Re: An Olympian proposal
From George Secor 26/05/2005
--- Dave Keenan <firstname.lastname@example.org
> At 06:03 AM 21/05/2005, George Secor wrote:
>> First off, I believe that the primary role of a symbol should be
>> *independent of the resolution* and that all primary roles should
>> therefore be *defined at the olympian level*.
> I agree, if primary role is defined as the role to be assumed in the
> absence of any other information. I recently took the use of "other
> information" to an extreme level in defining the athenian smart
> But the mere fact of knowing that the symbol is being used in the
> manner is additional information. And so
> defaults exist without even knowing what nominal and sharps or flats
> involved. It is these that should be used in the sag_jiX.par files
> converting from notation to ratio. Do you agree?
> It is these that I'm referring to. But you're right, I shouldn't call
> primary roles. Herculean defaults?
Yes, that's good.
>> Next, I would like to establish a "doctrine of reasonable
> I don't see much value in a name like that. There's no objective way
> determining what is a "reasonable expectation" other than by surveys.
Oh, come on! If we first introduce "e" (meaning any athenian symbol)
and then later ' and . as 5s-accents as something that can be added to
alter e, then it's reasonable to expect that 'e and .e will be the
notation for 5s-altered athenian-level commas. You don't need a survey
for that -- but perhaps I need a better, more specific name.
>> If two reasonably popular ratios differ by a 5-schisma, and if
>> one of the two has as its primary role an unaccented symbol, then we
>> would *reasonably expect* the other to be the primary role for the
>> symbol with the appropriate left-accent added. 7:11k and 11:35k fit
>> these conditions. (If one of the two ratios were of very little
>> popularity or usefulness or overly complex, we would then reasonably
>> expect a simpler ratio to be used in its place.)
> I agree it is a good principle that a 5-schisma difference between
> most-popular commas should be represented by a left accent difference
> between their symbols (the "5sC=LAS" pronounced "five sclas"
Okay, that's a better name than DRE, but your abbreviation is too long.
(What does "LAS" stand for? "Left-accented something"? Oh, I finally
managed to figure it out a day later: "left-accented symbol" -- duh!
> but it clashes with others.
Yes, I know some of these principles are going to conflict. But we
should go about this in such a way as to follow as many of them as
possible in a consistent manner.
> At the olympian level at least, it applies
> equally to these non-athenians:
> )| 19s .)| 5:19n
> ~| 17k .~| 85k
> ~~| 125C .~~| 25C
> )|~ 19C .)|~ 95C
> )/| 5:19C .)/| 19:25C
> ~|) 49S '~|) 245S
> |~) 5:13S '|~) 13:25M
> )//| 5:13M .)//| 13:25S (if these exist)
> (/| 49M '(/| 5:49M
> But applying it consistently in this way will lead to non-monotonic
> (core crossovers).
Yes, I agree that avoiding core-crossovers is also a desirable
> Even among athenian cores we have
> .|\ .(| |\ (|
Yes, I appreciate your point. I would say that 5sC=LAS would not be
applied to any symbol core if it resulted in a core-crossover with a
nearby athenian-cored symbol (thus excluding most non-athenian cores
from application of the 5sC=LAS principle). I think that will address
most of the examples you gave above.
I was thinking that there's no crossover with 5:49M, but I see that
/|\ 11M '/|\ 55M
would cross over (/| -- only 55M isn't very simple, so I don't think it
would be needed very much. Try notating 55/32 and you'll see that you
can't use '/|\ with 1/1 from C to C# -- only with G# as 1/1 do you
begin to encounter it as F'/|\, the principal spelling. So I would
recommend using an olympian sequence that excluded '/|\, such as this:
... /|\ /|\' /|\'' or (/|. (/| (/|' (/|'' '(/|. '(/|
with the choice of the 3rd symbol in that sequence depending on where
the herculean boundary between /|\ and (/| was set, in order to achieve
DAFO (drop accents for herculean -- from olympian). (Sorry, but I'm
not finished with the issue of herculean boundaries, as you'll see
But I see that this also requires choosing .(|)' in preference to |\),
since 49/32 won't require |\) until 1/1 is D#. Hmmm, looks like .(|)
should be in the herculean set instead of |\), but that (/| should
stay, which could give us this olympian sequence:
... '(/| .|\) .|\)' .(|). .(|) .(|)' (|)'' (|)' (|)
Although this would upset our penchant for symmetry, it has the
most-probably-used non-right-accented symbols. Perhaps
complement-symmetry should be mandatory only in ET symbol sequences.
