accuracy and notation

Accuracy
--------

Gene Ward Smith wrote...
>Is there general agreement among JI people that +-1/2 cent
>is close enough? I would think doing better would be very
>hard.

I'm still not clear on what you guys are discussing. The
required accuracy is wildly different in different situations.
The situation requiring the most accuracy that I am aware of
is the tuning of very fine pianos. It has been shown to my
satisfaction that piano tuners make adjustments as fine as
+- 0.1 or maybe even 0.05 cents. At least, I have it from the
fellow who makes Sanderson Accutuners that such accuracy is
needed. Such differences are inaudible except in the beating
of high harmonics when multiple strings are sounded together.
Adjustments at this scale are heard as a change in the _timbre_
of the instrument to most listeners (who can hear it at all).
And importantly, such adjustments may NOT necessarily be in
the direction of JI (or equivalently, defining the fundamental
of the pitches being tuned to this degree of accuracy is
somewhat arbitrary).

Another situation needing this accuracy may be the use of
electronic timbres for particular effects such as beat-counting
in extended-duration music (see recent mention of LaMonte
Young's installations on this list).

For ensembles of free-pitched monophonic instruments, the
most accurate examples I know of are brass quintets playing
5-limit music, maybe to +- 0.5 cents for sustained chords
in optimum voicings. Barbershop quartets may get +- 1 cent
on 7-limit otonalities. This is to say that at some time
during the sustained chord this accuracy is reached -- not
necessarily that the entire duration of the chord stays
within this range of JI (in fact I believe it is very important
to music to have 'noisy' 'attack effects' that help listeners
pick up new events).

For mixed ensembles playing music of a normal "Western" pace,
+- 2-5 cents seems about as good as can be done or heard.

None of this means, as far as I can tell, that applying these
random errors to a target of, say, 22-et, will sound the same
as applying them to a target of JI. So the whole 'they don't
play within that accuracy anyway' thing is a wash. And as
Paul/Ara pointed out (why do you use pseudonyms, Paul? -- it's
very rude), you can notate in 22 or what have you and still
bend to JI as well as any of the examples above (brass quintets,
barbershop quartets, etc.) bend from 12.

Notation
--------

As a composer and performer, my goals for the ideal notation of
melodic-harmonic music would be:

(1) Notate the basic scale as simply as possible. For example:
successive movements on a staff give successive steps through
the scale, one letter for each member of the scale, etc.

(2) Define accidentals only as needed to uniquely ennumerate
all the chords you want from their nearest approximation in
scale steps of the basic melodic scale.

(3) Being able to notate all the keys of the melodic scale
(its "Cartesian cross set") at once is a nice-to-have, which
is seems easy to commensurate with (1) if your basic scale is
an MOS (conventional notation, for example, conflates 25:24
and 2187:2048 in its accidentals). Key information can also
be specified with a clef.

If you want only JI chords, the accidentals can be numbers
showing the vertical relationships, and common tones can be
shown by connecting pitches between chords with a line.

If I wanted to write for an ensemble of instruments and
actually get my music performed, I would make an electronic
version. And if I still wanted an acoustic version I would
take the electronic version to them, with versions for each
instrument where the given instrument is on one one stereo
channel only, and the rest of the mix on the other. The
balance knob on the performers' home stereo then becomes a
mixer allowing for invaluable practice opportunities.

Then, judging from their willingness, and the rehearsal time
available, I would choose whether to issue parts in
xenharmonic notation (see items 1-4) or in the nearest
meantone (up to 31) approximation (tab). Where things break
down, your desired common tones can be linked with lines on
the score.

Until a musical culture springs up around extended meantone,
porcupine, pajara, or miracle, I would refrain from
"standardizing" notation based on 31, 15, 22, or 72.

If these 72-toners can actually play, well, let's face it:
they can't. If somebody wants to prove me wrong, it would be
quite simple: send them a score for a single, 11-limit
otonality and post the recording here. Or point me to an
existing recording where 11-limit otonalities can be heard.

