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Message: 6375 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 16:33:35

Subject: Re: naming temperaments

From: Carl Lumma

>{{As it stands, there's no good way to talk about the *blocks*
>behind popular temperaments.}}
>
>Why do you say blocks are behind temperaments?


Because that's the way I think of temperaments.

-Carl

Message: 6376 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 18:33:33

Subject: Re: Janata paper

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> 
wrote:

>>> How would you instruct someone to build such a torus? 
>> 

>> you can look at hall's paper where a plastic inflatable one is 
>> depicted, or take schoenberg's or krumhansl's diagrams and 
>> connect the opposite pairs of edges . . .
> 

> I mean, what leads you to the torus?


ultimately, it's that fact that you need two unison vectors to vanish 
in order to get from 5-limit to 12-equal. 5-limit comes about 
"naturally" in hall's case, but in schoenberg's and krumhansl's, 
it's really just a basis for 12-equal in terms of fifths and *minor* 
thirds -- fifths because the nearest key signatures are for tonics 
a fifth apart, and minor thirds because relative major and minor 
keys have their tonics a minor third apart.


>>> Janata uses key signatures, which is from where I get 7.
>> 

>> is the 7 just a result of the conventional naming, or is it more 
>> than that?
> 

> As I wrote earlier, I think Janata is saying the brain allocates
> groups of neurons to each of the 24 diatonic keys, in such a 
way
> that the distance between any pair of groups is related to the
> number of pitches shared by their associated diatonic keys.  
Was
> that your understanding?


i'll have to look at it again, but i thought it was roughly like that. 
thus the schoenberg-krumhansl torus used as the theoretical 
model.


>  If true, it's a fantastic justification
> for using partially-tempered periodicity blocks in music theory.

partially tempered??

Message: 6377 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 00:50:27

Subject: Re: Janata paper

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> 
wrote:

>>> Meanwhile, "chromatic period vector" is perfect,
>>> as far as a neuroimaging study by researchers at
>>> Dartmouth College is concerned.  They basically found,
>>> if I understand correctly, a map of meantone, as
>>> a quasi-tempered block, in patterns of brain activity
>>> of experienced listeners, when they hear chord
>>> progressions whose roots span the tuning.
>> 

>> Carl, *PLEASE* give us a link or some reference
>> to this interesting study!!!
> 
> The Cortical Topography of Tonal Structures Un... * [with cont.]  (Wayb.)
> 

> This paper has been the subject of some debate recently,
> on the SpecMus and PsyMus lists.
> 
> Also, 'quasi-tempered meantone' is ambiguous.  What the
> paper found is: each triad in 12-tET is associated with
> a region of maximum activity in the brain.  The particular
> area for each triad differs between listeners and between
> sessions for a given listener, but the distances between
> the areas is always related to the number of common pitches
> between the diatonic keys rooted on them.  For example,
> A major and F# minor have the same key signature, and AMaj
> and F#min chords activate the same regions in the brain of
> a given person on a given day.  Maybe one of our temperament
> gurus can tell us what temperaments(s) this 7-of-12 setup
> represents...where the pythagorean, syntonic, and augmented
> commas vanish and the 25:24 is chromatic?


i don't know where you're getting 7. they just used the good old 
12-equal torus.

Message: 6378 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 18:35:15

Subject: Re: Janata paper

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Carl Lumma <ekin@l...>" 
<ekin@l...> wrote:

>> but i would consider that the standard notation of 
>> 12-equal is defined by a vanishing syntonic comma, a 
chromatic 
>> 25:24, as well as a *systemic* vanishing unison vector 
(either 
>> the pythagorean comma, the diesis, or the diaschisma) . . .
> 

> Ah, this is the terminology I neeeded.  I knew of course, that
> Janata was using 12-tET, and the commas involved, but how 
to
> describe a *2-D* block with *one* chromatic and *two* 
vanashing
> commas. . .
> 
> -Carl


it's really a 7-tone block *and* a 12-tone block, operating 
simultaneously on different levels of cognition . . .

