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Message: 6325 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:14:05

Subject: Re: A common notation for JI and ETs

From: Carl Lumma

>> >ommatic UV seems okay to me.  The terminology comes from
>> Fokker, and refers to a quantity with magnitude and direction.
>> What would you suggest Gene?
> 

> We aren't in a vector space, so mathematically it's awfully
> dubious to be talking about vectors. I think it is confusing
> and excessively verbose. "Comma" is short and sweet.


But you can't force all commas to vanish.  So shall we count
you as vote #2 for "vanishing comma"?

-Carl

Message: 6326 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:17:04

Subject: Re: A common notation for JI and ETs

From: Carl Lumma

Graham Breed <graham@m...> wrote:

> Me:

>> Ratios are one of the insufficiently 
>> general representations -- they don't work for inharmonic
>> timbres.


Wow, Graham, what have you got up your sleeve?  Do I
understand correctly that you're doing away with the
'extraction of fundamental' abstraction that we've been
relying on here since the dawn of time?  Do we really
have the tools to, and would there be any benefit from,
consider all the partials all of the time?

-Carl

Message: 6327 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:23:19

Subject: Re: A common notation for JI and ETs

From: Graham Breed

Carl Lumma  wrote:


> Wow, Graham, what have you got up your sleeve?  Do I
> understand correctly that you're doing away with the
> 'extraction of fundamental' abstraction that we've been
> relying on here since the dawn of time?  Do we really
> have the tools to, and would there be any benefit from,
> consider all the partials all of the time?


I'm not sure what you're talking about there, but I don't think it 
applies to me.  All I do is find approximations to a set of consonant 
intervals, which may happen to be the logarithms of rational numbers, 
but don't need to be.  And I've been doing that for a while now.


                         Graham

Message: 6328 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:28:35

Subject: Re: A common notation for JI and ETs

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith 
<genewardsmith@j...>" <genewardsmith@j...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus 

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> 

>> what's wrong with "commatic unison vector"?
> 

> I'd prefer not to call positive rational numbers "vectors" in 
general.


how about "commatic unison"?

Message: 6329 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:32:38

Subject: Re: A common notation for JI and ETs

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" 
<d.keenan@u...> wrote:


> The prime-exponent vector is only one specific mathematical
> representation of these things. One could also argue that there is
> really only one "unison vector" and that's [0 0 0 ...].


in conventional theory, there's not only a "perfect unison" but also 
an "augmented unison", etc.


> Now with Paul's term "commatic unison vector", which is contrasted
> with "chromatic unison vector", we have a third sense of "comma".
> Meaning that which vanishes (or is distributed so you don't notice
> it). Could that be the original meaning of "comma"? No, it seems 
that
> they were so named purely because of their small size (but not
> undetectability).


this assumes that just intonation was actually used in practice. i 
disagree. the commas were found in JI theory, not in musical practice.


> "Commatic unison vector" translates to "commatic comma", which looks
> like a redundancy.


how do you make that translation?


> What's wrong with "vanishing comma" vs. "chromatic comma" or
> "distributed comma" versus "chromatic comma"?


"chromatic comma" seems like a contradiction. however, i have no 
problem with "vanishing comma" or "distributed comma".

Message: 6330 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 00:26:58

Subject: Re: A common notation for JI and ETs

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith
<genewardsmith@j...>" <genewardsmith@j...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx David C Keenan <d.keenan@u...>
wrote:
> 

>> Monz             George and Dave
>> --------------------------------
>> skhisma          schisma
>> kleisma          kleisma
>> comma            comma
>> small diesis     comma
>> great diesis     diesis
>> small semitone   ediesis (and other larger anomalies)
> 

> Will it cause confusion to call any small interval which vanishes in

a given temperament a "comma"? Some word is needed, and I'm not keen
on "unison vector".

>


I believe it would cause confusion to do that. For a start the term
"comma" is already overloaded with the job of being a general term as
well as suggesting a certain range of sizes. Folks have tried to
relieve it of one of these tasks. For the general term we also have
"unison vector", "anomaly" and "residue". Anyone know any others?
These all have problems: 

The prime-exponent vector is only one specific mathematical
representation of these things. One could also argue that there is
really only one "unison vector" and that's [0 0 0 ...].

An anomaly sounds like something unexpected - that failed to be
predicted by some theory.

A residue is something that remains, but on the contrary they often
"vanish".