-Carl

Carl,

Just a tiny thing in your post, most all of which I found quite
interesting:

--- In tuning@y..., Carl Lumma <carl@l...> wrote:
> And as Paul/Ara pointed out (why do you use pseudonyms, Paul? --
> it's very rude)

Ara is the keyboard player in Paul's band, and I think Paul has both
referred to him in topics, as well as possibly posted from Ara's
home, therefore giving a different user name.

I could be wrong about the details, but I would be very, very
surprised if Paul is purposely posting with a pseudonym. And Paul can
chime in on this if he wants...

Cheers,
Jon

Carl,

If you don't mind me asking, what exactly do you mean by this:

"If these 72-toners can actually play, well, let's face it: they
can't."

The "72-toners" I've played with, and I specifically mean Mat and Joe
Maneri, are hands down two of the finest musicians I've ever played
with... and I've been blessed over the years to have had the
opportunity to play with some great ones.

I read something like this and I say, well he must mean something
besides what he wrote, but what you wrote doesn't seem to leave much
elbowroom for misinterpretation:

"If these 72-toners can actually play, well, let's face it: they
can't. If somebody wants to prove me wrong, it would be quite simple:
send them a score for a single, 11-limit otonality and post the
recording here. Or point me to an existing recording where 11-limit
otonalities can be heard."

Everyone's entitled to their opinions of course, but to my mind this
is such a ridiculous statement two or three times over, and if I'm
missing or misreading something I sure would like to know what it
is...

take care,

--Dan Stearns

----- Original Message -----
From: "Carl Lumma" <carl@lumma.org>
To: <tuning@yahoogroups.com>
Sent: Sunday, March 03, 2002 12:36 PM
Subject: [tuning] accuracy and notation

