33,46/37,5/4
5/4,64/51,59/47
81/64,19/15,33/26
14/11,23/18,32/25
9/7
35/27,13/10
38/29,21/16
33/25,37/28
4/3
39/29,35/26,27/20
19/14,49/36
26/19,48/35,11/8
11/8,29/21
25/18,32/23,39/28
7/5,1024/729,45/32
24/17,17/12
10/7
23/16,36/25,49/34
16/11,8192/5625,35/24
22/15,69/47,72/49
37/25,40/27
3/2
53/35,50/33,1024/675
32/21,29/19,75/49
192/125,20/13,54/35
45/29,59/38,14/9
25/16,47/30,11/7
30/19,128/81,19/12
43/27,8/5,6561/4096
37/23
34/21,81/50,13/8
44/27,18/11,105/64
28/17,33/20
32768/19683,5/3
5/3,42/25,27/16
27/16,39/23,17/10
128/75,41/24,12/7
50/29,216/125,64/37
125/72,40/23,47/27
7/4,225/128
23/13,16/9
16/9,25/14
9/5,59049/32768
29/16,20/11
11/6
37/20,50/27,13/7
28/15
15/8,32/17,17/9
256/135,243/128,40/21
21/11,23/12,48/25
27/14,29/15,31/16
37/19,39/20,125/64
49/25,55/28,6144/3125
2025/1024,105/53
2/1

But if any of the given ratios falls midway, I will not accept tina as a
replacement for cents.

Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 17 May�s 2007 Per�embe 5:08
Subject: [tuning] Re: Wikipedia "tina" page

> Hi Oz,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> > These statements are not convincing. Demonstrate
> > to us its superiority by some examples first.
>
>
> The entire second quarter of my Encyclopedia page
>
> http://tonalsoft.com/enc/t/tina.aspx
>
> is taken up by a table showing how close the integer
> tina values are to their floating-point counterparts,
> for a wide variety of 31-limit JI intervals.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Hi Monz;

The uppermost link on the meantone page (http://tonalsoft.com/enc/m/
meantone.aspx) mentioned in this posting fails to trigger the applet.
It sends me to http://tonalsoft.com/enc/encyclopedia.aspx ; although
the lower applet link works and displays fine with Safari.
I think it's just an html linking problem.

As you're thinking about meantone as a spiral, you may find the Mac-
only animation and QuickTime movie (for other platforms), which I put
together a few years ago at:

http://lucytune.com/new_to_lt/recipe.html

could give you some ideas of how to express your concepts visually,
audibly, and dynamically, in one simple interactive 3D animation.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 17 May 2007, at 18:47, monz wrote:

> Hi Petr,
>
> --- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
> >
> > Monz wrote:
> >
> > > http://tonalsoft.com/enc/p/prime-space.aspx
> >
> > If this is the case, then those are prime space coordinates,
> > aren't they?
>
> Yes. The exponents listed in a "monzo" are exactly that:
> prime-space coordinates.
>
> Note that according to Gene's definition of "monzo",
> the coordinates must be integers, but i also allow
> non-integer rational numbers and give it the name
> "rational monzo".
>
> For example, a meantone which uses a tempering which
> is an exact rational part of the syntonic-comma
> (such as 1/4-comma or 2/7-comma, for example) can
> be plotted on the helical lattice as a spiral which
> has a few points falling at regular intervals exactly
> onto the tempered prime-space integer coordinates,
> but has other points between those which have rational
> coordinates, representing rational exponents of the
> prime-factors.
>
> I haven't yet created a good graphic of this, and
> Tonescape can't do it yet. But you can get an idea
> of what i'm talking about by looking at my "meantone"
> Encyclopedia entry:
>
> http://tonalsoft.com/enc/m/meantone.aspx
>
> under the section titled "MEANTONE COINCIDENCES OF
> JUST INTONATION INTERVAL CHAINS" and also looking at the
> graphic titled "1/4-comma meantone rational implications".
>
> My webpage "Ellis's Duodene and a 'best-fit' meantone"
> also illustrates this idea further:
>
> http://sonic-arts.org/monzo/meantone/lattices/PB-MT.htm
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Hi Oz,

OK ... arranged in the same format you used
in your list, i'm providing both tina and cent
values with percent error ...

Here are the integer tina values, with percent error
in parentheses, for your list of ratios:

98 (16), 124 (19), -153 (4)
194 (1), 211 (27), 10416 (1)
292 (17), 347 (4), 379 (8)
430 (12), 448 (2), 465 (7)
503 (11), 538 (4), 573 (9)
632 (11), 642 (3), 656 (7)
747 (15), 795 (6), 809 (4)
850 (6), 913 (5)
948 (10), 986 (6)
1021 (11), 1072 (9), 1104 (5)
1174 (14), 1197 (2)
1284 (5), 1298 (5)
1396 (12), 1451 (1)
1451 (1), 1510 (36)
1590 (12), 1645 (0)
1743 (16)
1789 (48), 1798 (3), 1801 (15)
1899 (1)
2024 (8), 2058 (3), 2093 (2)
2093 (2), 2148 (11), 2155 (13)
2246 (5), 2260 (5)
2364 (6), 2370 (14), 2392 (16)
2437 (5), 2472 (10), 2523 (10)
2558 (5), 2596 (9), 2603 (15)
2650 (1), 2674 (6), 2682 (17), 2749 (6)
2749 (6), 2797 (16), 2801 (25)
2902 (2), 2912 (11), 2937 (3)
2971 (8), 3020 (29), 3041 (11)
3096 (1)
3197 (4), 3232 (11)
3330 (25), 3350 (0)
3420 (19), 3434 (48)
3544 (1)
3650 (25), 3662 (11), 3697 (4)
3762 (5), 3798 (2)
3864 (0), 3891 (5), 3923 (9)
3923 (9), 3976 (30)
4047 (10), 4068 (30), 4082 (5)
4145 (6), 4186 (3), 4200 (7)
4248 (15), 4291 (15)
4394 (6)
4471 (30), 4492 (10), 4502 (16)
4616 (9), 4631 (23), 4648 (5)
4718 (15), 4730 (6), 4741 (2)
4830 (37), 4842 (4)
4995 (1)
5112 (23), 5119 (19), 5134 (13)
5189 (0), 5209 (25), 5244 (12)
5287 (16), 5307 (11), 5342 (4)
5413 (37), 5420 (16), 5443 (1)
5498 (11), 5531 (30), 5568 (8)
5627 (11), 5637 (2), 5661 (6)
5733 (11), 5790 (6), 5804 (4)
5857 (17)
5936 (15), 5943 (9), 5981 (5)
6016 (10), 6067 (10), 6099 (6)
6147 (16), 6169 (14)
6279 (5), 6293 (5)
6293 (5), 6391 (11), 6446 (2)
6446 (2), 6505 (35), 6537 (10)
6585 (12), 6597 (14), 6640 (1)
6711 (41), 6738 (15), 6750 (48)
6796 (16), 6817 (25), 6829 (35)
6894 (0), 6949 (12)
7029 (36), 7088 (1)
7088 (1), 7143 (12)
7241 (5), 7255 (5)
7326 (30), 7365 (14)
7467 (9)
7579 (42), 7591 (10), 7626 (5)
7689 (6)
7744 (6), 7792 (15), 7835 (14)
7883 (7), 7897 (3), 7938 (5)
7966 (9), 8015 (30), 8036 (11)
8091 (2), 8121 (36), 8148 (12)
8210 (47), 8227 (11), 8247 (17)
8290 (12), 8317 (3), 8328 (27)
8400 (13), 8422 (23)
8539 (0)

-----------

For comparison, here are the integer cents values,
with percent error in parentheses, for the same list
of ratios:

14 (21), 17 (40), -22 (49)
27 (26), 30 (39), 1464 (22)
41 (6), 49 (23), 53 (27)
60 (41), 63 (4), 65 (34)
71 (33), 76 (39), 81 (46)
89 (20), 90 (22), 92 (18)
105 (4), 112 (27), 114 (31)
119 (44), 128 (30)
133 (24), 139 (43)
143 (50), 151 (36), 155 (14)
165 (0), 168 (21)
180 (45), 182 (40)
196 (20), 204 (9)
204 (9), 212 (25)
223 (46), 231 (17)
245 (3)
251 (34), 253 (32), 253 (8)
267 (13)
284 (45), 289 (21), 294 (13)
294 (13), 302 (15), 303 (14)
316 (36), 318 (40)
332 (21), 333 (4), 336 (13)
342 (48), 347 (41), 355 (45)
359 (47), 365 (19), 366 (17)
372 (41), 376 (21), 377 (7), 386 (31)
386 (31), 393 (9), 394 (33)
408 (18), 409 (24), 413 (25)
418 (49), 424 (36), 427 (37)
435 (8)
449 (27), 454 (21)
468 (6), 471 (22)
481 (35), 483 (48)
498 (4)
513 (9), 515 (39), 520 (45)
529 (31), 534 (26)
543 (1), 547 (18), 551 (32)
551 (32), 559 (20)
569 (28), 572 (27), 574 (34)
583 (49), 588 (27), 590 (22)
597 (0), 603 (0)
617 (49)
628 (27), 631 (28), 633 (30)
649 (32), 651 (16), 653 (18)
663 (5), 665 (28), 666 (26)
679 (28), 680 (45)
702 (4)
718 (36), 719 (35), 722 (49)
729 (22), 732 (6), 737 (7)
743 (1), 746 (21), 751 (27)
761 (35), 762 (34), 765 (8)
773 (37), 777 (24), 782 (49)
791 (24), 792 (18), 796 (44)
806 (35), 814 (31), 816 (36)
823 (7)
834 (17), 835 (19), 841 (47)
845 (45), 853 (41), 857 (9)
864 (13), 867 (4)
882 (40), 884 (36)
884 (36), 898 (15), 906 (13)
906 (13), 914 (21), 919 (36)
925 (42), 927 (11), 933 (13)
943 (5), 947 (8), 949 (34)
955 (3), 958 (4), 960 (36)
969 (17), 977 (46)
988 (25), 996 (9)
996 (9), 1004 (20)
1018 (40), 1020 (45)
1030 (42), 1035 (0)
1049 (36)
1065 (3), 1067 (24), 1072 (30)
1081 (44)
1088 (27), 1095 (4), 1101 (5)
1108 (18), 1110 (22), 1116 (47)
1119 (46), 1126 (32), 1129 (33)
1137 (4), 1141 (31), 1145 (4)
1154 (17), 1156 (17), 1159 (6)
1165 (2), 1169 (19), 1170 (39)
1180 (45), 1184 (41)
1200 (0)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Ok then, let's see you approximate these:
>
> 126/125,100/99,80/81
> 64/63,3125/3072,55:54
> 128/125,36/35,33/32
> 729/704,28/27,27/26
> 25/24,117/112,22/21
> 20/19,256/243,135/128
> 17/16,16/15,2187/2048
> 15/14,14/13
> 27/25,13/12
> 88/81,12/11,35/32
> 11/10,54/49
> 65536/59049,10/9
> 28/25,9/8
> 9/8,26/23
> 256/225,8/7
> 144/125
> 37/32,81/70,125/108
> 7/6
> 33/28,13/11,32/27
> 32/27,25/21,81/68
> 6/5,19683/16384
> 63/52,40/33,17/14
> 39/32,11/9,27/22
> 16/13,100/81,21/17
> 31/25,41/33,46/37,5/4
> 5/4,64/51,59/47
> 81/64,19/15,33/26
> 14/11,23/18,32/25
> 9/7
> 35/27,13/10
> 38/29,21/16
> 33/25,37/28
> 4/3
> 39/29,35/26,27/20
> 19/14,49/36
> 26/19,48/35,11/8
> 11/8,29/21
> 25/18,32/23,39/28
> 7/5,1024/729,45/32
> 24/17,17/12
> 10/7
> 23/16,36/25,49/34
> 16/11,8192/5625,35/24
> 22/15,69/47,72/49
> 37/25,40/27
> 3/2
> 53/35,50/33,1024/675
> 32/21,29/19,75/49
> 192/125,20/13,54/35
> 45/29,59/38,14/9
> 25/16,47/30,11/7
> 30/19,128/81,19/12
> 43/27,8/5,6561/4096
> 37/23
> 34/21,81/50,13/8
> 44/27,18/11,105/64
> 28/17,33/20
> 32768/19683,5/3
> 5/3,42/25,27/16
> 27/16,39/23,17/10
> 128/75,41/24,12/7
> 50/29,216/125,64/37
> 125/72,40/23,47/27
> 7/4,225/128
> 23/13,16/9
> 16/9,25/14
> 9/5,59049/32768
> 29/16,20/11
> 11/6
> 37/20,50/27,13/7
> 28/15
> 15/8,32/17,17/9
> 256/135,243/128,40/21
> 21/11,23/12,48/25
> 27/14,29/15,31/16
> 37/19,39/20,125/64
> 49/25,55/28,6144/3125
> 2025/1024,105/53
> 2/1
>
>
> But if any of the given ratios falls midway, I will not accept tina as a
> replacement for cents.
>
> Oz.
>
>
> ----- Original Message -----
> From: "monz" <monz@...>
> To: <tuning@yahoogroups.com>
> Sent: 17 Mayýs 2007 Perþembe 5:08
> Subject: [tuning] Re: Wikipedia "tina" page
>
>
> > Hi Oz,
> >
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > > These statements are not convincing. Demonstrate
> > > to us its superiority by some examples first.
> >
> >
> > The entire second quarter of my Encyclopedia page
> >
> > http://tonalsoft.com/enc/t/tina.aspx
> >
> > is taken up by a table showing how close the integer
> > tina values are to their floating-point counterparts,
> > for a wide variety of 31-limit JI intervals.
> >
> >
> > -monz
> > http://tonalsoft.com
> > Tonescape microtonal music software
> >
> >
> >
>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Oz,
>
>
> OK ... arranged in the same format you used
> in your list, i'm providing both tina and cent
> values with percent error ...
>
>
> Here are the integer tina values, with percent error
> in parentheses, for your list of ratios:

And don't forget that in absolute terms,
50 percent of a tina is only 7 percent of a cent,
which means that the absolute errors of the tinas
are far smaller than almost all of the cent errors.

The point of measuring the relative error (percent)
is to show how closely the integer values approximate
the "real" floating-point values. The whole reason
i like tinas so much is because you won't accumulate
much rounding error if you ignore the decimal places.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Oz,

There were two typos in your list that
caused weird results in my calculations,
occurring in the first two lines of your
ratio list.

