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Message: 7025

Date: Fri, 11 Jul 2003 10:33:46

Subject: Re: Announcing Xenharmony.org

From: Carl Lumma


>> Christ Gene, what good are formats like ogg if they don't spare
>> us from bothersome CDs!?

>
>I think CDs are nifty,


Bluea.  Do you, by any chance, like florescent lights?

Seriously, I'd do anything to avoid bringing another cd into the
world.

-Carl
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Message: 7026

Date: Fri, 11 Jul 2003 20:24:10

Subject: Re: Announcing Xenharmony.org

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> >> Christ Gene, what good are formats like ogg if they don't spare
> >> us from bothersome CDs!?

> >
> >I think CDs are nifty,

> 
> Bluea.  Do you, by any chance, like florescent lights?


Have 'em all over the place in here.


> Seriously, I'd do anything to avoid bringing another cd into the
> world.


What's your favorite listening method?
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Message: 7027

Date: Fri, 11 Jul 2003 13:37:53

Subject: Re: Announcing Xenharmony.org

From: Carl Lumma


>> Bluea.  Do you, by any chance, like florescent lights?

>
>Have 'em all over the place in here.


Aaah- florescent lights and the number of the beast!  :)

"They hum like angels..."


>> Seriously, I'd do anything to avoid bringing another cd into the
>> world.

>
>What's your favorite listening method?


Right now, a limited selection of mp3s that I've ripped.  I'm hoping
that FLAC and $200 of hard drive get there soon, so I can rip my
entire cd collection and (literally) burn it.  I pay, even with the
most compact type of sleeve available, almost $200 per year just for
the floor space to store it.

-Carl
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Message: 7028

Date: Fri, 11 Jul 2003 21:59:03

Subject: Re: Announcing Xenharmony.org

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> >> Bluea.  Do you, by any chance, like florescent lights?

> >
> >Have 'em all over the place in here.

> 
> Aaah- florescent lights and the number of the beast!  :)
> 
> "They hum like angels..."


Mine are florescent lightbulbs. They don't hum and the light isn't 
blue.


> Right now, a limited selection of mp3s that I've ripped.  I'm hoping
> that FLAC and $200 of hard drive get there soon, so I can rip my
> entire cd collection and (literally) burn it.  I pay, even with the
> most compact type of sleeve available, almost $200 per year just for
> the floor space to store it.


A Fellowes sleeve holds two CDs in a very small space, and you can 
put hundreds of them in a box.

Why mp3s?
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Message: 7029

Date: Fri, 11 Jul 2003 15:24:13

Subject: Re: Announcing Xenharmony.org

From: Carl Lumma


>Mine are florescent lightbulbs. They don't hum and the light isn't 
>blue.


Actually, I have one of those in my room and another on the porch,
come to think of it.  But I don't often use them.  They have come
a long way, though.


>A Fellowes sleeve holds two CDs in a very small space, and you can 
>put hundreds of them in a box.


I fit over 1000 in 6 sq. ft. of floor space, using univenture
sleeves and cases, which are the best.  At $1050/mo. for 400 sq.
ft., do the math.  Not to mention constant worry about fire,
having to keep them in order so you can find one when you want
it, and actually getting them to where you want to listen to
them.  Plus every scratch degrades them.  20 years old.  Talk
about obsolete.


>Why mp3s?


Because they're portable, well-studied and going to be around for
a while, and suited to the data storage/transmission tech currently
available to me.

-Carl
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Message: 7030

Date: Fri, 11 Jul 2003 19:33:35

Subject: transformation?

From: Carl Lumma


>>The stuff Robert used was such a mapping, defined by a mapping from
>>generators to generators of p-limit JI. I have an old paper I recently
>>uncovered which my brother is supposed to scan for me, and which has
>>both a certain historical interest but also a practical one, in that
>>it explains this and goes on to transformations which are not note-
>>to-note.

>
>Cool; keep us posted on that, eh?


-Carl
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Message: 7031

Date: Fri, 11 Jul 2003 05:35:30

Subject: Announcing Xenharmony.org

From: Gene Ward Smith

This is the official announcement that my web site

Xenharmony * [with cont.]  (Wayb.)

is open for business. There is some theory discussion there, and will 
be more, but it is also a large and growing collection of retuned 
classical repertoire, as ogg files. If you, like me, have been having 
trouble dealing with 12-et music because it sounds too far out of 
tune, this might be just what you need. I think the best way to 
listen to these files is to download  them, convert them to wav 
files, and burn a CD.

