All;

Rather than naming every linear temperament of interest (and

presumably, every planar one also), why not name blocks of

interest, and use a prefix to denote which comma(s) vanish?

As it stands, there's no good way to talk about the *blocks*

behind popular temperaments.

An alternative would be to name the important commas, and then

name blocks and temperaments by concatenating the names of the

commas involved, with prefixes to indicate vanishing.

I would imagine the names we have so far would remain as

aliases.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> All;

>

> Rather than naming every linear temperament of interest (and

> presumably, every planar one also), why not name blocks of

> interest, and use a prefix to denote which comma(s) vanish?

i've been dreaming of a huge website where scales are organized by

blocks and one can click on which unison vectors to

temper/detemper . . .

> As it stands, there's no good way to talk about the *blocks*

> behind popular temperaments.

you mean naming all the just blocks? there are way too many; a given

temperament can apply to many blocks.

> An alternative would be to name the important commas, and then

> name blocks and temperaments by concatenating the names of the

> commas involved, with prefixes to indicate vanishing.

already there's the problem that the pythagorean comma doesn't vanish

in pythagorean tuning. but i like the idea . . . nevertheless, what

basis do you use? the TM basis for the 7-limit miracle kernel is

{225:224, 1029:1024}, yet the breedsma does vanish too, which this

wouldn't tell you by names alone . . .

>i've been dreaming of a huge website where scales are organized by

>blocks and one can click on which unison vectors to

>temper/detemper . . .

That would be truly awesome. The culmination of years of work.

>> As it stands, there's no good way to talk about the *blocks*

>> behind popular temperaments.

>

>you mean naming all the just blocks? there are way too many; a

>given temperament can apply to many blocks.

Ah, right.

>> An alternative would be to name the important commas, and then

>> name blocks and temperaments by concatenating the names of the

>> commas involved, with prefixes to indicate vanishing.

>

>already there's the problem that the pythagorean comma doesn't vanish

>in pythagorean tuning. but i like the idea . . . nevertheless, what

>basis do you use? the TM basis for the 7-limit miracle kernel is

>{225:224, 1029:1024}, yet the breedsma does vanish too, which this

>wouldn't tell you by names alone . . .

Good point. Maybe we need to name wedgies... does that solve the

problem?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >i've been dreaming of a huge website where scales are organized by

> >blocks and one can click on which unison vectors to

> >temper/detemper . . .

>

> That would be truly awesome. The culmination of years of work.

>

> >> As it stands, there's no good way to talk about the *blocks*

> >> behind popular temperaments.

> >

> >you mean naming all the just blocks? there are way too many; a

> >given temperament can apply to many blocks.

>

> Ah, right.

>

> >> An alternative would be to name the important commas, and then

> >> name blocks and temperaments by concatenating the names of the

> >> commas involved, with prefixes to indicate vanishing.

> >

> >already there's the problem that the pythagorean comma doesn't

vanish

> >in pythagorean tuning. but i like the idea . . . nevertheless,

what

> >basis do you use? the TM basis for the 7-limit miracle kernel is

> >{225:224, 1029:1024}, yet the breedsma does vanish too, which this

> >wouldn't tell you by names alone . . .

>

> Good point. Maybe we need to name wedgies... does that solve the

> problem?

>

> -Carl

naming wedgies is the same thing as naming temperaments, isn't it?

>naming wedgies is the same thing as naming temperaments, isn't it?

Yeah, probably. Looks like there's no good shorthand for talking

about this stuff. If there was, Dave would probably have already

found it! :)

-Carl

From: Carl Lumma <ekin@lumma.org>

{{Good point. Maybe we need to name wedgies... does that solve the

problem?}}

Naming wedgies is the same as naming temperaments, which is what we've

been doing.

Carl Lumma <ekin@lumma.org> writes:

{{Rather than naming every linear temperament of interest (and

presumably, every planar one also), why not name blocks of

interest, and use a prefix to denote which comma(s) vanish?}}

It seems to me that which commas vanish pretty well tells you what you

need to know right there. I also don't see why blocks in general warrant

names, though some clearly do.

