19/15 vs. 81/64---extremely subtle listening test

In all the fallout from the Well-Temperament listening tests, which
had most people radically *failing* to hear the differences very well
so often, and the talk of the 19-limit in recent WT threads, I thought
it would be fun to try this devilish listening test:

http://www.akjmusic.com/audio/chord_test.ogg
http://www.akjmusic.com/audio/chord_test.mp3

Can anyone tell an audible difference between 19/15 and 81/64?

First, two thirds are presented. Each third appears twice in random
order, for a total of four strikes of a major third. The choices are:

'A'
000.000
407.820 (81/64)
and
'B'
000.000
409.244 (19/15)

can you give the order?

Then, I'll present three triads, in random order:

'A'
000.000 cents
409.244 cents (19/15)
702.311 cents (4th root of 76/15)
'B'
000.000
407.820 (81/64)
701.955 (3/2)
'C'
000.000
409.244 (19/15)
701.955 (3/2)

can you give the order of the three strikes?

This brings to mind something for me...the defined limit of a wide
third for a WT is 81/64--perhaps it ought to be 19/15, since the
audible difference is virtually nil, and we can have some nice
rational 19-limit intervals to work with.

> http://www.akjmusic.com/audio/chord_test.ogg
> http://www.akjmusic.com/audio/chord_test.mp3
>
> Can anyone tell an audible difference between 19/15 and 81/64?
>
> First, two thirds are presented. Each third appears twice in
> random order, for a total of four strikes of a major third.
> The choices are:
>
> 'A'
> 000.000
> 407.820 (81/64)
> and
> 'B'
> 000.000
> 409.244 (19/15)
>
> can you give the order?

B A A B.

> Then, I'll present three triads, in random order:

You couldn't make separate files?

> 'A'
> 000.000 cents
> 409.244 cents (19/15)
> 702.311 cents (4th root of 76/15)
> 'B'
> 000.000
> 407.820 (81/64)
> 701.955 (3/2)
> 'C'
> 000.000
> 409.244 (19/15)
> 701.955 (3/2)
>
> can you give the order of the three strikes?

I could, but the baby is crying and some jackass is running
a leaf blower outside. But I think the point is, these 3rds
sound worse in a triad than they do by themselves.

> This brings to mind something for me...the defined limit of a wide
> third for a WT is 81/64--perhaps it ought to be 19/15, since the
> audible difference is virtually nil, and we can have some nice
> rational 19-limit intervals to work with.

But in this case the 19-limit interval sounds worse.
And I don't think there's any lock at 24/19, either. Listen
to nearby intervals and see if it stands out.

-Carl

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

> http://www.akjmusic.com/audio/chord_test.ogg
> http://www.akjmusic.com/audio/chord_test.mp3
>
> Can anyone tell an audible difference between 19/15 and 81/64?

I'll give it a shot, but geez. (19/15)/(81/64) = 1216/1215.
If anyone likes 19/15 better, they could try the (76/15)^(1/4) fifth I
guess; that's not too terribly far off from the 41-et fifth. Of course
if you are going to warp meantone like that, 46 (14/11 "meantone"
thirds) or even 22 (9/7 "meantone" thirds) come to mind. A simple
retuning via Scala and you are in business.

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...>
wrote:
>
> In all the fallout from the Well-Temperament listening tests, which
> had most people radically *failing* to hear the differences very
well
> so often, and the talk of the 19-limit in recent WT threads, I
thought
> it would be fun to try this devilish listening test:
>
> http://www.akjmusic.com/audio/chord_test.ogg
> http://www.akjmusic.com/audio/chord_test.mp3
>
> Can anyone tell an audible difference between 19/15 and 81/64?
>
> First, two thirds are presented. Each third appears twice in random
> order, for a total of four strikes of a major third. The choices
are:
>
> 'A'
> 000.000
> 407.820 (81/64)
> and
> 'B'
> 000.000
> 409.244 (19/15)
>
> can you give the order?

Darker, brighter, brighter, darker (but higher, lower, lower,
higher).

>
> Then, I'll present three triads, in random order:
>
> 'A'
> 000.000 cents
> 409.244 cents (19/15)
> 702.311 cents (4th root of 76/15)
> 'B'
> 000.000
> 407.820 (81/64)
> 701.955 (3/2)
> 'C'
> 000.000
> 409.244 (19/15)
> 701.955 (3/2)
>
> can you give the order of the three strikes?