So far we have:

Grail:

Mahler Symphony #1
Schubert Symphony #8

(These both seriously rock)

Copland Symphony #3, first movement

Eight Minutes of Mystery Music

Beethoven piano sonatas 27,29,30,31,32
(These are good!)

Bifrost:

Joe Monzo's Mahler #7, first movement

Tännhäuser Overture

Meantone:

Mozart Piano Sonata K. 331

Sullivan "Song to Sing"

Handel "Raging Flames"

Schumann "Foreign Lands and People"

Couperin "Le Tic-Toc Choc"
(people love this one)

Cauldron:

Brahms Symphony #2

Ratwolf:

Beethoven Symphony #1

Stars and Stripes Forever

Wilwolf:

Midsummer Night's Dream Overture

Coming soon are Bruckner, Symphony #7, Mozart, Piano concertos 15 and 
22, Bach, Mass in b minor
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Message: 7032

Date: Fri, 11 Jul 2003 00:00:09

Subject: Re: Announcing Xenharmony.org

From: Carl Lumma


>This is the official announcement that my web site
>
>Xenharmony * [with cont.]  (Wayb.)
>
>is open for business. There is some theory discussion there, and will 
>be more, but it is also a large and growing collection of retuned 
>classical repertoire, as ogg files. If you, like me, have been having 
>trouble dealing with 12-et music because it sounds too far out of 
>tune, this might be just what you need. I think the best way to 
>listen to these files is to download  them, convert them to wav 
>files, and burn a CD.


Christ Gene, what good are formats like ogg if they don't spare
us from bothersome CDs!?

-Carl
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Message: 7033

Date: Fri, 11 Jul 2003 07:25:57

Subject: Re: Announcing Xenharmony.org

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:


> Christ Gene, what good are formats like ogg if they don't spare
> us from bothersome CDs!?


I think CDs are nifty, but I suggested this since it seems to me the 
sound quality is better than you get by using the player on a 
computer (the same being true of mp3.)
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Message: 7034

Date: Sat, 12 Jul 2003 07:45:32

Subject: Re: transformation?

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> >>The stuff Robert used was such a mapping, defined by a mapping 

from

> >>generators to generators of p-limit JI. I have an old paper I 

recently

> >>uncovered which my brother is supposed to scan for me, and which 

has

> >>both a certain historical interest but also a practical one, in 

that

> >>it explains this and goes on to transformations which are not 

note-

> >>to-note.

> >
> >Cool; keep us posted on that, eh?

> 
> -Carl

.
.
Yahoo groups: /tuning-math/files/DJVU/GWS1983.... * [with cont.]
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Message: 7035

Date: Sat, 12 Jul 2003 00:57:14

Subject: Re: transformation?

From: Carl Lumma


>Yahoo groups: /tuning-math/files/DJVU/GWS1983.... * [with cont.] 


Oh, I have that.  :(

-Carl
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Message: 7036

Date: Mon, 14 Jul 2003 02:28:11

Subject: 12-tones of diminished

From: Carl Lumma

Graham, and all;

So if one wants 12-tones of diminished, and one isn't planning
on enforcing 300-cent octaves, it makes sense to take 4 periods
of 3 tones each, no?  And what is the optimal generator?

According to Paul's Incredibly, Very Awesome database, 94 cents
in the 5-limit, giving mapping [[4,0] [6,1] [9,1]] and 11 cents
RMS error.  That appears to agree with the 'linear temp from uvs'
script for 648/625, and with the 'from ets' script in the
5-limit with either 8,12 or 16,28.

Now, how to extend this to the 7-limit?  The 'from ets' script
gives...

16,28:  86-cent generator and [... [11, 1]] mapping,
$0.33 max error

8,12:   106-cent generator and [... [12, -2]] mapping,
$0.20 max error

8,28:   133-cent generator and [... [13, -4]] mapping,
$0.16 max error

...how do I tell what new commas are involved here?  Too bad the
script doesn't give RMS error also.

-Carl
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Message: 7037

Date: Mon, 14 Jul 2003 20:16:56

Subject: Re: 12-tones of diminished

From: Graham Breed

Carl Lumma wrote:


> So if one wants 12-tones of diminished, and one isn't planning
> on enforcing 300-cent octaves, it makes sense to take 4 periods
> of 3 tones each, no?  And what is the optimal generator?