>> This, taken together
>> with DAFA, is why I view an accented athenian core as being less
>> complex than a non-accented non-athenian core.
> The above are each the most popular commas for their respective
> submit that the application of this principle at the olympian level
> have little to do with athenianity and much to do with popularity.
> If you want to eliminate a core crossover, the symbol for the least
> comma should go.
Yes, I would tend to agree with that, and I think that would eliminate
most left-accented non-athenian cores.
> So in fact isn't DAFA the _only_ reason you view an accented athenian
> as being less complex than a non-accented non-athenian core? (which
> to me to be circular reasoning).
No, there are two other reasons:
1) Every non-athenian core introduced is one more core for which the
meaning must be remembered, thus, the more non-athenian cores
introduced, the more complex the notation. If you introduce a new
symbol core into herculean, you should have an extremely good reason
for doing so, as with the following five:
(/| is required, because accented /|\ and (|) symbols will not fill out
a complete sequence between the two unaccented symbols.
|\) was added, because it's the complement of (/| -- and now I'm
questioning whether it's really necessary (or even desirable) in
~~| is required, because an accented athenian symbol will not fill out
a complete sequence two degrees below /| .
|~ was added because 5sC=LAS would have given '~|(, which represents a
rather complex ratio.
~|) was added because 5sC=LAS would have given '(|, which represents a
rather complex ratio, and also to avoid a fairly complicated
combination of accents '(|' for an important notational comma, 49S.
2) I said that 5sC=LAS was a reason that was to be "taken together"
with DAFA for regarding accented athenian cores as less complex.
>> Besides, 11:35k isn't even the right number of minas for )~| to be
>> primary ratio.
> I remind you that 11:35k isn't the right number of minas for ')|( to
> it as primary comma either. We shifted )|( too.
Well, sure, if the (unaccented) core gets shifted, then so do its
So then what? Do we then shift whatever else might strike our fancy,
such as )|~ down one mina to use for 25C, or )~| *up* one mina for
5:17C, or /|~ down one mina for 23S?
Oops, we *did* do that last one some time ago -- tee hee! But,
then again, 23S doesn't have an athenian-cored symbol 4 minas distant
that could have been accented (and we didn't have accents at the time
we shifted its symbol).
My point is that left-accented athenians are *perfectly* good for
notating commas such as 11:35k, 5:17C, and 25C and since 5sC=LAS in
each of these instances, then there's a perfectly good reason *not* to
introduce a new symbol core for any of these. Now there is one
exception: |\. will be used for 7:55C instead of .(| to avoid crossing
over the unaccented athenian |\ symbol used for the more popular 55C.
If we replace |\) with .(|) in herculean, then we've limited the number
of non-athenian symbol cores to four, and only one of the four needs to
>> You were suggesting a one-mina downward shift in order
>> to accomplish this,
> Yes. Its the same shift as required for ~|) for 49S. So we
> the same alternative definition of ~: in both cases.
>> but I think I've given enough justification to use
>> a different comma-definition (143C) for that symbol.
> 143C is the most popular for 25 minas but it is far less popular than
> 11:35k. 23 deemed ocurrences versus 63. What's wrong with ')|(' for
There's nothing at all wrong with that. But the only reason we need
)~| is for promethean and to notate some ET's without using accents, so
I would give it only a token appearance in olympian: in only a single
mina (sequence shown below), without any accents. It would also appear
in promethean, where its default value would be 11:35k. That could
then serve as a basis for notating certain ET's "promethean-style",
without accents. ET's that require at least some left accents could be
notated "herculean-style", and ET's that require right accents would be
Herculean and promethean are opposite approaches to expanding the
spartan and athenian symbol sets: one simplifies by keeping the number
of symbol cores down, while the other simplifies by not requiring the
reading the accents.
> I'm sorry, I've forgotten your justification.
> When we add new unaccented symbols, shouldn't we use the most popular
> that's within one mina of its sum of flags. The only reason ')|( is
> is because we moved )|( to 7:11k.
Before the shift, 11:35k would have been ')|(', which is a bit more
complicated than ')|(, so the shift simplified the symbols for both
7:11k and 11:35k. So what's wrong with ')|( for 11:35k? In addition
to 5sCLAS, it would allow both DAFA and DAFO.
>> I might add that DRE would also mandate that the most popular ratio
>> mina higher than )~| get .~|( for 5:17C,
> 5sCLAS would have .~|( for 5:17C but DAFA and MTC (monotonic cores)
> would not.