False, consonant, wild-eyed. I try to go by character, then
worry about the ratio later.

Nice test!

> This brings to mind something for me...the defined limit of a wide
> third for a WT is 81/64--perhaps it ought to be 19/15, since the
> audible difference is virtually nil, and we can have some nice
> rational 19-limit intervals to work with.

Might be a good idea! As you can guess from the WT I posted, I did
try 19/15 (19/18,19/17,19/16...what's next?) but I wanted a soft
third on C so I didn't explore it further, although it sounded fine
in context.

-Cameron Bobro

I'm amazed that Carl and Cameron can hear any difference at all in the
thirds. I can't--I'm not hearing the 'bright dark dark bright' that
Cameron mentions. Or, if I hear it, it's so subtle it seems like
suggestion. It's an amazingly small difference. Maybe my ears aren't
working as well---I probably have more age/hearing loss than Carl, and
that might play into hearing up to the 19 limit for locking of sorts.

The chords are remarkably close, too, although I hear a subtle
difference in the beating between A and B.

No one so far has guessed the order of the chords (or I should say has
even tried)...no takers?

I won't reveal the answer for the first part until more people respond.

-A.

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@>
> wrote:
> >
> > In all the fallout from the Well-Temperament listening tests, which
> > had most people radically *failing* to hear the differences very
> well
> > so often, and the talk of the 19-limit in recent WT threads, I
> thought
> > it would be fun to try this devilish listening test:
> >
> > http://www.akjmusic.com/audio/chord_test.ogg
> > http://www.akjmusic.com/audio/chord_test.mp3
> >
> > Can anyone tell an audible difference between 19/15 and 81/64?
> >
> > First, two thirds are presented. Each third appears twice in random
> > order, for a total of four strikes of a major third. The choices
> are:
> >
> > 'A'
> > 000.000
> > 407.820 (81/64)
> > and
> > 'B'
> > 000.000
> > 409.244 (19/15)
> >
> > can you give the order?
>
> Darker, brighter, brighter, darker (but higher, lower, lower,
> higher).
>
> >
> > Then, I'll present three triads, in random order:
> >
> > 'A'
> > 000.000 cents
> > 409.244 cents (19/15)
> > 702.311 cents (4th root of 76/15)
> > 'B'
> > 000.000
> > 407.820 (81/64)
> > 701.955 (3/2)
> > 'C'
> > 000.000
> > 409.244 (19/15)
> > 701.955 (3/2)
> >
> > can you give the order of the three strikes?
>
> False, consonant, wild-eyed. I try to go by character, then
> worry about the ratio later.
>
> Nice test!
>
> > This brings to mind something for me...the defined limit of a wide
> > third for a WT is 81/64--perhaps it ought to be 19/15, since the
> > audible difference is virtually nil, and we can have some nice
> > rational 19-limit intervals to work with.
>
> Might be a good idea! As you can guess from the WT I posted, I did
> try 19/15 (19/18,19/17,19/16...what's next?) but I wanted a soft
> third on C so I didn't explore it further, although it sounded fine
> in context.
>
> -Cameron Bobro
>

Oh- I think it Pyth., 19/15, wonky-fifth for the chords, but
whatever the second chord turns out to be I'm calling it good.
BAAB for the thirds as I said, I went with my feeling of one
hearing on that but listened to the chords several times.

The thirds in the context of a triad is a different matter, isn't it!