Message: 6379 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 01:13:25

Subject: Re: Janata paper

From: wallyesterpaulrus

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

>> Maybe one of our temperament
>> gurus can tell us what temperaments(s) this 7-of-12 setup
>> s...where the pythagorean, syntonic, and augmented
>> commas vanish and the 25:24 is chromatic?
> 
> 12-tET
> 
> 
>                     Graham


yup, any two of those vanishing commas together define 
12-equal or a closed 12-tone tuning (although [0 3] and [12 0] 
together give a torsional 36-tone block, since their difference, [12 
3], is three syntonic commas) . . . meanwhile, using the 
vanishing syntonic comma along with a 25:24 chroma gives the 
7-tone diatonic system. i didn't go through it in _the forms of 
tonality_, but i would consider that the standard notation of 
12-equal is defined by a vanishing syntonic comma, a chromatic 
25:24, as well as a *systemic* vanishing unison vector (either 
the pythagorean comma, the diesis, or the diaschisma) . . .

you can get some weird mutants by deliberately doing it wrong
 . . . 
pyth. comma + 25:24 chroma
|12  0|
|         | = 25-tone scale (not the standard mapping for 25)
|-1   2|

diesis + 25:24 chroma
|0     3|
|          | = 3-tone scale
|-1    2|

diaschisma + 25:24 chroma = 10-tone scale

(who needs determinants when you can just read off the 
intersections of the lines at 
Definitions of tuning terms: equal temperament... * [with cont.]  (Wayb.) ?

Message: 6380 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 18:38:33

Subject: Re: That poor overloaded word "comma"

From: wallyesterpaulrus

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


>The etymology of "comma" relates purely to small size
> (originally short duration), not vanishingness and not 
>ignoredness.


i'm not so sure!


> You realise that this also makes it more contentious to use
> "chromatic". Since an un-notated but non-vanishing comma 

could well be

> considered to provide "colour".


hmm . . . that's a stretch.


> But if "chromatic" is OK then
> "achromatic" is obviously excellent as its opposite.


a lot of things are "achromatic". for example any diatonic interval.

Message: 6381 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 01:26:16

Subject: Re: Janata paper

From: wallyesterpaulrus

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


>  . . . 
> pyth. comma + 25:24 chroma
> |12  0|
> |         | = 25-tone scale (not the standard mapping for 25)
> |-1   2|


sorry, that should be 24, not 25 . . . and in fact it's the mapping 
where 5:4 is 7 steps of 24 . . . this has affinities to the medieval 
arabic system . . .

Message: 6382 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 18:40:38

Subject: Re: That poor overloaded word "comma"

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> 
wrote:

>> You adequately explain what you mean by "unison vector" and
>> "chromatic", but for "commatic" we could be forgiven for 
thinking you
>> were referring only to its small size.
>> 
>> Had you written, "Notationally it is evident that 25:24 or 
128:135
>> serves as a /chromatic/ unison vector while 80:81 serves as a
>> /achromatic/ unison vector." there would be no problem since 
most
>> people would take achromatic to be the opposite of 
chromatic.
> 

> I don't know about that.  I took the sentence to be invoking a
> definition for those terms.  Though I admit I also already knew
> what he was talking about, I doubt any different choice of
> emphasized words would have mattered if I didn't.  Maybe 
there
> just need to be some bandwidth devoted to the definitions 
here.
> 
> -Carl


the word "commatic" is being used here, not the word "comma". 
it's etymologically related, but it doesn't have to mean the same 
thing!

Message: 6383 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 03:00:58

Subject: Re: That poor overloaded word "comma"

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:

> Dave, i'd like you to go into more detail about
> Paul's concepts and your feelings about the use
> of "comma", if you don't mind.


For more detail on Paul's concepts you should ask Paul. You might ask
him to mail you "The Forms of Tonality: a preview" if he hasn't already.

I think I've made my feelings about the use of "comma" very clear.
Maybe you just need to click the "Up thread" button a few times until
you get to where the subject heading was "A Common Notation for JI and
ETs".

It's very simple. The word "comma" (and its adjective "commatic")
already has two commonly accepted meanings in tuning theory. It
doesn't need a third one. I think "commatic" should mean only
"relating to commas", and not have a third meaning of "vanishing".
There's nothing wrong with the word "vanishing" so why would anyone
feel the to use "commatic" in this way, unless it's because they want
something that rhymes with "chromatic". Well for that purpose I
propose "achromatic", literally "not causing a change of colour"
(where colour = pitch).

I suspect the existing use of "chroma" that Carl is referring to is
practically that, a synonym for "pitch". In this sense it is used to
refer to a quality of a sound and as such will only appear as "the
chroma of <something>" and not as "a chroma".

Message: 6384 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 21:42:04

Subject: Re: A common notation for JI and ETs

From: gdsecor

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

> --- In tuning-math@xxxxxxxxxxx.xxxx George Secor wrote:
> 

>> 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. ...
> 

> You've made some good points about ease of learning and first 
impressions. 
> But I don't understand why you would fail to imagine that there 

might be a 

> way to retain those benefits while eliminating the two problems I 
have 
> described regarding the X shafts.
> 
> I played around with various ideas by modifying a copy of your 
> Symbols6.gif. The first thing I decided was to retain the triple 
shafts 
> since I found I could not adequately distinguish wide and narrow V 
shafts. 


