Re:JI and the listening composer - reply to Paul

emotionaljourney22 wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > Why not just go the whole hog and catch the pure tone?
>
> there's nothing wrong with adopting this as a philosophy and an
> approach, and taking off from there. but we could pursue this
> argument again, so here goes.
>
> (a) in tuning zither strings, you'll always have
> (1) a certain imprecision in how you tune the fundamentals

Sure, to some extent there's always an element of imprecision. But every vibrating string or
struck bar has a fundamental and I'm happy that my strobe tuner is finding it and tuning it
perfectly ( to 0.1 cent) on a zither or steel tube marimba. The inharmonic partials with the
zither at least are so weak that they don't matter in pitch recognition though to my ears they
enhance or indeed define the timbre. At some point we must surely have to get down and work with
an instrument, inharmonic partials or not.

> (2) an inevitable tradeoff between getting the fundamentals in tune
> and getting the overtones in tune (due to the inharmonicity of the
> strings)
>
> (b) if you know what imprecision you're willing to tolerate (even if
> it's as small as 0.1 cent), you can "target" certain
> microtemperaments (not necessarily equal), and you will be more
> likely to end up with a larger number of intervals and chords that
> pass your criterion for "justness", than if you simply "targeted" a
> just scale.

But I can't get a better 1/1 - 7/6 - 4/3 - 3/2 - 7/4 - 2/1 other than by using those tones. An ET
would be pointless. I'd end up with more tones than I need and less precision.

> dave keenan has discussed the latter quite a bit, so you might want
> to contact him (i think he's still following the tuning-math list)
>
> anyway, alison, did i miss something? did you end up doing some
> direct comparisons and deciding that the intervals and chords in 72-
> equal were too far from just for you? if so, i'd like to know that,
> and you can rest assured that i'll never mention 72-equal to you
> again!
>

Not at all. I love working with the subsets of 72 that you and others have so skilfully explored.
I love the whole and the parts, the precisions and the imprecisions. At the moment I simply happen
to be up to the eyes in JI slendros and pelogs and hearing things I've never heard before. When I
get round to finishing what I started in 72 I'll be listening with fresh ears, for modulation,
voice leading and the like but also for "suggestive" tones and I'll report what I hear.

Best Wishes

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> An ET would be pointless. I'd end up with more tones than I need

this again?

"an et has too many tones, why do i need to tune up all those tones?"

"an et has too few tones, it's a cage that restricts me, while ji is
infinite"

both of these arguments have come up in the past few days, but
neither is relevant in the contexts actually being discussed here.

no matter how you tune a 5-tone scale, you still have only 5 tones!
no, the point of temperament is to tame the wolves of whatever scale
you're using, whether 5 notes or 31. and the equal, closed
temperaments i mentioned were only examples of a more general class
of temperaments that eliminate particular wolves.

for example, the most gross and unrefined usage of your scale 1/1 -
7/6 - 4/3 - 3/2 - 7/4 (- 2/1) might attempt to use 4/3 - 7/4 (which
is 27 cents off a pure fourth) as a consonant dyad, perhaps in some
larger chords. by gross and unrefined, i mean that i'm allowing
errors as large a 7 cents, so read the rest of this paragraph with
that caveat in mind. margo schulter has discussed this situation at
length in reference to her "hyper-pythagorean" tunings, and finds
such errors quite acceptable for many (but certainly not all)
timbres. 22-equal is only an example of a whole class of tunings
(most open and infinite) in which this 5-tone scale is preserved
pretty much intact, its consonances still recognizable as the same
consonant intervals, but 4/3 - 7/4 is tamed and becomes just another
such consonant interval. chords like 1/1 - 4/3 - 7/4 - 7/3 are
wonderful in such a tuning, possessing a lush beauty, all six dyads
within being consonances, while in just intonation the harshness of
the 4/3 - 7/4 interval sticks out like a sore thumb. in certain
timbres, to my ears, etc. etc.

now i'm guessing that this *particular* solution won't be of interest
to you for your zither. but this is merely to illustrate the kind of
thinking behind my post, and that you only need the 5 tones of your
scale to derive it -- that's it, just 5 tones.

deepest regards,
paul

emotionaljourney22 wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > An ET would be pointless. I'd end up with more tones than I need
>
> this again?

