Yahoo Tuning Groups Ultimate Backup tuning vanishing comma caper

On Fri, 8 Feb 2002 21:09:04 -0800, SOMEONE articulated, I'd better not
say who :

>hey, real quick, can someone post a list of
>all ETs (everything under 200-ET is ok)
>in which the syntonic comma vanishes?

"Pipeline in the pipeline for piping" ;)

http://www.ampcast.com/guiseppimendoza
http://www.ampfea.org/sln/browse.php?num=3&a_id=132

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗genewardsmith <genewardsmith@juno.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> hey, real quick, can someone post a list of
> all ETs (everything under 200-ET is ok)
> in which the syntonic comma vanishes?

Here is a complete list of what I, to Paul's occasional annoyance, call the "standard" ets which have 81/80 in the kernel:

5 7 12 19 24 26 31 36 38 43 45 50 55 57 62 67 69 74 76 81
86 88 93 98 100 105 117 129

🔗Guiseppi Mendoza <guiseppi@mendozadil.freeserve.co.uk>

On Fri, 08 Feb 2002 22:00:15 -0800, SOMEONE articulated, I'd better
not say who :

>hey i was about to say that!

Either I was wrong, or I read correctly the triggers for a trick
question ;)

"Pipeline in the pipeline for piping" ;)

http://www.ampcast.com/guiseppimendoza
http://www.ampfea.org/sln/browse.php?num=3&a_id=132

🔗Guiseppi Mendoza <guiseppi@mendozadil.freeserve.co.uk>

On Sat, 09 Feb 2002 06:12:18 -0000, SOMEONE articulated, I'd better
not say who :

>Here is a complete list of what I, to Paul's occasional annoyance, call the "standard" ets which have 81/80 in the kernel:

You forgot the comma's, observe:

5, 7, 12, 19, 24, 26, 31, 36, 38, 43, 45, 50, 55, 57, 62, 67, 69, 74,
76, 81, 86, 88, 93, 98, 100, 105, 117, 129

(oh dear ;)

"Pipeline in the pipeline for piping" ;)

http://www.ampcast.com/guiseppimendoza
http://www.ampfea.org/sln/browse.php?num=3&a_id=132

🔗monz <joemonz@yahoo.com>

hey Guiseppi,

> From: Guiseppi Mendoza <guiseppi@mendozadil.freeserve.co.uk>
> To: <tuning@yahoogroups.com>
> Sent: Friday, February 08, 2002 10:55 PM
> Subject: Re: [tuning] Re: vanishing comma caper
>
>
> On Sat, 09 Feb 2002 06:12:18 -0000, SOMEONE articulated,
> I'd better not say who :

why not? (it was Gene. THANKS very much for this, Gene!)

> > Here is a complete list of what I, to Paul's occasional
> > annoyance, call the "standard" ets which have 81/80 in
> > the kernel:
>
> 5 7 12 19 24 26 31 36 38 43 45 50 55 57 62 67 69 74 76 81
> 86 88 93 98 100 105 117 129
>
> You forgot the comma's, observe:
>
> 5, 7, 12, 19, 24, 26, 31, 36, 38, 43, 45, 50, 55, 57, 62,
> 67, 69, 74, 76, 81, 86, 88, 93, 98, 100, 105, 117, 129

but that's because i asked for all the temperaments in
which the commas v a n i s h !!! get it? :)

(you probably never intended it, Gene, but in hindsight
it seems pretty clever!)

-monz

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🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > hey, real quick, can someone post a list of
> > all ETs (everything under 200-ET is ok)
> > in which the syntonic comma vanishes?
>
> Here is a complete list of what I, to Paul's occasional annoyance,
call the "standard" ets which have 81/80 in the kernel:
>
> 5 7 12 19 24 26 31 36 38 43 45 50 55 57 62 67 69 74 76 81
> 86 88 93 98 100 105 117 129

my annoyance stems from the fact that gene (i believe) completely
ignores the approximation to the consonant 5/3 in this reckoning. as
the syntonic comma arises probably even more often as the difference
between three 3/2s and a 5/3, rather than as the difference between
four 3/2s and a 5/4, gene's method seems to involve a musically
unwarranted mathematical convenience.

in other words, there are often different 'valid' ways of using an
equal temperament, some in which the syntonic comma vanishes, some in
which it doesn't.

76 is one of my favorite examples. it doesn't take much effort to
come up with two perfectly nice-sounding ways of using 76, one in
which the syntonic comma vanishes, and one in which it doesn't vanish.

the equal temperaments where the answer is a clear-cut 'yes, it
vanishes' in my view are the ones along the line connecting 12 with
26 in this graph:

/tuning/files/perlich/equaltemp.jpg

as well as very small integer multiples of the smaller ones.

🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 12:49 PM
> Subject: [tuning] Re: vanishing comma caper
>
>
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > hey, real quick, can someone post a list of
> > > all ETs (everything under 200-ET is ok)
> > > in which the syntonic comma vanishes?
> >
> > Here is a complete list of what I, to Paul's occasional annoyance,
> > call the "standard" ets which have 81/80 in the kernel:
> >
> > 5 7 12 19 24 26 31 36 38 43 45 50 55 57 62 67 69 74 76 81
> > 86 88 93 98 100 105 117 129
>
> my annoyance stems from the fact that gene (i believe) completely
> ignores the approximation to the consonant 5/3 in this reckoning. as
> the syntonic comma arises probably even more often as the difference
> between three 3/2s and a 5/3, rather than as the difference between
> four 3/2s and a 5/4, gene's method seems to involve a musically
> unwarranted mathematical convenience.
>
> in other words, there are often different 'valid' ways of using an
> equal temperament, some in which the syntonic comma vanishes, some in
> which it doesn't.
>
> 76 is one of my favorite examples. it doesn't take much effort to
> come up with two perfectly nice-sounding ways of using 76, one in
> which the syntonic comma vanishes, and one in which it doesn't vanish.

hey, paul, thanks for elaborating on this. i was wondering
what your "annoyance" was, and this is very illuminating.

> the equal temperaments where the answer is a clear-cut 'yes, it
> vanishes' in my view are the ones along the line connecting 12 with
> 26 in this graph:
>
> /tuning/files/perlich/equaltemp.jpg

ok, got it!

... what's that number under the 69? is it 88?

can you make another version of this graph making the numbers
a couple of font sizes smaller, so they don't collide?
this is one of my favorites of all the graphics you've made.

> as well as very small integer multiples of the smaller ones.

huh? i'm sure i'd understand with a few examples. thanks.

-monz

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🔗clumma <carl@lumma.org>

>/tuning/files/perlich/equaltemp.jpg

Good one, Paul! This takes the 90-degree graphs by so many
authors (Wilson, Dave Hill) to the next level!

Howabout a version with smaller fonts, so the numbers don't
overlap? And maybe a smaller version in terms of pixels,
for those of us without 900 lines of vertical?

>as well as very small integer multiples of the smaller ones.

Not following the syntonic comma discussion here. Are you
saying that Gene's list only applies when the syntonic comma
is 4(3:2)=1(5:4), missing ets where it's defined on the minor
third? In this case, the lists would only differ on ets
which were not 5-limit consistent, right?

-Carl

🔗monz <joemonz@yahoo.com>

hi Carl,

me to Paul:

> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 1:22 PM
> Subject: Re: [tuning] Re: vanishing comma caper
>
>
> can you make another version of this graph making the numbers
> a couple of font sizes smaller, so they don't collide?
> this is one of my favorites of all the graphics you've made.

you to Paul:

> From: clumma <carl@lumma.org>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 1:25 PM
> Subject: [tuning] Re: vanishing comma caper
>
>
> >/tuning/files/perlich/equaltemp.jpg
>
> Good one, Paul! This takes the 90-degree graphs by so many
> authors (Wilson, Dave Hill) to the next level!
>
> Howabout a version with smaller fonts, so the numbers don't
> overlap? And maybe a smaller version in terms of pixels,
> for those of us without 900 lines of vertical?

w e sure are "in tune" today! ;-)

-monz

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🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> ... what's that number under the 69? is it 88?

yes. 88 = 69 + 19.

> can you make another version of this graph making the numbers
> a couple of font sizes smaller, so they don't collide?

maybe . . . i'll have to dive into matlab-techie-land :(

> this is one of my favorites of all the graphics you've made.

thanks.

> > as well as very small integer multiples of the smaller ones.
>
> huh? i'm sure i'd understand with a few examples. thanks.

24 is an example, since it 'collapses' to 12 in the 5-limit.

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "clumma" <carl@l...> wrote:
> >/tuning/files/perlich/equaltemp.jpg
>
> Good one, Paul! This takes the 90-degree graphs by so many
> authors (Wilson, Dave Hill) to the next level!
>
> Howabout a version with smaller fonts, so the numbers don't
> overlap?

you and monz have convinced me to try.

> And maybe a smaller version in terms of pixels,
> for those of us without 900 lines of vertical?

maybe . . .

> Not following the syntonic comma discussion here. Are you
> saying that Gene's list only applies when the syntonic comma
> is 4(3:2)=1(5:4), missing ets where it's defined on the minor
> third?

right.

> In this case, the lists would only differ on ets
> which were not 5-limit consistent, right?

right.

🔗genewardsmith <genewardsmith@juno.com>

🔗paulerlich <paul@stretch-music.com>

🔗dkeenanuqnetau <d.keenan@uq.net.au>

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > also look at this one, a 'zoomed-out' view on which 7-equal,
> 8-equal,
> > 9-equal, and 10-equal appear:
> >
> > /tuning/files/perlich/equaltemp2.jpg
>
> Hey Paul,
>
> There must be something wrong. This chart says that 12-tET has a
wide
> major third and implies that the unqualified major third is the
4:5.
> ;-)

great zinger, dave!