As far as I'm concerned, the triple-shaft question is more critical 
than the X-shaft issue.


> So I looked at just changing the X shafts, and in the end decided, 
surprise 
> surprise, that X's are best!
> 
> What I've come up with is simply a different X. Its two shafts 

cross at a 

> point that aligns with the note being modified, instead of the one 
below. 
> Of course when it is used with two concave or wavy flags it does 
look like 
> a V, but I think this is fine.


Yes, the place where recognition of the X is most important is with 
the /X\ and \Y/ symbols, and what you have looks good.  With the wavy 
and concave flags I'm less concerned, because these are for the more 
sophisticated user (who should be able to recognize them for what 
they are).


> Its shafts are slightly closer to vertical 
> than those of the previous X's, so there is no danger of confusing 
them 
> with straight flags, particularly since they (like all the shafts) 
are 
> longer and thinner than straight flags.

Yes.

> I've also modified a few of the two and three shaft symbols with 
two flags 
> to a side, to eliminate the cases where a shaft passed through the 
middle 
> of a flag. Previously this was done in some cases but not in 
others. And 
> I've added a conventional joined-double-flat symbol.


Okay, I'll buy that!


> By the way, I like all the flag-combinations the way you've done 
them. In 
> particular I prefer your ~)| to mine.
> 
> See
> Yahoo groups: /tuning-math/files/Dave/Symbols6... * [with cont.] 


Okay, then, let's run with it!

--George

Message: 6385 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 21:45:33

Subject: Re: A common notation for JI and ETs

From: gdsecor

--- In tuning-math@xxxxxxxxxxx.xxxx David C Keenan <d.keenan@u...> 
wrote [#5763]:

> --- 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


The way you have it, the kleisma-comma boundary is right at the 43 
comma.  If we put the kleisma-comma boundary at ~13.125c, or halfway 
between the 5:17 kleisma (~12.777c) and the 43 comma (~13.473c), then 
a Pythagorean comma up from this would be ~36.585c.  But if we put 
the comma-diesis boundary at ~37.144c, or halfway between the 5:17 
comma (~36.237c) and the 5:23 comma (~38.051c), then a Pythagorean 
comma down from this would be ~13.684c.  Why not split the difference 
and make the boundaries ~13.404c and ~36.864c?

--George

Message: 6387 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 14:19:20

Subject: Re: Janata paper

From: Carl Lumma

>> > mean, what leads you to the torus?
>

>ultimately, it's that fact that you need two unison vectors to vanish 
>in order to get from 5-limit to 12-equal.


Right, you get a torus when you join the two pairs of edges.
But IIRC Janata found that major triad activated the same
region on the torus as its relative minor.  I'll have to check
that...


>> If true, it's a fantastic justification
>> for using partially-tempered periodicity blocks in music theory.
>
>partially tempered??


To map the 24 diatonic keys down to 12, you'd need to appeal to
untempered dicot (the new name for "neutral thirds", I take it)
embedded in 12-equal, wouldn't you?

-Carl

Message: 6388 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 03:55:14

Subject: Re: That poor overloaded word "comma"

From: wallyesterpaulrus

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

> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> 
wrote:

>> Dave, i'd like you to go into more detail about
>> Paul's concepts and your feelings about the use
>> of "comma", if you don't mind.
> 

> For more detail on Paul's concepts you should ask Paul. You 
might ask
> him to mail you "The Forms of Tonality: a preview" if he hasn't 
already.
> 
> I think I've made my feelings about the use of "comma" very 
clear.
> Maybe you just need to click the "Up thread" button a few times 
until
> you get to where the subject heading was "A Common 

Notation for JI and

> ETs".
> 
> It's very simple. The word "comma" (and its adjective 
"commatic")
> already has two commonly accepted meanings in tuning 
theory. It
> doesn't need a third one. I think "commatic" should mean only
> "relating to commas", and not have a third meaning of 
"vanishing".
> There's nothing wrong with the word "vanishing" so why would 
anyone
> feel the to use "commatic" in this way,


in my paper, "commatic" doesn't necessarily mean "vanishing" -- 
it really just means "notationally ignored".

Message: 6390 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 03:58:51

Subject: Re: Janata paper

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> 
wrote:


> PsyMus isn't on Yahoo, and it costs money.
> 
> -Carl


?? i didn't pay for my membership . . .