Yes, and for a good reason. Why have an instrument with more tones than I need for a specific
musical application? That's what this means and it's a thoroughly reasonable point of view from
whatever angle.

>
> "an et has too many tones, why do i need to tune up all those tones?"

I never said this, but why indeed tune up 72 tones if I only want to work with 21?

>
> "an et has too few tones, it's a cage that restricts me, while ji is
> infinite"

As I'm in the mood I'll defend myself as I assume you're attributing this attitude to me. I don't
believe this to be true. Both are merely resources - only the music is good or bad.

> both of these arguments have come up in the past few days, but
> neither is relevant in the contexts actually being discussed here.
>
> no matter how you tune a 5-tone scale, you still have only 5 tones!
> no, the point of temperament is to tame the wolves of whatever scale
> you're using, whether 5 notes or 31. and the equal, closed
> temperaments i mentioned were only examples of a more general class
> of temperaments that eliminate particular wolves.
>
> for example, the most gross and unrefined usage of your scale 1/1 -
> 7/6 - 4/3 - 3/2 - 7/4 (- 2/1) might attempt to use 4/3 - 7/4 (which
> is 27 cents off a pure fourth) as a consonant dyad, perhaps in some
> larger chords. by gross and unrefined, i mean that i'm allowing
> errors as large a 7 cents, so read the rest of this paragraph with
> that caveat in mind. margo schulter has discussed this situation at
> length in reference to her "hyper-pythagorean" tunings, and finds
> such errors quite acceptable for many (but certainly not all)
> timbres. 22-equal is only an example of a whole class of tunings
> (most open and infinite) in which this 5-tone scale is preserved
> pretty much intact, its consonances still recognizable as the same
> consonant intervals, but 4/3 - 7/4 is tamed and becomes just another
> such consonant interval. chords like 1/1 - 4/3 - 7/4 - 7/3 are
> wonderful in such a tuning, possessing a lush beauty, all six dyads
> within being consonances, while in just intonation the harshness of
> the 4/3 - 7/4 interval sticks out like a sore thumb. in certain
> timbres, to my ears, etc. etc.

Many intervals in gamelan stick out like the dog's bollocks but the music is nonetheless
exquisitely beautiful. This time round I want the dissonances as they are. That's the challenge,
melodically and contrapuntally.

>
> now i'm guessing that this *particular* solution won't be of interest
> to you for your zither. but this is merely to illustrate the kind of
> thinking behind my post, and that you only need the 5 tones of your
> scale to derive it -- that's it, just 5 tones.
>
> deepest regards,
> paul

And kind regards also to you.

>
>
>

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> emotionaljourney22 wrote:
>
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> > > An ET would be pointless. I'd end up with more tones than I need
> >
> > this again?
>
> Yes, and for a good reason. Why have an instrument with more tones
> than I need for a specific
> musical application?

you shouldn't, and won't. hopefully my post made that clear. you
*won't* end up with any more tones if you temper your scale than if
you leave in in just intonation.

> That's what this means and it's a thoroughly reasonable point of
>view from
> whatever angle.

it seems that it merely misunderstands the proposal and nothing else.

> > "an et has too many tones, why do i need to tune up all those
tones?"
>
> I never said this,

isn't that what you're saying above?

> but why indeed tune up 72 tones if I only want
>to work with 21?

you don't -- you just tune up 21.

> > "an et has too few tones, it's a cage that restricts me, while ji
is
> > infinite"
>
> As I'm in the mood I'll defend myself as I assume you're
>attributing this attitude to me.

i wasn't -- i merely said (in the very next sentence) that it had
come up on this list very recently.

> Many intervals in gamelan stick out like the dog's bollocks but the
> music is nonetheless
> exquisitely beautiful.

speaking of pelog, i personally enjoy, both as a musician and from a
tuning-math standpoint (search the relevant list if interested), a
pelog scale which is generated by a chain of 677-cent fifths, rather
than any just intonation scale or close approximation thereof. it
seems more "rational" in a sense, more "authentic", and you're free
to add random deviations to the tuning for "flavor". have you ever
tried such an approach or anything like it?