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...>
wrote:
>
> I'm amazed that Carl and Cameron can hear any difference at all in
the
> thirds. I can't--I'm not hearing the 'bright dark dark bright' that
> Cameron mentions. Or, if I hear it, it's so subtle it seems like
> suggestion. It's an amazingly small difference. Maybe my ears
aren't
> working as well---I probably have more age/hearing loss than Carl,
and
> that might play into hearing up to the 19 limit for locking of
sorts.
>
> The chords are remarkably close, too, although I hear a subtle
> difference in the beating between A and B.
>
> No one so far has guessed the order of the chords (or I should say
has
> even tried)...no takers?
>
> I won't reveal the answer for the first part until more people
respond.
>
> -A.
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
wrote:
> >
> > --- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@>
> > wrote:
> > >
> > > In all the fallout from the Well-Temperament listening tests,
which
> > > had most people radically *failing* to hear the differences
very
> > well
> > > so often, and the talk of the 19-limit in recent WT threads, I
> > thought
> > > it would be fun to try this devilish listening test:
> > >
> > > http://www.akjmusic.com/audio/chord_test.ogg
> > > http://www.akjmusic.com/audio/chord_test.mp3
> > >
> > > Can anyone tell an audible difference between 19/15 and 81/64?
> > >
> > > First, two thirds are presented. Each third appears twice in
random
> > > order, for a total of four strikes of a major third. The
choices
> > are:
> > >
> > > 'A'
> > > 000.000
> > > 407.820 (81/64)
> > > and
> > > 'B'
> > > 000.000
> > > 409.244 (19/15)
> > >
> > > can you give the order?
> >
> > Darker, brighter, brighter, darker (but higher, lower, lower,
> > higher).
> >
> > >
> > > Then, I'll present three triads, in random order:
> > >
> > > 'A'
> > > 000.000 cents
> > > 409.244 cents (19/15)
> > > 702.311 cents (4th root of 76/15)
> > > 'B'
> > > 000.000
> > > 407.820 (81/64)
> > > 701.955 (3/2)
> > > 'C'
> > > 000.000
> > > 409.244 (19/15)
> > > 701.955 (3/2)
> > >
> > > can you give the order of the three strikes?
> >
> > False, consonant, wild-eyed. I try to go by character, then
> > worry about the ratio later.
> >
> > Nice test!
> >
> > > This brings to mind something for me...the defined limit of a
wide
> > > third for a WT is 81/64--perhaps it ought to be 19/15, since
the
> > > audible difference is virtually nil, and we can have some nice
> > > rational 19-limit intervals to work with.
> >
> > Might be a good idea! As you can guess from the WT I posted, I
did
> > try 19/15 (19/18,19/17,19/16...what's next?) but I wanted a soft
> > third on C so I didn't explore it further, although it sounded
fine
> > in context.
> >
> > -Cameron Bobro
> >
>

> I'm amazed that Carl and Cameron can hear any difference at
> all in the thirds.

I'm very confident that the 2nd third sounds sweeter than
the first, and I'm confident that means it's 81/64 and not
19/15, and I think I'm right about the 3rd third being the
same as the 2nd, but but by then the leaf blower had started
and I was, as usual, late for work.
I know I said harpsichord is an ideal timbre for testing
tunings, but I meant that in the context of moving music.
With isolated chords, the relatively long noisy attack and
short sustain mean a subtly-enveloped triangle wave would
probably be preferred (by me).

> No one so far has guessed the order of the chords (or I
> should say has even tried)...no takers?

I'll try to try again tonight.

-Carl

Aaron wrote:

> can you give the order of the three strikes?

I'm not sure but I think the one with the slightly wider fifth is played first. Perhaps it's ACB?

BTW: Maybe the overtones could get more pronounced with a sound in which they last longer -- or, even better, in a sustaining sound. Not a request, just an idea. When I wanted some people to set up some kind of meantone tempering on a regular piano at my former school a number of years ago, I made a CD full of sawtooth waves of the single tone periods, then the beat rates, and finally the major chords.

Petr

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > I'm amazed that Carl and Cameron can hear any difference at
> > all in the thirds.
>
> I'm very confident that the 2nd third sounds sweeter than
> the first, and I'm confident that means it's 81/64 and not
> 19/15, and I think I'm right about the 3rd third being the
> same as the 2nd, but but by then the leaf blower had started
> and I was, as usual, late for work.

This all sounds right.

> > No one so far has guessed the order of the chords (or I
> > should say has even tried)...no takers?
>
> I'll try to try again tonight.

I forgot what that part is about. What are we supposedly testing for,
by the way?

> > can you give the order of the three strikes?
>
> I'm not sure but I think the one with the slightly wider fifth
> is played first. Perhaps it's ACB?
>
> BTW: Maybe the overtones could get more pronounced with a sound
> in which they last longer -- or, even better, in a sustaining
> sound. Not a request, just an idea. When I wanted some people to
> set up some kind of meantone tempering on a regular piano at my
> former school a number of years ago, I made a CD full of sawtooth
> waves of the single tone periods, then the beat rates, and
> finally the major chords.