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> Here are the integer tina values, with percent error
> in parentheses, for your list of ratios:
>
>
> 98 (16), 124 (19), -153 (4)
> 194 (1), 211 (27), 10416 (1)
> <snip>
> -----------
>
> For comparison, here are the integer cents values,
> with percent error in parentheses, for the same list
> of ratios:
>
>
> 14 (21), 17 (40), -22 (49)
> 27 (26), 30 (39), 1464 (22)
> <snip>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > Ok then, let's see you approximate these:
> >
> > 126/125,100/99,80/81
> > 64/63,3125/3072,55:54
> > <snip>

"80/81" should have been "81/80",
so the values are the same but without
the negative sign.

"55:54" should have been "55/54" but i
didn't catch it at first. The correct
tina value is 226 (5), and the correct
cent value is 32 (23).

So replace the first two lines of each
list with:

tinas:

98 (16), 124 (19), 153 (4)
194 (1), 211 (27), 226 (5)

cents:

14 (21), 17 (40), 22 (49)
27 (26), 30 (39), 32 (23)

-monz
http://tonalsoft.com
Tonescape microtonal music software

You've done a tremendous job; but then again, you cannot so well
approximate:

37/32 (%48),
37/28 (%48),
37/25 (%37),
45/29 (%37),
39/23 (%35),
50/29 (%41),
64/37 (%48),
47/27 (%35),
23/13 (%36),
37/20 (%42),
29/15 (%36), and
37/19 (%47).

A replacement unit for the cent should have reduced roundoff errors for
these as much as 30 percent IMNSHO.

Thank you for the corrections.
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 18 May�s 2007 Cuma 6:10
Subject: [tuning] Re: Wikipedia "tina" page

Hi Oz,

OK ... arranged in the same format you used
in your list, i'm providing both tina and cent
values with percent error ...

Here are the integer tina values, with percent error
in parentheses, for your list of ratios:

98 (16), 124 (19), 153 (4)
194 (1), 211 (27), 226 (5)
292 (17), 347 (4), 379 (8)
430 (12), 448 (2), 465 (7)
503 (11), 538 (4), 573 (9)
632 (11), 642 (3), 656 (7)
747 (15), 795 (6), 809 (4)
850 (6), 913 (5)
948 (10), 986 (6)
1021 (11), 1072 (9), 1104 (5)
1174 (14), 1197 (2)
1284 (5), 1298 (5)
1396 (12), 1451 (1)
1451 (1), 1510 (36)
1590 (12), 1645 (0)
1743 (16)
1789 (48), 1798 (3), 1801 (15)
1899 (1)
2024 (8), 2058 (3), 2093 (2)
2093 (2), 2148 (11), 2155 (13)
2246 (5), 2260 (5)
2364 (6), 2370 (14), 2392 (16)
2437 (5), 2472 (10), 2523 (10)
2558 (5), 2596 (9), 2603 (15)
2650 (1), 2674 (6), 2682 (17), 2749 (6)
2749 (6), 2797 (16), 2801 (25)
2902 (2), 2912 (11), 2937 (3)
2971 (8), 3020 (29), 3041 (11)
3096 (1)
3197 (4), 3232 (11)
3330 (25), 3350 (0)
3420 (19), 3434 (48)
3544 (1)
3650 (25), 3662 (11), 3697 (4)
3762 (5), 3798 (2)
3864 (0), 3891 (5), 3923 (9)
3923 (9), 3976 (30)
4047 (10), 4068 (30), 4082 (5)
4145 (6), 4186 (3), 4200 (7)
4248 (15), 4291 (15)
4394 (6)
4471 (30), 4492 (10), 4502 (16)
4616 (9), 4631 (23), 4648 (5)
4718 (15), 4730 (6), 4741 (2)
4830 (37), 4842 (4)
4995 (1)
5112 (23), 5119 (19), 5134 (13)
5189 (0), 5209 (25), 5244 (12)
5287 (16), 5307 (11), 5342 (4)
5413 (37), 5420 (16), 5443 (1)
5498 (11), 5531 (30), 5568 (8)
5627 (11), 5637 (2), 5661 (6)
5733 (11), 5790 (6), 5804 (4)
5857 (17)
5936 (15), 5943 (9), 5981 (5)
6016 (10), 6067 (10), 6099 (6)
6147 (16), 6169 (14)
6279 (5), 6293 (5)
6293 (5), 6391 (11), 6446 (2)
6446 (2), 6505 (35), 6537 (10)
6585 (12), 6597 (14), 6640 (1)
6711 (41), 6738 (15), 6750 (48)
6796 (16), 6817 (25), 6829 (35)
6894 (0), 6949 (12)
7029 (36), 7088 (1)
7088 (1), 7143 (12)
7241 (5), 7255 (5)
7326 (30), 7365 (14)
7467 (9)
7579 (42), 7591 (10), 7626 (5)
7689 (6)
7744 (6), 7792 (15), 7835 (14)
7883 (7), 7897 (3), 7938 (5)
7966 (9), 8015 (30), 8036 (11)
8091 (2), 8121 (36), 8148 (12)
8210 (47), 8227 (11), 8247 (17)
8290 (12), 8317 (3), 8328 (27)
8400 (13), 8422 (23)
8539 (0)