So I'm stuck using "comma" for the general term as well as the
specific range, although I will use one of these others on occasion
where I'm wanting to use both senses of "comma" together.

Now with Paul's term "commatic unison vector", which is contrasted
with "chromatic unison vector", we have a third sense of "comma".
Meaning that which vanishes (or is distributed so you don't notice
it). Could that be the original meaning of "comma"? No, it seems that
they were so named purely because of their small size (but not
undetectability).

"Commatic unison vector" translates to "commatic comma", which looks
like a redundancy.

What's wrong with "vanishing comma" vs. "chromatic comma" or
"distributed comma" versus "chromatic comma"?

Although in size the chromatic ones are more usually small semitones
rather than commas.

Message: 6331 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:34:12

Subject: Re: A common notation for JI and ETs

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma <clumma@y...>" 
<clumma@y...> wrote:

>>> Will it cause confusion to call any small interval which
>>> vanishes in a given temperament a "comma"? Some word is
>>> needed, and I'm not keen on "unison vector".
>> 

>> what's wrong with "commatic unison vector"?
> 

> What's wrong with "comma", which has been standard on
> this list for years?
> 
> -Carl


some commas might not vanish in a given temperament.

Message: 6332 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 01:38:55

Subject: Re: Comment on notation

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith
<genewardsmith@j...>" <genewardsmith@j...> wrote:

> If we take the Hemiennealimmal temperament, which one gets by

ignoring the "schismninas" sagittal proposes to ignore, and then zeros
out one of the commas associated to 11-limit symbols as well, one gets
the following list of vals:

> 
> 729/704  [198, 312, 457, 554, 684]
> 
> 33/32  [18, 28, 41, 50, 62]
> 
> 36/35  [18, 30, 44, 52, 63]
> 
> 6561/6400  [90, 142, 208, 252, 311]
> 
> 45/44  [108, 170, 249, 302, 373]
> 
> 45927/45056  [306, 484, 709, 858, 1058]
> 
> 55/54  [36, 58, 85, 102, 125]
> 
> 81/80  [90, 142, 208, 252, 311]
> 
> 5120/5103  [198, 314, 460, 556, 685]


Why does this matter? Can you interpret it for me please.


> All of these except for the last, for 5120/5103, are non-standard.


I don't know what you mean by non-standard.


> Have you two notated the 198-et, by the way?


No, but I just tried, and it is difficult. The biggest problem is in
finding a valid symbol for 10deg198. Best I can come up with is 

198: )|(  |~  ~|(  /|  |\  /|~  (|(  ~|\  /|\  .(|\  (|)

You will see that I have resorted to using a 5-schisma flag to notate
10deg198 as the 7-ediesis 27:28. It could equally be '/|) the 7-diesis
57344:59049. This is rather ugly either way.

Why do you think it worth notating?


> If we take the ratio of two continguous intervals on the above list,

and toss 5120/5103 which we have already considered, we get the
following vals, all of which are standard, and in which the notation
simplies itself:

> 
> 413343/409600  [72, 114, 167, 202, 249]
> 
> 2200/2187  [126, 200, 293, 354, 436]
> 
> 243/242  [72, 114, 167, 202, 249]
> 
> 385/384  [72, 114, 167, 202, 249]
> 
> 8019/8000  [72, 114, 167, 202, 249]
> 
> 1240029/1239040  [342, 542, 794, 960, 1183]


I don't know why this matters either. More interpretation needed.

Message: 6333 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:39:28

Subject: Re: A common notation for JI and ETs

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Graham Breed <graham@m...> wrote:

> Dave Keenan  wrote:
> 

>> The prime-exponent vector is only one specific mathematical
>> representation of these things. One could also argue that there is
>> really only one "unison vector" and that's [0 0 0 ...].
> 

> There may be other representations, but all the sufficiently 
general 
> ones will be some kind of vector.  Ratios are one of the 
insufficiently 
> general representations -- they don't work for inharmonic timbres.
> 
> Unison vectors do become unisons in the resulting temperaments -- 
and 
> they really are vectors at that point, not ratios.  The usage of 
> "chromatic unison vector" for linear temperaments is suspect.  
Fokker 
> only considered equal temperaments, where all unison vectors vanish.


actually, fokker only considered just intonated periodicity blocks, 
where none of the unison vectors vanish.

Message: 6334 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 02:10:34

Subject: A few TM bases

From: Gene Ward Smith

In case it might be relevant, here are TM bases for the commas of
494 (11 and 13 limits) and 612 (11 limit.)

