Yahoo Tuning Groups Ultimate Backup tuning Well temperaments compared!

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> Sheer proximity to a target interval, alone, is not a musical
> judgement of its »accuracy« or usefulness. The handful of intervals
> I put into the Csound interval tester »high fifths for Gene«
> illustrate this very audibly. (You can flip the intervals around 3/2
> to hear them as meantone kinds of fifths and of course put in any
> ratios you want).
>
> Leaving out microscopic deviations from a target interval, and
> assuming a reasonable proximity for the tempered intervals (say 8-12
> cents deviation maximum, or a region centered on the target ideal
> about 16-24 cents wide, for musically functional reasons), it is
> plain to hear that an interval further from the target can have a
> character that makes it more suitable as a tempered interval than an
> interval which is »closer« in sheer frequency.
>
> This should be obvious, especially to anyone who puts any stock in
> simple ratios, primes, odd numbers, and the whole lot. How
> appropriate a tempered interval is may be a very subtle thing when
> heard in simple diad, but the flavor of the temperings permeates the
> whole tuning, and consequently the music.
>
> Anyway the whole business of considering everything as
> an »approximation« of a handful of just intervals is bogus- an
> interval should be good in and of itself, otherwise just put all
> effort to adaptive JI and leave it at that.
>
> -Cameron Bobro
>

I wouldn't be as dismissive of the temperament as approximation of JI
paradigm as you are. Temperaments, after all, are (usually) designed
to chase the pot-of-gold-at-the-end-of-the-rainbow that is JI, while
compromising so that the practical set of notes used can be much
smaller. So, unlike McLaren, or whoever else, I do think math tells us
*something* about the properties of a temperament/tuning.

That being said, you make some good points, and not every
tuning/temperament is/should be designed with JI in mind. In fact
there are some interesting things that happen when one decides to go
as far away from JI (or harmonic entropy if you will) as possible.

But I think Carl did some very thorough and good analysis, from the
typical "approach JI" POV.

-A.

🔗Carl Lumma <clumma@yahoo.com>

> Sheer proximity to a target interval, alone, is not a musical
> judgement of its accuracy

This is strictly true, which is why the *harmonic entropy* model
is preferrable. And that is one of the three methods I use in
my spreadsheet. However, the "basin of attraction" around a
phat JI consonance like 4:5:6 or 4:5:6:7 is so large that cents
error is a very good approximation of harmonic entropy, as long
as the error isn't too large.

> or usefulness.

I'm not claiming to measure the usefulness of sounds. I only
say that if you assume the point of a "well temperament" is to
make some keys better than others, the average key should not
be worse than 12-equal. Under any one of three consonance
measures in two JI "limits", I try to tell you for which
temperaments this is true.

> The handful of intervals I put into the Csound interval
> tester high fifths for Gene illustrate this very audibly.

I'm afraid I don't have CSound. Can you make some sound files
to illustrate your point?

> ... a region centered on the target ideal
> about 16-24 cents wide, for musically functional reasons), it is
> plain to hear that an interval further from the target can have a
> character that makes it more suitable as a tempered interval than
> an interval which is »closer« in sheer frequency.

None of the intervals in a "well temperament", as I've defined it,
are nearly that far off.

In the case of fifths, harmonic entropy predicts a steady rise in
dissonance on either side for about 50 cents. However when
roughness is taken into account I could imagine this being
somewhat different. But I'm certainly interested in hearing
your demo.

> This should be obvious, especially to anyone who puts any stock in
> simple ratios, primes, odd numbers, and the whole lot.

Well as I was just discussing with Ozan, prime limits don't
necessarily lead to simple ratios!

> How appropriate a tempered interval is may be a very subtle
> thing when heard in simple diad, but the flavor of the
> temperings permeates the whole tuning, and consequently
> the music.

Sure. Appropriateness is also very subjective.

> Anyway the whole business of considering everything as
> an »approximation« of a handful of just intervals is bogus- an
> interval should be good in and of itself,

I don't agree. All intervals are good in and of themselves,
but if you happen to want highly consonant music, for example
evangelical hymnody, the kind of thing I've been talking
about works.

> otherwise just put all effort to adaptive JI and leave it
> at that.

Some people want a well temperament, to put on their piano
or whatever.