300 cent octaves don't make sense anyway, because an octave is a long 
way from 300 cents.  4 periods of 2 tones each will do you (this is the 
octatonic scale, right?


> According to Paul's Incredibly, Very Awesome database, 94 cents
> in the 5-limit, giving mapping [[4,0] [6,1] [9,1]] and 11 cents
> RMS error.  That appears to agree with the 'linear temp from uvs'
> script for 648/625, and with the 'from ets' script in the
> 5-limit with either 8,12 or 16,28.


Yes, about 94 cents.


> Now, how to extend this to the 7-limit?  The 'from ets' script
> gives...
> 
> 16,28:  86-cent generator and [... [11, 1]] mapping,
> $0.33 max error
> 
> 8,12:   106-cent generator and [... [12, -2]] mapping,
> $0.20 max error
> 
> 8,28:   133-cent generator and [... [13, -4]] mapping,
> $0.16 max error
> 
> ...how do I tell what new commas are involved here?  Too bad the
> script doesn't give RMS error also.


The Python library can do it, which you have always been able to 
download.  It's giving different mappings for ET pairs, probably because 
I switched from nearest-prime to optimal mappings.  Anyway, here are the 
results, and as it's getting hot and sticky in here I'll post them 
verbatim rather than interpret them:


 >>> temper.Temperament(16,28,temper.limit7)


3/11, 83.3 cent generator

basis:
(0.25, 0.069401894665888031)

mapping by period and generator:
[(4, 0), (6, 1), (9, 1), (12, -3)]

mapping by steps:
[(28, 16), (44, 25), (65, 37), (78, 45)]

highest interval width: 4
complexity measure: 16  (28 for smallest MOS)
highest error: 0.015561  (18.673 cents)
unique

 >>> temper.Temperament(12,8,temper.limit7)


2/5, 86.3 cent generator

basis:
(0.25, 0.071928094887362182)

mapping by period and generator:
[(4, 0), (6, 1), (9, 1), (11, 1)]

mapping by steps:
[(12, 8), (19, 13), (28, 19), (34, 23)]

highest interval width: 1
complexity measure: 4  (8 for smallest MOS)
highest error: 0.027608  (33.129 cents)

 >>> temper.Temperament(8,28,temper.limit7)


4/9, 133.8 cent generator

basis:
(0.25, 0.11147098441152084)

mapping by period and generator:
[(4, 0), (5, 3), (8, 3), (9, 5)]

mapping by steps:
[(28, 8), (44, 13), (65, 19), (78, 23)]

highest interval width: 5
complexity measure: 20  (28 for smallest MOS)
highest error: 0.013034  (15.641 cents)
unique

 >>> def rmsError(m, n):

... 	lt = temper.Temperament(m, n, temper.limit7)
... 	lt.optimizeRMS()
... 	return lt.getRMSError()
...

 >>> rmsError(16, 28)*1200

13.982572846883539

 >>> rmsError(8, 28)*1200

11.750812084722009

 >>> rmsError(8, 12)*1200

20.963524907544105

 >>> map(temper.getRatio, 

temper.Temperament(8,28,temper.limit7).getUnisonVectors())
[(648, 625), (686, 675)]

 >>> map(temper.getRatio, 

temper.Temperament(16,28,temper.limit7).getUnisonVectors())
[(525, 512), (648, 625)]

 >>> map(temper.getRatio, 

temper.Temperament(8,12,temper.limit7).getUnisonVectors())
[(36, 35), (50, 49)]


                       Graham
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Message: 7038

Date: Mon, 14 Jul 2003 12:59:56

Subject: Re: 12-tones of diminished

From: Carl Lumma


>> So if one wants 12-tones of diminished, and one isn't planning
>> on enforcing 300-cent octaves, it makes sense to take 4 periods
>> of 3 tones each, no?  And what is the optimal generator?

>
>300 cent octaves don't make sense anyway, because an octave is a
>long way from 300 cents.


Exactly.


>4 periods of 2 tones each will do you (this is the 
>octatonic scale, right?


I want 12 tones, I think I need 3 tones / period.


>> Now, how to extend this to the 7-limit?  The 'from ets' script
>> gives...
>> 
>> 16,28:  86-cent generator and [... [11, 1]] mapping,
>> $0.33 max error
>> 
>> 8,12:   106-cent generator and [... [12, -2]] mapping,
>> $0.20 max error
>> 
>> 8,28:   133-cent generator and [... [13, -4]] mapping,
>> $0.16 max error
>> 
>> ...how do I tell what new commas are involved here?  Too bad the
>> script doesn't give RMS error also.