494 11-limit
[131072/130977, 234375/234256, 3025/3024, 4375/4374]

494 13-limit
[31250/31213, 1716/1715, 2080/2079, 3025/3024, 4096/4095]

612 11-limit
[2401/2400, 3025/3024, 4375/4374, 184549376/184528125]

Message: 6335 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 21:55:35

Subject: Re: A common notation for JI and ETs

From: gdsecor

--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" 
<d.keenan@u...> wrote:

> Here's another data point relevant to the comma-name boundaries
> discussion.
> 
> 49:125  E-13.469   Fb-36.929  
> 
> 36.929 c must be notated as ~|) which should make it a comma.
> Therefore 13.469 c ought to be a kleisma, as it would be with a 
13.47
> c boundary.


I haven't had a chance to keep up with all of your latest boundary 
changes, but your method makes sense, and assuming you haven't make 
any miscalculations, what you have should be okay.  (I'm dropping my 
proposal for a 120:121 boundary, because it serves no useful purpose, 
except to suggest a ballpark value.)


> As for the names of the categories - how about
> 
> hypodiesis
> diesis
> hyperdiesis
> 
> Which can be abbreviated to 
> 
> odiesis
> diesis
> ediesis


I think that the idea is good, but I have two suggestions.

1) I was thinking of having three different prefixes (such as mini, 
midi, and maxi, although probably not those three) and 
allowing "diesis" to remain a more general term that would cover all 
three.

2) The three prefixes should be more than just a single letter -- 
odiesis and ediesis sound too much alike.

I was about to suggest three prefixes used in organic chemistry: 
ortho, meta, and para.  The original 125:128 diesis would then 
appropriately be termed an orthodiesis.  The abbreviations o-diesis, 
m-diesis, and p-diesis would even work.  Unfortunately, the 
particular dieses that we're using the o and m characters for are 
both in the para category.  Perhaps we could use meta for the largest 
group (the meaning, "beyond," would still apply) and find a couple of 
other prefixes that wouldn't conflict with (and might even tie in 
with) the letters q and n for the small and middle ranges.

--George

Message: 6336 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 03:50:09

Subject: Re: A common notation for JI and ETs

From: Carl Lumma

>> >ill it cause confusion to call any small interval which
>> vanishes in a given temperament a "comma"? Some word is
>> needed, and I'm not keen on "unison vector".
>

>what's wrong with "commatic unison vector"?


What's wrong with "comma", which has been standard on
this list for years?

-Carl

Message: 6337 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 22:29:16

Subject: Vectors? (was: A common notation for JI and ETs)

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx Graham Breed <graham@m...> wrote:

> Carl Lumma  wrote:
> 

>> Wow, Graham, what have you got up your sleeve?  Do I
>> understand correctly that you're doing away with the
>> 'extraction of fundamental' abstraction that we've been
>> relying on here since the dawn of time?  Do we really
>> have the tools to, and would there be any benefit from,
>> consider all the partials all of the time?
> 

> I'm not sure what you're talking about there, but I don't think it 
> applies to me.  All I do is find approximations to a set of consonant 
> intervals, which may happen to be the logarithms of rational numbers, 
> but don't need to be.  And I've been doing that for a while now.
> 
> 
>                          Graham

Hey guys,


How about changing the title of this thread. It hasn't had anything to
do with the common notation for quite some time.

Message: 6338 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 14:30:13

Subject: Re: A common notation for JI and ETs

From: David C Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "gdsecor <gdsecor@y...>" <gdsecor@y...> 
wrote:

 > --- In tuning-math@xxxxxxxxxxx.xxxx David C Keenan <d.keenan@u...>
 > wrote:

>> ... [re boundaries]
>> To summarise:
>> 0
>> schismina
>> 0.98
>> schisma
>> 4.50
>> kleisma
>> 13.58
>> comma
>> 37.65
>> carcinoma
>> 45.11
>> diesis
>> 56.84
>> ediasis
>> 68.57
>> ...
>> On second thoughts, 13.47 cents might be a better choice for the
 > kleisma-comma boundary.
 >

 > I don't know where you're getting the numbers 13.58 and 13.47 cents.


Sorry I ran out of time to explain that yesterday. I'm getting them from a 
bloody great spreadsheet that generates all the commas satisfying certain 
criteria, for ratios N in popularity order, and when given the category 
boundaries tells me for each N how many are in each category.

I can then fiddle with the boundaries and see how far down the list I have 
to go before I get 2 in the same category.