-Carl

🔗Aaron Krister Johnson <aaron@dividebypi.com>

🔗Carl Lumma <clumma@yahoo.com>

> > Believe in harmonic entropy?
> > Don't use a well temperament - use ET.
>
> Carl,
>
> questions:
>
> 1) I assume you mean 12-eq, right?
> 2) If so, is this prescription based on the idea that the
> higher the prime, the greater the error in 12-eq (at least
> to the 11 limit)?
>
> -A.

Hi A.,

I meant 12-equal, but it may hold true for other numbers of
tones/octave as well... As for *why* it is, this is my guess:
- With cents error, if you make one key closer to JI some
other key goes farther away from JI, but the two can cancel.
It is, in other words, possible to have a well temperament
without any of what George S. calls "harmonic waste" (I think
that was you, George).
- But the way harmonic entropy is scaled, they don't cancel,
and if you consider all keys entropy tells you your best bet
is equal. This would apparently be supported by the historical
move towards equal temperament as music used more and more
modulation. But some present-day listeners do seem to prefer
the effect of some inequality even when using all keys. I
once heard Jerry Kuderna play Op.110, which is in Ab, at point-
blank range in a tuning with a wolf fifth on Ab. I would
have preferred ET in such a case, but apparently Jerry did not.

Anyway, that's just a guess - I haven't really looked at the
math. I should also say that by "entropy" here, I mean the
"sum of the dyadic entropies of a 2:3:4:5:6 chord" in each key,
averaged over all keys.

-Carl

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...>
wrote:

> I wouldn't be as dismissive of the temperament as approximation of
>JI paradigm as you are. Temperaments, after all, are (usually)
>designed to chase the pot-of-gold-at-the-end-of-the-rainbow that is
>JI, while compromising so that the practical set of notes used can
>be much smaller. So, unlike McLaren, or whoever else, I do think
>math tells us *something* about the properties of a
>temperament/tuning.

Well, I use a kind of "well temperament" as my principle tuning, and
it's all rational intervals with an ear on keeping all intervals
relatively simple (864/575 is the most complex "fifth", IIRC).
This is purely a matter of what sounds right to me, which is some
kind of "extended JI" I guess.

As far as math, number is adjective, not noun. It's the choice of
adjectives that's important: I don't dismiss all description just
because I find some descriptions inapproriate or incomplete.

It's the looking only at the first few "classic" JI intervals, and
primes, judging all tunings by how well the intervals "represent"
or "approximate" those classics, and doing that judgement by rank
proximity of frequency, that bothers me. I'll keep trying to explain
what I mean, and why...

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> However, the "basin of attraction" around a
> phat JI consonance like 4:5:6 or 4:5:6:7 is so large that cents
> error is a very good approximation of harmonic entropy, as long
> as the error isn't too large.

It's the nature of the "basin of attraction" that is my concern,
more below.

> > or usefulness.
>
> I'm not claiming to measure the usefulness of sounds. I only
> say that if you assume the point of a "well temperament" is to
> make some keys better than others, the average key should not
> be worse than 12-equal. Under any one of three consonance
> measures in two JI "limits", I try to tell you for which
> temperaments this is true.

How would a tuning with, say 7 very smooth JI keys and 5 clangorous
leftovers, if such a thing exists, rate in this system? How about a
tuning with a hole in the primes, so to speak, say bad 3s and
wonderful 5s? What about tunings based on higher primes, because you
can get quite smooth near-12EDO intervals using higher primes?

> > The handful of intervals I put into the Csound interval
> > tester high fifths for Gene illustrate this very audibly.
>
> I'm afraid I don't have CSound. Can you make some sound files
> to illustrate your point?

I'll try to do that this week, because it's far more clear than my
words.

> > ... a region centered on the target ideal
> > about 16-24 cents wide, for musically functional reasons), it is
> > plain to hear that an interval further from the target can have
>>a
> > character that makes it more suitable as a tempered interval than
> > an interval which is »closer« in sheer frequency.
>
> None of the intervals in a "well temperament", as I've defined it,
> are nearly that far off.

Didn't think so- that's a kind of "outer limit", I think. But I'll
send you a recording of something very interesting indeed :-)
>
> In the case of fifths, harmonic entropy predicts a steady rise in
> dissonance on either side for about 50 cents. However when
> roughness is taken into account I could imagine this being
> somewhat different. But I'm certainly interested in hearing
> your demo.

