Re: [tuning] A common notation for JI and ETs

> From: dkeenanuqnetau <d.keenan@uq.net.au>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, February 23, 2002 12:16 AM
> Subject: [tuning] A common notation for JI and ETs (was: 27 & 58-EDO
Scavengers)
>
>
> ...
>
> We can have one consistent set of symbols for notating both JI and
> ETs. The previous sentence should probably be in flashing lights.
> I'll say it again.
>
> * WE CAN HAVE ONE SMALL SET OF SYMBOLS FOR NOTATING BOTH JI AND ETS *
>
> This seems like something we should have had a long time ago. Many
> thanks to Gene for pushing the idea.
>
> The beauty is, that with this choice of commas, there is no need to go
> past 19-limit for notating all the ETs of interest, well into the
> hundreds. 19-limit means we only need 6 new pairs of symbols. This is
> far fewer than Rapoport's 5-limit system as used in Scala. This is
> because Rapoport needs all those 1/n-comma symbols. Because the 17 and
> 19 commas are so small, we don't need these 1-step symbols.
>
> These 17 and 19 commas just happen to step down in size from the
> syntonic and septimal comma in an almost perfect trinary system!: 27c,
> 9c, 3c. <etc.>
>
> ...
>
> To get the best approximation of that chord in _any_ ET you would just
> omit the symbols for any commas that vanish in that ET, and replace
> any symbols for higher primes with those of lower primes that
> correspond to the same number of steps. And sometimes we may use
> _pairs_ of symbols for lower primes in place of those for a higher
> prime.
>
> For example, in 12-tET the best approximation (athough not a usable or
> recognisable approximation) of that complete 19-limit otonality is
> notated as.
> G:D:B:F:A:C:Eb:F#:G#:Bb
> We simply dropped all the comma symbols.
>
> Is not such a system very much worth having????????????

absolutely, yes.

is this not very much like what i've been doing all along? back
in the 1980s, when i was first developing my JI theories, i had
decided on a 19-limit because there seemed to be no real need
to go beyond it in constructing a very large and comprehensive
rational tuning system and notation, and later when i got interested
in EDOs my notational ideas followed along the same lines. what
you wrote here, Dave, looks very familiar to me.

see my HEWM page if not clear about my notations
http://www.ixpres.com/interval/hewm.htm

which, BTW, has a big new update on Daniel Wolf's notational ideas.

-monz

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

/tuning/topicId_34739.html#34739

>
> is this not very much like what i've been doing all along? back
> in the 1980s, when i was first developing my JI theories, i had
> decided on a 19-limit because there seemed to be no real need
> to go beyond it in constructing a very large and comprehensive
> rational tuning system and notation, and later when i got interested
> in EDOs my notational ideas followed along the same lines. what
> you wrote here, Dave, looks very familiar to me.
>
> see my HEWM page if not clear about my notations
> http://www.ixpres.com/interval/hewm.htm
>
> which, BTW, has a big new update on Daniel Wolf's notational ideas.
>

***That address is wrong.

It's:

http://www.ixpres.com/interval/dict/hewm.htm

JP

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, February 23, 2002 8:58 AM
> Subject: [tuning] Re: A common notation for JI and ETs
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> ...
>
> > see my HEWM page if not clear about my notations
> > <incorrect URL snipped>
> >
> > which, BTW, has a big new update on Daniel Wolf's notational ideas.
> >
>
> ***That address is wrong.
>
> It's:
>
> http://www.ixpres.com/interval/dict/hewm.htm

oops... my bad. thanks, Joe!

-monz

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

> see my HEWM page if not clear about my notations
> http://www.ixpres.com/interval/hewm.htm

It's not there. Do you use the same commas up to the 19 limit?

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> is this not very much like what i've been doing all along? back
> in the 1980s, when i was first developing my JI theories, i had
> decided on a 19-limit because there seemed to be no real need
> to go beyond it in constructing a very large and comprehensive
> rational tuning system and notation, and later when i got interested
> in EDOs my notational ideas followed along the same lines. what
> you wrote here, Dave, looks very familiar to me.
>
> see my HEWM page if not clear about my notations
> http://www.ixpres.com/interval/dict/hewm.htm
>
> which, BTW, has a big new update on Daniel Wolf's notational ideas.

Thanks for that. It was great to read Wolf's ideas. Yes, this idea has
been popular for notating _rational_ scales for a long time, but
everyone seems to use different commas once we get past prime 11.

I can find nothing on your excellent web page that even suggests that
this notation could be or should be applied to ETs. And I don't see
where you say 19 is enough (for ETs). Have you said these things
somewhere else?

The only such suggestions I know of are those recent ones by George
Secor, who stops at 11 and does not keep the commas separate, so that
his notation is not suitable for notating rational scales, and that of
Rapoport who in the conclusion of his paper, in which he develops his
ET-notation based entirely on 5-limit commas, (the one used (slightly
modified) by Manuel in Scala), writes:

"The use of any of the above signs may not completely mitigate the
complications inherent in this manner of notating close approximations
to just tunings ... More concise signs are needed which represent the
higher harmonics better ..."

Neither of these authors specifically suggest a common notation for JI
and ETs.

If anyone is aware of anyone else working on such a common
JI/ET notation please let us know. Maybe Rapoport went on to do
something in this regard.

The application of 19-limit JI notation to ETs wipes out the
disagreement about which commas to use, once we realise that optimal
accidentals form a trinary sequence, and that we want the commas to
vanish in 12-tET, or a 12-tone Pythagorean chain.

> From: dkeenanuqnetau <d.keenan@uq.net.au>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 25, 2002 12:26 AM
> Subject: [tuning] Re: A common notation for JI and ETs
>
>
> I was previously able to reject the use of \ / as comma symbols and
> therefore the whole (for want of a better term) "European" system of
> \/ <> v^ for 5, 7 11. If they make \ / not be left-right confusable in
> real life (as above), then I can't reject them. Those guys seem pretty
> adamant about keeping v^ for quarter tones (and hence the 11-diesis)
> and it fits with George Secor's stuff too. The fact that Manuel Op de
> Coul isn't about to change Scala to correspond to the Sims notation,
> is fairly serious.
>
> ...
>
> So Monz, how about you stop supporting + and - as accidentals on
> actual scores and consider them only as ASCII approximations of \ and
> /-with-a short-vertical-line-thru-it?
>
> I'd hate it if the whole idea of notating ETs the same as 19-limit JI
> got rejected on either side of the Atlantic just because it chose the
> wrong set of symbols.

i'd known all along about the fairly long tradition of using
arrows for 1/4-tones, which is one reason why i've adhered so
strongly to keeping v^ for the 1/4-tones.

\ and /-with-a short-vertical-line-thru-it are essentially,
to my mind, the same as -+ . see the commentary i wrote about
Daniel Wolf's notation (and also Wolf's update) at:
http://www.ixpres.com/interval/dict/hewm.htm

it seems to me that the essential problem with using -+ in scores
is that people feel that the horizontal lines will get lost among
the staff lines and other horizontal symbols (for example, the
minus sign looks exacly like the "tenuto" symbol). the symbols
you propose are simply -+ with the horizontal line slanted ...
that's fine with me for score notation. and -+ remain for ASCII.

so, are we reaching a consensus on notation now? i sure hope so,
because i'm not planning to change anything i've written either.