I agree with Petr -- the harpsichord's attacks help in moving
passages, but can even become a bit deafening in listening
tests with isolated chords.
And the last chord seems to start fading out before sounding as
long as the first two. Plus, this *is* a harder test, with
two variables and only one trial per. But I'm guessing CBA.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:

> > I'm very confident that the 2nd third sounds sweeter than
> > the first, and I'm confident that means it's 81/64 and not
> > 19/15, and I think I'm right about the 3rd third being the
> > same as the 2nd, but but by then the leaf blower had started
> > and I was, as usual, late for work.
>
> This all sounds right.

So that would be BAAB, which means you, Carl, and I are in
agreement about this (except that I find the second one
simply brighter, not sweeter, even though it sounds lower)
>
> > > No one so far has guessed the order of the chords (or I
> > > should say has even tried)...no takers?
> >
> > I'll try to try again tonight.
>
> I forgot what that part is about. What are we supposedly testing
for,
> by the way?
>

Just say which one of the chords you think is which, Aaron gave
the three possibilities. I'm interested to know which of three
you guys prefer, too (I think the second chord is the most
consonant).

The timbre is just fine and the test quite clear, seems to me.

Cameron wrote...
> (I think the second chord is the most
> consonant).

Agree.

-Carl

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...> wrote:
>
> In all the fallout from the Well-Temperament listening tests, which
> had most people radically *failing* to hear the differences very well
> so often, and the talk of the 19-limit in recent WT threads, I thought
> it would be fun to try this devilish listening test:
>
> http://www.akjmusic.com/audio/chord_test.ogg
> http://www.akjmusic.com/audio/chord_test.mp3
>
> Can anyone tell an audible difference between 19/15 and 81/64?
>
> First, two thirds are presented. Each third appears twice in random
> order, for a total of four strikes of a major third. The choices are:
>
> 'A'
> 000.000
> 407.820 (81/64)
> and
> 'B'
> 000.000
> 409.244 (19/15)
>
> can you give the order?

Carl and Cameron, I'm impressed as hell. You guys heard it correctly: BAAB

> Then, I'll present three triads, in random order:
>
> 'A'
> 000.000 cents
> 409.244 cents (19/15)
> 702.311 cents (4th root of 76/15)
> 'B'
> 000.000
> 407.820 (81/64)
> 701.955 (3/2)
> 'C'
> 000.000
> 409.244 (19/15)
> 701.955 (3/2)
>
> can you give the order of the three strikes?

Interesting...Petr nailed this. 'ACB' was the order. Carl and Cameron
found the 1/1 - 19/15 - 3/2 to be most consonant! Perhaps there is
some subtle locking in the 19-limit for you guys?

> This brings to mind something for me...the defined limit of a wide
> third for a WT is 81/64--perhaps it ought to be 19/15, since the
> audible difference is virtually nil, and we can have some nice
> rational 19-limit intervals to work with.

I still think this above paragraph might have something to it, given
the results of Carl and Cameron above.

-A.

> > Then, I'll present three triads, in random order:
> >
> > 'A'
> > 000.000 cents
> > 409.244 cents (19/15)
> > 702.311 cents (4th root of 76/15)
> > 'B'
> > 000.000
> > 407.820 (81/64)
> > 701.955 (3/2)
> > 'C'
> > 000.000
> > 409.244 (19/15)
> > 701.955 (3/2)
> >
> > can you give the order of the three strikes?
>
> Interesting...Petr nailed this. 'ACB' was the order. Carl
> and Cameron found the 1/1 - 19/15 - 3/2 to be most consonant!
> Perhaps there is some subtle locking in the 19-limit for
> you guys?

Harumph.