It's the "steady rise" bit that bothers me, because I find that to
be audibly not true. It simply doesn't explain why I have found a
stinker three cents closer to the "ideal" 3/2 than another, more
distant, interval which is both more consonant sounding and "fifth"
in character.
>
> > This should be obvious, especially to anyone who puts any stock
>>in
> > simple ratios, primes, odd numbers, and the whole lot.
>
> Well as I was just discussing with Ozan, prime limits don't
> necessarily lead to simple ratios!

Yes it's a complex thing- you beat me to the punch with the 5/4
81/64 bit, the exact example that occured to me in that other
thread. The whole n/x2 family, ie harmonic overtones, for example,
can wolf down big primes with no signs of indigestion.

Anyway, "you know what I mean": if intervals do have recognizable
character by virtue of rational properties, whatever or however many
factors go into the making of that character, doesn't it stand to
reason that, for example, a relatively simple interval which shares
properties with a rational "target" interval and is 3 cents from
that target, is going to better "represent" that target than an
irrational interval two cents away? Better than "represent", it
could even be a "better" interval.

I've mentioned several times that I work with "regions", but I don't
mean that anything goes within those regions, or that the
theoretical center of the region is the goal. What I mean is, those
intervals of the same musical family which fall in that region "go".

George Secor's 17WT wasn't made thinking this way, as far as I can
tell from his writings, but it audibly fulfills the criterion. I
think it clear as to why- the two "fifths" he chose are
simply "right", and can probably be reproduced as two
somehow-related ratios, or irrational proportions within a
don't-be-silly distance of those ratios. So even though he
says "better/worse keys", I hear only different keys; in other
words, I haven't heard a tone which is crying out for a split key
because it's a sad attempt at being something else rather than what
it literally IS.

> Appropriateness is also very subjective.

Yes indeed- 12-EDO seems an insane choice for a band that plays the
same 3 chords in the same key for 30 years, for example, hahaha!
They could hone that key to custom perfection and dump every comma,
llama and wolf-o-rama anywhere else, and the same thing is true to
different degrees for anyone else who isn't doing Giant Steps or
Elektra.

>
> > Anyway the whole business of considering everything as
> > an »approximation« of a handful of just intervals is bogus- an
> > interval should be good in and of itself,
>
> I don't agree. All intervals are good in and of themselves,
> but if you happen to want highly consonant music, for example
> evangelical hymnody, the kind of thing I've been talking
> about works.

By "good" I mean, something you want. Not an approximation of
something you want.

> > otherwise just put all effort to adaptive JI and leave it
> > at that.
>
> Some people want a well temperament, to put on their piano
> or whatever.

Certainly, I use a kind of "well-temperament" as a central tuning
myself, not just because of the number and size of my fingers, but
because I much prefer the sound to that of classic adaptive JI! And
that's whole point of what I mean- it should be what you want
("need" is probably more accurate), not some lesser-of-evils.

Sorry if you thought I was knocking your groovy spreadsheet, I think
it's really good. In fact it's excellent, because I can't think of a
better tool for actually testing the very premises on which the
ratings are based!

-Cameron Bobro

🔗Carl Lumma <clumma@yahoo.com>

> > I'm not claiming to measure the usefulness of sounds. I only
> > say that if you assume the point of a "well temperament" is to
> > make some keys better than others, the average key should not
> > be worse than 12-equal. Under any one of three consonance
> > measures in two JI "limits", I try to tell you for which
> > temperaments this is true.
>
> How would a tuning with, say 7 very smooth JI keys and 5 clangorous
> leftovers, if such a thing exists, rate in this system?

Depends. Give me an example and I'll tell you.

> How about a
> tuning with a hole in the primes, so to speak, say bad 3s and
> wonderful 5s? What about tunings based on higher primes, because
> you can get quite smooth near-12EDO intervals using higher primes?

You shuold use an error function that measures the error of the
intervals you desire to measure the error of. :) For well
temperaments, I make some assumptions about that (see my
spreadsheets). But Aaron, along with LaMonte Young and many
others no doubt, have used 12-tone scales with, for example,
have good 3s and 7s but bad 5s. Such things don't aren't
generally considered "well temperaments", but that doesn't make
them any less interesting.