> > > The only feasible way of notating all ETs so that the notation
> > > indicates shifts from 12-tET, is the Johnny Reinhardt method of
> > > writing the + or - cents next to the notes.
> >
> > I imagine some other unit than cents would be feasible, for
> starters.
>
> Depends what you mean by "feasible". I meant "sufficiently accurate
> while being easily understood by performers with ordinary training".

i think Gene meant, for example, 612edo, which gives 5-limit ratios
with hardly any error and so is great as an integer measurement.
it's a lot better than 1200edo (cents) in that respect. for that
matter, for 5-limit, 118edo is terrific. see
http://www.ixprs.com/interval/dict/eqtemp.htm

-monz

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--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> Because cents are already a standard, and even if they weren't, most
> people are used to understanding and estimating percentages in daily
> life. Performers will far more easily understand, estimate and produce
> a certain _percent_ of the distance between 12-tET notes, compared to
> a certain number of fifty-oneths of it.

Gene: I doubt it. Do you really think someone can learn to make something 37 cents
above 300 by mental math?

Johnny: It may be that I am misunderstanding something, but yes, 37 above a notehead at 300 (a C compared down to an A) is rather easy to prepare mentally. Frankly, there seems to be a lot of spinning wheels with notation. I think it is a red herring and is holding things up, in termas of other more important accomplishments.

Either one is inventing notation for oneself, or for a small cadre. Musicians the world over have learned to read cents at 100 per semitone. Please let us use this information to make music. Special symbols only trip us up.

Best, Johnny Reinhard

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

> i think Gene meant, for example, 612edo, which gives 5-limit ratios
> with hardly any error and so is great as an integer measurement.

It's actually a good 7, 9 and 11-limit system also.

--- In tuning@y..., Afmmjr@a... wrote:

> Johnny: It may be that I am misunderstanding something, but yes, 37 above a notehead at 300 (a C compared down to an A) is rather easy to prepare mentally.

Presumably you need to learn to do this, however, and don't just leap right in knowing how to find 37 cents since it is 37% of a semitone.

Frankly, there seems to be a lot of spinning wheels with notation. I think it is a red herring and is holding things up, in termas of other more important accomplishments.

How is it holding things up?

Gene: Presumably you need to learn to do this, however, and don't just leap right
in knowing how to find 37 cents since it is 37% of a semitone.

Johnny: It's all part of training, certainly. But most all instruments have an envelope of a semitone that they can play through anyway. Think about it, winds, strings, all have ample manuverability in pitch. So when the mind sees 37 cents sharp from the norm, then it places it linearly just below the quartertone, and in combination with the harmonic balace, zeroes in on the exact pitch needed.

p.s. I hope you believe me

Johnny

Messian wrote that there are 2 things wrong with microtonal music:
1. New instruments
2. New notation that will be prohibitive

These 2 restrictions are no restrictions at all, unless one insists on them. Notation independence is great for spinning mental wheels, and it might even make a particular item more accurate. But cents notation makes all microtonal music fit musical training.

On 2/25/02 2:14 PM, "monz" <joemonz@yahoo.com> wrote:

>>> I imagine some other unit than cents would be feasible, for
>>> starters.
>>
>> Depends what you mean by "feasible". I meant "sufficiently accurate
>> while being easily understood by performers with ordinary training".
>
>
> i think Gene meant, for example, 612edo, which gives 5-limit ratios
> with hardly any error and so is great as an integer measurement.
> it's a lot better than 1200edo (cents) in that respect. for that
> matter, for 5-limit, 118edo is terrific. see
> http://www.ixprs.com/interval/dict/eqtemp.htm
>

118 gives you ratios but if you start using too many intervals, they start
falling on the wrong side from each other.

For that matter, 118 equates eight perfect fourths with a major third.

It's not so much the point for point accuracy that led me to use 4296, it's
more the fact that you retain the relative size of very small intervals.

> From: Orphon Soul, Inc. <tuning@orphonsoul.com>
> To: Tuning List <tuning@yahoogroups.com>
> Sent: Monday, February 25, 2002 5:11 PM
> Subject: [tuning] 4296 says hello (Re: A common notation for JI and Ets)
>
>
> On 2/25/02 2:14 PM, "monz" <joemonz@yahoo.com> wrote:
>
> >>> I imagine some other unit than cents would be feasible, for
> >>> starters.
> >>
> >> Depends what you mean by "feasible". I meant "sufficiently accurate
> >> while being easily understood by performers with ordinary training".
> >
> >
> > i think Gene meant, for example, 612edo, which gives 5-limit ratios
> > with hardly any error and so is great as an integer measurement.
> > it's a lot better than 1200edo (cents) in that respect. for that
> > matter, for 5-limit, 118edo is terrific. see
> > http://www.ixprs.com/interval/dict/eqtemp.htm
> >
>
> 118 gives you ratios but if you start using too many intervals, they start
> falling on the wrong side from each other.
>
> For that matter, 118 equates eight perfect fourths with a major third.
>
> It's not so much the point for point accuracy that led me to use 4296,
it's
> more the fact that you retain the relative size of very small intervals.

to my mind, both of those mean pretty much the same thing.
the "point for point accuracy" is going to determine whether
or not the "relative size of very small intervals" remains
consistent.

i simply picked 612 as an example of something that Gene would
use, since he's mentioned it in the past and the question was
directed at him.

but yes, 4296 as an integer interval measurement, at least for
the 5-limit, can't be beat by any lower-cardinality EDO.

i just calculated the amount of error of the degrees of 4296edo
for the 3x5 lattice where 7^1 and 11^1, and both of them have
a rather large degree of error. because the 3x5 lattice in
4296edo has essentially no error, the error for the individual
ratios 7:4 and 11:8 will be duplicated for a large section of
the 3x5 lattice where each of those prime-factors = 1, and the
converse amount of error where they are -1.

so each 4296edo degreee is off at 7^1 by +0.4 of a 4296edo degree,
and at 7^-1 by -0.4 degree, and each 4296edo degree is off at 11^1
by -0.3 of a degree, and at 11^-1 by +0.3 degree.

so anyway, yes, 4296 is superb for the 5-limit, but nowhere near
as good for higher limits, which is what we really need for
comprehensive notational purposes.

i've added some 7- and 11-limit lattices to that page,
for 118edo and 612edo.

-monz

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--- In tuning@y..., "monz" <joemonz@y...> wrote:
> \ and /-with-a short-vertical-line-thru-it are essentially,
> to my mind, the same as -+ . see the commentary i wrote about
> Daniel Wolf's notation (and also Wolf's update) at:
> http://www.ixpres.com/interval/dict/hewm.htm
>
> it seems to me that the essential problem with using -+ in scores
> is that people feel that the horizontal lines will get lost among
> the staff lines and other horizontal symbols (for example, the
> minus sign looks exacly like the "tenuto" symbol). the symbols
> you propose are simply -+ with the horizontal line slanted ...

Yes. But slanted in a specific way, as per Daniel Wolf, so as to agree
with the Fokker slashes, - = \ and + = /, and the vertical line is
much shorter than the slanted one.

> that's fine with me for score notation. and -+ remain for ASCII.

Great! That's _some_ progress at least.