You could have both MTC and DAFH for both 11:35K and 5:17c if the
olympian sequence were:
... ')|( )~| .~|( .~|(' ~|(.. ~|(. ~|( ~|(' |~.. |~. |~ ...
and the herculean step for ')|( were subdivided into ')|( and .~|( --
something I'm seriously considering (among other things) as a result of
our latest discussion.
You could also have DAFA if the althenian lowerbound of ~|( were
lowered about 2 minas, but I'm not recommending that at this point,
because it's probably too much. I'll just accept the idea that you
can't have everything everywhere. You also won't have DAFO if 11:35k
is )~| and ')|( is used in herculean; however, if you have )~| for
11:35k in both olympian and herculean, then you won't have DAFA.
>> so I anticipate that the )~|
>> might never be used with any accents (except to subdivide a mina,
>> possibly for 11:35C).
> Note that I'm saying that both ')|( and )~| should be 11:35k. The
> I see for )~| is for ETs that would otherwise have only one or two
> symbols, to avoid accents entirely.
Yes, I was thinking about this for the past couple of days, hence my
suggestion above for )~| as primary ratio of 143C but with 11:35k as
its *promethean default*. This minimizes the number of symbol cores in
other (herculean-style) contexts, but allows this (and other) symbol
cores to come to the fore with their own (not necessarily primary)
promethean default ratios, as needed.
BTW, I happened to notice that )~| is valid as 11:35k, 143C, 5:17C, and
as the sum of its flags in 270, 306, 364, 388, 400, and 494. It's also
valid for all of these less one in 288 (not for 143C) and 311 (not as
sum of flags, which is not a problem). So it looks as if this is going
to be a very useful symbol, albeit within a somewhat limited scope.
>>>> 8* '~|( 85C 2^27:3^13*5*17 ***
>>>> Degree 8 has a complex ratio, hence will be an opportunity to
>>>> a non-athenian (unaccented) symbol (guess which one!).
>>> There is of course only one. |~ as 23C.
>>> The most popular commas for 8degHerc are
>>> 7:25C 45 deemed occurrences |~..
>>> 23C 39 |~
>>> 1225C 38 |~.
>>> So it would be difficult to argue for .~~|
>>> However, it looks like |~ should have primary role 7:25C in
>>> 23C in olympian.
>> Two comments:
>> 1) I think that primary roles should be independent of resolution,
>> would regard |~ as approximating 7:25C in herculean;
> OK. But 7:25C is the most likely value for it in Herculean and so
> the default listed in sag_ji3.par. But I agree not to call this a
> role" in future, but rather the "herculean default".
>> 2) For 25/14 of C, 7:25C would be used as an alternate spelling
>> after the preferred spelling Bb'|(, whereas |~ is used in the main
>> spelling of 23/16.
> Agreed. But even so, 7:25 is so much more popular than 23 that this
> alternate spelling of 7:25 could well be a more popular use of the |~
> symbol than 23 in herculean. But it is close.
Yes, that's possible. I see 3 possible cases of alternate spellings:
1) When there are two possible spellings, each of the two will likely
be used, but generally one more often than the other.
2) If there are three possible spellings, and one of them is clearly
preferred far ahead of the other two, then the other two will rarely be
3) If there are three possible spellings, but none is clearly preferred
far ahead of the other two, then one of them will almost never be used,
and this will, for all practical purposes, be the same as case 1.
For 28/25 you have the following three olympian spellings with C=1/1:
Cx!/' D.!( Ebb|~..
I would classify this one as case 2. For 25/14 it's case 3, with
Cbb|\. being the almost-never-used spelling. The picture may change
slightly when you use a different nominal as 1/1, but you get the
>>>> Degree 9 will require a new non-athenian symbol, since no
>>>> athenian-cored symbol is possible.
>>> Most popular commas for 9deg58-EDA
>>> 125C 63 do (deemed occurrences)
>>> 11:49C 30 do
>>> 11:25C 30 do
>>> 95C 23 do
>>> 125C is [26 -12, -3>, the comma least likely to be used to notate
>>> formula distributes the 2,3-reduced occurrences of 125 in the
>>> as follows
>>> 125S 326 do
>>> 125M 103 do
>>> 125C 63 do
>> You'll have to explain how you came up with that, because at this
>> I'm not buying it.
> Darn. I was hoping you weren't gonna ask me that. 'Cause I've
> spreadsheet and can't remember. I'll look some more, but in the
> why not tell me how you would distribute them.