> > > The handful of intervals I put into the Csound interval
> > > tester high fifths for Gene illustrate this very audibly.
> >
> > I'm afraid I don't have CSound. Can you make some sound files
> > to illustrate your point?
>
> I'll try to do that this week, because it's far more clear than
> my words.

Great!

> Didn't think so- that's a kind of "outer limit", I think. But I'll
> send you a recording of something very interesting indeed :-)

By all means!

> > In the case of fifths, harmonic entropy predicts a steady rise
> > in dissonance on either side for about 50 cents. However when
> > roughness is taken into account I could imagine this being
> > somewhat different. But I'm certainly interested in hearing
> > your demo.
>
> It's the "steady rise" bit that bothers me, because I find that to
> be audibly not true. It simply doesn't explain why I have found a
> stinker three cents closer to the "ideal" 3/2 than another, more
> distant, interval which is both more consonant sounding and "fifth"
> in character.

What are these intervals?

> Anyway, "you know what I mean": if intervals do have recognizable
> character by virtue of rational properties, whatever or however
> many factors go into the making of that character, doesn't it
> stand to reason that, for example, a relatively simple interval
> which shares properties with a rational "target" interval and is
> 3 cents from that target, is going to better "represent" that
> target than an irrational interval two cents away?

Why should it?

> Better than "represent", it
> could even be a "better" interval.

Why should it be?

> > > Anyway the whole business of considering everything as
> > > an »approximation« of a handful of just intervals is bogus- an
> > > interval should be good in and of itself,
> >
> > I don't agree. All intervals are good in and of themselves,
> > but if you happen to want highly consonant music, for example
> > evangelical hymnody, the kind of thing I've been talking
> > about works.
>
> By "good" I mean, something you want. Not an approximation of
> something you want.

Well, that's pretty subjective. If you define what you want,
then we can talk about how to get it!

> Certainly, I use a kind of "well-temperament" as a central tuning
> myself, not just because of the number and size of my fingers, but
> because I much prefer the sound to that of classic adaptive JI!

Classic adaptive JI is something of an oxymoron. Do you
mean "classic JI" or "adaptive JI", or do you have a new
knid of adaptive JI you haven't told us about yet?

-Carl

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> > How would a tuning with, say 7 very smooth JI keys and 5
>> clangorous
> > leftovers, if such a thing exists, rate in this system?
>
> Depends. Give me an example and I'll tell you.

Don't know of any examples, but I'm guessing things along these
lines must exist...have to think about how to generate such a thing.
>
> > How about a
> > tuning with a hole in the primes, so to speak, say bad 3s and
> > wonderful 5s? What about tunings based on higher primes, because
> > you can get quite smooth near-12EDO intervals using higher
>>primes?
>
> You shuold use an error function that measures the error of the
> intervals you desire to measure the error of. :)

What I should have said is: in Paul Ehrlich's 22 paper, if I
understood correctly, his comparison of various ETs against a set of
primes, via "harmonic entropy", WOULD give a poor rating to a tuning
that "scores well" in all intervals except one bomb, referring to...

> But Aaron, along with LaMonte Young and many
> others no doubt, have used 12-tone scales with, for example,
> have good 3s and 7s but bad 5s.

...this kind of thing. And I'll checking if you're taking the same
approach.

> > It's the "steady rise" bit that bothers me, because I find that
>>to
> > be audibly not true. It simply doesn't explain why I have found
>>a stinker three cents closer to the "ideal" 3/2 than another,
>>more distant, interval which is both more consonant sounding
>>and "fifth"
> > in character.

> What are these intervals?

How accurate is the tuning of your synthesis method? I tested
them "blind", which I think is a good idea. Try out these ratios and
tell me which ones stink:

3/2 701.955 cents
864/575 704.963 cents
176/117 706.880 cents
325/216 707.290 cents
450/299 707.735 cents
414/275 708.239 cents
529/351 710.156 cents
104/69 710.298 cents
299/198 713.574 cents

You can mirror them against 3/2 to make lower tempered fifths (at
least one of them is a classic meantone fifth mirrored upwards) but
that weakens the test quite a bit, I think, because fifths tempered
down are so familiar.

> > Anyway, "you know what I mean": if intervals do have
>recognizable
> > character by virtue of rational properties, whatever or however
> > many factors go into the making of that character, doesn't it
> > stand to reason that, for example, a relatively simple interval
> > which shares properties with a rational "target" interval and is
> > 3 cents from that target, is going to better "represent" that
> > target than an irrational interval two cents away?
>
> Why should it?