Now, why not \+ in ASCII, or \/, apart from the fact that -+ is what
you're used to?

> so, are we reaching a consensus on notation now? i sure hope so,
> because i'm not planning to change anything i've written either.

No. We reached consensus on that months ago, except for you and Manuel
(who disagree with each other, regarding the ASCII).

I guess I'm trying get you and Manuel to agree, so we're at least down
to 2 notations instead of 3.

Hey Manuel, how about changing from L7 to <> for the septimal comma
and also from ;| to <> for the Richter-Herf 1/6-tones. Dan Wolf likes
<>, according to Monz's HEWM page.

The 7 is too easily taken to be an octave number, or as specifying a
seventh chord.

You describe | and ; as
| semitone fraction sharp (1/n semitone = one step)
; semitone fraction flat (1/n semitone = one step)
As currently used for the Richter-Herf 72-tET notation, these do not
correspond to 1 step.

And how about using some symbols other than v^ for the diaschisma, so
we at least only have 2 uses of these symbols instead of 3. How about
"u" and "n". I think these bear more resemblance to Rapoport's
diaschisma symbols than v and ^ do.

And for comma fractions, how about using \- and -/ instead of < and
>. This would then be consistent with your diesis fraction symbols (-
and -).

All these suggestions are so that, since you're not adopting the Sims
notation or its ASCII equivalent, you are at least minimising the
number of clashes.

> i think Gene meant, for example, 612edo, which gives 5-limit ratios
> with hardly any error and so is great as an integer measurement.
> it's a lot better than 1200edo (cents) in that respect. for that
> matter, for 5-limit, 118edo is terrific. see
> http://www.ixprs.com/interval/dict/eqtemp.htm

Well that's nice, but we're talking ETs and 19-limit JI here. 612-tET
isn't even 13-limit consistent. And for approximating a multitude of
ETs, it is irrelevant how accurately multiples of the unit approximate
ratios. All that matters in that case is the size of the unit. Cents
are obviously more accurate than 1/612ths of an octave for this
purpose. Although 1/612ths may well be accurate enough for most
purposes, there is no incentive to change from a well established
unit.

Gene wrote, in response to Johnny:
> Presumably you need to learn to do this, however,
> and don't just leap right in
> knowing how to find 37 cents since it is 37% of a
> semitone.

Of course they can't hit 37 +- 0.5c without a lot of practice (and
most players will never get that sort of accuracy repeatably) but the
point is that a player of say a fretless stringed instrument or
a sliding wind/brass instrument _can_, even on the very first time
they encounter this notation, just leap right in there knowing how to
find _approximately_ 37 cents because it is 37% of a semitone.

For those kinds of continuous pitch instruments, or instruments where
the pitches must be obtained by bending 12-tET pitches, this notation
seems ideal, to me. I don't see the point in rounding to the nearest
step of 72-tET or 144-tET or 612-tET and then using some new symbols
(unless of course your piece is actually _in_ one of these ETs).

However this sort of notation (cents written near the noteheads) seems
to me like it would be next-to-useless for telling a performer which
key or fret or hole to use on an instrument that is designed or tuned
(or merely has its open strings tuned) to something other than
12-tET, e.g. generalised keyboards or remapped Halberstadts or
non-12-equal guitars or other specially built or modified instruments.
Nor does this cents notation make things easy for a composer who wants
to think in terms of JI or near-JI sonorities, whether composing in JI
or a temperament.

Johnny, for these purposes I (and a lot of others) see that a notation
based on a 12-note (or less) chain of the best 2:3 approximations in
the tuning (or a multiple if it has none), augmented by symbols that
correspond to higher-prime commas, is the best system. We're just
trying to standardise (a) the commas to be used and (b) the symbols
that will stand for those commas.

The cents-near-the-notehead notation does not meet all needs. We enjoy
working out this kind of stuff cooperatively. I don't see how it is
holding anything up. If anything, it's the lack of standardisation of
these Pythagorean-based notations that's holding things up.

It's all that bloody Ezra Sims fault. ;-) Whatever posessed the guy to
use full-arrows for 1/12-tones. Aaargh.

Dave,

When I was looking at multiples of 12 (for notation and consistency),
I noticed that 12*52, 624-tet, was consistent through the 27-limit
with all errors under 1�. Now nearest approximations with extremely
large ETs are always going to have extremely low errors, but so large
a consistency is a rarer bird.

Learning 72-tet is a proven, logical leap for players already up to
their eyebrows in 12, and 144 is just a crosshatch away from that. At
144-tet you have a pretty damn reliable way to get someone grounded in
12-tet confidently close to most any notes one would use in the
continuum (extreme or unusual cases aside). Finishing type adjustments
from there are a given and provisional to whatever the piece at hand
may be.

You could conceivably look at 72, and, even more so I think, 144
notation as cents notation training wheels... a good, reliable way to
teach those who may have difficulty making abstract leaps to a 12-tet
written note and some number. Glyphs are good, unless they're not!

take care,

--Dan Stearns

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Monday, February 25, 2002 6:38 PM
Subject: [tuning] Re: A common notation for JI and ETs