Hello Paul!
Why don't you tune your 22 equal to a 612 subset. How about 4296,
8592,
12,276,
16,572,
20868,
25,164
29460
33144
37440
41736
46032
49716
54012
58308
62604
66900
70584
74880
but it hard to beat12,276 (11 limit)
but the list goes on
You all seem completely obsessed with ETs that you will propose any high number ET just so you
can "convert" the person away from JI. It really is absurd on all your part. and frankly find it
nothing more than self serving. This little group seems more concerned being the ones coming up
with the answers than with the answers themselves. If this is what working with ETs does to people
maybe it has some really psychotic effects

emotionaljourney22 wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> >
> > emotionaljourney22 wrote:
> >
> > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> > >
> > > > An ET would be pointless. I'd end up with more tones than I need
> > >
> > > this again?
> >
> > Yes, and for a good reason. Why have an instrument with more tones
> > than I need for a specific
> > musical application?
>
> you shouldn't, and won't. hopefully my post made that clear. you
> *won't* end up with any more tones if you temper your scale than if
> you leave in in just intonation.
>
> > That's what this means and it's a thoroughly reasonable point of
> >view from
> > whatever angle.
>
> it seems that it merely misunderstands the proposal and nothing else.
>
> > > "an et has too many tones, why do i need to tune up all those
> tones?"
> >
> > I never said this,
>
> isn't that what you're saying above?
>
> > but why indeed tune up 72 tones if I only want
> >to work with 21?
>
> you don't -- you just tune up 21.
>
> > > "an et has too few tones, it's a cage that restricts me, while ji
> is
> > > infinite"
> >
> > As I'm in the mood I'll defend myself as I assume you're
> >attributing this attitude to me.
>
> i wasn't -- i merely said (in the very next sentence) that it had
> come up on this list very recently.
>
> > Many intervals in gamelan stick out like the dog's bollocks but the
> > music is nonetheless
> > exquisitely beautiful.
>
> speaking of pelog, i personally enjoy, both as a musician and from a
> tuning-math standpoint (search the relevant list if interested), a
> pelog scale which is generated by a chain of 677-cent fifths, rather
> than any just intonation scale or close approximation thereof. it
> seems more "rational" in a sense, more "authentic", and you're free
> to add random deviations to the tuning for "flavor". have you ever
> tried such an approach or anything like it?
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Oh!
did i forget to mention 1848
or 6691 oh there is just too many
and should keep the tuning math list busy for a while
Kraig Grady wrote:

> Hello Paul!
> Why don't you tune your 22 equal to a 612 subset. How about 4296,
> 8592,
> 12,276,
> 16,572,
> 20868,
> 25,164
> 29460
> 33144
> 37440
> 41736
> 46032
> 49716
> 54012
> 58308
> 62604
> 66900
> 70584
> 74880
> but it hard to beat12,276 (11 limit)
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Hello Paul!
> Why don't you tune your 22 equal to a 612 subset. How about 4296,
> 8592,
> 12,276,
> 16,572,
> 20868,
> 25,164
> 29460
> 33144
> 37440
> 41736
> 46032
> 49716
> 54012
> 58308
> 62604
> 66900
> 70584
> 74880
> but it hard to beat12,276 (11 limit)
> but the list goes on
> You all seem completely obsessed with ETs that you will propose
> any high number ET just so you
> can "convert" the person away from JI.

this bears no relation to the truth. i thought i already cleared this
up with you, just yesterday. you seemed to acknowledge my actual
position, which has no resemblance to this in any aspect, but instead
concerned absorbing certain commas. i then acknowledged your
alternate aesthetic preferences, and we left, i thought, with an
understanding of why the other was doing what they are doing, and, it
seemed, a much improved relationship.

now this post? did the post get delayed in the mail?

i have no interest in high number ets and no desire to convert anyone
from ji. why have you reverted so quickly to this misunderstanding? i
see more obsession with high number ets in your list above than in
any of the ideas i've presented.

> It really is absurd on all your part. and frankly find it
> nothing more than self serving. This little group seems more
> concerned being the ones coming up
> with the answers than with the answers themselves. If this is what
> working with ETs does to people
> maybe it has some really psychotic effects

what kinds of effects are at work behind someone who comes to an
understanding of someone one day and then reverts to a previous
misunderstanding the next? or maybe this is merely a yahoo glitch --
i sincerely hope so.