Why should it? In the case of a "fifth", wouldn't the more consonant
sounding of two tempered intervals be more like 3/2? I don't think a
sour dissonance either "represents" or takes the stead of 3/2, but I
guess that's subjective, too.

> > Better than "represent", it
> > could even be a "better" interval.
>
> Why should it be?

Could be "better" becuase it simply sounds "better", in addition to
being more functional in the context of the tuning.

> > By "good" I mean, something you want. Not an approximation of
> > something you want.
>
> Well, that's pretty subjective. If you define what you want,
> then we can talk about how to get it!

Well, I define what I want by, for example, stopping a string on a
fretless guitar with a butterknife and singing along. :-) Defining
the intervals has fortunately not been too hard- measure, take a
guess as to the ratio, put it in Csound and listen (CPS defined by
the ratio). There is a cohesion and are by now fairly predictable
patterns, so it goes quickly. Besides, once I nail a couple of
things I really like, I then work with the difference tones
so I now have more delightful toys than I have time to play with.

Haven't got around to defining the "soft" (low) "major thirds" I
like best, those may be a challenge to work into tunings, we'll see.
But- going by rank proximity to 5/4 certainly isn't going to help-
how could be it when I know there's a friendly one around 388 cents
and a cheerful one around 392 and a putrid one right in between?

>>Classic adaptive JI is something of an oxymoron. Do you
>>mean "classic JI" or "adaptive JI", or do you have a new
>>kind of adaptive JI you haven't told us about yet?

Gee whiz, man. How about "Classic", "adaptive" or "what-have-you" ,
or 5/4 and Mj minor triad-centric low-prime-simple-ratio JI". :-P

-Cameron Bobro

🔗Carl Lumma <clumma@yahoo.com>

> > > How about a
> > > tuning with a hole in the primes, so to speak, say bad 3s and
> > > wonderful 5s? What about tunings based on higher primes,
> > > because you can get quite smooth near-12EDO intervals using
> > > higher primes?
> >
> > You shuold use an error function that measures the error of
> > the intervals you desire to measure the error of. :)
>
> What I should have said is: in Paul Ehrlich's 22 paper, if I
> understood correctly, his comparison of various ETs against a
> set of primes, via "harmonic entropy", WOULD give a poor rating
> to a tuning that "scores well" in all intervals except one
> bomb, referring to...

I don't think harmonic entropy existed when he wrote that paper.
Are you thinking of another paper, or am I all wet?

http://lumma.org/tuning/erlich

> > But Aaron, along with LaMonte Young and many
> > others no doubt, have used 12-tone scales with, for example,
> > have good 3s and 7s but bad 5s.
>
> ...this kind of thing. And I'll checking if you're taking the
> same approach.

Since 5-limit intervals are a part of every evaluation in my
spreadsheet, these scales would do poorly indeed.

> > What are these intervals?
>
> How accurate is the tuning of your synthesis method? I tested
> them "blind", which I think is a good idea. Try out these ratios
> and tell me which ones stink:
>
> 3/2 701.955 cents
> 864/575 704.963 cents
> 176/117 706.880 cents
> 325/216 707.290 cents
> 450/299 707.735 cents
> 414/275 708.239 cents
> 529/351 710.156 cents
> 104/69 710.298 cents
> 299/198 713.574 cents

I have Cool Edit, which is very tedious to work with by I assume
very accurate. Other than that, it's the wavetable synth that
came with Windows. ;-P Is there any chance you could dump
these into some wave files?

>>> if intervals do have recognizable
>>> character by virtue of rational properties, whatever or however
>>> many factors go into the making of that character, doesn't it
>>> stand to reason that, for example, a relatively simple interval
>>> which shares properties with a rational "target" interval and is
>>> 3 cents from that target, is going to better "represent" that
>>> target than an irrational interval two cents away?
>>
>> Why should it?
>
> Why should it? In the case of a "fifth", wouldn't the more
> consonant sounding of two tempered intervals be more like 3/2?
> I don't think a sour dissonance either "represents" or takes
> the stead of 3/2, but I guess that's subjective, too.

