Tuning-Math Digests messages 3926 - 3950

This is an Opt In Archive . We would like to hear from you if you want your posts included. For the contact address see About this archive. All posts are copyright (c).

Contents Hide Contents S 4

Previous Next

3000 3050 3100 3150 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 3700 3750 3800 3850 3900 3950

3900 - 3925 -



top of page bottom of page down


Message: 3926

Date: Thu, 21 Feb 2002 10:40:35

Subject: Re: 4296

From: genewardsmith

--- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> If you run the Brun algorithm with ONLY the fourth or fifth, 4296 shows up
> as a 3rd limit temperament.  But the fact that it also shows up in so many
> 5th limit algorithms with so many different shaped convergence webs, I found
> it
to be extremely ductile.

It is a semiconvergent for *both* log2(3) and log2(5) (reducing
9975/4296 to 3325/1432 in the case of log2(5)). This is a rather
amazing property, and it would be interesing to know what else, if
anything, shares it.


top of page bottom of page up down


Message: 3928

Date: Thu, 21 Feb 2002 12:17:42

Subject: Re: 4296

From: paulerlich

--- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> On 2/20/02 2:02 AM, "genewardsmith" <genewardsmith@j...> wrote:
> 
> > The first comma is the smallest one on my list of best 5-limit temperaments,
> > and gvies us the map [[0, 49, 15], [1,-6,0]]. This divides the 5 into 15
> > parts, and if we tempered 71 or 84 notes by it, we would get a lot of
> > essentially just ratios. If Mark has no objection, perhaps the "Jones" would
> > be a good name for this temperament; the Jones generator being 665/4296,
> > slightly short of satanic. If we take the Jones comma and wedge it with ...
> 
> Err I didn't see this part before.
> 
> (Wrinkling eyebrows, smacking stale aftertaste...)
> 
> I umm... Naming a TEMPERAMENT after me?  Jeesh.  Which one are you saying?
> 665
or 4296?

neither. gene is talking about the _linear_ temperament, not _equal_
temperament, whose _generator_ is about 665/4296 of an octave, but not
exactly -- its tuning can be optimized in various ways, so that it
will be (inaudibly) different from 4296-equal. kind of like the
optimal meantone generator is about 29/50 of an octave, but not
exactly . . .


top of page bottom of page up down


Message: 3929

Date: Thu, 21 Feb 2002 12:20:49

Subject: Re: 4296

From: paulerlich

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> 
> > If you run the Brun algorithm with ONLY the fourth or fifth, 4296 shows up
> > as a 3rd limit temperament.  But the fact that it also shows up in so many
> > 5th limit algorithms with so many different shaped convergence webs, I found
> > it to be extremely ductile.
> 
> It is a semiconvergent for *both* log2(3) and log2(5) (reducing 9975/4296 to 3325/1432 in the case of log2(5)).

don't forget to try log2(5/3).

>This is a rather amazing property, and it would be interesing to know what >else, if anything, shares it.

if you're allowed to reduce like this, 12 does, because 28/12 = 7/3.


top of page bottom of page up down


Message: 3930

Date: Thu, 21 Feb 2002 20:57:43

Subject: comments sought

From: paulerlich

Chapt. One, IV.4. Group Theory *


top of page bottom of page up down


Message: 3932

Date: Thu, 21 Feb 2002 23:32:44

Subject: monz's et graph (from my lumma.gif)

From: paulerlich

hey guys, in the first graph here:

Definitions of tuning terms: equal temperament, (c) 1998 by Joe Monzo *

there's no label on the linear temperament that goes through 12, 73, 
61, 49, and 37. what is it?


top of page bottom of page up down


Message: 3933

Date: Thu, 21 Feb 2002 19:09:54

Subject: Re: 4296

From: genewardsmith

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

> if you're
allowed to reduce like this, 12 does, because 28/12 = 7/3.

Yes, this occurred to me after I posted. It would be interesting to
know if anything is a semiconvergent for 3/2, 5/3, and 5/4, but these
should be finite in number, and if you don't get one fairly quickly
you will probably not get one at all.


top of page bottom of page up down


Message: 3934

Date: Thu, 21 Feb 2002 17:05:34

Subject: Re: magma

From: Carl Lumma

>>>> may be of interest to some here:
>>>> Magma Computational Algebra System Home Page *
>>>
>>>are you sure that's the correct link?
>> 
>>Yes. -C.
>
>well, i just get "The page cannot be displayed"

It's been coming through fine here.  Maybe something
between you and it is just down.  Try "refresh"
lately?

>carl, why won't you answer us on the tuning list? we're asking about 
>the cd you made for me of various a capella groups. could you discuss 
>them please on tuning?