 > I indicated earlier a rationale for a lower limit for a comma:
 >
 > << The point here is that I thought that the comma (120:121,
 > ~14.367c) between the next smaller pair of superparticular ratios
 > (10:11 and 11:12) should be smaller than the lower size limit for a
 > comma. >>


But it is a rationale that bears little relationship to the reason we want 
these boundaries, which is to make it so there is at most one instance of 
each category for a given popular N. I take it instead as an argument for 
putting the boundary "in that ballpark", with 1 cent either way not 
mattering very much.


 > So I suggest that the upper limit for a kleisma should be 120:121
 > (~14.367c), and that a comma would be anything infinitesimally larger
 > than that, unless there is something between 13.47 and 14.37 cents
 > that we need to have in the comma category.


I believe there is. Namely the 7:125-comma and the 43-comma.

N      From C with cents   Popularity  Ocurrence
                            ranking
------------------------------------------------
7:125  Ebb-9.67  D+13.79    35          0.21%
43     E#+9.99   F-13.473   58          0.10%
143    Ebb-11.40 D+12.06    66          0.09%
17:19  D+11.35   Ebb-12.11  72          0.08%

The 143 (=11*13) and 17:19 cases above are not a problem because we'd be 
forced to notate them all as ~)| anyway.

The question really becomes: How far either side of the half Pythagorean 
comma would a pair of "commas" have to be before we'd notate them using two 
different symbols?

In size order we have
~)|
.~|(
'~)|
~|(

The 5:17-kleisma of 12.78 cents is notated exactly as .~|( and it needs to 
be called a kleisma because there is also a 5:17-comma at 36.24 cents 
(unless we were going to pull the comma-carcinoma boundary down below 
36.24, which I don't recommend).

I propose that if it's notated as ~)| or .~|( then it's a kleisma and if 
its notated as ~|( or '~)| it's a comma.

So in size order we have:
~)|    primarily the 17:19-kleisma 11.35 c
               (but the 143-kleisma 12.06 c is more popular)
.~|(   primarily the  5:17-kleisma 12.78 c
'~)|                      43-comma 13.473 c
            or possibly 7:125 comma 13.79 c
~|(    primarily the      17-comma 14.73 c

The boundary then is most tightly defined between .~|( and '~)|. We already 
have the 5:17-kleisma at 12.78 cents for .~|(. The most popular thing I can 
find that _might_ be notated as '~)| is the 7:125-comma of 13.79 cents. It 
would otherwise be notated as ~|( so it would still be called a comma. 
However the most popular that _needs_ to be notated as '~)| is the 43-comma 
of 13.473 cents.

Similarly the comma-carcinoma boundary should be between
~|)  primarily the 5:17-comma 36.24 c
/|~  primarily the 5:23-carcinoma 38.05 c

These are less than a 5-schisma apart and so there are no combinations with 
the 5-schisma flag to confuse the issue. Halfway is at 37.14 cents.

Many commas come in pairs that differ by a Pythagorean comma, so it would 
be an advantage to have the distance from the kleisma-comma boundary to the 
comma-carcinoma boundary being exactly a Pythagorean comma. That way we are 
guaranteed never to find such a pair falling into the comma category.

A Pythag comma up from 13.47 is 36.93 cents, which will do nicely.

To summarise:
0
schismina
0.98
schisma
4.50
kleisma
13.47
comma
36.93
carcinoma
45.11
diesis
56.84
ediasis
68.57

Message: 6339 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 23:12:24

Subject: Re: A common notation for JI and ETs

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma <clumma@y...>" <clumma@y...> wrote:


> But you can't force all commas to vanish.  So shall we count
> you as vote #2 for "vanishing comma"?


What I say is "commas of temperament T", meaning those which belong to the kernal of T, or vanish.

Message: 6340 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 04:36:35

Subject: Re: A common notation for JI and ETs

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "gdsecor <gdsecor@y...>"
<gdsecor@y...> wrote:

> I think that if we can't think of anything else, then it will have to 
> be either * and k or * and c.  I agree that the k character is rather 
> large, so I would tend to prefer * and c, even if they aren't very 
> good as opposites.
> 
> I like the pair a and e, because the letters are small.  True, they 
> don't look much like the 5:7 kleima symbols, but at this point 
> nothing will.  I don't know which one should be up and which down -- 
> a (for ascending) and e for (d_e_scending) might therefore be as good 
> a choice as any.
> 
> But of the two above, I think I would go for * and c, which, like the 
> 17 comma, have a special character and letter as a pair.