{{As it stands, there's no good way to talk about the *blocks*

behind popular temperaments.}}

Why do you say blocks are behind temperaments?

>{{As it stands, there's no good way to talk about the *blocks*

>behind popular temperaments.}}

>

>Why do you say blocks are behind temperaments?

Because that's the way I think of temperaments.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> All;

>

> Rather than naming every linear temperament of interest (and

> presumably, every planar one also), why not name blocks of

> interest, and use a prefix to denote which comma(s) vanish?

But Carl,

I believe that musicians, as opposed to mathematicians, think of

strange temperaments more in terms of what the generator(s) and period

are, rather than what commas vanish.

--- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

<d.keenan@u...> wrote:

> --- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > All;

> >

> > Rather than naming every linear temperament of interest (and

> > presumably, every planar one also), why not name blocks of

> > interest, and use a prefix to denote which comma(s) vanish?

>

> But Carl,

>

> I believe that musicians, as opposed to mathematicians, think of

> strange temperaments more in terms of what the generator(s) and

period

> are, rather than what commas vanish.

this is why musicians have such trouble with two-dimensional systems

such as planar temperaments or 5-limit strict ji.

--- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

<d.keenan@u...> wrote:

> I believe that musicians, as opposed to mathematicians, think of

> strange temperaments more in terms of what the generator(s) and

period

> are, rather than what commas vanish.

all the more reason monz should update the table of commas and

temperaments here:

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> --- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

> <d.keenan@u...> wrote:

>

> > I believe that musicians, as opposed to mathematicians, think of

> > strange temperaments more in terms of what the generator(s) and

> period

> > are, rather than what commas vanish.

>

> all the more reason monz should update the table of commas and

> temperaments here:

>

> http://sonic-arts.org/dict/eqtemp.htm

This is an extraordinarily beautiful and informative graphic.

I assume you mean he should add generator and period to the table of

commas and temperaments. Absolutely!

--- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

<d.keenan@u...> wrote:

> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus

> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> > --- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

> > <d.keenan@u...> wrote:

> >

> > > I believe that musicians, as opposed to mathematicians, think of

> > > strange temperaments more in terms of what the generator(s) and

> > period

> > > are, rather than what commas vanish.

> >

> > all the more reason monz should update the table of commas and

> > temperaments here:

> >

> > http://sonic-arts.org/dict/eqtemp.htm

>

> This is an extraordinarily beautiful and informative graphic.

thanks -- i can't believe this is your first time seeing it.

> I assume you mean he should add generator and period to the table of

> commas and temperaments. Absolutely!

yes, the data is already in the yahoo tuning database.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> --- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

> <d.keenan@u...> wrote:

> > > http://sonic-arts.org/dict/eqtemp.htm

> >

> > This is an extraordinarily beautiful and informative graphic.

>

> thanks -- i can't believe this is your first time seeing it.

I think I saw a very early version and hadn't looked at it since.

--- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

<d.keenan@u...> wrote:

> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus

> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> > --- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

> > <d.keenan@u...> wrote:

> > > > http://sonic-arts.org/dict/eqtemp.htm

> > >

> > > This is an extraordinarily beautiful and informative graphic.

> >

> > thanks -- i can't believe this is your first time seeing it.

>

> I think I saw a very early version and hadn't looked at it since.

since you're interested in 217, 494 and the like, be sure to use the

mouse-over zoom feature.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> --- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

> <d.keenan@u...> wrote:

> > --- In tuning-math@yahoogroups.com, "wallyesterpaulrus

> > <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> > > --- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

> > > <d.keenan@u...> wrote:

> > > > > http://sonic-arts.org/dict/eqtemp.htm

> > > >

> > > > This is an extraordinarily beautiful and informative graphic.

> > >

> > > thanks -- i can't believe this is your first time seeing it.