There definitely is some locking in the beating vs. 81:64 --
I heard it in Scala when playing these triads last night. But
it's incredibly subtle, doesn't lead to more consonance, is
is masked when a fifth is present, almost couldn't be used
in the real world to set a third, and I couldn't hear it at
all in these files. I think I'll chalk my dismal result up to
randomness and possibly poisoning by reading Cameron's post.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > Then, I'll present three triads, in random order:
> > >
> > > 'A'
> > > 000.000 cents
> > > 409.244 cents (19/15)
> > > 702.311 cents (4th root of 76/15)
> > > 'B'
> > > 000.000
> > > 407.820 (81/64)
> > > 701.955 (3/2)
> > > 'C'
> > > 000.000
> > > 409.244 (19/15)
> > > 701.955 (3/2)
> > >
> > > can you give the order of the three strikes?
> >
> > Interesting...Petr nailed this. 'ACB' was the order. Carl
> > and Cameron found the 1/1 - 19/15 - 3/2 to be most consonant!
> > Perhaps there is some subtle locking in the 19-limit for
> > you guys?
>
> Harumph.
>
> There definitely is some locking in the beating vs. 81:64 --
> I heard it in Scala when playing these triads last night. But
> it's incredibly subtle, doesn't lead to more consonance, is
> is masked when a fifth is present, almost couldn't be used
> in the real world to set a third, and I couldn't hear it at
> all in these files. I think I'll chalk my dismal result up to
> randomness and possibly poisoning by reading Cameron's post.

Not dismal *at all*---you and Cameron heard a difference in the thirds
(alone, not in the chords, obviously) that I really couldn't if you
put a gun to my head. Go figure....and Petr, he must have super-ears
to hear the triads as well...funny, I heard more difference in the
triads, because I think the other two pitches made it less subtle for
me, but I'm not sure I would've figured which was which.

-A.

> There definitely is some locking in the beating vs. 81:64 --
> I heard it in Scala when playing these triads last night. But
> it's incredibly subtle, doesn't lead to more consonance, is
> is masked when a fifth is present, almost couldn't be used
> in the real world to set a third, and I couldn't hear it at
> all in these files. I think I'll chalk my dismal result up to
> randomness and possibly poisoning by reading Cameron's post.
>
> -Carl
>

Errata:

I heard it in Scala when playing these THIRDS last night

is masked when a fifth is present, almost CERTAINLY
couldn't be used

-C.

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@>
wrote:
> >
> > In all the fallout from the Well-Temperament listening tests,
which
> > had most people radically *failing* to hear the differences very
well
> > so often, and the talk of the 19-limit in recent WT threads, I
thought
> > it would be fun to try this devilish listening test:
> >
> > http://www.akjmusic.com/audio/chord_test.ogg
> > http://www.akjmusic.com/audio/chord_test.mp3
> >
> > Can anyone tell an audible difference between 19/15 and 81/64?
> >
> > First, two thirds are presented. Each third appears twice in
random
> > order, for a total of four strikes of a major third. The choices
are:
> >
> > 'A'
> > 000.000
> > 407.820 (81/64)
> > and
> > 'B'
> > 000.000
> > 409.244 (19/15)
> >
> > can you give the order?
>
> Carl and Cameron, I'm impressed as hell. You guys heard it
correctly: BAAB
>
> > Then, I'll present three triads, in random order:
> >
> > 'A'
> > 000.000 cents
> > 409.244 cents (19/15)
> > 702.311 cents (4th root of 76/15)
> > 'B'
> > 000.000
> > 407.820 (81/64)
> > 701.955 (3/2)
> > 'C'
> > 000.000
> > 409.244 (19/15)
> > 701.955 (3/2)
> >
> > can you give the order of the three strikes?
>
> Interesting...Petr nailed this. 'ACB' was the order. Carl and
Cameron
> found the 1/1 - 19/15 - 3/2 to be most consonant! Perhaps there is
> some subtle locking in the 19-limit for you guys?
>
> > This brings to mind something for me...the defined limit of a
wide
> > third for a WT is 81/64--perhaps it ought to be 19/15, since the
> > audible difference is virtually nil, and we can have some nice
> > rational 19-limit intervals to work with.
>
> I still think this above paragraph might have something to it,
given
> the results of Carl and Cameron above.
>
> -A.
>

I thought it was BCA. One interval I was certain of, "C", 19/15,
knowing from previous experience with *19/x and x/*19 goofing around
that it's a very consonant third (it's 3/2 complement of 45/38 is
fine too) but mixed up A and B. I'm kind of surprised that I heard
the unusual fifth as "false", I'm working with high fifths all the
time, but not too surprised that the Pyth. triad seemed "wild-eyed"
in context, it really is a pretty unrestful third, in any context.