Message: 6391 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 22:52:45

Subject: Re: a tuning-math question

From: wallyesterpaulrus

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

> I have a tuning-math question that I'm hoping someone can answer in 
a 
> purely mathematical fashion.
> 
> If you were to divide a line segment into a given number of parts 
> of a given number of sizes, what strategies could you use to order 
> those parts? 
> 
> (I'm hoping the strategies would be general enough so that the 
number 
> of parts and separate sizes would be irrelevant--thanks.)


hi dan -- great to have you back!

how about ordering them from left to right?

(i'm probably not understanding your question . . .)

-paul

Message: 6392 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 04:01:07

Subject: Re: Janata paper

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> 
wrote:

>> i don't know where you're getting 7. they just used the good 
old 
>> 12-equal torus.
> 

> How would you instruct someone to build such a torus? 


you can look at hall's paper where a plastic inflatable one is 
depicted, or take schoenberg's or krumhansl's diagrams and 
connect the opposite pairs of edges . . .


> Janata uses
> key signatures, which is from where I get 7.
> 
> -Carl


is the 7 just a result of the conventional naming, or is it more 
than that?

Message: 6393 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 22:55:06

Subject: Re: Janata paper

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

>>> I mean, what leads you to the torus?
>> 

>> ultimately, it's that fact that you need two unison vectors to 
vanish 
>> in order to get from 5-limit to 12-equal.
> 

> Right, you get a torus when you join the two pairs of edges.
> But IIRC Janata found that major triad activated the same
> region on the torus as its relative minor.  I'll have to check
> that...
> 

>>> If true, it's a fantastic justification
>>> for using partially-tempered periodicity blocks in music theory.
>> 
>> partially tempered??
> 

> To map the 24 diatonic keys down to 12, you'd need to appeal to
> untempered dicot (the new name for "neutral thirds", I take it)
> embedded in 12-equal, wouldn't you?


not at all. if a key is identified with its relative minor, that 
might mean that 81:80 is vanishing, but it sure doesn't mean 25:24 is 
vanishing!

dicot tunings include 7-equal, 10-equal, and one mapping of 17-
equal . . . but not 12-equal!

Message: 6394 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 15:06:09

Subject: naming temperaments

From: Carl Lumma

All;

Rather than naming every linear temperament of interest (and
presumably, every planar one also), why not name blocks of
interest, and use a prefix to denote which comma(s) vanish?

As it stands, there's no good way to talk about the *blocks*
behind popular temperaments.

An alternative would be to name the important commas, and then
name blocks and temperaments by concatenating the names of the
commas involved, with prefixes to indicate vanishing.

I would imagine the names we have so far would remain as
aliases.

-Carl

Message: 6395 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 23:15:53

Subject: Re: naming temperaments

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> All;
> 
> Rather than naming every linear temperament of interest (and
> presumably, every planar one also), why not name blocks of
> interest, and use a prefix to denote which comma(s) vanish?


i've been dreaming of a huge website where scales are organized by 
blocks and one can click on which unison vectors to 
temper/detemper . . .


> As it stands, there's no good way to talk about the *blocks*
> behind popular temperaments.


you mean naming all the just blocks? there are way too many; a given 
temperament can apply to many blocks.


> An alternative would be to name the important commas, and then
> name blocks and temperaments by concatenating the names of the
> commas involved, with prefixes to indicate vanishing.


already there's the problem that the pythagorean comma doesn't vanish 
in pythagorean tuning. but i like the idea . . . nevertheless, what 
basis do you use? the TM basis for the 7-limit miracle kernel is 
{225:224, 1029:1024}, yet the breedsma does vanish too, which this 
wouldn't tell you by names alone . . .

Message: 6396 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 05:03:08

Subject: Re: Janata paper

From: Carl Lumma

> but i would consider that the standard notation of 
> 12-equal is defined by a vanishing syntonic comma, a chromatic 
> 25:24, as well as a *systemic* vanishing unison vector (either 
> the pythagorean comma, the diesis, or the diaschisma) . . .


Ah, this is the terminology I neeeded.  I knew of course, that
Janata was using 12-tET, and the commas involved, but how to
describe a *2-D* block with *one* chromatic and *two* vanashing
commas. . .

-Carl

Message: 6397 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 15:23:16

Subject: Re: naming temperaments

From: Carl Lumma

>i've been dreaming of a huge website where scales are organized by 
>blocks and one can click on which unison vectors to 
>temper/detemper . . .


That would be truly awesome.  The culmination of years of work.