> >

> > I think I saw a very early version and hadn't looked at it since.

>

> since you're interested in 217, 494 and the like, be sure to use the

> mouse-over zoom feature.

Awesome!

Except I found I wanted a 333&1/3 zoom so I could see 217 and 494 (and

possibly 612) on the same plot. Some people are never satisfied. ;-)

I couldn't find any explanation of why some numbers are in various

hues of red, orange and magenta. Only some stuff about red lines not

drawn.

>{{As it stands, there's no good way to talk about the *blocks*

>behind popular temperaments.}}

>

>Why do you say blocks are behind temperaments?

What do you call meantone without the 81:80 tempered out? Paul

tried to deny the existence of such beasts, but this hardly

seems possible in light of adaptive JI.

-Carl

hi Dave,

> From: <d.keenan@uq.net.au>

> To: <tuning-math@yahoogroups.com>

> Sent: Monday, February 10, 2003 10:29 PM

> Subject: [tuning-math] poking monz (was: Re: naming temperaments(

>

>

re: http://sonic-arts.org/dict/eqtemp.htm

> I couldn't find any explanation of why some numbers

> are in various hues of red, orange and magenta. Only

> some stuff about red lines not drawn.

since you were sort-of offlist for a while,

you may not know that i too have been mostly

offlist since last March. i really needed

a vacation over the summer (when i was enjoying

riding my new motorcycle a lot), and then around

September i got a lot busier with work (which

is real good, because i needed the money).

i slapped paul's graphics into this page and created

the javascript mouseover "zoom" feature, but

unfortunately haven't yet invested the time in

cleaning up the table and text that go along with

these graphics ... as paul has already mentioned

in this thread.

so ... be patient, i'll get around to it eventually.

-monz

Carl Lumma wrote:

> i've been dreaming of a huge website where scales are organized by > blocks and one can click on which unison vectors to > temper/detemper . . .

> > That would be truly awesome. The culmination of years of work.

Then the sooner we start, the sooner it'll be ready.

What do you mean by "blocks"? Planar temperaments?

I can see how it would be nice to have a dynamic version of Monz's diagram, where you could click on equal temeperaments or pairs of equal temperaments to get linear temperaments. But what you want seems to be the other way round -- starting with commas rather than equal temperaments. The problem with that is that it becomes multidimensional.

Planar temperaments combine with equal temperaments to give linear temperaments, but planar temperaments combining with other planar temperaments won't work in general.

>>>An alternative would be to name the important commas, and then

>>>name blocks and temperaments by concatenating the names of the

>>>commas involved, with prefixes to indicate vanishing.

>>

>>already there's the problem that the pythagorean comma doesn't vanish >>in pythagorean tuning. but i like the idea . . . nevertheless, what >>basis do you use? the TM basis for the 7-limit miracle kernel is >>{225:224, 1029:1024}, yet the breedsma does vanish too, which this >>wouldn't tell you by names alone . . .

> > Good point. Maybe we need to name wedgies... does that solve the

> problem?

Wedgies or mappings will tell you if a given comma vanishes in a given temperament. You can start with a list of known commas and keep all those that vanish in each temperament -- no need to restrict yourself to the TM basis. What do you want them for?

Graham

Carl Lumma <ekin@lumma.org> writes:

>What do you call meantone without the 81:80 tempered out?

>tried to deny the existence of such beasts, but this hardly

>seems possible in light of adaptive JI.

Paul is right. Adaptive JI either removes the 81/80 or it doesn't; if it

doesn't, it isn't meantone.

>> i've been dreaming of a huge website where scales are organized by

>> blocks and one can click on which unison vectors to

>> temper/detemper . . .

>>

>> That would be truly awesome. The culmination of years of work.

>

>Then the sooner we start, the sooner it'll be ready.

>

>What do you mean by "blocks"? Planar temperaments?

Periodicity blocks. No temperament.

