Tuning-Math Digests messages 6375 - 6399

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Message: 6375

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


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Message: 6383

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".


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Message: 6387

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

Subject: Re: Janata paper

From: Carl Lumma

>> 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?

-Carl


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Message: 6394

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


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Message: 6396

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


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Message: 6397

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


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Message: 6398

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.


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