Sold!

Message: 6341 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 23:16:11

Subject: Re: A common notation for JI and ETs

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:


> how about "commatic unison"?


Ick. If threatened, I'll pull inside my shell and start saying "kernel elements".

Message: 6342 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 04:43:53

Subject: Re: A common notation for JI and ETs

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma <clumma@y...>"
<clumma@y...> wrote:

>>> Will it cause confusion to call any small interval which
>>> vanishes in a given temperament a "comma"? Some word is
>>> needed, and I'm not keen on "unison vector".
>> 

>> what's wrong with "commatic unison vector"?
> 

> What's wrong with "comma", which has been standard on
> this list for years?


Because simply calling something a comma should not imply that it
vanishes.

Message: 6343 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 04:49:30

Subject: Re: A common notation for JI and ETs

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>"
<d.keenan@u...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "gdsecor <gdsecor@y...>"
> <gdsecor@y...> wrote:

>> I think that if we can't think of anything else, then it will have to 
>> be either * and k or * and c.  I agree that the k character is rather 
>> large, so I would tend to prefer * and c, even if they aren't very 
>> good as opposites.
>> 
>> I like the pair a and e, because the letters are small.  True, they 
>> don't look much like the 5:7 kleima symbols, but at this point 
>> nothing will.  I don't know which one should be up and which down -- 
>> a (for ascending) and e for (d_e_scending) might therefore be as good 
>> a choice as any.
>> 
>> But of the two above, I think I would go for * and c, which, like the 
>> 17 comma, have a special character and letter as a pair.
> 
> Sold!


I'm going to push on here and suggest we use $ and z for the 23-comma
symbols |~ and !~

That way we have a single ascii character for every flag, and could
could then have at most two-character abbreviations for all the
single-shaft symbols.

Message: 6344 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 07:26:51

Subject: Re: A common notation for JI and ETs

From: Dave Keenan

Here's another data point relevant to the comma-name boundaries
discussion.

49:125  E-13.469   Fb-36.929  

36.929 c must be notated as ~|) which should make it a comma.
Therefore 13.469 c ought to be a kleisma, as it would be with a 13.47
c boundary.

As for the names of the categories - how about

hypodiesis
diesis
hyperdiesis

Which can be abbreviated to 

odiesis
diesis
ediesis

Message: 6345 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 09:11:57

Subject: Re: A common notation for JI and ETs

From: Carl Lumma

>> >hat's wrong with "comma", which has been standard on
>> this list for years?
>

>Because simply calling something a comma should not imply
>that it vanishes.


Oh, I thought the issue was about making "comma" mean
"syntonic comma", which would be a horrendous disaster.

Commatic UV seems okay to me.  The terminology comes from
Fokker, and refers to a quantity with magnitude and direction.
What would you suggest Gene?

While I'm at it, I'll once again throw wounding darts in the
general direction of any excess in prescriptive defining.  I
think we have the right and obligation to revise standard
music-theory terminology *when necessary*.  That is, when
creating a context that makes the standard term(s) clear is
*unusually difficult*.  Anything more is a waste of time, IMHO.

-Carl

Message: 6346 - Contents - Hide Contents

Date: Thu, 06 Feb 2003 09:50:30

Subject: Re: A common notation for JI and ETs

From: Graham Breed

Dave Keenan  wrote:


> The prime-exponent vector is only one specific mathematical
> representation of these things. One could also argue that there is
> really only one "unison vector" and that's [0 0 0 ...].


There may be other representations, but all the sufficiently general 
ones will be some kind of vector.  Ratios are one of the insufficiently 
general representations -- they don't work for inharmonic timbres.

Unison vectors do become unisons in the resulting temperaments -- and 
they really are vectors at that point, not ratios.  The usage of 
"chromatic unison vector" for linear temperaments is suspect.  Fokker 
only considered equal temperaments, where all unison vectors vanish.


> Now with Paul's term "commatic unison vector", which is contrasted
> with "chromatic unison vector", we have a third sense of "comma".
> Meaning that which vanishes (or is distributed so you don't notice
> it). Could that be the original meaning of "comma"? No, it seems that
> they were so named purely because of their small size (but not
> undetectability).


The original meaning of "comma" seems closest to anomaly from what I've 
read.


> What's wrong with "vanishing comma" vs. "chromatic comma" or
> "distributed comma" versus "chromatic comma"?