> Accuracy
> --------
>
> Gene Ward Smith wrote...
> >Is there general agreement among JI people that +-1/2 cent
> >is close enough? I would think doing better would be very
> >hard.
>
> I'm still not clear on what you guys are discussing. The
> required accuracy is wildly different in different situations.
> The situation requiring the most accuracy that I am aware of
> is the tuning of very fine pianos. It has been shown to my
> satisfaction that piano tuners make adjustments as fine as
> +- 0.1 or maybe even 0.05 cents. At least, I have it from the
> fellow who makes Sanderson Accutuners that such accuracy is
> needed. Such differences are inaudible except in the beating
> of high harmonics when multiple strings are sounded together.
> Adjustments at this scale are heard as a change in the _timbre_
> of the instrument to most listeners (who can hear it at all).
> And importantly, such adjustments may NOT necessarily be in
> the direction of JI (or equivalently, defining the fundamental
> of the pitches being tuned to this degree of accuracy is
> somewhat arbitrary).
>
> Another situation needing this accuracy may be the use of
> electronic timbres for particular effects such as beat-counting
> in extended-duration music (see recent mention of LaMonte
> Young's installations on this list).
>
> For ensembles of free-pitched monophonic instruments, the
> most accurate examples I know of are brass quintets playing
> 5-limit music, maybe to +- 0.5 cents for sustained chords
> in optimum voicings. Barbershop quartets may get +- 1 cent
> on 7-limit otonalities. This is to say that at some time
> during the sustained chord this accuracy is reached -- not
> necessarily that the entire duration of the chord stays
> within this range of JI (in fact I believe it is very important
> to music to have 'noisy' 'attack effects' that help listeners
> pick up new events).
>
> For mixed ensembles playing music of a normal "Western" pace,
> +- 2-5 cents seems about as good as can be done or heard.
>
> None of this means, as far as I can tell, that applying these
> random errors to a target of, say, 22-et, will sound the same
> as applying them to a target of JI. So the whole 'they don't
> play within that accuracy anyway' thing is a wash. And as
> Paul/Ara pointed out (why do you use pseudonyms, Paul? -- it's
> very rude), you can notate in 22 or what have you and still
> bend to JI as well as any of the examples above (brass quintets,
> barbershop quartets, etc.) bend from 12.
>
>
> Notation
> --------
>
> As a composer and performer, my goals for the ideal notation of
> melodic-harmonic music would be:
>
> (1) Notate the basic scale as simply as possible. For example:
> successive movements on a staff give successive steps through
> the scale, one letter for each member of the scale, etc.
>
> (2) Define accidentals only as needed to uniquely ennumerate
> all the chords you want from their nearest approximation in
> scale steps of the basic melodic scale.
>
> (3) Being able to notate all the keys of the melodic scale
> (its "Cartesian cross set") at once is a nice-to-have, which
> is seems easy to commensurate with (1) if your basic scale is
> an MOS (conventional notation, for example, conflates 25:24
> and 2187:2048 in its accidentals). Key information can also
> be specified with a clef.
>
> If you want only JI chords, the accidentals can be numbers
> showing the vertical relationships, and common tones can be
> shown by connecting pitches between chords with a line.
>
> If I wanted to write for an ensemble of instruments and
> actually get my music performed, I would make an electronic
> version. And if I still wanted an acoustic version I would
> take the electronic version to them, with versions for each
> instrument where the given instrument is on one one stereo
> channel only, and the rest of the mix on the other. The
> balance knob on the performers' home stereo then becomes a
> mixer allowing for invaluable practice opportunities.
>
> Then, judging from their willingness, and the rehearsal time
> available, I would choose whether to issue parts in
> xenharmonic notation (see items 1-4) or in the nearest
> meantone (up to 31) approximation (tab). Where things break
> down, your desired common tones can be linked with lines on
> the score.
>
> Until a musical culture springs up around extended meantone,
> porcupine, pajara, or miracle, I would refrain from
> "standardizing" notation based on 31, 15, 22, or 72.
>
> If these 72-toners can actually play, well, let's face it:
> they can't. If somebody wants to prove me wrong, it would be
> quite simple: send them a score for a single, 11-limit
> otonality and post the recording here. Or point me to an
> existing recording where 11-limit otonalities can be heard.
>
> -Carl
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
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> CLICK HERE to search
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>

Dan,

Please understand that this was not a jab at Maneri, or any
other 72-tone instrumentalist. I was trying to clarify
things for people on this list. Producing extended JI in an
ensemble of free-pitched instruments is very, very, very hard.
Producing extended JI and keeping a good standard of pitch is
even harder. But playing in exact 72 is _impossible_. So
when people here say 72, they mean extended JI notated as if
the 225:224 vanishes. When Maneri says 72 (from the interview
I read), he means 6th tones. There's a difference.

I think it can be done, but the fact that it hasn't yet been
done above the 7-limit is one thing you need to consider when
coming up with optimal notation schemes.

-Carl

>If you don't mind me asking, what exactly do you mean by this:
>
>"If these 72-toners can actually play, well, let's face it: they
>can't."
>
>The "72-toners" I've played with, and I specifically mean Mat and
>Joe Maneri, are hands down two of the finest musicians I've ever
>played with... and I've been blessed over the years to have had
>the opportunity to play with some great ones.

No Dan, I didn't mean they can't play good music. I meant they
can't do what people claim they can, which is play accurately in
72-et. I understand that extended JI wasn't Maneri's goal, and
that's fine, but if these guys can play accurate 72, it will be
very easy to make me eat my hat -- point me to a recording of an
11-limit otonality.