With C=1/1, there are only 2 spellings: C'\\! and B/|) -- case 1,
second spelling perhaps more likely, but only slightly.
With E=1/1, there are 3 spellings: E'\\! D#/|) Fb~~! -- case 3, third
spelling almost never used.
With Db=1/1, there are 3 spellings: Db'\\! C/|) B#.|)' -- case 3,
third spelling almost never used.
I imagine it would translate into something like 54% for 125M, 45% for
125S, and 1% for 125C.
>>> Agreed. But if |~) is ever used, I think its primary role should
>>> be 5:13S.
>> We'll be discussing that when we get to olympian.
> I think we have to do olympian, herculean and promethean (if we have
> all) more or less simultaneously.
Yes, you're right! And I hope I've strengthened the justification for
the existence of promethean by what I said above.
> Is it conceivable that 1 in 10 occurrences of 125 (with various
> 2 and 3) might be notated by using 125C? I guess you're saying no.
Yes, that's a "no".
>> So I don't imagine that we'll need an exact olympian-level symbol
>> 125C. You've taken this (slope, I believe) into account in your
>> comma-popularity rankings, but I think you've given much too much
>> weight to third-place spellings that will hardly ever be used.
> That's funny, because when I designed the distribution formula I
> thinking that although I personally wouldn't bother with third-place
> high-slope spellings, you seemed to often think them worthwhile,
I did? Well yes, I guess I did say that symbols should be provided for
all possible spellings, but that doesn't mean that third-place
spellings have to be the *primary* roles for their symbols.
> so I'd
> better not weight them too low. It seems I may have overdone it.
Caution: Our thoughts are subject to oscillation. :~}
> But be aware that if I change it in some uniform way, you may not
> effect it has on other (e.g. second-place) alternate spellings.
You'll have to look at some examples and figure out what sort of
adjustment is appropriate for the relative powers of 3. When you see
double-sharps or double-flats, then I would say you're somewhere around
the 1-percent category.
>> On the basis of usefulness, the contest for the primary ratio for
>> is between 11:49C and 11:25C. I would select 11:25C, because it has
>> lower combination of primes. Subdividing the mina would give 11:49C
>> |~'' as its exact symbol. Then let 125C be approximated by one of
> OK. So I'll fiddle the formula (if I ever find it) to make 125C come
> just slightly less popular than both 11:25C or 11:49C. I expect
> win then too.
Wait a minute -- 11:25C and 11:49C should each be much more popular
than 125C! Those would each be used for the preferred spellings of the
ratios they notate (case 2).
>> Okay. I couldn't tell that from your olympian.xls table, since you
>> only ordered them *within* each mina. I don't remember whether you
>> gave me an extensive popularity listing.
> I'll send you one when I fix the 125C thing.
I just might want to see an extensive popularity listing for the ratios
taken collectively, without any allowance for powers of 3. Thus 125
would be listed without specifying whether it's M, S, or C.
>>> I'm totally confused as to what you intend here.
>> Sorry! I used a left-accent when I meant a *right* one.
> Oh dear. I thought no one would ever do that. But of course it
> happened because it was a non-athenian core. Right accented athenians
> so much simpler.
Yes, especially in herculean, where you can't see the accents. d-;
>> This is the
>> sort of olympian sequence I had in mind:
>> minas symbol exact ratio
>> ----- ------ -----------
>> 70 (|'' 17:25S
>> 71 ~|).. ??? instead of '(|. 847S = 7*11*11S
>> 72 ~|). 25:49S instead of '(|
>> 73 ~|) 49S
>> 74 ~|)' 5:17S
>> 75 .(|(. 11:23S instead of ~|)''
>> This allows one to drop accents for herculean (from olympian, DAFH)
>> the above range of symbols (plus quite a bit more above and below).
> That's OK, but when we get to olympian,
The above symbols *are* olympian.
> what about the 5sCLAS principle and the DAFA principle
> and the MTC (monotonic cores) principle?
> 77 '~|) 245S = 5*49S
Well, with a non-athenian symbol core you can't have DAFA no matter how
you look at it. My sequence *does* have MTC, although that eliminates
5sCLAS. So that's one out of three.
If it's any consolation, note that 254S is not the preferred spelling
for 49/25 (taking C=1/1):
second: Cb.(|(' or Cb'~|)
> For what it's worth, I have 847S = 7*11*11S for ~|).. at 71 minas.
Yes, that's nice. I was looking for something simpler than 17:19S.