>I can see how it would be nice to have a dynamic version of Monz's

>diagram, where you could click on equal temeperaments or pairs of equal

>temperaments to get linear temperaments. But what you want seems to be

>the other way round -- starting with commas rather than equal

>temperaments.

Right.

Paul's database and zoom-graphs already go a long way...

-Carl

>>What do you call meantone without the 81:80 tempered out?

>>tried to deny the existence of such beasts, but this hardly

>>seems possible in light of adaptive JI.

>

>Paul is right. Adaptive JI either removes the 81/80 or it doesn't;

>if it doesn't, it isn't meantone.

It wouldn't be JI if it removed it. But it's more than random

JI, it's JI treating the 81:80 as a unison. What do you call

that?

-Carl

Carl Lumma <ekin@lumma.org> writes:

>It wouldn't be JI if it removed it. But it's more than random

>JI, it's JI treating the 81:80 as a unison. What do you call

>that?

Comma drift.

>>It wouldn't be JI if it removed it. But it's more than random

>>JI, it's JI treating the 81:80 as a unison. What do you call

>>that?

>

>Comma drift.

???

What do you call _the scale_?

Did you read _The Forms of Tonality_?

-Carl

--- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

<d.keenan@u...> wrote:

> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus

> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> > --- In tuning-math@yahoogroups.com, "Dave Keenan <d.keenan@u...>"

> > <d.keenan@u...> wrote:

> > > --- In tuning-math@yahoogroups.com, "wallyesterpaulrus

> > > <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> > > > --- In tuning-math@yahoogroups.com, "Dave Keenan

<d.keenan@u...>"

> > > > <d.keenan@u...> wrote:

> > > > > > http://sonic-arts.org/dict/eqtemp.htm

> > > > >

> > > > > This is an extraordinarily beautiful and informative

graphic.

> > > >

> > > > thanks -- i can't believe this is your first time seeing it.

> > >

> > > I think I saw a very early version and hadn't looked at it

since.

> >

> > since you're interested in 217, 494 and the like, be sure to use

the

> > mouse-over zoom feature.

>

> Awesome!

>

> Except I found I wanted a 333&1/3 zoom so I could see 217 and 494

(and

> possibly 612) on the same plot. Some people are never satisfied. ;-)

>

> I couldn't find any explanation of why some numbers are in various

> hues of red, orange and magenta. Only some stuff about red lines not

> drawn.

the bluish ets are consistent, the reddish ones inconsistent (and may

appear in more than one place on the graph). i used different shades

of each because some numbers lie right on top of one another.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >{{As it stands, there's no good way to talk about the *blocks*

> >behind popular temperaments.}}

> >

> >Why do you say blocks are behind temperaments?

>

> What do you call meantone without the 81:80 tempered out?

i would *not* call it "untempered dicot"!

> Paul

> tried to deny the existence of such beasts,

i did?

> but this hardly

> seems possible in light of adaptive JI.

please fill in the blanks for us, carl.

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

> unfortunately haven't yet invested the time in

> cleaning up the table

monz, the table you have there now was simply pasted in from a link i

gave you -- except that you fixed some of the scientifically notated

ratios so that they didn't look like unisons.

the table at the original url now includes the ratios in full decimal

representation, as well as important info like the generator of each.

so it would seem that you simply need to do the pasting again -- does

it take a lot of time? my impression was that it was an instantaneous

operation -- please correct me if i'm wrong.

sorry for poking,

paul

--- In tuning-math@yahoogroups.com, Graham Breed <graham@m...> wrote:

> Carl Lumma wrote:

> > i've been dreaming of a huge website where scales are organized

by

> > blocks and one can click on which unison vectors to

> > temper/detemper . . .

> >

> > That would be truly awesome. The culmination of years of work.

>

> Then the sooner we start, the sooner it'll be ready.

>

> What do you mean by "blocks"? Planar temperaments?

when i wrote blocks in the sentence above, i meant *finite* scales.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >>What do you call meantone without the 81:80 tempered out?

