Yahoo Tuning Groups Ultimate Backup tuning 144? 72? Partch?

[me, Monz:]
>> I have to agree, because of your eloquent argument,
>> that Dan Stearns was right and I should have just left
>> Partch alone.
>
[Paul Erlich:]
> That's too bad, because I think Partch in 72-tET is a
> wonderful thing.

But Paul, we're debating the merits/(non-)usefulness
of 144-tET, not 72! I agree with you on 72, and I like
it, and I've been using it ever since I found out about
the Sims/Herf notations.

PS - Partch on my new 'octave'-specific lattice
is a wonderful thing!

[Erlich:]
> (I'm thinking string players and
> singers trained in 72-tET, which is happening here in Boston).
^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^
[emphasis mine]

And this is a really excellent thing!

-monz

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

>[Monz:]
>>> I have to agree, because of your eloquent argument,
>>> that Dan Stearns was right and I should have just left
>>> Partch alone.
>>
>[Paul Erlich:]
>> That's too bad, because I think Partch in 72-tET is a
>> wonderful thing.

>But Paul, we're debating the merits/(non-)usefulness
>of 144-tET, not 72! I agree with you on 72, and I like
>it, and I've been using it ever since I found out about
>the Sims/Herf notations.

But Dan Stearns' argument would speak against using 72 just as much as
against using 144.

[monz:]
>>> in addition, because 11 * 13 = 143,
>>> 144-eq approximates 11-eq and 13-eq extremely well:

[Erlich/Barbaro:]
>> No it doesn't. It only approximates the smallest intervals
>> of 11-eq and 13-eq extremely well, as you show:

><etc., quoting me>

>> For larger intervals the approximation is nothing special.

>Ahem...

>So a max error of ~3.79 cents isn't good enough
>*for a notation* to call it 'special'?

We're talking about approximations in 144-tET, where no approximation can
possibly be more than 4.17 cents off. In that context, the approximation of
a scale with a max error of 3.79 cents is certainly not special.

>Ditto for max error = ~3.85 cents?

That's right.

IN OTHER WORDS, IF YOU LOOK AT HOW WELL 144-tET APPROXIMATES SMALL ETs, 11
AND 13 ARE NOT AMONG THE BETTER ONES (i.e., nothing special).

>24-eq: 24-ET cents
> ratio cents degree cents 'error'
>
> 11/6 10.49 21 10.50 0.64
> 12/11 1.51 3 1.50 -0.64
> 16/11 6.49 13 6.50 1.32
> 11/8 5.51 11 5.50 -1.32
> 4/3 4.98 10 5.00 1.96
> 3/2 7.02 14 7.00 -1.96
> 11/9 3.47 7 3.50 2.59
> 18/11 8.53 17 8.50 -2.59
> 64/33 11.47 23 11.50 3.27
> 33/32 0.53 1 0.50 -3.27
> 35/32 1.55 3 1.50 -5.14
> 39/32 3.42 7 3.50 7.52
> 13/8 8.41 17 8.50 9.47
> 13/12 1.39 3 1.50 11.43
> 5/4 3.86 8 4.00 13.69
> 9/7 4.35 9 4.50 14.92
> 14/9 7.65 15 7.50 -14.92
> 20/11 10.35 21 10.50 15.00
> 11/10 1.65 3 1.50 -15.00
> 12/7 9.33 19 9.50 16.87
> 7/6 2.67 5 2.50 -16.87
> 8/7 2.31 5 2.50 18.83
> 7/4 9.69 19 9.50 -18.83
> 25/24 0.71 1 0.50 -20.67
> 32/21 7.29 15 7.50 20.78
> 21/16 4.71 9 4.50 -20.78
> 25/16 7.73 15 7.50 -22.63
> 63/32 11.73 23 11.50 -22.74

I have a big problem with this table because many of the approximations are
not consistent with one another. The ratios with 7 in them can't be
consistently approximated in 24-tET if you try to improve on 12-tET's
approximations.

>I honestly don't think that these inconsistencies are
>bothersome in actual practice. You're dealing here
>with 144 steps to the 'octave'. I haven't played with
>144-eq audibly (i.e., *as* a tuning system) to hear
>what that sounds like, but we've been talking about
>it strictly as an approximative notational representation
>of other pitches, anyway.

144-tET _is_ consistent with the 11-limit; it's just that the correct
approximations of 11-limit intervals would never lead you to use the ~ sign;
in other words, you'd end up using 72-tET.

>With so many fine shadings of pitch available to the
>notation, in my experience of using it *merely as a
>notation*, those inconsistencies don't phase me.

The word is faze. Unless you were trying for a cute pun.

🔗monz@xxxx.xxx

> But Dan Stearns' argument would speak against using 72
> just as much as against using 144.

Well, you're right about that, but...
Partch's argument would speak out against both, too.

I think Dan's point was that using Partch was a bad
example because Partch was so insistent on the use
of ratios to represent pitch that any equivocation,
however small or minor it may be, goes contrary
to the fundamentals of his theories.

> We're talking about approximations in 144-tET, where no
> approximation can possibly be more than 4.17 cents off.
> In that context, the approximation of a scale with a
> max error of 3.79 cents is certainly not special.

Oh, OK... that's a different viewpoint than the angle
I was seeing it. I can buy that line of reasoning.

> The ratios with 7 in them can't be consistently
> approximated in 24-tET if you try to improve on 12-tET's
> approximations.

This is true, but - you can indicate the 7-limit ratios
to the performers with better approximation if you use
the quarter-tones in the *notation*!

The point that I'm so doggedly belaboring here is that
what is necessary or desirable in a tuning system does
not necessarily equate, transport, or sometimes even
approximate what works for a notation.

Look at the usual sheet-music notation for harmony:
letter-names, numbers, and a handful of symbols. And
that's enough to describe what John Coltrane did?

Apparently so, because I know a *lot* of musicians
whose only paleographic understanding of Coltrane's music
is that small heap of chord notations. And yet, they
can reproduce it as faithfully as their technique
will allow.

Of course, they're doing it by using their ears,
but that's exactly my point. Musicians will be
very forgiving, or possibly ignorant (on purpose),
of any notation if they are gifted with good intonation.
If anything, a good sense of intonation usually
*encourages* musicians to mark the music with extra
symbols to indicate subtle shades of tuning.

>> those inconsistencies don't phase me.

> The word is faze. Unless you were trying for a cute pun.

uh..... y----eah... that's it - that's the ticket...

-monz

144? 72? Partch?

🔗monz@juno.com

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

🔗monz@xxxx.xxx