Gee, I thought I did respond... here it is: 34636.  I've switched
to digest mode for tuning and single e-mails for this group and
harmonic entropy (stayed web for metatuning), so tuning may take a
little longer.

BTW Gene, those ad blocking services work by filtering all your
http traffic through their server.  I think it's safe to say this
cannot be a good idea, even without resorting to paranoia.

-Carl


top of page bottom of page up down


Message: 3935

Date: Thu, 21 Feb 2002 17:52:34

Subject: Re: comments sought

From: Carl Lumma

() Any article on Mozart introducing his works by their location
in the movie "Amadeus" is automatically disqualified.

() Mozart's "formula" doesn't look like very much of a formula
at all to me.  It looks a loose description -- a lot like the
standard music theory the author (correctly) criticizes at the
beginning of the article.  Let's see the "formula" applied from
scratch into something that sounds like Mozart; then we'll talk.

() "practically every musical composition has mathematical
underpinnings"  You can use math to describe almost anything.
How deep these descriptions are, how much explanatory power
they have for why we like music, is another thing... "the
chromatic scale is a simple logarithmic equation", for example,
explains nothing.

() "Thus, the beginning of Beethoven's Fifth symphony, when
translated into mathematical language, reads just like the first
chapter of a textbook on group theory, almost sentence for
sentence!"  I'll leave this to Gene and those who know group
theory.  Doesn't strike me that that much is being said here,
other than a discussion (as opposed to a prediction) of the 5th
symphony using fancy lingo.

() "He wanted to implant the idea of the theme in our brain
before we heard it!"  Okay, okay.  So what?

() There seems to be a lot of good advice on practicing the piano
on this site, though I'm still working my way through it.

-Carl


top of page bottom of page up down


Message: 3936

Date: Thu, 21 Feb 2002 19:37:35

Subject: Re: comments sought

From: monz

> From: Orphon Soul, Inc. <tuning@xxxxxxxxxx.xxx>
> To: Tuning Math <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Thursday, February 21, 2002 3:25 PM
> Subject: Re: [tuning-math] comments sought
>
>
> ...
> I keep going back to Beethoven's first piano sonata, it's almost like a
> fractal structure the way things move around and fold into each other.
> Almost like origami.


hmmm... that's really interesting, marc.  i can see a lot of
Beethoven's work in that light, now that you mention it.


> I can't ever say exactly what it means to the general
> public but I can tell be all the fidget factors he had a solid grip on
being
> able to balance and calm the mind enraged.  Only because if he didn't, in
> certain states of mind I wouldn't be able to listen to him.


that's really interesting.


> There's a sense
> of nested scales in his variations as well.  A melody will move up into
> arpeggiating a different chord, one note will be a diatonic step away, one
> note will be a chromatic step away etc.  Well not etc.  I don't recall any
> specific 17 or 19 implications in altered intervals as they evolved.


hmm ... i don't recall Beethoven using anything that resembles 19,
but i'd say that he certainly implied 17 a  l o t  in his compositions,
both melodically (the "flat 9th" or "flat 2nd") and harmonically
(frequent "diminished-7th" chords which imply 10:12:14:17).


it's amazing to me how Beethoven could capture in his piano pieces
what i  c l e a r l y   hear as improvisations.  in good performances
of much of his piano music, i can almost see Ludwig himself sitting
at the keyboard making it up on the spot.


> Other than the fact that there's an Fb on the first page of the first
> piano sonata.  I thought that was so cool.


whoa! -- it's getting scary now, you and i have thought so
many similar things.  when i first bought an old used copy
of the _32 Sonatas, volume 1_ at Settlement Music School back
in the 1970s, i opened to the first page and that was my exact
response when i saw the Fb: "wow, that's so cool!".


> Oh actually, no, in his first few piano sonatas at least,
> IIRC he [Beethoven] works with a span of 19 fifths.  Heh.


it's been a few months now since i worked on it, but i recall
that Mozart used a span of 20 "5ths" in the 1st movement of his
40th Symphony.  the Symphony is in G-minor, so G=1/1 gives a
meantone chain from -8 (Cb) to +11 (B#) "5th" generators.

in my MIDI rendition of the beginning of the piece in 55edo
Mozart's tuning: 55-EDO,  (c) 2001 by Joseph L. Monzo *
i was careful to tune the sharps and flats differently to
reflect Mozart's notation, which had to be done by hand
because none of the programs i know of (Manuel's Scala,
Graham's Midiconv, John deLaubenfels adaptune) can retune
to more than 12 tones per octave.


-monz






_________________________________________________________

Do You Yahoo!?