-Carl

hi Carl,

> From: Carl Lumma <carl@lumma.org>
> To: <tuning@yahoogroups.com>
> Sent: Monday, March 04, 2002 9:53 AM
> Subject: [tuning] Re: accuracy and notation
>
>
> Dan,
>
> Please understand that this was not a jab at Maneri, or any
> other 72-tone instrumentalist. I was trying to clarify
> things for people on this list. Producing extended JI in an
> ensemble of free-pitched instruments is very, very, very hard.
> Producing extended JI and keeping a good standard of pitch is
> even harder. But playing in exact 72 is _impossible_. So
> when people here say 72, they mean extended JI notated as if
> the 225:224 vanishes. When Maneri says 72 (from the interview
> I read), he means 6th tones. There's a difference.
>
> I think it can be done, but the fact that it hasn't yet been
> done above the 7-limit is one thing you need to consider when
> coming up with optimal notation schemes.

see my latest post to tuning-math, and my addition near the
end of the description of my version of HEWM notation
(just before the part about Daniel Wolf's version)
http://www.ixpres.com/interval/dict/hewm.htm
concerning the differences between the JI and 72edo versions
of HEWM.

72edo simplifies the notation, because of the fact that
equivalencies of duplicated symbols sometimes allows them
to cancel each other out, leaving a simpler glyph for
a complicated ratio. because of the incommensurability of
higher powers of prime-factors, the JI version can never
do this, and must always include all the symbols for accuracy.

when you saying "there's a difference", are you referring
simply to the different perspectives of EDO vs. JI, or
is there more to that? please clarify and expound.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

>Ara is the keyboard player in Paul's band, and I think Paul has both
>referred to him in topics, as well as possibly posted from Ara's
>home, therefore giving a different user name.
>
>I could be wrong about the details, but I would be very, very
>surprised if Paul is purposely posting with a pseudonym. And Paul can
>chime in on this if he wants...

Yeah, I've met Ara. Absolutely a fantastic fellow (*wave*, hello
Ara!). I just don't think those two messages were Ara. If Paul was
using his e-mail address, it just would have taken a name at the
bottom of the message to be in good form. No huge deal, just thought
I'd mention it.

-Carl

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> Carl,
>
> Just a tiny thing in your post, most all of which I found quite
> interesting:
>
> --- In tuning@y..., Carl Lumma <carl@l...> wrote:
> > And as Paul/Ara pointed out (why do you use pseudonyms, Paul? --
> > it's very rude)
>
> Ara is the keyboard player in Paul's band, and I think Paul has
both
> referred to him in topics, as well as possibly posted from Ara's
> home, therefore giving a different user name.
>
> I could be wrong about the details, but I would be very, very
> surprised if Paul is purposely posting with a pseudonym. And Paul
can
> chime in on this if he wants...
>
> Cheers,
> Jon

thanks jon.

i don't recall this ever happening before, but you're quite correct.

i was at ara's home. he has a yahoo e-mail address, and is subscribed
to this list. therefore, when i logged on, i was taken straight to
the tuning list website, without having to sign in. by force of
habit, i simply posted, unaware of the 'pseudonym' that my message
would appear under.

so, my apologies to ara, carl, or whoever this was rude to.

and good on you, carl, for recognizing my writing!

Carl,

Both Mat and Joe have extraordinary ears, and a rare technical command
as well. I'd reckon both play as accurate a 72 as they do a 12--plenty
accurate enough in other words. But this is not what their music is
all about. Neither are 11-limit otonalities. So it's irrelevant to
me... these are not the types of things you're not going to find them
in their recordings, not by a long shot!

Something you may or may not know, is that Joe has a specially
designed 72-tet keyboard in the room he composes and practices in...
and if there's something he wants to check or try beyond what he's
able to hear in his head or play on his reeds, it's right there... he
knows what 72-tet sounds like...