-----------

For comparison, here are the integer cents values,
with percent error in parentheses, for the same list
of ratios:

14 (21), 17 (40), 22 (49)
27 (26), 30 (39), 32 (23)
41 (6), 49 (23), 53 (27)
60 (41), 63 (4), 65 (34)
71 (33), 76 (39), 81 (46)
89 (20), 90 (22), 92 (18)
105 (4), 112 (27), 114 (31)
119 (44), 128 (30)
133 (24), 139 (43)
143 (50), 151 (36), 155 (14)
165 (0), 168 (21)
180 (45), 182 (40)
196 (20), 204 (9)
204 (9), 212 (25)
223 (46), 231 (17)
245 (3)
251 (34), 253 (32), 253 (8)
267 (13)
284 (45), 289 (21), 294 (13)
294 (13), 302 (15), 303 (14)
316 (36), 318 (40)
332 (21), 333 (4), 336 (13)
342 (48), 347 (41), 355 (45)
359 (47), 365 (19), 366 (17)
372 (41), 376 (21), 377 (7), 386 (31)
386 (31), 393 (9), 394 (33)
408 (18), 409 (24), 413 (25)
418 (49), 424 (36), 427 (37)
435 (8)
449 (27), 454 (21)
468 (6), 471 (22)
481 (35), 483 (48)
498 (4)
513 (9), 515 (39), 520 (45)
529 (31), 534 (26)
543 (1), 547 (18), 551 (32)
551 (32), 559 (20)
569 (28), 572 (27), 574 (34)
583 (49), 588 (27), 590 (22)
597 (0), 603 (0)
617 (49)
628 (27), 631 (28), 633 (30)
649 (32), 651 (16), 653 (18)
663 (5), 665 (28), 666 (26)
679 (28), 680 (45)
702 (4)
718 (36), 719 (35), 722 (49)
729 (22), 732 (6), 737 (7)
743 (1), 746 (21), 751 (27)
761 (35), 762 (34), 765 (8)
773 (37), 777 (24), 782 (49)
791 (24), 792 (18), 796 (44)
806 (35), 814 (31), 816 (36)
823 (7)
834 (17), 835 (19), 841 (47)
845 (45), 853 (41), 857 (9)
864 (13), 867 (4)
882 (40), 884 (36)
884 (36), 898 (15), 906 (13)
906 (13), 914 (21), 919 (36)
925 (42), 927 (11), 933 (13)
943 (5), 947 (8), 949 (34)
955 (3), 958 (4), 960 (36)
969 (17), 977 (46)
988 (25), 996 (9)
996 (9), 1004 (20)
1018 (40), 1020 (45)
1030 (42), 1035 (0)
1049 (36)
1065 (3), 1067 (24), 1072 (30)
1081 (44)
1088 (27), 1095 (4), 1101 (5)
1108 (18), 1110 (22), 1116 (47)
1119 (46), 1126 (32), 1129 (33)
1137 (4), 1141 (31), 1145 (4)
1154 (17), 1156 (17), 1159 (6)
1165 (2), 1169 (19), 1170 (39)
1180 (45), 1184 (41)
1200 (0)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Ok then, let's see you approximate these:
>
> 126/125,100/99,81/80
> 64/63,3125/3072,55/54
> 128/125,36/35,33/32
> 729/704,28/27,27/26
> 25/24,117/112,22/21
> 20/19,256/243,135/128
> 17/16,16/15,2187/2048
> 15/14,14/13
> 27/25,13/12
> 88/81,12/11,35/32
> 11/10,54/49
> 65536/59049,10/9
> 28/25,9/8
> 9/8,26/23
> 256/225,8/7
> 144/125
> 37/32,81/70,125/108
> 7/6
> 33/28,13/11,32/27
> 32/27,25/21,81/68
> 6/5,19683/16384
> 63/52,40/33,17/14
> 39/32,11/9,27/22
> 16/13,100/81,21/17
> 31/25,41/33,46/37,5/4
> 5/4,64/51,59/47
> 81/64,19/15,33/26
> 14/11,23/18,32/25
> 9/7
> 35/27,13/10
> 38/29,21/16
> 33/25,37/28
> 4/3
> 39/29,35/26,27/20
> 19/14,49/36
> 26/19,48/35,11/8
> 11/8,29/21
> 25/18,32/23,39/28
> 7/5,1024/729,45/32
> 24/17,17/12
> 10/7
> 23/16,36/25,49/34
> 16/11,8192/5625,35/24
> 22/15,69/47,72/49
> 37/25,40/27
> 3/2
> 53/35,50/33,1024/675
> 32/21,29/19,75/49
> 192/125,20/13,54/35
> 45/29,59/38,14/9
> 25/16,47/30,11/7
> 30/19,128/81,19/12
> 43/27,8/5,6561/4096
> 37/23
> 34/21,81/50,13/8
> 44/27,18/11,105/64
> 28/17,33/20
> 32768/19683,5/3
> 5/3,42/25,27/16
> 27/16,39/23,17/10
> 128/75,41/24,12/7
> 50/29,216/125,64/37
> 125/72,40/23,47/27
> 7/4,225/128
> 23/13,16/9
> 16/9,25/14
> 9/5,59049/32768
> 29/16,20/11
> 11/6
> 37/20,50/27,13/7
> 28/15
> 15/8,32/17,17/9
> 256/135,243/128,40/21
> 21/11,23/12,48/25
> 27/14,29/15,31/16
> 37/19,39/20,125/64
> 49/25,55/28,6144/3125
> 2025/1024,105/53
> 2/1
>
>
> But if any of the given ratios falls midway, I will not accept tina as a
> replacement for cents.
>
> Oz.
>
>
>