Sorry, I wasn't very clear. I mean, what sort of property
can a 3-cents-sharp-from-3/2 interval have that a 2-cents-
sharp-from-3/2 one doesn't? I guess one has to hear it. My
experinece tuning pianos suggests these intevals sound almost
identical, except the former beats slightly faster.

> >>Classic adaptive JI is something of an oxymoron. Do you
> >>mean "classic JI" or "adaptive JI", or do you have a new
> >>kind of adaptive JI you haven't told us about yet?
>
> Gee whiz, man. How about "Classic", "adaptive" or "what-have-you" ,
> or 5/4 and Mj minor triad-centric low-prime-simple-ratio JI". :-P

Sorry about that... you're "entering a world of pain" (think
John Goodman in Lebowski) with the terminology around here.
"Classic JI" is one way we refer to the style of 'take a scale
consisting of some ratios and play it'. Allowing rapid root
changes might be called "extended reference". "Adaptive JI"
is like extended reference with root changes by irrational
intervals. Finally there is "adaptive tuning", in which the
vertical consonances are very slightly tempered along with
the root-change intervals. Unless you're talking to Bill
Sethares, when "adaptive tuning" means the the tuning is varied
according the total *partials* in play at any given time.
Since Bill's usage came first, I've suggested we call the former
thing "adaptive temperament". . .

See what I mean? I've been on this list for almost 10 years
and I'm still not sure I got that right. So you've just got
to give examples of everything, is what I try to do anyway.

-Carl

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

>
> I don't think harmonic entropy existed when he wrote that paper.
> Are you thinking of another paper, or am I all wet?

My bad- Forms of Tonality.

>
> > > But Aaron, along with LaMonte Young and many
> > > others no doubt, have used 12-tone scales with, for example,
> > > have good 3s and 7s but bad 5s.
> >
> > ...this kind of thing. And I'll checking if you're taking the
> > same approach.
>
> Since 5-limit intervals are a part of every evaluation in my
> spreadsheet, these scales would do poorly indeed.

I knew that: rhetorical question. :-)

> I have Cool Edit, which is very tedious to work with by I assume
> very accurate. Other than that, it's the wavetable synth that
> came with Windows. ;-P Is there any chance you could dump
> these into some wave files?

Man you really should get Csound, it is a godsend, and free! (and
the free frontend/editor WinXsoundPro if you're on windows). Then
it's cut-n-paste and click to get examples which are tuned, as far
as I know, to the highest accuracy possible today- I've got plenty
of microtuning-friendly code to share, and teach the thing sometimes.

The tuning accuracy of CoolEdit is fine IIRC, you can type in Hz to
so many decimal places, right? The problem is that it probably uses
tiny wavetables and all sounds are actually distorted (that's what
it sounds like).

> Sorry, I wasn't very clear. I mean, what sort of property
> can a 3-cents-sharp-from-3/2 interval have that a 2-cents-
> sharp-from-3/2 one doesn't? I guess one has to hear it. My
> experinece tuning pianos suggests these intevals sound almost
> identical, except the former beats slightly faster.

I just described on MMM what I believe is the source of difference.
If you try the intervals and find that the dissonance skips around
as you move away from 3/2, rather than steadily increasing...
something other than sheer proximity/distance to the 3/2 is going on.
The piano is a metallic percussion instrument so... I don't know.

> Sorry about that... you're "entering a world of pain" (think
> John Goodman in Lebowski) with the terminology around here.
> "Classic JI" is one way we refer to the style of 'take a scale
> consisting of some ratios and play it'. Allowing rapid root
> changes might be called "extended reference". "Adaptive JI"
> is like extended reference with root changes by irrational
> intervals. Finally there is "adaptive tuning", in which the
> vertical consonances are very slightly tempered along with
> the root-change intervals. Unless you're talking to Bill
> Sethares, when "adaptive tuning" means the the tuning is varied
> according the total *partials* in play at any given time.
> Since Bill's usage came first, I've suggested we call the former
> thing "adaptive temperament". . .

Oh goodness gracious. :-) Okay, I'll just say, hey, I often prefer
the sound of pretty complex ratios to simple ones, and "higher
primes" to lower.

-Cameron Bobro

🔗Carl Lumma <clumma@yahoo.com>

> > I don't think harmonic entropy existed when he wrote that paper.
> > Are you thinking of another paper, or am I all wet?
>
> My bad- Forms of Tonality.