Get your free @yahoo.com address at Yahoo! Mail Setup *


top of page bottom of page up down


Message: 3937

Date: Fri, 22 Feb 2002 00:27:30

Subject: Re: monz's et graph (from my lumma.gif)

From: Carl Lumma

>Definitions of tuning terms: equal temperament, (c) 1998 by Joe Monzo *
>
>there's no label on the linear temperament that goes through 12, 73, 
>61, 49, and 37. what is it?

In Herman Miller's version, you can see that 25 is on the other side
of 37 from 12.

The 64:63 vanishes as a 7-limit comma in 27, 37, 49, and 12, and as
a 9-limit comma in 61.  I can't seem to get it to vanish in 73.

The generator could be 98 cents... 6/73 gives MOS of 61, 49, 37, 25,
13, and 12 according to Scala.

As a method for finding generators from a series of equal temperaments,
maybe a spreadsheet that graphs each temperament's intervals on a line.
Where the lines get close, you have common generators.  Any Excel
wizards out there think this is a good idea?

More to the point, every line on this plane is a linear temperament,
right?  So what makes low-numbered (less than 100) equal temperaments
cluster on some of them?

Finally, re the jumping jacks / ideal comma question... what's the
question?  How are we defining "most powerful" comma?  Have we decided?
What's the relationship between a comma vanishing and a map?  I say
the most powerful maps are the ones with the smallest numbers in them.
Sum of abs value would work.  What do y'all think?

-Carl


top of page bottom of page up down


Message: 3938

Date: Fri, 22 Feb 2002 03:45:12

Subject: Re: magma

From: genewardsmith

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> > BTW Gene, those ad blocking services work by filtering all your
> > http traffic through their server.
> 
> are
you serious?? someone tell me this isn't so.

It's not true of Proxomitron, at least, since that is a program, not a
service:

Some time ago I began to notice that many of the wonderful new
features added to web browsers, far from making pages better, were
instead making the web a more and more hostile place! Cramped frames,
pop-up windows, music you can't shut off, stroboscopic animations, and
and ever increasing deluge of slow loading advertising content were
making web viewing something akin to trying to read a novel in the
middle of Times Square on New Years Eve!

I decided to try and create a general purpose solution - one that
could not only stop the aggravations of today, but also any demonic
HTML tags lurking in the future. Thus the Proxomitron was born!

At it's heart is a powerful text matching engine. Similar to wildcards
and regular expressions, but specially designed for HTML, it can
re-write web pages on the fly. Think of it like a very powerful "Search and Replace" for the web. Troublesome HTML can be altered or
removed and new content can be added - even your own JavaScripts!

By simply selecting some of the many included filters, you can say
goodbye to common nuisances like animated GIFs, pop-up windows,
advertising banners, dynamic HTML and more. Best of all, these rules
are not hard-coded. More than simply flexible - You can completely
change them, make them more powerful, and of course, add rules of your
own! If it can be written in HTML, it can probably be controlled by
the Proxomitron.

The final power is yours!

Not only can the filters stop general aggravations, but web pages you
visit often can be completely customized to suit your own taste. Don't
like someone else's choice of colors, fonts, or backgrounds? Use your
own instead. Delete useless frames or even change their JavaScripts to
work the way you want. There's really no limit!


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


top of page bottom of page up down


Message: 3939

Date: Fri, 22 Feb 2002 07:30:20

Subject: Re: comments sought

From: monz

> From: <manuel.op.de.coul@xxxxxxxxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Friday, February 22, 2002 5:20 AM
> Subject: Re: [tuning-math] Re: comments sought
>
>
> > What do you mean?  Midiconv doesn't have any 12-fetishism! 
> > I don't think Scala does either.
> 
> They don't, but Joe means the MIDI 12-fetishism. If there's
> a F# and a Gb in the score, we aren't able to guess which
> because they have the same note number in the MIDI-file.


thanks for clarifying that, Manuel.  yes, the fault is not
with the software designers but with MIDI.



> Still doing _all_ notes by hand what Joe does is a waste
> of time.


that's true, Manuel, and i thank you publicly here for
providing me with the entire Mozart 40th retuned to a
12-tone subset of 55edo by Scala.  when i ever find time
to go back to this project, i can continue by starting from
your file and simply changing the pitch-bend on the few
required notes (at least i hope it's a few!).



-monz


 



_________________________________________________________

Do You Yahoo!?

Get your free @yahoo.com address at Yahoo! Mail Setup *


top of page bottom of page up down


Message: 3940

Date: Fri, 22 Feb 2002 00:32:44

Subject: Re: monz's et graph (from my lumma.gif)

From: Carl Lumma

>The 64:63 vanishes as a 7-limit comma in 27, 37, 49, and 12,

That's supposed to be *25*, 37, 49...