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

i wrote,

> or maybe this is merely a yahoo glitch --
> i sincerely hope so.

i just noticed that kraig was quoting my post today -- so this was
not the result of a glitch.

in which the only tuning i proposed was a non-equal-temperament, non-
just MOS scale.

so his response is all the more puzzling to me.

i felt so pleased at the hard-won progress that had been made in
understanding.

and then it all disappears, as if it all never happened.

such are the heartbreaks of life, i suppose. i am deeply saddened.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> Oh!
> did i forget to mention 1848
> or 6691 oh there is just too many
> and should keep the tuning math list busy for a while

i feel ridiculous answering this on behalf the tuning math list,
which is generally engaged in far more useful subjects -- but we did
spend a day or two, way back when, looking at the completely
musically pointless and irrelevant (i mean this with all sincerity!)
question of high number equal temperaments, into 6 or 7 digit
numbers. we found some truly startling patterns, totally unexpected,
and which gene thought may actually be of considerable number
theoretic interest . . . and which shed some light on the patterns in
*low-number* equal temperaments which have been known for quite some
time, but with little accompanying understanding. look at these
posts, for example:

/tuning-math/message/1869

/tuning-math/message/1915

/tuning-math/message/1918

hello Paul!
My objection from the start was the badgering of people who state they like a JI with 612
temperments when it isn't asked for or even implied. You are not interested in high number ET's
then what is 612?
I continue you find Yours, Genes, and Grahams relentless in push 612 down Alison's JI scale. what
could possibly be gained by proposing 612 temperment on a 10 tone scale. Am i really missing
something?.

>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> hello Paul!
> My objection from the start was the badgering of people who
state they like a JI with 612
> temperments when it isn't asked for or even implied. You are not
interested in high number ET's
> then what is 612?

i never proposed 612, in fact i tried to explain what i saw in gene's
proposal that had nothing to do with any equal temperament or with
612 notes per se. didn't you get it? from your response, it seemed
that you had . . .

> I continue you find Yours, Genes, and Grahams relentless in push
>612 down Alison's JI scale.

what on earth are you talking about? did i even mention 612 to
alison??

> what
> could possibly be gained by proposing 612 temperment on a 10 tone
>scale. Am i really missing
> something?.

as i explained before, the 10 tone scale in question gains more
almost-pure consonances when certain commas are tempered out. 612-
equal is only one example of such a tuning, just as 31-equal is only
one example of a meantone tuning. in general, though, such tunings
are not closed/finite -- nor are they just.

we've been down this road before, also to the point of mutual
understanding -- i thought. remember those color blackjust lattices
which showed the 21-tone ji scale and the "wolves" they contain? you
remarked that you liked how the lattice showed the mistuned
consonances and that you'd like to retain those "wolves" to use them
for position-finding and for their own unique characteristics. i
appreciated that, meanwhile others would prefer to "tame the wolves"
and use a miracle temperament. 72-equal is an *example* of a tuning
supporting miracle temperament. but it's still only a 21-tone scale.
joseph is now working on his third (?) composition in this scale. so
if he says he's using 72-equal, are you going to castigate him for it?

maintaining hope,
paul

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> But I can't get a better 1/1 - 7/6 - 4/3 - 3/2 - 7/4 - 2/1 other
than by using those tones. An ET
> would be pointless. I'd end up with more tones than I need and less
precision.

We're not talking about ETs or adding more tones. There are many other
kinds of temperament besides ETs. But in this case, you're right. With
only 5 notes and such a tight (and I'd say unrealistic for a
wood-framed stringed instrument) error tolerance, I don't know of any
microtemperament that can introduce any new JI intervals into the same
5 notes.

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

we found some truly startling patterns, totally unexpected,
> and which gene thought may actually be of considerable number
> theoretic interest . . .

I'm thinking of giving a talk on it, and wondered if you would object to my calling it "Erlich's Phenomenon".

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
>
> we found some truly startling patterns, totally unexpected,
> > and which gene thought may actually be of considerable number
> > theoretic interest . . .
>
> I'm thinking of giving a talk on it, and wondered if you would
>object to my calling it "Erlich's Phenomenon".

i'd be honored! personally, i like how suggests and explanation the
familiar bumps, like in 5-limit we have 19-22, 31-34, 41-43, 53-55,
pairs of good ets that cluster together in this regular pattern with
nothing noteworthy in-between. the 15:16 ratio is responsible for
this. the relative "power" of various superparticulars still seems a
bit of a mystery, though if graham is right, it comes down to nothing
more than a simple unweighted complexity metric . . .