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > \ and /-with-a short-vertical-line-thru-it are essentially,
> > to my mind, the same as -+ . see the commentary i wrote about
> > Daniel Wolf's notation (and also Wolf's update) at:
> > http://www.ixpres.com/interval/dict/hewm.htm
> >
> > it seems to me that the essential problem with using -+ in scores
> > is that people feel that the horizontal lines will get lost among
> > the staff lines and other horizontal symbols (for example, the
> > minus sign looks exacly like the "tenuto" symbol). the symbols
> > you propose are simply -+ with the horizontal line slanted ...
>
> Yes. But slanted in a specific way, as per Daniel Wolf, so as to
agree
> with the Fokker slashes, - = \ and + = /, and the vertical line is
> much shorter than the slanted one.
>
> > that's fine with me for score notation. and -+ remain for ASCII.
>
> Great! That's _some_ progress at least.
>
> Now, why not \+ in ASCII, or \/, apart from the fact that -+ is what
> you're used to?
>
> > so, are we reaching a consensus on notation now? i sure hope so,
> > because i'm not planning to change anything i've written either.
>
> No. We reached consensus on that months ago, except for you and
Manuel
> (who disagree with each other, regarding the ASCII).
>
> I guess I'm trying get you and Manuel to agree, so we're at least
down
> to 2 notations instead of 3.
>
> Hey Manuel, how about changing from L7 to <> for the septimal comma
> and also from ;| to <> for the Richter-Herf 1/6-tones. Dan Wolf
likes
> <>, according to Monz's HEWM page.
>
> The 7 is too easily taken to be an octave number, or as specifying a
> seventh chord.
>
> You describe | and ; as
> | semitone fraction sharp (1/n semitone = one step)
> ; semitone fraction flat (1/n semitone = one step)
> As currently used for the Richter-Herf 72-tET notation, these do not
> correspond to 1 step.
>
> And how about using some symbols other than v^ for the diaschisma,
so
> we at least only have 2 uses of these symbols instead of 3. How
about
> "u" and "n". I think these bear more resemblance to Rapoport's
> diaschisma symbols than v and ^ do.
>
> And for comma fractions, how about using \- and -/ instead of < and
> >. This would then be consistent with your diesis fraction symbols
(-
> and -).
>
> All these suggestions are so that, since you're not adopting the
Sims
> notation or its ASCII equivalent, you are at least minimising the
> number of clashes.
>
> > i think Gene meant, for example, 612edo, which gives 5-limit
ratios
> > with hardly any error and so is great as an integer measurement.
> > it's a lot better than 1200edo (cents) in that respect. for that
> > matter, for 5-limit, 118edo is terrific. see
> > http://www.ixprs.com/interval/dict/eqtemp.htm
>
> Well that's nice, but we're talking ETs and 19-limit JI here.
612-tET
> isn't even 13-limit consistent. And for approximating a multitude of
> ETs, it is irrelevant how accurately multiples of the unit
approximate
> ratios. All that matters in that case is the size of the unit. Cents
> are obviously more accurate than 1/612ths of an octave for this
> purpose. Although 1/612ths may well be accurate enough for most
> purposes, there is no incentive to change from a well established
> unit.
>
> Gene wrote, in response to Johnny:
> > Presumably you need to learn to do this, however,
> > and don't just leap right in
> > knowing how to find 37 cents since it is 37% of a
> > semitone.
>
> Of course they can't hit 37 +- 0.5c without a lot of practice (and
> most players will never get that sort of accuracy repeatably) but
the
> point is that a player of say a fretless stringed instrument or
> a sliding wind/brass instrument _can_, even on the very first time
> they encounter this notation, just leap right in there knowing how
to
> find _approximately_ 37 cents because it is 37% of a semitone.
>
> For those kinds of continuous pitch instruments, or instruments
where
> the pitches must be obtained by bending 12-tET pitches, this
notation
> seems ideal, to me. I don't see the point in rounding to the nearest
> step of 72-tET or 144-tET or 612-tET and then using some new symbols
> (unless of course your piece is actually _in_ one of these ETs).
>
> However this sort of notation (cents written near the noteheads)
seems
> to me like it would be next-to-useless for telling a performer which
> key or fret or hole to use on an instrument that is designed or
tuned
> (or merely has its open strings tuned) to something other than
> 12-tET, e.g. generalised keyboards or remapped Halberstadts or
> non-12-equal guitars or other specially built or modified
instruments.
> Nor does this cents notation make things easy for a composer who
wants
> to think in terms of JI or near-JI sonorities, whether composing in
JI
> or a temperament.
>
> Johnny, for these purposes I (and a lot of others) see that a
notation
> based on a 12-note (or less) chain of the best 2:3 approximations in
> the tuning (or a multiple if it has none), augmented by symbols that
> correspond to higher-prime commas, is the best system. We're just
> trying to standardise (a) the commas to be used and (b) the symbols
> that will stand for those commas.
>
> The cents-near-the-notehead notation does not meet all needs. We
enjoy
> working out this kind of stuff cooperatively. I don't see how it is
> holding anything up. If anything, it's the lack of standardisation
of
> these Pythagorean-based notations that's holding things up.
>
> It's all that bloody Ezra Sims fault. ;-) Whatever posessed the guy
to
> use full-arrows for 1/12-tones. Aaargh.
>
>
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In a message dated 2/25/02 9:40:06 PM Eastern Standard Time,
d.keenan@uq.net.au writes:

> However this sort of notation (cents written near the noteheads) seems
> to me like it would be next-to-useless for telling a performer which
> key or fret or hole to use on an instrument that is designed or tuned
> (or merely has its open strings tuned) to something other than
> 12-tET, e.g. generalised keyboards or remapped Halberstadts or
> non-12-equal guitars or other specially built or modified instruments.
> Nor does this cents notation make things easy for a composer who wants
> to think in terms of JI or near-JI sonorities, whether composing in JI
> or a temperament.
>

Gene, you guys are a bunch'a "comma-nists" for sure! ; ) The whole point of
cents notation is for the performer. Composers can grab whatever they want,
even as to pencil or computer. With some better experiences you might trust
players more to navigate through the cents. It could be that I trust
musicians so much they actually play microtonally in tune to match my
expectations.

> Johnny, for these purposes I (and a lot of others) see that a notation
> based on a 12-note (or less) chain of the best 2:3 approximations in
> the tuning (or a multiple if it has none), augmented by symbols that
> correspond to higher-prime commas, is the best system. We're just
> trying to standardise (a) the commas to be used and (b) the symbols
> that will stand for those commas.
>

I collaborated with Gardner Reed when he wrote his book Microtonal Notation.
The conclusion of the book is that there are almost as many notations as
there are systems. Don't even start about non-systems. Rudolf Rasch wrote a
scathing review of the book because Gardner's book didn't demonstrate why
particular symbols were appropriate to the particular fractioning that they
were representative of. Gardner was stunned in his response. But it always
seemed clear to me.

It is frustrating that a notation cannot be all things to all people. In my
head all the tunings are there with all the pitches. Why should I get
excited about symbols that are like reading Etruscan today? I'm sorry if it
seems like I"m a pill at a party, but reading music is what I do. Composers
describe in notation. However, performers read prescribed notation. They
are not the same thing. Musicians can read cents so take advantage of it
before it becomes a lost art.

And by the way, 1200 cents abstracts the continuum of music enough that the
"raison d'etre" of the tuning or feel will be intuited by any musician worth
their salt. If the composer can feel it and imagine it in a plastic form ("a
piece") then the listener is susceptible as well.

> The cents-near-the-notehead notation does not meet all needs.

But it will get your music played.

> working out this kind of stuff cooperatively. I don't see how it
> is
> holding anything up.

I only meant it in the transcendental sense.

If anything, it's the lack of standardisation of
> these Pythagorean-based notations that's holding things up.
>

Pythagorus had nothing to do with those notations. I cannot accept
(half-jokingly) that the supposed personage Pythagorus is getting even newer
false credentials worthy of Isacoff. More seriously, I know that the
accurate mapping of specific symbols are vital to your confidence in the
system itself. This is true for me as well so I cannot understand not
wanting to feel nauseous with the pitch. All I want to say is that if you
use cents for performers everyone will be happy. You'll see, every tuning
will be on an equal footing. Accuracy is what you'll get.

> It's all that bloody Ezra Sims fault. ;-) Whatever posessed the guy to
> use full-arrows for 1/12-tones. Aaargh.
>
>

Arrows are especially egregious because they always imply infinity. What I
am trying to say that they point towards a direction, but they don't say
convincingly how far. A legend will suffice, but it is back to the
idiosyncratic piece to piece. I've spent most of my adult life training
musicians to play in cents notation and it is now quite pervasive in big
cities. Please use this resource composers.

Best, Johnny Reinhard

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Learning 72-tet is a proven, logical leap for players already up to
> their eyebrows in 12,

Absolutely. Its existence almost makes one believe in God. ;-)

> and 144 is just a crosshatch away from that.

Yes. Possibly one crosshatch too many.

> You could conceivably look at 72, and, even more so I think, 144
> notation as cents notation training wheels... a good, reliable way
to
> teach those who may have difficulty making abstract leaps to a
12-tet
> written note and some number. Glyphs are good, unless they're not!

I like that! "72-tET as training wheels for cents notation". Yes. But
I think they should then (if they need to go to cents notation at all)
go from from 72-tET notation to seeing +-17, 33 and 50 cents on the
scores and then other numbers.