I don't see that in FoT. Can you give a page number? Or
maybe you're talking about his "middle path" paper (which
is so far not online)?

> > I have Cool Edit, which is very tedious to work with by I assume
> > very accurate. Other than that, it's the wavetable synth that
> > came with Windows. ;-P Is there any chance you could dump
> > these into some wave files?
>
> Man you really should get Csound, it is a godsend, and free! (and
> the free frontend/editor WinXsoundPro if you're on windows). Then
> it's cut-n-paste and click to get examples which are tuned, as far
> as I know, to the highest accuracy possible today- I've got plenty
> of microtuning-friendly code to share, and teach the thing=
> sometimes.

I've tried before and had trouble. And right now, it's just far
too much for me to install any more software on my machine (I
have something like 200 titles on here). I don't have the
time/energy to tackle it right now. The list has to get by on
what each of us can contribute without blowing the rest of our
lives out of whack.

> The tuning accuracy of CoolEdit is fine IIRC, you can type in
> Hz to so many decimal places, right?

Yes. Actually you type in a fundamental as Hz. and a bunch
of partials as factors. So for rationals it's fairly easy,
but still an extra step to convert to a factor and type it
in a tiny box.

> The problem is that it probably uses tiny wavetables and all
> sounds are actually distorted (that's what it sounds like).

No, it's a simple synth. I used inv. sine waves or something
like that.

> > Sorry about that... you're "entering a world of pain" (think
> > John Goodman in Lebowski) with the terminology around here.
> > "Classic JI" is one way we refer to the style of 'take a scale
> > consisting of some ratios and play it'. Allowing rapid root
> > changes might be called "extended reference". "Adaptive JI"
> > is like extended reference with root changes by irrational
> > intervals. Finally there is "adaptive tuning", in which the
> > vertical consonances are very slightly tempered along with
> > the root-change intervals. Unless you're talking to Bill
> > Sethares, when "adaptive tuning" means the the tuning is varied
> > according the total *partials* in play at any given time.
> > Since Bill's usage came first, I've suggested we call the former
> > thing "adaptive temperament". . .
>
> Oh goodness gracious. :-) Okay, I'll just say, hey, I often prefer
> the sound of pretty complex ratios to simple ones, and "higher
> primes" to lower.

Incidentally, you can see Paul's account of this on page 10
of erlich-tFoT.pdf. He calls classic JI "strict JI",
extended reference "free-style JI", and this is the sense
of "adaptive tuning" which is predated by Sethares' usage.

-Carl

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > I don't think harmonic entropy existed when he wrote that
>>paper.
> > > Are you thinking of another paper, or am I all wet?
> >
> > My bad- Forms of Tonality.
>
> I don't see that in FoT. Can you give a page number? Or
> maybe you're talking about his "middle path" paper (which
> is so far not online)?

Hmmm...have to go through printouts! Maybe it was in someone else's
paper? It must be somewhere because my sirens went off when I read
it. :-)

> I've tried before and had trouble.

Know the feeling...

>And right now, it's just far
> too much for me to install any more software on my machine (I
> have something like 200 titles on here). I don't have the
> time/energy to tackle it right now. The list has to get by on
> what each of us can contribute without blowing the rest of our
> lives out of whack.

Yes I certainly understand. Right now I've got the latest Csound and
all this stuff on the laptop at home (no internet there)- my main
music computer is here at the studio but it's more of a giant
taperecorder now. And the computer I'm on now is just for the
Internet, yikes. (my studio is in the basement of a cybercafe). This
week I should be able to get you some .wav files, though.

> > The problem is that it probably uses tiny wavetables and all
> > sounds are actually distorted (that's what it sounds like).
>
> No, it's a simple synth. I used inv. sine waves or something
> like that.

The software synths all (almost- there's one exception I know of,
which takes a monster computer) read wavetables. Big wavetables take
a great deal time and memory, a huge wavetable read with cubic
interpolation is a kind of ideal. Even a sine read from a small
wavetable has harmonics and inharmonics. Anyway in this case tuning
accuracy and a non-painful timbre is most important.

> Incidentally, you can see Paul's account of this on page 10
> of erlich-tFoT.pdf. He calls classic JI "strict JI",
> extended reference "free-style JI", and this is the sense
> of "adaptive tuning" which is predated by Sethares' usage.