>> As it stands, there's no good way to talk about the *blocks*
>> behind popular temperaments.
>

>you mean naming all the just blocks? there are way too many; a
>given temperament can apply to many blocks.

Ah, right.


>> An alternative would be to name the important commas, and then
>> name blocks and temperaments by concatenating the names of the
>> commas involved, with prefixes to indicate vanishing.
>

>already there's the problem that the pythagorean comma doesn't vanish 
>in pythagorean tuning. but i like the idea . . . nevertheless, what 
>basis do you use? the TM basis for the 7-limit miracle kernel is 
>{225:224, 1029:1024}, yet the breedsma does vanish too, which this 
>wouldn't tell you by names alone . . .


Good point.  Maybe we need to name wedgies... does that solve the
problem?

-Carl

Message: 6398 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 06:33:28

Subject: Re: That poor overloaded word "comma"

From: Dave Keenan

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

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

>> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> 
> wrote:

>>> Dave, i'd like you to go into more detail about
>>> Paul's concepts and your feelings about the use
>>> of "comma", if you don't mind.
>> 

>> For more detail on Paul's concepts you should ask Paul. You 
> might ask

>> him to mail you "The Forms of Tonality: a preview" if he hasn't 
> already.
>> 

>> I think I've made my feelings about the use of "comma" very 
> clear.

>> Maybe you just need to click the "Up thread" button a few times 
> until

>> you get to where the subject heading was "A Common 

> Notation for JI and
>> ETs".
>> 

>> It's very simple. The word "comma" (and its adjective 
> "commatic")

>> already has two commonly accepted meanings in tuning 
> theory. It

>> doesn't need a third one. I think "commatic" should mean only
>> "relating to commas", and not have a third meaning of 
> "vanishing".

>> There's nothing wrong with the word "vanishing" so why would 
> anyone

>> feel the to use "commatic" in this way,
> 

> in my paper, "commatic" doesn't necessarily mean "vanishing" -- 
> it really just means "notationally ignored".


OK. I don't think "commatic" should be pressed into service to mean
that either. The etymology of "comma" relates purely to small size
(originally short duration), not vanishingness and not ignoredness.

You realise that this also makes it more contentious to use
"chromatic". Since an un-notated but non-vanishing comma could well be
considered to provide "colour". But if "chromatic" is OK then
"achromatic" is obviously excellent as its opposite.

Now that I read your paper as if I didn't already know what you were
talking about, I notice that you don't actually explain what you (or
Paul Hahn) mean by "commatic". The first ocurrence I can find is in
the sentence, "Notationally it is evident that 80:81 serves as a
/commatic/ unison vector, while 25:24 or 128:135 serves as a
/chromatic/ unison vector."

Well it might be "evident" if I already knew what you meant by
commatic. It's obviously an adjective from "comma", but I can't find
where you describe what essential properties of a comma something
would have to have in order to be called commatic. To that point the
only thing we know about commas is that 80:81 is called the syntonic
comma and that it's smaller than the chromatic semitone and major limma.

You adequately explain what you mean by "unison vector" and
"chromatic", but for "commatic" we could be forgiven for thinking you
were referring only to its small size.

Had you written, "Notationally it is evident that 25:24 or 128:135
serves as a /chromatic/ unison vector while 80:81 serves as a
/achromatic/ unison vector." there would be no problem since most
people would take achromatic to be the opposite of chromatic.

Message: 6399 - Contents - Hide Contents

Date: Mon, 10 Feb 2003 23:32:15

Subject: Re: naming temperaments

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

>> i've been dreaming of a huge website where scales are organized by 
>> blocks and one can click on which unison vectors to 
>> temper/detemper . . .
> 

> That would be truly awesome.  The culmination of years of work.
> 

>>> As it stands, there's no good way to talk about the *blocks*
>>> behind popular temperaments.
>> 

>> you mean naming all the just blocks? there are way too many; a
>> given temperament can apply to many blocks.
> 
> Ah, right.
> 

>>> An alternative would be to name the important commas, and then
>>> name blocks and temperaments by concatenating the names of the
>>> commas involved, with prefixes to indicate vanishing.
>> 

>> already there's the problem that the pythagorean comma doesn't 
vanish 
>> in pythagorean tuning. but i like the idea . . . nevertheless, 
what 
>> basis do you use? the TM basis for the 7-limit miracle kernel is 
>> {225:224, 1029:1024}, yet the breedsma does vanish too, which this 
>> wouldn't tell you by names alone . . .
> 

> Good point.  Maybe we need to name wedgies... does that solve the
> problem?
> 
> -Carl


naming wedgies is the same thing as naming temperaments, isn't it?

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