Note that I believe that players of some instrument (continuous pitch
and bendable-12-equal) will prefer cents-based notation, but that
JI-oriented composers and players of purpose-built fixed-pitch
instruments (whether JI, ET or linear temperament) will prefer a
comma-based notation. Fewer accidentals for one thing.

72-tET is great because the notation comes out the same whether you
are using the accidentals to indicate shifts in cents from 12-tET or
higher-prime comma shifts from a Pythagorean approximation. This is
because (a) its "Pythagorean approximation" happens to be 12-tET, and
(b) the three primes 5,7 and 11 just happen to have their commas map
to 1, 2 and 3 steps. So 72-tET is also training wheels for comma
notation. 144-tET isn't.

To give 144-tET the same dual-purpose training-wheel properties, your
new accidental would have to represent the 13-comma, which corresponds
to 5 steps (the 5,7,11 commas correspond to 2,4,6 steps). This would
be very messy, and one rarely needs to go past the 11-comma in
notating most tunings of interest, using Pythagorean-comma notation.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_34739.html#34837

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > i think Gene meant, for example, 612edo, which gives 5-limit
ratios with hardly any error and so is great as an integer
measurement.
>
> It's actually a good 7, 9 and 11-limit system also.

***So... then we get 51 degrees for each "semi-tone"...?

That may take a little "getting used to..." :)

JP

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Dave,
>
> When I was looking at multiples of 12 (for notation and consistency),
> I noticed that 12*52, 624-tet, was consistent through the 27-limit
> with all errors under 1¢. Now nearest approximations with extremely
> large ETs are always going to have extremely low errors, but so large
> a consistency is a rarer bird.

Now how about 1236? :)

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_34739.html#34855

> Dave,
>
> When I was looking at multiples of 12 (for notation and
consistency), I noticed that 12*52, 624-tet, was consistent through
the 27-limit with all errors under 1¢. Now nearest approximations
with extremely large ETs are always going to have extremely low
errors, but so large a consistency is a rarer bird.
>
> Learning 72-tet is a proven, logical leap for players already up to
> their eyebrows in 12, and 144 is just a crosshatch away from that.
At 144-tet you have a pretty damn reliable way to get someone
grounded in 12-tet confidently close to most any notes one would use
in the continuum (extreme or unusual cases aside). Finishing type
adjustments from there are a given and provisional to whatever the
piece at hand may be.
>
> You could conceivably look at 72, and, even more so I think, 144
> notation as cents notation training wheels... a good, reliable way
to teach those who may have difficulty making abstract leaps to a 12-
tet written note and some number. Glyphs are good, unless they're not!
>

***I wholeheartedly agree with this post!

J. Pehrson

Johnny,

I believe what you say, as far as it goes, but you didn't seem to
address this:

"However this sort of notation (cents written near the noteheads)
seems to me like it would be next-to-useless for telling a performer
which key or fret or hole to use on a [fixed pitch] instrument that is
designed or tuned (or merely has its open strings tuned) to something
other than 12-tET, e.g. generalised keyboards or remapped Halberstadts
or non-12-equal guitars or other specially built or modified
instruments. [Such as the Partch instruments or those Alison
Monteith is building]"

Yup. We're comma-nists all right. We are expecting the "withering away
of the stave" any time now.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_34739.html#34864

> I like that! "72-tET as training wheels for cents notation". Yes.
But I think they should then (if they need to go to cents notation at
all) go from from 72-tET notation to seeing +-17, 33 and 50 cents on
the scores and then other numbers.
>

***Well, I told Johnny Reinhard that I would be willing to write a
17, 33 or 50 above every glyph in my 72-tET-notated score. I think,
though, when he realized there were only *three* numbers in the
entire piece, he felt it was less necessary...

JP

In a message dated 2/25/02 11:23:46 PM Eastern Standard Time,
d.keenan@uq.net.au writes:

> Johnny,
>
> I believe what you say, as far as it goes, but you didn't seem to
> address this:
>
> "However this sort of notation (cents written near the noteheads)
> seems to me like it would be next-to-useless for telling a performer
> which key or fret or hole to use on a [fixed pitch] instrument that is
> designed or tuned (or merely has its open strings tuned) to something
> other than 12-tET, e.g. generalised keyboards or remapped Halberstadts
> or non-12-equal guitars or other specially built or modified
> instruments. [Such as the Partch instruments or those Alison
> Monteith is building]"
>
>

Ah, that's why we have a common pitch frequency. I recommend A=440.
Partch's G at 4 cents lower can be difficult, but that's why I just did for
my last Canadian tour. I wrote a piece in 43-Partch which was premiered in
Winnipeg and played again in Vancouver called "September 11th." Since the
chromelodeon adaptation was tuned to Partch's G I had a tough time...not
ideal...but certainly doable.

When I play with Jon Catler I have to do his 60 cycles tuning which brings
down whatever tuning he is doing down an obscenely specific interval, and I
do it. And I improvise in it and I believe in it. Trust the players to play
the music, or play it yourself. There does not seem to be much alternative.

Best, Johnny Reinhard

On 2/25/02 8:54 PM, "monz" <joemonz@yahoo.com> wrote:

> so anyway, yes, 4296 is superb for the 5-limit, but nowhere near
> as good for higher limits, which is what we really need for
> comprehensive notational purposes.
>

Ahh, so true. I forget because my use of higher harmonics is usually
incidental, or derived from different simpler melodies, depending on the
temperament. Like having a Bb to G# as a 7:4 in 31, etc.

Dave wrote:

"Hey Manuel, how about changing from L7 to <> for the septimal comma"

It can't, <> are already used for the syntonic comma fraction,
which they resemble most.

"and also from ;| to <> for the Richter-Herf 1/6-tones."

Okay, I see no obstacle here.

"The 7 is too easily taken to be an octave number, or as specifying a
seventh chord."

That's true, but there are only so many ascii symbols. Besides
octave numbers are always separated by a point in Scala.

"And how about using some symbols other than v^ for the diaschisma, so
>we at least only have 2 uses of these symbols instead of 3."

I agree it's not ideal. But as long as they don't bite each other
I see no real advantage to change. And "u" and "v" would be
difficult to distinguish.

"And for comma fractions, how about using \- and -/ instead of < and
>. This would then be consistent with your diesis fraction symbols (-
and -)."

Oh no, I'm not so happy with the combinations )-) and ((- but they
occur very rarely. Having /-/ instead of /> would make it much more
difficult to read. And /> combines into one graphic symbol, otherwise
you'd have to imagine _three_ ascii symbols combining to one symbol.

Manuel

/tuning/topicId_7071.html#7078

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> > Dave,
> >
> > When I was looking at multiples of 12 (for notation and
consistency),
> > I noticed that 12*52, 624-tet, was consistent through the 27-limit
> > with all errors under 1¢. Now nearest approximations with
extremely
> > large ETs are always going to have extremely low errors, but so
large
> > a consistency is a rarer bird.
>
> Now how about 1236? :)

Gene:

1236 is inconsistent at the 19 limit.

Before anyone considered 72-ET practical, 31-ET was often thought to
be the most marketable system for the rest of the musical world at
large. In this regard, 224-ET (or 8*31) might have been considered a
basis for JI notation, with its 15-limit consistency.