I'd say trust me (as I was there and have some experiential basis in
reality for what I'm telling you), but I know better! Oh well, know
that I understand what you're getting at a bit better, I don't much
care one way or the other anyway.

take care,

--Dan Stearns

----- Original Message -----
From: "Carl Lumma" <carl@lumma.org>
To: <tuning@yahoogroups.com>
Sent: Monday, March 04, 2002 9:25 AM
Subject: [tuning] Re: accuracy and notation

> >If you don't mind me asking, what exactly do you mean by this:
> >
> >"If these 72-toners can actually play, well, let's face it: they
> >can't."
> >
> >The "72-toners" I've played with, and I specifically mean Mat and
> >Joe Maneri, are hands down two of the finest musicians I've ever
> >played with... and I've been blessed over the years to have had
> >the opportunity to play with some great ones.
>
> No Dan, I didn't mean they can't play good music. I meant they
> can't do what people claim they can, which is play accurately in
> 72-et. I understand that extended JI wasn't Maneri's goal, and
> that's fine, but if these guys can play accurate 72, it will be
> very easy to make me eat my hat -- point me to a recording of an
> 11-limit otonality.
>
> -Carl
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> FREE COLLEGE MONEY
> CLICK HERE to search
> 600,000 scholarships!
> http://us.click.yahoo.com/iZp8OC/4m7CAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
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>
> You do not need web access to participate. You may subscribe
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>
>

>But this is not what their music is all about. Neither are
>11-limit otonalities. So it's irrelevant to me... these are
>not the types of things you're not going to find them
>in their recordings, not by a long shot!

I know, and acknowledged it in both of my posts.

>Something you may or may not know, is that Joe has a
>specially designed 72-tet keyboard in the room he composes
>and practices in... and if there's something he wants to
>check or try beyond what he's able to hear in his head or
>play on his reeds, it's right there... he knows what 72-tet
>sounds like...

I didn't know that. Cool!

72 can sound like a lot of thing, Dan. I doubt Maneri,
or anyone else on this planet, has heard a fraction of
them.

>I'd say trust me (as I was there and have some experiential
>basis in reality for what I'm telling you), but I know better!

Good. Because if they haven't any practice playing in
extended JI, the chances of them doing it out-of-the-box
from JI notated in 72 is nil, nil, plus nil. It doesn't
mean they'll never do it. They might pick it up relatively
quickly. But there will be rehearsal time involved, and
enough of it to be a potential problem for any composer
trying to get his work performed. This, Dan, I know from
experience. That was all I was saying.

-Carl

> when you saying "there's a difference", are you referring
> simply to the different perspectives of EDO vs. JI, or
> is there more to that? please clarify and expound.

I don't know what EDO vs. JI means here, but hopefully my
subsequent two posts in this thread have (or will) clear
up your questions. If not, please re-phrase, and I'll
try my best to explain.

-Carl

--- In tuning@y..., "clumma" <carl@l...> wrote:

> Good. Because if they haven't any practice playing in
> extended JI, the chances of them doing it out-of-the-box
> from JI notated in 72 is nil, nil, plus nil. It doesn't
> mean they'll never do it. They might pick it up relatively
> quickly. But there will be rehearsal time involved, and
> enough of it to be a potential problem for any composer
> trying to get his work performed. This, Dan, I know from
> experience. That was all I was saying.

on the other hand, so much of what maneri and the royal jelly dance
collective were doing *sounded* like 11-limit ji. i agree with monz
that the 11-limit ji implications of 72-equal are virtually
unavoidable.

>on the other hand, so much of what maneri and the royal jelly dance
>collective were doing *sounded* like 11-limit ji.

I'd better get up to speed on that, then.

>i agree with monz that the 11-limit ji implications of 72-equal are
>virtually unavoidable.

Well, you could play all day in the 5-limit or 7-limit... you have
to have music that supports it first. I'm saying, that may be enough.
Of course you have to notate this music, and 72 may be a logical way
to do that. But you could do it in 31, or even 12. I believe the
attraction of 11-limit JI, or lack thereof, is the gating factor here
for free-pitched ensembles, not 72. So to me, your statment is
equivalent for free-pitched ensembles to: "the 11-limit implications
of the pitch continuum are unavoidable". Which is, judging from the
rarity of 11-limit music, not true.

-Carl

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

> >i agree with monz that the 11-limit ji implications of 72-equal are
> >virtually unavoidable.
>
> Well, you could play all day in the 5-limit or 7-limit... you have
> to have music that supports it first. I'm saying, that may be
enough.

enough for what?