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_37538.html#37706

>> i'd be honored! personally, i like how suggests and explanation
the
> familiar bumps, like in 5-limit we have 19-22, 31-34, 41-43, 53-55,
> pairs of good ets that cluster together in this regular pattern
with
> nothing noteworthy in-between. the 15:16 ratio is responsible for
> this. the relative "power" of various superparticulars still seems
a
> bit of a mystery, though if graham is right, it comes down to
nothing more than a simple unweighted complexity metric . . .

***I'll bet that was something discussed on *Tuning Math* since I
don't remember it from here. Could I please have a couple
of "layman's" sentences elaborating on this, if it's possible??

Thanks!

Joseph

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
>
> /tuning/topicId_37538.html#37706
>
> >> i'd be honored! personally, i like how suggests and explanation
> the
> > familiar bumps, like in 5-limit we have 19-22, 31-34, 41-43, 53-
55,
> > pairs of good ets that cluster together in this regular pattern
> with
> > nothing noteworthy in-between. the 15:16 ratio is responsible for
> > this. the relative "power" of various superparticulars still
seems
> a
> > bit of a mystery, though if graham is right, it comes down to
> nothing more than a simple unweighted complexity metric . . .
>
>
> ***I'll bet that was something discussed on *Tuning Math* since I
> don't remember it from here. Could I please have a couple
> of "layman's" sentences elaborating on this, if it's possible??

well, this surely is an oversimplification, but it's sorta like this:

16:15 is the *smallest* ji interval derivable from two 5-limit
consonances (4:3 / 5:4 = 16:15).

if a tuning has a very good approximation to the 5-limit consonances,
it will also have a pretty good approximation to 16:15.

for an et to have a pretty good approximation to 16:15, the 16:15
will have to be close to an integer number of steps in the ET.

16:15 fits in an octave 10.74 times.

so you'd expect the good 5-limit ets to have numbers of notes close
to multiples of 10.74 -- while ets *not* close to multiples of 10.74
are unlikely to be good in the 5-limit.

here are some multiples of 10.74:

10.74
21.48
32.22
42.96
53.70

so you'd expect the good 5-limit ets to cluster around these values,
and they do:

10, 12 are close to 10.74
19, 22 are close to 21.48
31, 34 are close to 32.22
41, 43 are close to 42.96
53, 55 are close to 53.70

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_37538.html#37758

>
> so you'd expect the good 5-limit ets to cluster around these
values,
> and they do:
>
> 10, 12 are close to 10.74
> 19, 22 are close to 21.48
> 31, 34 are close to 32.22
> 41, 43 are close to 42.96
> 53, 55 are close to 53.70

***That's really interesting, Paul... quite a way to figure things
out. Isn't that a bit the method you used to find the optimal
Miracle generator size as well??

Joseph

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
>
> /tuning/topicId_37538.html#37758
>
> >
> > so you'd expect the good 5-limit ets to cluster around these
> values,
> > and they do:
> >
> > 10, 12 are close to 10.74
> > 19, 22 are close to 21.48
> > 31, 34 are close to 32.22
> > 41, 43 are close to 42.96
> > 53, 55 are close to 53.70
>
>
> ***That's really interesting, Paul... quite a way to figure things
> out. Isn't that a bit the method you used to find the optimal
> Miracle generator size as well??

don't see any relationship, joseph, but perhaps i'm missing something!

'dja get that CD?

i wrote,

> 16:15 is the *smallest* ji interval derivable from two 5-limit
> consonances (4:3 / 5:4 = 16:15).

sorry folks -- that would be 25:24 -- i did say it was an
oversimplifications!

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_37538.html#37795

>> >
> > ***That's really interesting, Paul... quite a way to figure
things
> > out. Isn't that a bit the method you used to find the optimal
> > Miracle generator size as well??
>
> don't see any relationship, joseph, but perhaps i'm missing
something!
>

***Hmm. Well, maybe the processes *weren't* so similar..., obviously

> 'dja get that CD?

***Yes! Sounds great. More offlist!

Joseph

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_37538.html#37810

> i wrote,
>
> > 16:15 is the *smallest* ji interval derivable from two 5-limit
> > consonances (4:3 / 5:4 = 16:15).
>
> sorry folks -- that would be 25:24 -- i did say it was an
> oversimplifications!

***Now I'm lost. Regrettably, I *got* it the *first* time... :)

J. Pehrson