Of course, there's always the (41-limit) consistency champ, 311-ET,
which comes pretty close to a tenfold division of 31.

But for a notational basis my vote rests with 72-ET. It's easy to
understand, takes in the 24 & 36-ET folks, and finds the commonality
between 31 & 41-ET (via Miracle). Besides, its so-so representation
of 13 gives you the option of mapping it into either of two
positions: the lower one keeps it distinct from ratios of 11, and the
higher one allows bridging to ratios of 11 by conflating 352:351.

--George

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

>
> Before anyone considered 72-ET practical, 31-ET was often thought
to
> be the most marketable system for the rest of the musical world at
> large. In this regard, 224-ET (or 8*31) might have been considered
a
> basis for JI notation, with its 15-limit consistency.

hope this isn't too 'mathy' for this list, but george, 8*31 is 248,
and 248-equal isn't 15-limit consistent.

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> Dave wrote:
>
> "Hey Manuel, how about changing from L7 to <> for the septimal
comma"
>
> It can't, <> are already used for the syntonic comma fraction,
> which they resemble most.
>
> "And for comma fractions, how about using \- and -/ instead of <
and
> >. This would then be consistent with your diesis fraction symbols
(-
> and -)."
>
> Oh no, I'm not so happy with the combinations )-) and ((- but they
> occur very rarely. Having /-/ instead of /> would make it much more
> difficult to read. And /> combines into one graphic symbol,
otherwise
> you'd have to imagine _three_ ascii symbols combining to one symbol.

Yeah, you're right, two-character symbols suck. But I just noticed
that you're already using ` and ' for a syntonic comma fraction in V31
notation. Why not use them everywhere and thereby free up <> for
septimal-comma/1/6-tone?

> "And how about using some symbols other than v^ for the diaschisma,
so
> >we at least only have 2 uses of these symbols instead of 3."
>
> I agree it's not ideal. But as long as they don't bite each other
> I see no real advantage to change.

OK. So you're saying that the diaschisma and 11-diesis never occur in
the same notation, so you don't care about distinguishing them.

> And "u" and "v" would be difficult to distinguish.

Hmm. Now you seem to be saying that my proposal wouldn't distinguish
them _enough_? Are you contradicting yourself?

--- In tuning@y..., Afmmjr@a... wrote:
> Ah, that's why we have a common pitch frequency.

No. That's not what I'm referring to. Assume we're using a common
reference pitch.

What use is a cents-near-the-note-head notation for someone playing a
keyboard or any other fixed-pitch instrument in a JI tuning or in an
ET that isn't related to 12-tET, say 22-tET?

On 2/26/02 4:30 PM, "paulerlich" <paul@stretch-music.com> wrote:

> /tuning/topicId_7071.html#7078
>

Nice to see. Until a month or so ago I hadn't really thought about 4296
since like the early 90s.

On 2/27/02 1:48 AM, "dkeenanuqnetau" <d.keenan@uq.net.au> wrote:

> --- In tuning@y..., Afmmjr@a... wrote:
>> Ah, that's why we have a common pitch frequency.
>
> No. That's not what I'm referring to. Assume we're using a common
> reference pitch.
>
> What use is a cents-near-the-note-head notation for someone playing a
> keyboard or any other fixed-pitch instrument in a JI tuning or in an
> ET that isn't related to 12-tET, say 22-tET?

That's kind of what I was thinking. After the point where I didn't even
know wind instruments were capable of microtones, I would imagine that's a
good way to notate it for non-linear instruments. But for a keyboard or
guitar, ehh. Guitar anyway it would make more visual sense to me to take
plus or minus actual notes from a recognizeable diatonic note. There have
been objections to using "+/-" notes at any cost, which I think I only
leaned toward because of the actual shift in single notes. I do like the
idea, though, of having a certain sense of harmonic placement, notating with
different commas and such. That's pretty interesting.

Funny also that off on my own, I too thought of using "v ^" for syntonic
commas, where the carat was an inverted Roman V, and either "< >" or "L 7"
as septimal, where they were all actual rotated sevens. Which, like I said,
was more a convenience for notes that were otherwise useable but
diatonically hairy, triple sharps and quadruple flats otherwise.

Marc

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

> > Now how about 1236? :)
>
> Gene:
>
> 1236 is inconsistent at the 19 limit.

It's a possibility before that, though.

> Of course, there's always the (41-limit) consistency champ, 311-ET,
> which comes pretty close to a tenfold division of 31.

I just ran a search of good 27-limit systems, and like the look of
1578 (which has some serious chops in lower limits as well, always a nice feature, and isn't bad up to the 35 limit.)

Here's a log-flat 27-limit badness measure up to the 2000-et:

7 1.141144471
10 1.240708486
12 1.217053950
19 1.144720218
31 1.099480243
34 1.288827753
46 1.270499309
50 1.260187317
53 1.173390659
72 1.254791028
80 1.123712041
87 1.205817116
94 1.201939694
111 1.166266558
118 1.214045944
130 1.229083008
140 1.179895167
149 1.016202123
159 .9683644384
183 1.198219614
193 1.146671047
217 1.142301757
282 .9635806968
311 .9616350579
388 1.029878729
422 .9410929149
525 1.280088703
624 1.112379903
653 1.241393090
730 1.239910729
882 1.276056679
935 1.117235218
1012 1.260570163
1106 1.252348988
1125 1.287802625
1171 1.120767718
1323 1.124992388
1395 1.260905588
1578 .7802221111
1600 1.221930048
1889 1.203554173
2000 1.264725343

The Woolhouse 730 makes it to this list, I see, as do 10, 50, 80, 1600
and 2000, which suggests some decimal possibilities.

> But for a notational basis my vote rests with 72-ET. It's easy to
> understand, takes in the 24 & 36-ET folks, and finds the commonality
> between 31 & 41-ET (via Miracle).

It won't work for some temperaments, however.

On 2/27/02 5:20 AM, "genewardsmith" <genewardsmith@juno.com> wrote:

> I just ran a search of good 27-limit systems, and like the look of
> 1578 (which has some serious chops in lower limits as well, always a nice
> feature, and isn't bad up to the 35 limit.)
>
> Here's a log-flat 27-limit badness measure up to the 2000-et:

What exactly is *27* limit?

This I'm having a hard time with lately. From what I heard years ago, I was
under the impression that "limit" was used to describe the highest *prime*
number in use, which if you're considering things up to 27, would be 23 in
this case.

Besides the Orphon definitions, I think I need to air a group of
definitions, all of which mean something to me but in use by other people
here means something different.

Is there a term for that circulating though? Say if you're only using
combinations of 3rd 5th and 7th harmonics to calculate intervals? (e.g.
{25:21, 343:243, 7:5} etc) I was under the impression that was called "7th
limit".

Marc

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

> What exactly is *27* limit?

Unfortunately, there is prime limit *and* odd limit. 27 limit means
take the set S27 of odd numbers from 1 to 27 inclusive, and form the set of ratios R27 = {p/q| p, q are in S27}. The octave equivalence classes for which R27 are representatives are the consonant intervals of the 27-limit. A temperament which is being used to represent the 27 limit then is judged on how well it represents every element of
R27, assuming pure octaves. One can take eg rms error, or as I did in this calculation, maximum error, and use that as a basis for a "badness" measure, perhaps after further adjustments, as I did here.