Looks like maybe specific examples and avoiding the terminology
altogether is the best bet, hahaha!

-Cameron Bobro

🔗Carl Lumma <clumma@yahoo.com>

> > I don't see that in FoT. Can you give a page number? Or
> > maybe you're talking about his "middle path" paper (which
> > is so far not online)?
>
> Hmmm...have to go through printouts! Maybe it was in someone
> else's paper? It must be somewhere because my sirens went off
> when I read it. :-)

I think he did say something like this, but I couldn't find
it either.

>(my studio is in the basement of a cybercafe)

Rock on! Free wireless. :)

> This week I should be able to get you some .wav files, though.

Great!

> > > The problem is that it probably uses tiny wavetables and all
> > > sounds are actually distorted (that's what it sounds like).
> >
> > No, it's a simple synth. I used inv. sine waves or something
> > like that.
>
> The software synths all (almost- there's one exception I know of,
> which takes a monster computer) read wavetables.

There are lots of synths that don't read wavetables.
Cameleon5000 and VirSyn Cube are additive synths, any of the
modeling synths from Arturia, Sculpture (part of Apple Logic),
and AAS String Studio... Reaktor.... Synful Orchestra, and
definitely Cool Edit.
None of them are particularly taxing of compute power.

The crappy Windows MIDI synth I use to play MIDI *is*
wavetable, and of the worst sort.

> Big wavetables take
> a great deal time and memory, a huge wavetable read with cubic
> interpolation is a kind of ideal. Even a sine read from a small
> wavetable has harmonics and inharmonics. Anyway in this case
> tuning accuracy and a non-painful timbre is most important.

Like CSound, Cool Edit is generating these mathematically.
Or I'll eat a bug (but I get to pick which kind).

-Carl

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >(my studio is in the basement of a cybercafe)
>
> Rock on! Free wireless. :)

Yes I'm very grateful for such a nice situation!

> There are lots of synths that don't read wavetables.
> Cameleon5000 and VirSyn Cube are additive synths, any of the
> modeling synths from Arturia, Sculpture (part of Apple Logic),
> and AAS String Studio... Reaktor.... Synful Orchestra, and
> definitely Cool Edit.
> None of them are particularly taxing of compute power.

Hehe, I just wrote a big thing on "technically speaking..." about
wavetables, more appropriate for MMM or KVR, but I just looked at
Wikipedia and realize that the term has been corrupted by commercial
uses and misuses to the point where it's come to mean "sample
playback". There's also inaccurate information in the Wikipedia
article, what a surprise.

The synths you mention above aren't sample-playback synths, that's
where our wires are crossed. There's a huge difference between
the "wavetable synth" in the cheesey soundcard, or an expensive GM
keyboard for that matter, and for example Reaktor (which I own),
which is a wavetable synth in a big way, also exploiting the non-
oscillator uses of the wavetable. The additive synths reads sines
from wavetables (with one exception that I know of) and so on.

Anyway there was a big discussion at KVR about this, back to tuning!

-Cameron Bobro

🔗Carl Lumma <clumma@yahoo.com>

> Hehe, I just wrote a big thing on "technically speaking..." about
> wavetables, more appropriate for MMM or KVR, but I just looked at
> Wikipedia and realize that the term has been corrupted by
> commercial uses and misuses to the point where it's come to
> mean "sample playback". There's also inaccurate information in
> the Wikipedia article, what a surprise.
> The synths you mention above aren't sample-playback synths, that's
> where our wires are crossed.

I'm aware of a distinction between wavetable and sample
playback, but I once tried to track it down on the web and
came to the conclusion that it no longer exists
linguistically (in English, anyway), and therefore the
material difference was also impossible to discern.

> There's a huge difference between the "wavetable synth" in the
> cheesey soundcard, or an expensive GM keyboard for that matter,
> and for example Reaktor (which I own), which is a wavetable
> synth in a big way, also exploiting the non-oscillator uses
> of the wavetable. The additive synths reads sines from
> wavetables (with one exception that I know of) and so on.

Yes, I understand that it's an array that can hold digital
sample *values* in sequence. Right? I'm not sure what the
use of this technique means ... something about distortion?
And what is the one synth, requiring major power, that you
know of?

> Anyway there was a big discussion at KVR about this, back to tuning!

Got a link?

-Carl