"Vanishing comma" sounds good to me.


                         Graham

Message: 6347 - Contents - Hide Contents

Date: Fri, 07 Feb 2003 01:01:10

Subject: partial-specific theory

From: Carl Lumma

>> >ow, Graham, what have you got up your sleeve?  Do I
>> understand correctly that you're doing away with the
>> 'extraction of fundamental' abstraction that we've been
>> relying on here since the dawn of time?  Do we really
>> have the tools to, and would there be any benefit from,
>> consider all the partials all of the time?
> 

> I'm not sure what you're talking about there, but I don't
> think it applies to me.


What were you writing about ratios being insufficient?

"Intervals are defined as vectors in terms of a minimal subset
of the partials relative to the fundamental (which, for inharmonic 
timbres, will probably be the whole set)."

etc.

-C.

Message: 6348 - Contents - Hide Contents

Date: Fri, 07 Feb 2003 14:30:02

Subject: Re: A common notation for JI and ETs

From: David C Keenan

Was: Comment on Notation


>--- In tuning-math@xxxxxxxxxxx.xxxx "gdsecor <gdsecor@y...>"
><gdsecor@y...> wrote:
>--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>"
><d.keenan@u...> wrote:

>> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith
>> 

>>> Have you two notated the 198-et, by the way?
>> 

>> No, but I just tried, and it is difficult. The biggest problem is in
>> finding a valid symbol for 10deg198. Best I can come up with is
>> 
>> 198: )|(  |~  ~|(  /|  |\  /|~  (|(  ~|\  /|\  .(|\  (|)
>> 
>> You will see that I have resorted to using a 5-schisma flag to
>notate

>> 10deg198 as the 7-ediesis 27:28. It could equally be '/|) the 7-
>diesis

>> 57344:59049. This is rather ugly either way.
>

>Ugly is a good way of putting it, since it is evident that (/| and
>|\) aren't a cure-all for our half-apotome problems.  The cleanest
>way to do it here (as well as in a lot of those divisions that
>require something very close to 1/2-apotome) would be '|)).  The
>thing that has been keeping us from using it is that we don't have a
>rational complement for |)).  But should that stop us from
>having '|)), which is its own rational complement?


No. What the heck! I'm in a "throw caution to the winds" kinda mood today.


>I hesitate to suggest this, but with the pinch we're in, we could
>possibly allow ''|)) as the rational complement of |)) -- if we could
>this once allow a double-5-schisma, just as we allowed a double-5
>comma.


Yech! Not that much of a mood. :-)


>I've noticed that the 19-schisma is only rarely twice the
>number of degrees in an ET as the 5-schisma, or I might have
>suggested )|)), even if it's a three-flagger.


Gee. A choice between a 3-flagger and a 2-flag-on-the-same-side-er with 
double accents. Sounds like the proverbial rock and hard place.

Tell me again why we can't use (/| as 49-diesis and '(/| as 
self-complementing 5:49 diesis, or indeed with complement .|\) ?

Is it that whenever you need to use it it has inconsistent symbol 
arithmetic based on summing the flags? Examples?

-- Dave Keenan
Brisbane, Australia
Dave Keenan's Home Page * [with cont.]  (Wayb.)

Message: 6349 - Contents - Hide Contents

Date: Fri, 7 Feb 2003 13:13:55

Subject: A common notation for JI and ETs

From: George Secor

--- In tuning-math@xxxxxxxxxxx.xxxx David C Keenan <d.keenan@u...>
wrote [#5713]:

> Hi George,
>--- In tuning-math@xxxxxxxxxxx.xxxx "gdsecor <gdsecor@y...>"
<gdsecor@y...> wrote:

>> --- In tuning-math@xxxxxxxxxxx.xxxx David C Keenan <d.keenan@u...>
wrote:

>>> This problem is not with the existence of single sagittal symbols
between
>>> sharp and double-sharp or flat and double-flat, but specifically
with the
>>> appearance of their shafts. There is a Ted Mook type objection
>>> (sight-reading in bad light) to the triple-shafts, which I refer
to as
>>> 2-3-confusability. We addressed that partially by agreeing not to
pack the
>>> triple-shafts into the same width as the double-shafts, but I
believe the
>>> problem still remains.
>

>> When I did some legibility testing with a few subjects last year, I
>> found that the distance at which the number of shafts could be
easily
>> distinguished was greater than that at which wavy flags could easily
>> be distinguished from concave ones.  Given that, I don't believe
that
>> there is a problem such as you describe.