> Is there a term for that circulating though? Say if you're only using
> combinations of 3rd 5th and 7th harmonics to calculate intervals? (e.g.
> {25:21, 343:243, 7:5} etc) I was under the impression that was called "7th
> limit".

It is, and perhaps we should come up with better terminology.

> > What use is a cents-near-the-note-head notation for someone playing a
> > keyboard or any other fixed-pitch instrument in a JI tuning or in an
> > ET that isn't related to 12-tET, say 22-tET?
>
>

Dave, there is no use in using cents for notating an inflexible pitched
instrument. Only indications of where to put the fingers will make any
difference, or "tabulature." Partch realized this even as he came up with
several alternatives for flexible pitched instruments.

Best, Johnny Reinhard

On 2/27/02 6:11 AM, "genewardsmith" <genewardsmith@juno.com> wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>
>> What exactly is *27* limit?
>
> Unfortunately, there is prime limit *and* odd limit.

That in itself isn't really all that bad a distinction.

> 27 limit means
> take the set S27 of odd numbers from 1 to 27 inclusive, and form the set of
> ratios R27 = {p/q| p, q are in S27}.

Errr... You mean 3:1, 5:3, 7:5, 11:7, etc? The sort of umm
superduperparticular? Or are you including *all* permutations, like 7:3,
11:3, 17:5 and so on.

> The octave equivalence classes for which R27 are representatives are the
> consonant intervals of the 27-limit. A temperament which is being used to
> represent the 27 limit then is judged on how well it represents every element
> of R27, assuming pure octaves. One can take eg rms error, or as I did in this
> calculation, maximum error, and use that as a basis for a "badness" measure,
> perhaps after further adjustments, as I did here.

Alright thanks. That seems like a good study.

>> Is there a term for that circulating though? Say if you're only using
>> combinations of 3rd 5th and 7th harmonics to calculate intervals? (e.g.
>> {25:21, 343:243, 7:5} etc) I was under the impression that was called "7th
>> limit".
>
> It is, and perhaps we should come up with better terminology.

I mostly got into the idea of limit as a basis for expansion of the Brun
algorithm. Take a step or so within a certain harmonic scheme and then
start working in the next one. This is how I've been mumbling it to myself,
as of about 1991:

"Limit" - like I first heard it, the highest prime number used.
"Exclusion" - the prime numbers NOT used in a limit.
"Indulgence" - the scheme actually used within the limit.
"Abstinence" - the scheme actually not used within the limit.
"Forcing" - using a prime outside of the scheme lower than the limit.
"Exploring" - using a prime outside of the scheme higher than the limit.

I noticed this same binary arrangement recently, only for odd numbers
instead of prime. This I think we called a binary indulgence something or
other. I'll have to ask Fred. And yes of course there's a double size
scheme when you intermix lack of octave:

2: 2nd limit. Octave.

2 3: 3rd limit. 3L. Pythagorean.

2 3 5: 5th limit. 5L. Quint, or Quint-essential. (ha)

2 3 7: 7th limit, 5th exclusion. (If you notice the "O P Q ? S"
progression, we used to just call this "R". Most of our checking it out was
based on 6:7:8 melodies.)
2 3 5 7: 7th limit. Septimal.

2 3 11: 11th limit, 5th and 7th exclusion.
2 3 5 11: 11th limit, 7th exclusion.
2 3 7 11: 11th limit, 5th exclusion.
2 3 5 7 11: 11th limit.

Almost like jazz chords, actually, add this, no that. I'm surprised Fred
never came up with that. I'm REALLY surprised. Like after we coined
"diatonic aperture" he said "what about shutter speed?" There's logic in
facetiousness; it was that comment that started me on a lot of time studies.

Again, it wasn't so much just dealing with these loose floating limits in
arbitrary just intonation experimentation. We were very concerned with the
Brun algorithm more than a lot of other things we worked on. So we're not
just talking about a simple test of whether the harmonics are good in any
one particular temperament, but if that temperament actually showed up in an
algorithm, the convergence web implied was the concern. From THERE, then we
used the aforementioned terms.

Actually we used the {2:1, 3:2, 5:4, 11:10} convergence a lot, which yielded
19, 22, 41, 46, 65... All of which show up in several algorithms involving
7th harmonics. So what we did with this bunch, a lot of the post production
on the K-Ram 22 stuff went like this:

"11th limit, 7 exclusion; forced 7s, 3rd and 7th indulgence."
Or, "2 3 5 11" algorithms with "2 3 7" arbitrary webs.

It's funny because the Toronto stuff was all from that same exact algorithm,
but it was implimenting webs taken from 5th limit algorithms. Oh well
actually it was based on the fact that 46 showed up in the {2:1, 5:3, 4:3},
and the web from THAT was taken and 19, 22 and 41 were shoved through that
web. Or something like that. Not all Toronto, just Blueberry. Ugh it's
been so long. Anyway I was saying, from the same algorithm, {2:1, 3:2, 5:4,
11:10}, those two groups never sounded alike. Even with the same guitars.
But that's really just like comparing classical piano with jazz piano. It's
a different style within the same instrument. This was just temperament.

I think of ANYTHING historical, the only thing we ever stuck by was the Brun
algorithm and variations of it we came up with. But then again we never
read any Partch. At that point we couldn't even get a hold of any. Once we
saw the way temperaments synergize, and once we saw the relative error
decreasing systematically, AND once we made the convergence web discovery,
well that seemed to take up a lot of our time for a few years. Hence all
the talk of 1171 and 1342 and such.

Sorry to babble. Coffee time.

Marc

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> > But for a notational basis my vote rests with 72-ET. It's easy
to
> > understand, takes in the 24 & 36-ET folks, and finds the
commonality
> > between 31 & 41-ET (via Miracle).
>
> It won't work for some temperaments, however.

meantone is the biggie, of course. at least 152-equal can do adaptive
(as in adaptive ji) meantone.

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> On 2/27/02 5:20 AM, "genewardsmith" <genewardsmith@j...> wrote:
>
> > I just ran a search of good 27-limit systems, and like the look of
> > 1578 (which has some serious chops in lower limits as well,
always a nice
> > feature, and isn't bad up to the 35 limit.)
> >
> > Here's a log-flat 27-limit badness measure up to the 2000-et:
>
>
> What exactly is *27* limit?
>
> This I'm having a hard time with lately. From what I heard years
ago, I was
> under the impression that "limit" was used to describe the highest
*prime*
> number in use,

not by harry partch, but by others who came after him. have you
checked monz' dictionary? look up 'limit'.

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> On 2/27/02 6:11 AM, "genewardsmith" <genewardsmith@j...> wrote:
>
> > --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> >
> >> What exactly is *27* limit?
> >
> > Unfortunately, there is prime limit *and* odd limit.
>
> That in itself isn't really all that bad a distinction.

yes, we usually make that distinction here, unless context makes it
obvious which one we mean. when we're talking about infinite ji
tuning systems, it's prime limit . . . when we're talking about
evaluating temperaments or a composer's threshold of consonance, it's
odd limit . . .