> >>tried to deny the existence of such beasts, but this hardly

> >>seems possible in light of adaptive JI.

> >

> >Paul is right. Adaptive JI either removes the 81/80 or it doesn't;

> >if it doesn't, it isn't meantone.

>

> It wouldn't be JI if it removed it. But it's more than random

> JI, it's JI treating the 81:80 as a unison. What do you call

> that?

>

> -Carl

if you use strict JI but treat 81:80 as a unison, you're still in the

realm of the diatonic system as explained in my paper "the forms of

tonality" -- and very far from any kind of dicot system.

>> What do you call meantone without the 81:80 tempered out?

>

>i would *not* call it "untempered dicot"!

Oh, neither would I. I switched the example.

>> Paul tried to deny the existence of such beasts,

>

>i did?

Well, you asked "dicot is a temperament, generated by neutral

thirds. in what sense does it make sense to speak of an untempered

temperament?

>> but this hardly seems possible in light of adaptive JI.

>

>please fill in the blanks for us, carl.

Do you not argue in the Forms of Tonality that PBs are fundamental

musical structures?

Is there a difference between music written for meantone and

music written for 5-limit JI? Does that difference go away

when the former is rendered in adaptive JI?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >> What do you call meantone without the 81:80 tempered out?

> >

> >i would *not* call it "untempered dicot"!

>

> Oh, neither would I. I switched the example.

ok, so what are we talking about exactly?

> >> Paul tried to deny the existence of such beasts,

> >

> >i did?

>

> Well, you asked "dicot is a temperament, generated by neutral

> thirds. in what sense does it make sense to speak of an untempered

> temperament?

now we *are* talking about "untempered dicot" again? make up your

mind!

> >> but this hardly seems possible in light of adaptive JI.

> >

> >please fill in the blanks for us, carl.

>

> Do you not argue in the Forms of Tonality that PBs are fundamental

> musical structures?

yes . . . ?

> Is there a difference between music written for meantone and

> music written for 5-limit JI?

there can be . . . but most western music is simply written for 7

nominals, sharps, and flats . . .

> Does that difference go away

> when the former is rendered in adaptive JI?

it might not, depending on the music and how it's notated. the forms

of tonality argues that the diatonic model holds up quite well in all

these alternatives (i think i list 5).

>ok, so what are we talking about exactly?

What terminology should be used when discussing

untempered PBs.

You said many different PBs might represent a

single untempered temperament.* Would they all

still share some essential feature?

* I assumed this happens like: given a bunch of

commas, one can swap factors around between them

and come up with a different bunch of commas,

that generate a different block, but the temperament

would map both blocks to the same pitches.

>>>>Paul tried to deny the existence of such beasts,

>>>

>>>i did?

>>

>>Well, you asked "dicot is a temperament, generated by neutral

>>thirds. in what sense does it make sense to speak of an untempered

>>temperament?"

>

>now we *are* talking about "untempered dicot" again? make up your

>mind!

It was the "in what sense..." part that I was referring to.

>>Is there a difference between music written for meantone and

>>music written for 5-limit JI?

>

>there can be . . .

Ok, that's an answer. Forget Western music. I've always

believed in an affirmative answer here, too, though I realize

I'm at a loss as to how I'd test for it. So I asked.

>> Does that difference go away

>> when the former is rendered in adaptive JI?

>

>it might not, depending on the music and how it's notated. the forms

>of tonality argues that the diatonic model holds up quite well in all

>these alternatives (i think i list 5).

Ok, so it does make sense to talk about an untempered temperament.

What's the appropriate way to talk about it?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >ok, so what are we talking about exactly?

>

> What terminology should be used when discussing

> untempered PBs.

well, there are fokker periodicity blocks, other things

like "semiblocks" that gene's defined . . . and of course you might

have commatic unison vectors even in the untempered case . . .

> You said many different PBs might represent a

> single untempered temperament.* Would they all

> still share some essential feature?