>
>The Python library can do it, which you have always been able to 
>download.


url?


>It's giving different mappings for ET pairs, probably because I
>switched from nearest-prime to optimal mappings.


What's nearest-prime?  By optimal, do you mean least badness?


> >>> rmsError(16, 28)*1200

>13.982572846883539

> >>> rmsError(8, 28)*1200

>11.750812084722009

> >>> rmsError(8, 12)*1200

>20.963524907544105


So the best mapping is out of the range of a 12-tone tuning.

But the 2nd-best mapping (the worst according to max error)
is in range, giving...

!
 12 tones of 7-limit diminished.
 12
!
  86.
 172.
 300.
 386.
 472.
 600.
 686.
 772.
 900.
 986.
 1072.
 2/1
!

...with unforch. some nasty fifths.  The 106-cent mapping gives...

!
 12 tones of 7-limit diminished.
 12
!
 106.
 212.
 300.
 406.
 512.
 600.
 706.
 812.
 900.
 1006.
 1112.
 2/1
!

...and looks like the best bet.


> >>> map(temper.getRatio, 

>temper.Temperament(8,28,temper.limit7).getUnisonVectors())
>[(648, 625), (686, 675)]

> >>> map(temper.getRatio, 

>temper.Temperament(16,28,temper.limit7).getUnisonVectors())
>[(525, 512), (648, 625)]

> >>> map(temper.getRatio, 

>temper.Temperament(8,12,temper.limit7).getUnisonVectors())
>[(36, 35), (50, 49)]


Cool.  Tx.

-Carl
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Message: 7039

Date: Mon, 14 Jul 2003 17:52:06

Subject: Re: 12-tones of diminished

From: Carl Lumma


>Automatically generated temperaments * [with cont.]  (Wayb.)


Ah!  (I've never seen that before)


>The optimial mapping is that with the smallest worst 
>error, which is one badness measure for equal temperaments.


I must be missing how complexity is part of it (making it a
badness measure).


>> What's nearest-prime?  By optimal, do you mean least badness?

>
>Nearest-prime takes the nearest approximation to the logarithm
>of each prime number.


Sounds like another error-only measure.  I'm surprised you
get finite results without some sort of badness cutoff.


>> So the best mapping is out of the range of a 12-tone tuning.
>> 
>> But the 2nd-best mapping (the worst according to max error)
>> is in range, giving...

>
>No, it's the worst tuned one by either measure.


According to your results, 8,12 has higher RMS error than
16,28 (the 86-cent mapping in question)...


> >>> rmsError(16, 28)*1200

>13.982572846883539

> >>> rmsError(8, 12)*1200

>20.963524907544105


-Carl
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Message: 7040

Date: Tue, 15 Jul 2003 12:03:10

Subject: Re: 12-tones of diminished

From: Carl Lumma


>>>The optimial mapping is that with the smallest worst 
>>>error, which is one badness measure for equal temperaments.

>> 
>> I must be missing how complexity is part of it (making it a
>> badness measure).

>
>It's only being used to compare equal temperaments with the same 
>number of notes, so the only thing that changes is the error.


But the ets aren't what we care about.  Changing the mapping *does*
change the number of notes needed to express the target chord
(in this case 4:5:6:7, and with linear temperaments, you get the
utonal version for free), which is my definition of complexity.


>>>Nearest-prime takes the nearest approximation to the logarithm
>>>of each prime number.

>> 
>> Sounds like another error-only measure.  I'm surprised you
>> get finite results without some sort of badness cutoff.

>
>I get one finite result for one number of notes to the octave.  For a 
>list of equal temperaments, I start at 1 note to the octave and count up 
>until I've got all I need.  The error's calculated in terms of scale 
>steps.


Ah.


>> According to your results, 8,12 has higher RMS error than
>> 16,28 (the 86-cent mapping in question)...

>
>And 8,12 has a higher maximum error as well and is the 86-cent mapping.


8,12 is the 86-cent mapping?


>This goes back to what I said about the results I get being different 
>to what the website gives, because it uses a different version of the 
>library.


SOB.