> Of course you have to notate this music, and 72 may be a logical way
> to do that. But you could do it in 31,

not unique for 11-limit consonances.

> or even 12.

ditto.

> I believe the
> attraction of 11-limit JI, or lack thereof, is the gating factor
here
> for free-pitched ensembles, not 72.

the gating factor? what does that mean? in regard to what?

> So to me, your statment is
> equivalent for free-pitched ensembles to: "the 11-limit implications
> of the pitch continuum are unavoidable".

absolutely not. if choosing intervals randomly from the pitch
continuum, there's only a 19% chance of being within 4 cents of an 11-
limit consonance. if choosing intervals randomly from 72-equal, that
goes up to 40%. and if you look at maneri's book, you'll note that
considerably more than 40% the vertical intervals landed on in his
exercises are the 11-limit ones. either this is a remarkable
coincidence, which would still reverberate in the music of his
students, or it is an indication of the intuitive 'attraction' of
these intervals. the only point here is that 72-equal trained
musicians do very often play clear 11-limit intervals, whether
they're aware of it or not -- and especially if you concentrate on
those who are aware of it, such as those from the sims/tenney rather
than the maneri school, you're certainly going to get far better
results than you did from the ensemble that played your piece at afmm.

>But you could do it in 31,
>
>not unique for 11-limit consonances.

Yeah, you have to go to 41. I'm a stickler
for uniquness. Still, non-uniqueness doesn't
prevent impressive 7-limit music notated in
12 (plenty o' b-shop doesn't obey extended-
meantone accidentals).

>>I believe the attraction of 11-limit JI, or lack thereof, is
>>the gating factor here for free-pitched ensembles, not 72.
>
>the gating factor? what does that mean? in regard to what?

Limiting factor. I realize we only say this at work.

-Carl

--- In tuning@y..., "clumma" <carl@l...> wrote:
> >But you could do it in 31,
> >
> >not unique for 11-limit consonances.
>
> Yeah, you have to go to 41.

still not unique for 11-limit consonances. 11/10 "=" 10/9.

> I'm a stickler
> for uniquness.

then you better take another look at 41. partch's diamond of 29 notes
becomes 27 notes in 41, and thus his whole 43-tone scale becomes the
full 41 tones.

> >>I believe the attraction of 11-limit JI, or lack thereof, is
> >>the gating factor here for free-pitched ensembles, not 72.
> >
> >the gating factor? what does that mean? in regard to what?
>
> Limiting factor.

still don't know how what this sentence means, or how it ties into
your argument.

clumma wrote:

> >But you could do it in 31,
> >
> >not unique for 11-limit consonances.
>
> Yeah, you have to go to 41. I'm a stickler
> for uniquness. Still, non-uniqueness doesn't
> prevent impressive 7-limit music notated in
> 12 (plenty o' b-shop doesn't obey extended-
> meantone accidentals).

Not 41. 10:9 =~ 11:10

Graham

> From: Carl Lumma <carl@lumma.org>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, March 07, 2002 9:35 PM
> Subject: [tuning] Re: accuracy and notation
>
>
> > [paul erlich, IIRC]
> > i agree with monz that the 11-limit ji implications of 72-equal are
> > virtually unavoidable.
>
> Well, you could play all day in the 5-limit or 7-limit... you have
> to have music that supports it first. I'm saying, that may be enough.
> Of course you have to notate this music, and 72 may be a logical way
> to do that. But you could do it in 31, or even 12. I believe the
> attraction of 11-limit JI, or lack thereof, is the gating factor here
> for free-pitched ensembles, not 72. So to me, your statment is
> equivalent for free-pitched ensembles to: "the 11-limit implications
> of the pitch continuum are unavoidable". Which is, judging from the
> rarity of 11-limit music, not true.

i think you're not entirely understanding what paul is
saying here.