> I understood that these subjects were only involved in deciding
whether they 
> preferred the middle shaft shortened or not, and that the distance
recognition tests 
> were only conducted with yourself as subject. Is this correct?
> 
> Can you tell me something about your subjects and the test. How many?
What 
> were their musical backgrounds? Were they likely to be impartial or
were they 
> friends or relatives who might pick up subliminal cues as to which
you preferred? 
> What instructions were they given? How was the test conducted?


I will quote here a considerable portion of the email that I sent you
on 29 April 2002, which will answer some of those questions.

<< I also got an answer from the tests that I ran this past weekend.  I
printed out your test page and also your adaptive JI page with the
staves approximately the same size.  Both were just slightly larger
than most printed music.

Using five different test subjects, I explained in advance the
difference between the top and bottom lines and the purpose of the
middle-shaft modification, but I didn't give any indication of my
personal preference.  Four preferred the 3-shaft symbols the same
length and one preferred the shorter middle shafts.  Although all were
definite in their preferences, they all thought that the difference in
legibility between the two choices was small.

I also ran more extensive tests using myself as a test subject.  When I
placed your test page and your adaptive JI page beside each other and
gradually backed away from them, I observed that (at a distance of
somewhat more than a meter) it became more difficult to tell the
difference between a wavy left and a straight left symbol sooner it did
to tell the difference between the two-shaft and three-shaft arrow
symbols (regardless of the length of the middle shaft).  I also
observed that the difference in legibility between the two
sesqui-symbol choices was small, with the equal-length choice having a
very slight edge.

One conclusion that I can draw from this is that, given that it is more
of a problem to distinguish the flag shapes, there is definitely no
point in making the arrow shafts thicker than they are.  I found that a
normal reading distance of about 75 centimeters presents no problems in
distinguishing either the flags or the number of shafts (with either
sesqui option), but since orchestral players might have to read at a
somewhat greater distance, I would highly recommend using staves
somewhat larger than usual for orchestral parts.

So I personally don't think it matters much whether the middle shaft is
shorter or the same length when it comes to distinguishing how many.

Another question that may be asked is whether a vertical difference in
shaft length might be distracting in that it may tend to draw the eye
away from the end of the symbol having the flags.  The differences
between the various flags is perceived *vertically*, while the number
of shafts is perceived only *horizontally* if all are the same length. 
I tried reading quickly from one chord to another in one of your 19-Apr
files (two staves below the one labeled "prime comma symbols", and I
found that I had to make an effort to force my attention *away* from
the shaft ends of the sesqui symbols to concentrate on the flags,
whereas I didn't have this problem with the two-shaft symbols.  In
other words, once I was close enough to clearly see the difference in
length between the shafts, the difference wasn't necessary and I found
this feature to be a distraction.

So I would say that I would prefer the three lines the same length with
the sesqui symbols, but not for the reason that we were debating. >>

Now to answer the rest.

My testing was not done under controlled conditions -- much was out of
my control, and there was only a very limited time (only about 10
minutes) available, but I thought it was better than nothing.  It was
done at my church, and the subjects were the music director, three
musicians from the group that plays for the service, and my daugher
(tested separately from the others, inasmuch as she had already seen my
version of the symbols.  Let me state outright that I value my
daughter's opinion very highly, because she's very outspoken and, when
I ask her opinion about something, she speaks her mind, whether I like
it or not).  As for the other four subjects, I tried not to influence
their decision in any way by my facial expressions (which I suppose
still would't guarantee that I didn't).  About the only conclusion that
I could safely make from so small a sample is that it was unanimous
that the difference in legibility between a 3-shaft symbol that has an
equal-length or shortened middle shaft is marginal.

By the way, I do seem to remember asking one of my subjects whether he
thought it might be too difficult to distinguish a concave from a wavy
flag, and he said that he could tell them apart without any trouble.

As it turned out, I also ended up being one of the subjects, inasmuch
as I discovered that the experience of viewing the symbols on a printed
page was a bit different than of seeing them on a computer screen
(particularly the ones with concave and wavy flags), and I very quickly
observed a couple of things that I hadn't planned to test with my other
subjects.  One of these was that, as I moved farther away from the
page, it was evident that it was much easier to distinguish a 2-shaft
symbol from a 3-shaft one of the same type than it was to distinguish a
wavy flag from a concave flag in a single-shaft symbol (and that a flag
distinction was easier if the symbols had multiple shafts).  I also
observed that with the 3-shaft symbols with shortened center shaft, my
eye was continually drawn away from the flags toward the shaft ends,
which I found to be a distraction, inasmuch as I wanted my attention to
be centered on the flags themselves.  With the equal-length shafts I
had no problem distinguishing 3 shafts from 2 or X with my attention
centered on the flags (reading at the farthest distance at which I
could comfortably distinguish a wavy from a concave flag.