> > 27 limit means
> > take the set S27 of odd numbers from 1 to 27 inclusive, and form
the set of
> > ratios R27 = {p/q| p, q are in S27}.
>
> Errr... You mean 3:1, 5:3, 7:5, 11:7, etc? The sort of umm
> superduperparticular? Or are you including *all* permutations,
like 7:3,
> 11:3, 17:5 and so on.

*all* permutations.

> It's funny because the Toronto stuff

gee i wish i knew what you were talking about :)

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

> > 27 limit means
> > take the set S27 of odd numbers from 1 to 27 inclusive, and form the set of
> > ratios R27 = {p/q| p, q are in S27}.

> Errr... You mean 3:1, 5:3, 7:5, 11:7, etc? The sort of umm
> superduperparticular? Or are you including *all* permutations, like 7:3,
> 11:3, 17:5 and so on.

I'm including the lot--p and q are in S27 is the only condition.

> I think of ANYTHING historical, the only thing we ever stuck by was the Brun
> algorithm and variations of it we came up with.

That sounds like an interesting topic for tuning-math.

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

> meantone is the biggie, of course. at least 152-equal can do adaptive
> (as in adaptive ji) meantone.

If we really want to get serious about using a micro-et to represent everything JI, there's always 2460. I thought seriously about adopting it as a system before settling on 612, and it does just about everything.

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
> There have
> been objections to using "+/-" notes at any cost, which I think I
only
> leaned toward because of the actual shift in single notes.

The objection is to using "+" and "-" as accidentals on the staff,
without slanting their horizontal strokes as / and \. I don't have any
objection to cents written e.g. +14 or -38 on the staff.

In a message dated 2/27/02 10:41:01 PM Eastern Standard Time,
d.keenan@uq.net.au writes:

> The objection is to using "+" and "-" as accidentals on the staff,
> without slanting their horizontal strokes as / and \. I don't have any
> objection to cents written e.g. +14 or -38 on the staff.
>
>
>

Marc, you don't need both + and - (plus and minus). Positive numbers are
already + so only - (minus) is needed to indicate subtraction. Of course,
above the staff makes more sense as its an easier read.

Best, Johnny Reinhard

--- In tuning@y..., Afmmjr@a... wrote:
> Dave, there is no use in using cents for notating an inflexible
pitched
> instrument.

Good. We agree.

> Only indications of where to put the fingers will make
any
> difference, or "tabulature." Partch realized this even as he came
up with
> several alternatives for flexible pitched instruments.

Right. So for performers we are suggesting that the best notations
are:
1. cents-near-the-notehead for flexible-pitch instruments
2. finger-numbers near the noteheads or tablature for fixed-pitch
instruments.

Wouldn't you add scordatura, for fixed pitch instruments such as
re-mapped keyboards and re-fretted guitars.

For other readers:
Tablature is essentially a series of diagrams showing where to put
your fingers.
Scordatura looks exactly like conventional staff notation, but would
sound awful if you played it on a standard-tuned instrument. It's only
purpose is to get you to put your fingers in the right place by having
you _pretend_ that your instrument is still in standard tuning.

So Gene Smith, George Secor etc.,

It seems there isn't much of a place for a notation based on a
pythagorean A to G, with sharps and flats and comma accidentals, as
far as performers go.

If we instead look at the use of notations in analysis and
composition, it seems like it would be better to use notations based
on specific linear temperaments like Graham Breed's Miracle decimal
and Paul Erlich's Pajara decatonic and Herman Millers's Porcupine
heptatonic (for which I warn against using the letters A to G).

I wonder would Joseph Pehrson find it worthwhile to compose in decimal
if he could automatically convert it to Sims notation for the
performers? Joseph, I understand you view the Sims accidentals
primarily as cents-near-the-notehead and not as 5,7 and 11 commas. Is
that correct. Of course that's the beauty of these 72-tET notations,
they can be viewed either way.

Of course the pythag A to G with # and b, _is_ the specific notation
for the linear temperaments called meantone and pythagorean. But is
there any point in forcing it to fit other unrelated linear
temperaments?

I hope someone can come up with some good reasons, 'cause I was having
fun. :-)

It seems like an awful lot of people have proposed these
pythag-plus-commas notations, and they are not all purely theorists.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> Of course the pythag A to G with # and b, _is_ the specific
notation
> for the linear temperaments called meantone and pythagorean.

yup.

> But is
> there any point in forcing it to fit other unrelated linear
> temperaments?

i find the idea ugly, aesthetically speaking. especially when there
isn't a 7-tone periodicity block (in the case of a linear
temperament, an mos) at the center of it.

> It seems like an awful lot of people have proposed these
> pythag-plus-commas notations, and they are not all purely theorists.

right -- monz calls it 'hewm' (helmholtz-ellis-wolf-monzo), though
the full list extends far into the past (to eitz at least) and of
course is much more extensive than four names.

In a message dated 3/1/02 2:12:07 AM Eastern Standard Time,
d.keenan@uq.net.au writes:

> Wouldn't you add scordatura, for fixed pitch instruments such as
> re-mapped keyboards and re-fretted guitars.
>
>

Absolutely--my recent guitar solo is in scordatura. The guitarist reads
straight placements of fingers on strings (AKA tablature). (Too bad tuning
the open strings is so challenging to this guitarist...but he sight read the
whole piece down on my stoop after I tuned it up for him.)

Notation for performance is for the ease of the performer to play the most
complex requests at their earliest.

Peace, Johnny Reinhard

"Orphon Soul, Inc." schrieb:

> That's kind of what I was thinking. After the point where I didn't even
> know wind instruments were capable of microtones, I would imagine that's a
> good way to notate it for non-linear instruments. But for a keyboard or
> guitar, ehh. Guitar anyway it would make more visual sense to me to take
> plus or minus actual notes from a recognizeable diatonic note. There have
> been objections to using "+/-" notes at any cost, which I think I only
> leaned toward because of the actual shift in single notes. I do like the
> idea, though, of having a certain sense of harmonic placement, notating with
> different commas and such. That's pretty interesting.

just trying to catch up at all; still i beg to add my humble
opinion largely concurring with marc:

for brass instruments, the built in intervals are harmonics,
and it would make sense to notate deviations from the
harmonic series or else use the comma based accidentals.
it's a pity that this presupposes that either the composer
or the instrumentalist understand exactly what they are
doing.
for fretted guitars, negative deviations are just confusing.

klaus

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

/tuning/topicId_34739.html#35063

>
> I wonder would Joseph Pehrson find it worthwhile to compose in
decimal if he could automatically convert it to Sims notation for the
> performers?

***I gather you believe, Dave, that somehow if I were to use Graham's
*decimal* notation that I would have a firmer mental command of the
compositional structure of the pieces.

Well, maybe, but I am so used to using *letter names* A-G that, it's
*that* system that facilitates my compositional thinking. I'm not
sure I could get used to the other one, despite whatever advantages.
(I've been using "letter names" for 30, maybe 40 years with
juvenalia... of composing :) )

Joseph, I understand you view the Sims accidentals
> primarily as cents-near-the-notehead and not as 5,7 and 11 commas.
Is that correct. Of course that's the beauty of these 72-tET
notations, they can be viewed either way.

****I really don't know about that, Dave, because I think I am *also*
thinking commas not cents deviations when I use 72-tET.

For example, the very simple G-Bv-D in Blackjack, I'm
surely "thinking" syntonic comma, just as a very simple case...

jp