>>>> The only non-athenian symbol available to compete for the
>>>> '|~), which has a couple of possible ratios: 7:115M and 187M.
>>> Huh? What about 13:25M for '|~) ?
>> If //|'' is 5:13S, then I would reasonably expect 13:25M (a
>> larger) to be '//|'', which could become '//| in herculean.
> What has that got to do with whether '|~), if used, should have
> role 13:25M or not?
I'm having trouble with two different symbols having the same primary
role. If you have a spreadsheet to give you the olympian notation,
then there would be more than one result. There's a solution to this,
but I don't have time to elaborate on it now.
>>>> think I've found a good reason for a double-right accent in
>>>> with a left accent.
>>> Maybe you've found a good reason for a new unaccented symbol for
>>> region. With primary role 5:13M. e.g. )//|
>> Then ')//| would be exactly 13M. Were you also thinking of having
>> instead of ./|) in herculean? I'm questioning whether there's
>> sufficient justification for another symbol that introduces even
>> redundancy in that:
>> 13:25M could be either )//|. or '|~), which are equivalent to '//|''
>> Double-right accents show up only in olympian, and it's simple
>> to understand and remember how they work, and this is a region where
>> they can be dropped quite easily for olympian-to-herculean
>> If '//| and ./|) will cover the herculean range in this area, why
>> introduce a new symbol core?
> It's the same reason as for the existence of other non-athenians (and
> non-herculeans) - to notate some large ETs which would otherwise have
> or two accented symbols.
>>> Then 13:25M could be )//|. (right accent).
>>> But why wouldn't 13:25M be '|~) in olympian?
>> Only if |~) is 5:13S. That, plus the question of how (and whether)
>> 5:13S and 7:23S should have separate (exact) symbols, is an issue
>> have to take up when we discuss olympian.
> Since we've agreed on herculean, it looks like we're now discussing
> olympian or promethean. I think both of them require a decision on
> Then there's the possibility that |~) is not used in any JI notation,
> only in large ETs. We'd still have to decide what comma it is. And
> wouldn't it be the simplest in range?
I've been thinking about that and have an answer, but since this is
still subject to oscillation, I'll tell you later.
>>>> So here's what I get for the herculean symbol sequence:
>>>> '| )| |( '|( )|( ')|( ~|( |~ ~~|
>>>> ./| /| '/| .|) |) '|) |\ (| ~|)
>>>> .(|( (|( .//| //| '//| ./|) /|) '/|)
>>>> /|\ (/| '(/| |\) (|) .(|\ (|\ '(|\
>> Evidently we agree (whew!).
> It isn't pretty, and it isn't memorable. It would be nice to have a
> reasonably short account of why it's the best. A few principles
> consistently applied. Even if it's not exactly how we arrived at it.
> Because people are going to ask. I want to be able to make a
> that comes up with it automatically. The boundary tweaking seems
> particularly difficult to justify.
I have an idea for herculean boundaries that gives up equidistance in
order to gain more 5sC=LAS, DAFA, DAFH, and MTC, and also fewer
instances of symbols having both left and right accents when you add
accents for olympian. Rather than elaborate on it now and run the risk
of oscillating back and forth on the details, I need to work on it and
see how well it comes together before I say any more. I'll need at
least a few days (it covers everything from athenian through olympian),
so it will probably not be till next week before I've settled most of
>> Then only thing about which we disagree, then, as far as herculean
>> concerned, is whether symbol definitions should be independent of
>> resolution (which is more of a theoretical than a practical issue).
>> And the only thing remaining is to finalize the boundary tweaking
>> those couple of degrees that require it.
So I thought -- before my latest brainstorm.
> Yes. Will you put together the relevant sag_ji3.par file?
> Let's not send it to Manuel until we have the olympian and possibly
> promethean too.
Yes, I agree.
>> Thank God it's almost the weekend -- I desperately need a break from
>> all of this!
> Yes. Congratulations, we have agreed on herculean symbols and
> for the first time ever.
No, not the boundaries yet. (Groan!) Not till my latest brainstorm
runs its course.
> I'm sorry you had to drag me kicking and screaming
> for so much of the way.
I hope I don't have you kicking and screaming too much next week.
> How about a 455nC=RAS principle and a ???nC=DRAS principle?
Huh? What? Duh -- now I get it! I don't know how often we could
apply that. There might also be a 4375nC=RAS alternative where 455n
doesn't work. And that other one might be a 65:77nC=DRAS principle.