But, you cannot satisfactorily express some ratios as whole numbers. The
whole point of an interval unit is to quantize most ratios, so that the
roundoff errors are mathematically negligible. The errors for

37/32 (%48),
37/28 (%48),
37/25 (%37),
45/29 (%37),
39/23 (%35),
50/29 (%41),
64/37 (%48),
47/27 (%35),
23/13 (%36),
37/20 (%42),
29/15 (%36), and
37/19 (%47)

are relatively significant. I hence itch for a better measurement unit.

Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 18 May�s 2007 Cuma 7:12
Subject: [tuning] Re: Wikipedia "tina" page

> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
> >
> > Hi Oz,
> >
> >
> > OK ... arranged in the same format you used
> > in your list, i'm providing both tina and cent
> > values with percent error ...
> >
> >
> > Here are the integer tina values, with percent error
> > in parentheses, for your list of ratios:
>
>
> And don't forget that in absolute terms,
> 50 percent of a tina is only 7 percent of a cent,
> which means that the absolute errors of the tinas
> are far smaller than almost all of the cent errors.
>
> The point of measuring the relative error (percent)
> is to show how closely the integer values approximate
> the "real" floating-point values. The whole reason
> i like tinas so much is because you won't accumulate
> much rounding error if you ignore the decimal places.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

What about using 1/30030 of an octave as a unit?
30030=2*3*5*7*11*13

Ozan Yarman wrote:
> But, you cannot satisfactorily express some ratios as whole numbers. The
> whole point of an interval unit is to quantize most ratios, so that the
> roundoff errors are mathematically negligible. The errors for
>
> 37/32 (%48),
> 37/28 (%48),
> 37/25 (%37),
> 45/29 (%37),
> 39/23 (%35),
> 50/29 (%41),
> 64/37 (%48),
> 47/27 (%35),
> 23/13 (%36),
> 37/20 (%42),
> 29/15 (%36), and
> 37/19 (%47)
>
> are relatively significant. I hence itch for a better measurement unit.
>
> Oz.
>
> ----- Original Message -----
> From: "monz" <monz@tonalsoft.com>
> To: <tuning@yahoogroups.com>
> Sent: 18 May�s 2007 Cuma 7:12
> Subject: [tuning] Re: Wikipedia "tina" page
>
>
> >> --- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>> >>> Hi Oz,
>>>
>>>
>>> OK ... arranged in the same format you used
>>> in your list, i'm providing both tina and cent
>>> values with percent error ...
>>>
>>>
>>> Here are the integer tina values, with percent error
>>> in parentheses, for your list of ratios:
>>> >> And don't forget that in absolute terms,
>> 50 percent of a tina is only 7 percent of a cent,
>> which means that the absolute errors of the tinas
>> are far smaller than almost all of the cent errors.
>>
>> The point of measuring the relative error (percent)
>> is to show how closely the integer values approximate
>> the "real" floating-point values. The whole reason
>> i like tinas so much is because you won't accumulate
>> much rounding error if you ignore the decimal places.
>>
>>
>> -monz
>> http://tonalsoft.com
>> Tonescape microtonal music software
>>
>>
>> >
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
>
>
>
>
>

What's its specialty? How well does it approximate?

Oz.

----- Original Message -----
From: "Aaron K. Johnson" <aaron@akjmusic.com>
To: <tuning@yahoogroups.com>
Sent: 18 May�s 2007 Cuma 15:26
Subject: Re: [tuning] Re: Wikipedia "tina" page

>
> What about using 1/30030 of an octave as a unit?
> 30030=2*3*5*7*11*13
>
>

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> But, you cannot satisfactorily express some ratios
> as whole numbers. The whole point of an interval unit
> is to quantize most ratios, so that the roundoff errors
> are mathematically negligible. The errors for
>
> 37/32 (%48),
> 37/28 (%48),
> 37/25 (%37),
> 45/29 (%37),
> 39/23 (%35),
> 50/29 (%41),
> 64/37 (%48),
> 47/27 (%35),
> 23/13 (%36),
> 37/20 (%42),
> 29/15 (%36), and
> 37/19 (%47)
>
> are relatively significant. I hence itch for a
> better measurement unit.