🔗paulerlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

----- Original Message -----
From: paulerlich <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, February 13, 2002 11:51 PM
Subject: [tuning] Re: vanishing comma caper

> --- In tuning@y..., "clumma" <carl@l...> wrote:
> > >/tuning/files/perlich/equaltemp.jpg
> >
> > Good one, Paul! This takes the 90-degree graphs by so many
> > authors (Wilson, Dave Hill) to the next level!
> >
> > Howabout a version with smaller fonts, so the numbers don't
> > overlap? And maybe a smaller version in terms of pixels,
> > for those of us without 900 lines of vertical?
>
> /tuning/files/perlich/lumma.gif

thanks, paul!! hmmm ... seeing it in this nice small version
makes me wonder now: is there any rhyme or reason to the way
different ETs group together along various linear axis here?

-monz

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🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> thanks, paul!! hmmm ... seeing it in this nice small version
> makes me wonder now: is there any rhyme or reason to the way
> different ETs group together along various linear axis here?
>
>
>
> -monz

you betcha! this was all covered around the time i made the original
postings, and earlier by herman miller:

/tuning/topicId_29265.html#29650

🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, February 14, 2002 12:25 AM
> Subject: [tuning] Re: vanishing comma caper
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > thanks, paul!! hmmm ... seeing it in this nice small version
> > makes me wonder now: is there any rhyme or reason to the way
> > different ETs group together along various linear axis here?
> >
> > -monz
>
> you betcha! this was all covered around the time i made the original
> postings, and earlier by herman miller:
>
> /tuning/topicId_29265.html#29650

excellent!

i've used this info to make an adaptation of paul's graph
which i've placed, along with explanatory comment, in my
newly updated "equal temperament" Dictionary entry:
http://www.ixpres.com/interval/dict/eqtemp.htm

-monz

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🔗clumma <carl@lumma.org>

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > From: paulerlich <paul@s...>
> > To: <tuning@y...>
> > Sent: Thursday, February 14, 2002 12:25 AM
> > Subject: [tuning] Re: vanishing comma caper
> >
> >
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > > thanks, paul!! hmmm ... seeing it in this nice small version
> > > makes me wonder now: is there any rhyme or reason to the way
> > > different ETs group together along various linear axis here?
> > >
> > > -monz
> >
> > you betcha! this was all covered around the time i made the
original
> > postings, and earlier by herman miller:
> >
> > /tuning/topicId_29265.html#29650
>
>
> excellent!
>
> i've used this info to make an adaptation of paul's graph
> which i've placed, along with explanatory comment, in my
> newly updated "equal temperament" Dictionary entry:
> http://www.ixpres.com/interval/dict/eqtemp.htm
>
>
>
> -monz

nice!!

be careful, monz . . . you didn't put in an appropriate comma for
kleismic, which is easily remedied, as it's the kleisma . . . but for
miracle? can miracle really make sense in the 5-limit?

🔗monz <joemonz@yahoo.com>

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, February 14, 2002 12:27 PM
> Subject: [tuning] Re: vanishing comma caper
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > i've used this info to make an adaptation of paul's graph
> > which i've placed, along with explanatory comment, in my
> > newly updated "equal temperament" Dictionary entry:
> > http://www.ixpres.com/interval/dict/eqtemp.htm
> >
> >
>
> nice!!

thanks.

> be careful, monz . . . you didn't put in an appropriate comma for
> kleismic, which is easily remedied, as it's the kleisma . . .

ah, i know . . . it's because i can never remember the ratio for
the kleisma off the top of my head. i'll look it up and add it
tonight.

> but for miracle? can miracle really make sense in the 5-limit?

hmmm . . . good point. i was just following Gene's lead when
he mentioned that 41,72,31 were all on the MIRACLE line.

-monz

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🔗genewardsmith <genewardsmith@juno.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> > but for miracle? can miracle really make sense in the 5-limit?
>
>
> hmmm . . . good point. i was just following Gene's lead when
> he mentioned that 41,72,31 were all on the MIRACLE line.

h31^h41 = 34171875/33554432, Ampersand's comma. This is the basic
5-limit comma of miracle, but if you object to miracle as the name of a 5-limit temperament, you could always call it ampersand.

🔗paulerlich <paul@stretch-music.com>

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > > but for miracle? can miracle really make sense in the 5-limit?
> >
> >
> > hmmm . . . good point. i was just following Gene's lead when
> > he mentioned that 41,72,31 were all on the MIRACLE line.
>
> h31^h41 = 34171875/33554432, Ampersand's comma. This is the basic
> 5-limit comma of miracle, but if you object to miracle as the name
of a 5-limit temperament, you could always call it ampersand.

sounds good. anyone know who ampersand was, and what he talked about?