he's referring to statements i've made about the Maneri/van Duyne
72edo ear-training book: with my foreknowledge of 11-limit JI
a n d how well 72edo approximates it, i found it impossible
to do the exercises in that book without "hearing" (in my mind)
the 11-limit JI implications.

i think your confusion is over the fact that paul and i are
n o t referring o n l y to ratios which include 11 as
a factor, but rather to e v e r y t h i n g within the
11-limit.

so when i saw an exercise in the Maneri book which has,
for example (and adapting to the ASCII notational transcription)
C Eb< , i found it i m p o s s i b l e not to "hear"
a 7:6 ratio.

-monz

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

/tuning/topicId_35176.html#35379

>
> so when i saw an exercise in the Maneri book which has,
> for example (and adapting to the ASCII notational transcription)
> C Eb< , i found it i m p o s s i b l e not to "hear"
> a 7:6 ratio.
>
>

***I guess the question is whether players *should* be trying
to "adjust" 72-tET *toward* Just as an *intention* or whether they
should be trying for *accurate* 6th tones and 12th tones.

??

Or is the distinction again the *3 Penny Opera* perhaps too little to
really worry about??

Oh Monz... I don't mind the chic lowercase, of course, but when you
*emphasize* could you use *this* or _this_ rather than t h i s??

I find t h a t v e r y d i f f i c u l t to read!

jp

>>>But you could do it in 31,
>>>
>>>not unique for 11-limit consonances.
>>
>>Yeah, you have to go to 41. I'm a stickler
>>for uniquness. Still, non-uniqueness doesn't
>>prevent impressive 7-limit music notated in
>>12 (plenty o' b-shop doesn't obey extended-
>>meantone accidentals).
>
>Not 41. 10:9 =~ 11:10

Oh, right. I was remembering the 9-limit for
some reason. You need to go to 58.

-Carl

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_35176.html#35379
>
> >
> > so when i saw an exercise in the Maneri book which has,
> > for example (and adapting to the ASCII notational
transcription)
> > C Eb< , i found it i m p o s s i b l e not to "hear"
> > a 7:6 ratio.
> >
> >
>
> ***I guess the question is whether players *should* be trying
> to "adjust" 72-tET *toward* Just as an *intention* or whether
they
> should be trying for *accurate* 6th tones and 12th tones.
>
> ??
>
> Or is the distinction again the *3 Penny Opera* perhaps too
little to
> really worry about??

i'm sticking with the latter. i'm going to take the "amazing randi"
point of view here, and i want to see an example, where the
music really moves along at a decent clip, and someone really
can play the difference between these two systems on a
conventional musical instrument. the pitches produced must be
measured in an *objective* manner.

how about simply *hearing* the difference? we should be able to
concoct some listening examples without too much trouble . . .
but let's conclude the "jerries" first, shall we?

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

/tuning/topicId_35176.html#35460

> >
> > Or is the distinction again the *3 Penny Opera* perhaps too
> little to
> > really worry about??
>
> i'm sticking with the latter. i'm going to take the "amazing randi"
> point of view here, and i want to see an example, where the
> music really moves along at a decent clip, and someone really
> can play the difference between these two systems on a
> conventional musical instrument. the pitches produced must be
> measured in an *objective* manner.
>
> how about simply *hearing* the difference? we should be able to
> concoct some listening examples without too much trouble . . .
> but let's conclude the "jerries" first, shall we?

***Good idea, Paul! But, I fear if Ezra Sims can't hear the
difference between 72-tET and Just, *I* won't be able to either...

jp

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> ***Good idea, Paul! But, I fear if Ezra Sims can't hear the
> difference between 72-tET and Just, *I* won't be able to either...

ezra sims may have been overly-ji-zealous in attempting a
retuning of bach, which is naive by either delaubenfels or
reinhard standards. does that mean he had no ear when it came
to his own music? not necessarily -- and arguing that it does
follow is tantamount to calling him a charlatan.