>

> * I assumed this happens like: given a bunch of

> commas, one can swap factors around between them

> and come up with a different bunch of commas,

> that generate a different block, but the temperament

> would map both blocks to the same pitches.

not if one or more the the "commas generating the block", or unison

vectors, is chromatic. then you might end up with a chromatically

altered block.

> >>>>Paul tried to deny the existence of such beasts,

> >>>

> >>>i did?

> >>

> >>Well, you asked "dicot is a temperament, generated by neutral

> >>thirds. in what sense does it make sense to speak of an untempered

> >>temperament?"

> >

> >now we *are* talking about "untempered dicot" again? make up your

> >mind!

>

> It was the "in what sense..." part that I was referring to.

ok, so in a sense, my paper discusses, as one

possibility, "untempered meantone". in which comma drift can occur.

how are we doing?

>> What terminology should be used when discussing

>> untempered PBs.

>

>well, there are fokker periodicity blocks, other things

>like "semiblocks" that gene's defined . . . and of course you might

>have commatic unison vectors even in the untempered case . . .

//

>ok, so in a sense, my paper discusses, as one

>possibility, "untempered meantone". in which comma drift can occur.

>

>how are we doing?

Good! So how can one quickly refer to blocks that correspond

to temperaments? Do I have to say "the 7-tone PB which has

commatic uv x and chromatic uv y"? Does it make sense to say

"untempered [temperament-x]"? etc.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Good! So how can one quickly refer to blocks that correspond

> to temperaments? Do I have to say "the 7-tone PB which has

> commatic uv x and chromatic uv y"?

it helps . . .

> Does it make sense to say

> "untempered [temperament-x]"? etc.

>

> -Carl

untempered meantone would not be enough to tell you how many notes

are in the block, just that you won't have any 81:80 pairs in it.

hi paul,

> From: <wallyesterpaulrus@yahoo.com>

> To: <tuning-math@yahoogroups.com>

> Sent: Tuesday, February 11, 2003 2:32 PM

> Subject: [tuning-math] poking monz (was: Re: naming temperaments(

>

>

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

>

> > unfortunately haven't yet invested the time in

> > cleaning up the table

>

> monz, the table you have there now was simply pasted in from a link i

> gave you -- except that you fixed some of the scientifically notated

> ratios so that they didn't look like unisons.

>

> the table at the original url now includes the ratios in full decimal

> representation, as well as important info like the generator of each.

> so it would seem that you simply need to do the pasting again -- does

> it take a lot of time? my impression was that it was an instantaneous

> operation -- please correct me if i'm wrong.

>

> sorry for poking,

> paul

no need to apologize -- i try to stay on top of my webpages

to make sure they're correct and as up-to-date as i can make

them, and i know that you've sent me (several times) some

stuff that i still need to incorporate. i've just been real

busy lately ... sorry.

can you please post the link to the table again?

i'll try to get right on it.

-monz

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

>

> hi paul,

>

>

> > From: <wallyesterpaulrus@y...>

> > To: <tuning-math@yahoogroups.com>

> > Sent: Tuesday, February 11, 2003 2:32 PM

> > Subject: [tuning-math] poking monz (was: Re: naming temperaments(

> >

> >

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

> >

> > > unfortunately haven't yet invested the time in

> > > cleaning up the table

> >

> > monz, the table you have there now was simply pasted in from a

link i

> > gave you -- except that you fixed some of the scientifically

notated

> > ratios so that they didn't look like unisons.

> >

> > the table at the original url now includes the ratios in full

decimal

> > representation, as well as important info like the generator of

each.

> > so it would seem that you simply need to do the pasting again --

does

> > it take a lot of time? my impression was that it was an

instantaneous

> > operation -- please correct me if i'm wrong.

> >

> > sorry for poking,

> > paul

>

>

>

> no need to apologize -- i try to stay on top of my webpages

> to make sure they're correct and as up-to-date as i can make

> them, and i know that you've sent me (several times) some

> stuff that i still need to incorporate. i've just been real

> busy lately ... sorry.