Thus I found that unequal shaft lengths would be of little (if any)
value in distinguishing 2 from 3, while introducing a problem that I
did not encounter with the equal lengths.  I didn't test anybody else
regarding this, because there wasn't any time left even to explain what
I wanted to determine.


> We both know the answers to these questions in the case of the

subject Ted Mook. 

> He has been involved in trying out various microtonal notations as a
performer. 
> He only knows me from one previous email exchange in which I asked
him why 
> he didn't like the tartini symbols. I expect you still have the email
exchange 
> relating to the test. The test was conducted by email, 

> so subliminal cues would be difficult. Ted preferred the shortened
middle shaft. 
> But I acknowledge that a result from a single subject means almost
nothing.


But there was no variation in the kinds of flags that were used in the
symbols that Ted saw, hence he would have had no reason to find a short
middle shaft an objectionable distraction, as I did.


> Even if we assume your results are valid above, your argument from

them is a 

> non-sequitur. It might only mean that we have a bigger problem with 
> distinguishing wavy flags than we do with distinguishing triple

shafts. But even 

> this is not the case, because the consequences of mistaking a wavy

flag for a 

> straight one are not very serious musically (about 15 cents), while
mistaking a 
> triple shaft for a double is very serious (about 100 cents).


So something that is slightly less readable has less serious
consequences if it is misread.  That sounds okay to me -- certainly not
a reason to change anything.


>> [GS:]
>> (Do we
>> have to go through all this again?  I think we are still agreeing to
>> disagree.  But now, after having written everything else in this
>> message, I've come back to this point, because I think I've figured
>> out why you've brought all of this up.  You're testing me to see if
I
>> still feel the same way about all of this, because you don't want to
>> do a lot of work on the font, only to have me change my mind.)
> 

> It's the font work, yes - as I already said in a subsequent post. But

> I'm not testing you to see if you still feel the same way. I'm trying

> to brutally force you to have the rational discusion that I gave up 
> on previously when I got the "sacred cow" feeling. Or maybe its 
> not so much a sacred cow, but it's just that you have been using 
> them yourself for a long time and would find in very inconvenient 
> to change. But (and I'm always saying this to someone in these 
> standardisation efforts) you are only one person. What is your 
> inconvenience compared to that of all those who may come after 
> you?


I have given a lot of thought to those who may come after me,
particularly the novice.  I want the first step in learning the
single-symbol version of the notation to be *conceptually* as simple as
possible.  The notation for 24-ET (considered either alone or as a
subset of 72-ET) or 31-ET is so simple that even a child would be able
to understand and remember the symbols with minimal effort.  Unless I
see some *compelling* reason that one to three shafts and X, along with
an up or down arrowhead, is too difficult to *read* or *distinguish*,
then I must reject any departure from this as an unnecessary
*complication* that would make the notation more *difficult to learn*. 
I want someone's reaction to the first lesson in microtonal notation to
be, "Hey, this is a lot easier than I expected!"  We should remember
that first impressions are very important.  Therein lies the "sacred
cow" that you're up against.

If you take away the simplicity of:

| is 1 degree
|| is 2 degrees
||| is 3 degrees
X is 4 degrees
^ is up
v is down

by adopting something like your latest proposal:


> |    0/2 apotome
> ||   1/2 apotome
> \/   2/2 apotome  (note these are shafts not straight flags)
> \ /  3/2 apotome


then that simplicity has been compromised.  My daughter's reaction to
your latest for 2/2 and 3/2 apotome was immediate (as if she had read
my mind): the shafts would look too much like straight flags.  A major
advantage of the vertical lines (and even the X) is that they don't
interfere with or otherwise detract from the perception or
identification of the flags, because they look completely different.

I hope I've adequately (and rationally) addressed the issues you
raised.  If you still want to make some sort of symbol proposal based
on what you sketched above -- some actual symbols in a graphic, then
I'd be happy to look at them.  Otherwise, I can't imagine how something
like that could be an improvement.

--George


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