Six of the largest errors here are for the six ratios
which contain 37 as a prime-factor. I explicitly stated
back at the beginning of my advocacy for 8539-edo tinas
that 37 is the only prime-factor up to the 41-limit
which is not approximated well by 8539-edo.

I'd be happy to find the best candidates for integer
logarithmic interval measurement units for exactly
the list of ratios you provided ... but it will have
to wait until i can find time to work on it.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> You've done a tremendous job; but then again, you cannot so well
> approximate:
>
> 37/32 (%48),
> 37/28 (%48),
> 37/25 (%37),
> 45/29 (%37),
> 39/23 (%35),
> 50/29 (%41),
> 64/37 (%48),
> 47/27 (%35),
> 23/13 (%36),
> 37/20 (%42),
> 29/15 (%36), and
> 37/19 (%47).
>
> A replacement unit for the cent should have reduced roundoff errors
for
> these as much as 30 percent IMNSHO.

You seem to want to go as high as the 47-limit. Is this all you need,
or do you want even more? And *why* do you need to get that high-
limit?

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 19 May�s 2007 Cumartesi 22:21
Subject: [tuning] Re: Wikipedia "tina" page

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > You've done a tremendous job; but then again, you cannot so well
> > approximate:
> >
> > 37/32 (%48),
> > 37/28 (%48),
> > 37/25 (%37),
> > 45/29 (%37),
> > 39/23 (%35),
> > 50/29 (%41),
> > 64/37 (%48),
> > 47/27 (%35),
> > 23/13 (%36),
> > 37/20 (%42),
> > 29/15 (%36), and
> > 37/19 (%47).
> >
> > A replacement unit for the cent should have reduced roundoff errors
> for
> > these as much as 30 percent IMNSHO.
>
> You seem to want to go as high as the 47-limit. Is this all you need,
> or do you want even more? And *why* do you need to get that high-
> limit?
>
>

Ah, that was the second simplest ratio for the 64th step of 80 MOS 159-tET
after 40/23. Even if we were to forget that one, there is a 13-limit ratio
in that list that demands better representation.

Oz.

> > > 37/32 (%48),
> > > 37/28 (%48),
> > > 37/25 (%37),
> > > 45/29 (%37),
> > > 39/23 (%35),
> > > 50/29 (%41),
> > > 64/37 (%48),
> > > 47/27 (%35),
> > > 23/13 (%36),
> > > 37/20 (%42),
> > > 29/15 (%36), and
> > > 37/19 (%47).

> > You seem to want to go as high as the 47-limit. Is this all you need,
> > or do you want even more? And *why* do you need to get that high-
> > limit?

> Ah, that was the second simplest ratio for the 64th step of 80 MOS 159-tET
> after 40/23. Even if we were to forget that one, there is a 13-limit ratio
> in that list that demands better representation.

None of the ratios given is 13-limit. The lowest limit listed is 23, which no doubt has something to do with the fact that tinas work very well through the 21-limit.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 21 May�s 2007 Pazartesi 21:35
Subject: [tuning] Re: Wikipedia "tina" page

> > > > 37/32 (%48),
> > > > 37/28 (%48),
> > > > 37/25 (%37),
> > > > 45/29 (%37),
> > > > 39/23 (%35),
> > > > 50/29 (%41),
> > > > 64/37 (%48),
> > > > 47/27 (%35),
> > > > 23/13 (%36),
> > > > 37/20 (%42),
> > > > 29/15 (%36), and
> > > > 37/19 (%47).
>
> > > You seem to want to go as high as the 47-limit. Is this all you need,
> > > or do you want even more? And *why* do you need to get that high-
> > > limit?
>
> > Ah, that was the second simplest ratio for the 64th step of 80 MOS
> 159-tET
> > after 40/23. Even if we were to forget that one, there is a 13-limit
> ratio
> > in that list that demands better representation.
>
> None of the ratios given is 13-limit. The lowest limit listed is 23,

Mine was a typo.

> which no doubt has something to do with the fact that tinas work very
> well through the 21-limit.
>

But not so well through 37.

Oz.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
Monz wrote:
> > The only really accurate way of describing a "monzo"
> > is to call it a "prime-factor-exponent vector". Gene's
> > whole purpose in giving it the short name (that i
> > obviously like) was that he didn't want to have to
> > keep typing that much longer term over and over again.

That's a bit disingenous isn't it? No one ever called them
"prime-factor-exponent vectors" that I am aware of. I call them "prime
exponent vectors", but "exponent vector" is sufficient since what else
would they be exponents of, in this field? In fact regular
mathematicians already call them that. See
http://mathworld.wolfram.com/ExponentVector.html

If you really must have something shorter, call them EV's or PEV's.