>

> can you please post the link to the table again?

> i'll try to get right on it.

>

>

> -monz

the table can be sorted any way you please, but i think most helpful

for the user would be alphabetically by temperament name, so that one

can see a green line on the graph and immediately find the relevant

info:

/tuning/database?

method=reportRows&tbl=10&sortBy=6

my second choice would be sorting by the "odd limit" of the vanishing

comma's ratio:

/tuning/database?

method=reportRows&tbl=10&sortBy=4

feel free to replace the 60+-digit numerators and denominators with

the scientific notation on your current table, if you wish.

thanks again and let me know when you have time again to revisit your

wonderful Dictionary, so that i may help improve it.

-paul

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

> i'll try to get right on it.

while we're at it, here's a more complete "small 5-limit intervals"

chart to replace the one on your equal temperament page:

/tuning-math/files/Paul/small.gif

due to the triangular/hexagonal geometry, it has the magical property

that each vector points in exactly the same direction -- that is, has

exactly the same slope -- as the green line for the corresponding

temperament in the graphs above. check it out!

moreover, this chart could be used in conjunction with a set of

hexagonal bingo cards . . . as you know, i've made quite a few

already, and can make more in about 2 seconds apiece . . . so that

one can see exactly *how* a given small interval vanishes, or fails

to, in a given equal temperament.

then this chart would have a dual function . . .

let me know,

paul

hi monz . . .

i just noticed that some of the + signs and - signs are reversed on

the "zoom 100" graph.

please allow me to fix them.

thanks,

paul

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> hi monz . . .

>

> i just noticed that some of the + signs and - signs are reversed on

> the "zoom 100" graph.

>

> please allow me to fix them.

>

> thanks,

> paul

here is the corrected "zoom 100" graph:

/tuning-math/files/Paul/zooms.gif

and here's the updated "zoom 1" graph:

/tuning-math/files/Paul/zoomq.gif

sorry for all the harassment,

paul

hi paul,

> From: <wallyesterpaulrus@yahoo.com>

> To: <tuning-math@yahoogroups.com>

> Sent: Wednesday, February 12, 2003 2:40 PM

> Subject: [tuning-math] poking monz (was: Re: naming temperaments(

>

>

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

>

> > i'll try to get right on it.

>

> while we're at it, here's a more complete "small 5-limit intervals"

> chart to replace the one on your equal temperament page:

>

> /tuning-math/files/Paul/small.gif

done.

> due to the triangular/hexagonal geometry, it has the magical property

> that each vector points in exactly the same direction -- that is, has

> exactly the same slope -- as the green line for the corresponding

> temperament in the graphs above. check it out!

>

> moreover, this chart could be used in conjunction with a set of

> hexagonal bingo cards . . . as you know, i've made quite a few

> already, and can make more in about 2 seconds apiece . . . so that

> one can see exactly *how* a given small interval vanishes, or fails

> to, in a given equal temperament.

>

> then this chart would have a dual function . . .

>

> let me know,

> paul

i'd like to include hexagonal graphs for *all* the EDOs on my

"equal temperament" page *and* on the "bingo lattice" page.

it's just a matter of me finding the opportunity to do it.

keep sending me stuff ... i'll incorporate it as i have the chance.

-monz

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

> i'd like to include hexagonal graphs for *all* the EDOs on my

> "equal temperament" page *and* on the "bingo lattice" page.

> it's just a matter of me finding the opportunity to do it.

i'll make the lattices, you just need to upload them :)

seriously, there's no point in going much beyond 72-equal with these

lattices, is there?

> keep sending me stuff ... i'll incorporate it as i have the chance.

thanks!

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> > can you please post the link to the table again?

> > i'll try to get right on it.

> >

> >

> > -monz

>

> the table can be sorted any way you please, but i think most

helpful

> for the user would be alphabetically by temperament name, so that

one

> can see a green line on the graph and immediately find the relevant

> info:

>

> /tuning/database?