-Ca.


top of page bottom of page up down


Message: 3941

Date: Fri, 22 Feb 2002 03:46:39

Subject: Re: comments sought

From: genewardsmith

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

> Chapt. One, IV.4. Group Theory *

If you take out the drivel pretending to be math, you are left with an analysis of how Mozart and Beethoven use motives to build themes.


top of page bottom of page up down


Message: 3942

Date: Fri, 22 Feb 2002 17:10:44

Subject: Re: comments sought

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

Another possibility is to see if there are unused note
numbers in the MIDI-file, change the note numbers of the
special notes to those free ones, and retune the whole
file in one go with Scala using a 128-note scale with
the right pitches. Then you don't need to calculate
pitch bends, and you can try different tunings too with
very little effort.

Manuel


top of page bottom of page up down


Message: 3943

Date: Fri, 22 Feb 2002 08:41:37

Subject: Re: proxomitron

From: genewardsmith

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> Ad blocking software still doesn't address many of my concerns.

It doesn't address all my concerns either, but it seems clear a Usenet
group isn't about to happen.


top of page bottom of page up down


Message: 3944

Date: Fri, 22 Feb 2002 09:08:25

Subject: Re: [tuning] Monzo's lines

From: monz

> From: genewardsmith <genewardsmith@xxxx.xxx>
> To: <tuning@xxxxxxxxxxx.xxx>
> Sent: Friday, February 15, 2002 12:12 AM
> Subject: [tuning] Monzo's lines
>
>
> Here are more comma for the lines on Joe's graph at:
> 
> Definitions of tuning terms: equal temperament, (c) 1998 by Joe Monzo *
> 
> ..
> The 59-71-12 line goes with 2^29 3^-8 5^-7 = 536870192/512578125.
> ...
> Finally the Orwell line of 22-75-53-84-31 is associated to the
> semicomma, which is 2^29 3^-8 5^-7 = 2109375/2097152.


there's a typo here.  i'm assuming that the ratio for the
semicomma is correct, in which case the prime-factoring is
[2 3 5]**[-21 3 7].  Gene, where did you get the name "semicomma"?



-monz


 



_________________________________________________________

Do You Yahoo!?

Get your free @yahoo.com address at Yahoo! Mail Setup *


top of page bottom of page up down


Message: 3945

Date: Fri, 22 Feb 2002 00:51:11

Subject: Re: proxomitron

From: Carl Lumma

>It doesn't address all my concerns either, but it seems clear a Usenet
>group isn't about to happen.

I've never used the usenet, but it seems like it would be so much
better.

-Carl


top of page bottom of page up down


Message: 3946

Date: Fri, 22 Feb 2002 09:18:53

Subject: Re: [tuning] Re: Monzo's lines

From: monz

> From: genewardsmith <genewardsmith@xxxx.xxx>
> To: <tuning@xxxxxxxxxxx.xxx>
> Sent: Friday, February 15, 2002 9:22 PM
> Subject: [tuning] Re: Monzo's lines
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >  
> > here are a few more linear axes that i can see
> > on my adaptation of paul's graph of 5-limit ETs:
> > 
> > Definitions of tuning terms: equal temperament, (c) 1998 by Joe Monzo *
>
> ...
>
> > 26-99-73
> 
> 2^10 3^40 5^23


that's a typo: the minus sign is missing from 3^-40.
the correct prime-factoring is [2 3 5]**[10 -40 23] .



-monz


 



_________________________________________________________

Do You Yahoo!?

Get your free @yahoo.com address at Yahoo! Mail Setup *


top of page bottom of page up down


Message: 3947

Date: Fri, 22 Feb 2002 08:51:50

Subject: Re: monz's et graph (from my lumma.gif)

From: genewardsmith

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> The generator could be 98 cents... 6/73 gives MOS of 61, 49, 37, 25,
> 13, and 12 according to Scala.

Right--the comma is 262144/253125, and the rms generator 98.317 cents.


top of page bottom of page up down


Message: 3948

Date: Fri, 22 Feb 2002 18:20:08

Subject: Re: [tuning] Monzo's lines

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

> Gene, where did you get the name "semicomma"?

From Fokker, via the Scala interval list.

Manuel


top of page bottom of page up down


Message: 3949

Date: Fri, 22 Feb 2002 00:52:53

Subject: Re: monz's et graph (from my lumma.gif)

From: Carl Lumma

>>there's no label on the linear temperament that goes through 12, 73, 
>>61, 49, and 37. what is it?
>
>In Herman Miller's version, you can see that 25 is on the other side
>of 37 from 12.

He also gives the 5-limit comma for this series as [-4 -5].

-Carl


top of page bottom of page up

Previous Next

3000 3050 3100 3150 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 3700 3750 3800 3850 3900 3950

3900 - 3925 -

top of page