> On Graham's website, I saw something called "ratiospace". IIRC, if
was just
> the same thing. And, as far as I understood his words, the idea had
already
> been promoted by Fokker and others. In case I'm right, then I agree
that the
> name "ratiospace" contains a small bit of explanation in it. When I
first
> read about monzos, I thought I'm missing something like a brand new
way of
> describing JI intervals. Then, when I realized it was the same as what I
> knew was being called ratiopsace, I began to doubt if I actually didn't
> misunderstand the concept of ratiospace. But until now, I think I
didn't.
> That doesn't mean anything else than the fact that I can't see any
> difference between ratiospace and monzo.

I totally agree that eponyms or other non-descriptive names for well
known concepts just serve to obscure.

-- Dave Keenan

Hi Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, Petr Parízek <p.parizek@> wrote:
> Monz wrote:
> > > The only really accurate way of describing a "monzo"
> > > is to call it a "prime-factor-exponent vector". Gene's
> > > whole purpose in giving it the short name (that i
> > > obviously like) was that he didn't want to have to
> > > keep typing that much longer term over and over again.
>
> That's a bit disingenous isn't it? No one ever called
> them "prime-factor-exponent vectors" that I am aware of.
> I call them "prime exponent vectors", but "exponent vector"
> is sufficient since what else would they be exponents of,
> in this field? In fact regular mathematicians already call
> them that. See
> http://mathworld.wolfram.com/ExponentVector.html

Well, Gene does use all kinds of numbers as generators,
not only the prime-factors. So in his usage, the exponents
can be attached to many different kinds of bases.

-monz
http://tonalsoft.com
Tonescape microtonal music software

This old footage from twenty years ago, has recently appeared on YouTube.

It was a stunt for one of the first LucyTuned pop singles.

http://www.youtube.com/watch?v=wOi0szA_oac

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

Posted by: "Dave Keenan" d.keenan@bigpond.net.au
<mailto:d.keenan@bigpond.net.au?Subject=%20Re%3A%20Wikipedia%20%22tina%22%20page>
dkeenanuqnetau <http://profiles.yahoo.com/dkeenanuqnetau>

Sun May 20, 2007 8:49 pm (PST)

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Petr Par�zek <p.parizek@.
..> wrote:

>> That doesn't mean anything else than the fact that I can't see any
>> difference between ratiospace and monzo.

> I totally agree that eponyms or other non-descriptive names for well
> known concepts just serve to obscure.

"Exponent vector" is used rather loosely. Normally you don't precisely define a vector space or a group, nor do you give the dimension or rank of the group. Finally, it usually is the case that the "vector" itself isn't regarded as actually representing a positive rational number, but is merely the list of exponents of a positive rational number. Nor is it set up in such a way that there is specifically a dual concept involved, and the dual to the free group of infinite rank of "exponent vectors" is actually one with a different structure to it, not a free group, and probably not what we want to consider. I think it is much clearer if you know in advance that you have an element of a group of a particular rank, and that this element defines, by definition, a p-limit rational number, not any possible rational number. And the bra-ket notation we've adopted has clarified many confusions in my opinion.

Hence, whether or not you call them "exponent vectors" and the dual concept "prime mappings", or do what I did and call them "monzo" and "val", precisely defining them to have a particular fixed dimension or rank I think is important in some contexts.

However, "exponent vector" would be what I'd probably use if I was writing a paper--in fact, I think I may have used it. But it's really better to have a precisely defined word which means exactly what we want it to mean, which "exponent vector" doesn't quite do.

--- In tuning@yahoogroups.com, Gene Ward Smith <genewardsmith@...> wrote:
> "Exponent vector" is used rather loosely. Normally you don't precisely
> define a vector space or a group, nor do you give the dimension or rank
> of the group.

It seems it's good enough for Mathworld. I suspect it's just that
algebraists like to define it rather more tightly than the rest of us.

> Finally, it usually is the case that the "vector" itself
> isn't regarded as actually representing a positive rational number, but
> is merely the list of exponents of a positive rational number.

That's a bit of a hairsplit don't you think? I don't know about you,
but I can oscillate back and forth between seeing it one way and
seeing it the other at will.

> Nor is it
> set up in such a way that there is specifically a dual concept
involved,
> and the dual to the free group of infinite rank of "exponent
vectors" is
> actually one with a different structure to it, not a free group, and
> probably not what we want to consider. I think it is much clearer if
you
> know in advance that you have an element of a group of a particular
> rank, and that this element defines, by definition, a p-limit rational
> number, not any possible rational number.

I suspect that few people apart from yourself even consider such
things. They are just taken for granted or don't even make it on the
radar.

> And the bra-ket notation we've
> adopted has clarified many confusions in my opinion.

Oh absolutely. I'm 100% with you on that one brother.

> Hence, whether or not you call them "exponent vectors" and the dual
> concept "prime mappings", or do what I did and call them "monzo" and
> "val", precisely defining them to have a particular fixed dimension or
> rank I think is important in some contexts.

Sure.

> However, "exponent vector" would be what I'd probably use if I was
> writing a paper--in fact, I think I may have used it. But it's really
> better to have a precisely defined word which means exactly what we
want
> it to mean, which "exponent vector" doesn't quite do.

Oh well. Each to their own.

-- Dave K