> method=reportRows&tbl=10&sortBy=6

>

> my second choice would be sorting by the "odd limit" of the

vanishing

> comma's ratio:

>

> /tuning/database?

> method=reportRows&tbl=10&sortBy=4

>

> feel free to replace the 60+-digit numerators and denominators with

> the scientific notation on your current table, if you wish.

>

> thanks again and let me know when you have time again to revisit

your

> wonderful Dictionary, so that i may help improve it.

>

> -paul

hi monz,

i see you've incorporated my other corrections for your equal

temperament page -- THANKS!! -- but haven't updated the table

discussed above.

is there something i can do to the format to make it easier for you?

a third useful way of sorting the table would be according to

decreasing rms error -- how close the green line comes to the origin:

/tuning/database?

method=reportRows&tbl=10&sortBy=10&sortDir=up

hopefully one of these three sorting methods will be satisfactory for

you.

btw, credit for this table (which i compiled) belongs not only to

carl lumma, but to pretty much the entire tuning-math team, and

primarily gene.

thanks,

paul

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

> i'd like to include hexagonal graphs for *all* the EDOs on my

> "equal temperament" page *and* on the "bingo lattice" page.

>

> keep sending me stuff ... i'll incorporate it as i have the chance.

i've done them for all ets from 7 through 80 which are both 5-limit

consistent and "non-torsional".

they're the first 50 or so files on this page:

enjoy!

see below. i've just updated the table, as well as the zoom-100 graph

/tuning-math/files/Paul/zooms.gif

and the zoom-1000 graph

/tuning-math/files/Paul/zoomt.gif

to include "counterschismic" -- the family that includes three of

monz's favorites, 53, 306, and 730 . . .

the table below not only needs to replace the table on the equal

temperament page, but would also be (and so would the new small 5-

limit intervals hexagonal graph) a fine addition to the small 5-limit

intervals page and to the linear temperament page . . .

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus

> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

>

> > > can you please post the link to the table again?

> > > i'll try to get right on it.

> > >

> > >

> > > -monz

> >

> > the table can be sorted any way you please, but i think most

> helpful

> > for the user would be alphabetically by temperament name, so that

> one

> > can see a green line on the graph and immediately find the

relevant

> > info:

> >

> > /tuning/database?

> > method=reportRows&tbl=10&sortBy=6

> >

> > my second choice would be sorting by the "odd limit" of the

> vanishing

> > comma's ratio:

> >

> > /tuning/database?

> > method=reportRows&tbl=10&sortBy=4

> >

> > feel free to replace the 60+-digit numerators and denominators

with

> > the scientific notation on your current table, if you wish.

> >

> > thanks again and let me know when you have time again to revisit

> your

> > wonderful Dictionary, so that i may help improve it.

> >

> > -paul

>

> hi monz,

>

> i see you've incorporated my other corrections for your equal

> temperament page -- THANKS!! -- but haven't updated the table

> discussed above.

>

> is there something i can do to the format to make it easier for you?

>

> a third useful way of sorting the table would be according to

> decreasing rms error -- how close the green line comes to the

origin:

>

> /tuning/database?

> method=reportRows&tbl=10&sortBy=10&sortDir=up

>

> hopefully one of these three sorting methods will be satisfactory

for

> you.

>

> btw, credit for this table (which i compiled) belongs not only to

> carl lumma, but to pretty much the entire tuning-math team, and

> primarily gene.

>

> thanks,

> paul

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

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

>

> > i'd like to include hexagonal graphs for *all* the EDOs on my

> > "equal temperament" page *and* on the "bingo lattice" page.

>

> >

> > keep sending me stuff ... i'll incorporate it as i have the

chance.

>

> i've done them for all ets from 7 through 80 which are both 5-limit

> consistent and "non-torsional".

>

> they're the first 50 or so files on this page:

>

> /tuning-math/files/Paul/

>

> enjoy!