-Carl
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Message: 7041

Date: Tue, 15 Jul 2003 19:24:07

Subject: Re: 12-tones of diminished

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> Graham, and all;

> So if one wants 12-tones of diminished, and one isn't planning
> on enforcing 300-cent octaves, it makes sense to take 4 periods
> of 3 tones each, no?  And what is the optimal generator?


(1) You could take 12 tones of diminished and not enfore a uniform 
size of generator as well, and optimize for that.

(2) Are you asking about a non-octave version of diminished?
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Message: 7042

Date: Tue, 15 Jul 2003 01:44:04

Subject: Re: 12-tones of diminished

From: Graham Breed

Carl Lumma wrote:


> url?


Automatically generated temperaments * [with cont.]  (Wayb.)


> What's nearest-prime?  By optimal, do you mean least badness?


Nearest-prime takes the nearest approximation to the logarithm of each 
prime number.  The optimial mapping is that with the smallest worst 
error, which is one badness measure for equal temperaments.


> So the best mapping is out of the range of a 12-tone tuning.
> 
> But the 2nd-best mapping (the worst according to max error)
> is in range, giving...


No, it's the worst tuned  one by either measure.


                    Graham
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Message: 7043

Date: Tue, 15 Jul 2003 12:28:20

Subject: Re: 12-tones of diminished

From: Carl Lumma


>> So if one wants 12-tones of diminished, and one isn't planning
>> on enforcing 300-cent octaves, it makes sense to take 4 periods
>> of 3 tones each, no?  And what is the optimal generator?

>
>(1) You could take 12 tones of diminished and not enforce a
>uniform size of generator as well, and optimize for that.


Yeah, I'm not particularly interested in that, but I'm willing
to view examples.


>(2) Are you asking about a non-octave version of diminished?


Diminished *is* non-octave.

-Carl
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Message: 7044

Date: Tue, 15 Jul 2003 20:58:19

Subject: Re: 12-tones of diminished

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:


> >(2) Are you asking about a non-octave version of diminished?

> 
> Diminished *is* non-octave.


absolutely false!!
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Message: 7045

Date: Tue, 15 Jul 2003 10:57:50

Subject: Re: 12-tones of diminished

From: Graham Breed

Carl Lumma wrote:


>>The optimial mapping is that with the smallest worst 
>>error, which is one badness measure for equal temperaments.

> 
> I must be missing how complexity is part of it (making it a
> badness measure).


It's only being used to compare equal temperaments with the same number 
of notes, so the only thing that changes is the error.


>>Nearest-prime takes the nearest approximation to the logarithm
>>of each prime number.

> 
> Sounds like another error-only measure.  I'm surprised you
> get finite results without some sort of badness cutoff.


I get one finite result for one number of notes to the octave.  For a 
list of equal temperaments, I start at 1 note to the octave and count up 
  until I've got all I need.  The error's calculated in terms of scale 
steps.


> According to your results, 8,12 has higher RMS error than
> 16,28 (the 86-cent mapping in question)...


And 8,12 has a higher maximum error as well and is the 86-cent mapping. 
  This goes back to what I said about the results I get being different 
to what the website gives, because it uses a different version of the 
library.


                       Graham
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Message: 7046

Date: Tue, 15 Jul 2003 16:37:05

Subject: Re: 12-tones of diminished

From: Carl Lumma


>> >(2) Are you asking about a non-octave version of diminished?

>> 
>> Diminished *is* non-octave.

>
>absolutely false!!


That depends on how you read that sentence.

-Carl
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Message: 7047

Date: Thu, 17 Jul 2003 20:15:25

Subject: Obvious things proven

From: Graham Breed

Everything you already knew about maximally even scales:

Maximal Evenness Proofs * [with cont.]  (Wayb.)


                     Graham
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Message: 7048

Date: Thu, 17 Jul 2003 21:05:08

Subject: Re: Obvious things proven

From: Gene Ward Smith

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


> Everything you already knew about maximally even scales:


Great stuff! 

By the way, what would you and Carl think of starting a web ring? You 
only need four websites for a webring.com website.
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Message: 7049

Date: Thu, 17 Jul 2003 21:58:07

Subject: Re: Obvious things proven

From: Carl Lumma


>> Everything you already knew about maximally even scales:

>
>Great stuff! 
>
>By the way, what would you and Carl think of starting a web ring?
>You only need four websites for a webring.com website.


I don't have a site, yet.  But I also prefer just linking to
friends in the conventional way, or using google's similar
pages feature.

-Carl
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