The first 4 diads seemed clear- 19/15 is smoother and darker yet
physically higher (wider), so when I heard it drop yet brighten
(or become more metallic might be a better description) on the
second one, there it was.

Thanks for the groovy test, Aaron! Time to start tuning up some 19-y
WTs if you ask me. :-)

-Cameron Bobro

Cameron wrote:

> Thanks for the groovy test, Aaron! Time to start tuning up some 19-y WTs if you ask me. :-)

Don't know which version of Manuel's scale archive you have but there's a couple of my 19-limit WTs. They're listed as "parizek_jiweltmp", "parizek_jiwt2" and "parizek_jiwt3".

Petr

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

> I think I'll chalk my dismal result up to
> randomness and possibly poisoning by reading Cameron's post.

I thought two of the chords sounded awfully similar and handn't gotten
around to trying to sort it out.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
> Don't know which version of Manuel's scale archive you have but
>there's a couple of my 19-limit WTs. They're listed
>as "parizek_jiweltmp", "parizek_jiwt2" and "parizek_jiwt3".

Yes, I found them a while ago when I did "compare scale" on one of my
experiments and found that it was identical to one of yours, in a
different key. That's how I found these groups in the first place, by
the way- pretty much randomly googling stuff from what I was working
on.

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

> Harumph.
>
> There definitely is some locking in the beating vs. 81:64 --
> I heard it in Scala when playing these triads last night. But
> it's incredibly subtle, doesn't lead to more consonance, is
> is masked when a fifth is present, almost couldn't be used
> in the real world to set a third, and I couldn't hear it at
> all in these files. I think I'll chalk my dismal result up to
> randomness and possibly poisoning by reading Cameron's post.
>
> -Carl

You would have named the chords if you hadn't based your judgement
on the idea that the most consonant triad must be the 81/64 triad,
I'm quite sure.

19/15 is just dandy, why for goodness' sake shouldn't it be as or
more consonant in a triad than 81/64? Further away from 5/4? That's
insane- if there's anything to the attraction of simpler intervals,
14/11 and even 9/7 are the nearest major planets, and that idea
would favor 19/15 over 81/64 anyway.

Prime limit? Prime limit without considering exponents is nuts, as
you know very well, 19/15 is simpler there, too.

N*D? 19/15 is 18 times as simple.

Harmonic series? the 81st partial? get outta here. As far as
overtones, 19/15 is the equivalent of a simple interval (15/8) above
a subharmonic major sixth. They're probably on equal footing as far
as M3 credentials coming from the harmonic series.

Familiarity? You're on record saying how you don't like Pyth.
thirds.

Why don't you just trust your ears? I've reevaluted my position on
81/64. In this context I heard it as "wild-eyed" and I still do on
listening again. I realize that I DON'T like it as a M3, but as a
ditone, which is what it is. CDE chord in Pyth., cool! Scala lists
81/64 as a M3 and 19/15 as a ditone but I think this is wrong. 19/15
would be the ditone of what? Certainly not a simple ratio, while
81/64 = (9/8)(9/8).

> > Harumph.
> >
> > There definitely is some locking in the beating vs. 81:64 --
> > I heard it in Scala when playing these triads last night. But
> > it's incredibly subtle, doesn't lead to more consonance, is
> > is masked when a fifth is present, almost couldn't be used
> > in the real world to set a third, and I couldn't hear it at
> > all in these files. I think I'll chalk my dismal result up to
> > randomness and possibly poisoning by reading Cameron's post.
> >
> > -Carl
>
> You would have named the chords if you hadn't based your judgement
> on the idea that the most consonant triad must be the 81/64 triad,
> I'm quite sure.

I don't think so.

> Further away from 5/4? That's
> insane- if there's anything to the attraction of simpler intervals,
> 14/11 and even 9/7 are the nearest major planets, and that idea
> would favor 19/15 over 81/64 anyway.

What makes you so sure?

> N*D? 19/15 is 18 times as simple.

N*D doesn't work when the product is this high.

> Why don't you just trust your ears?

Why must you make assumptions about what I did. I notice
you didn't get it right either!

-Carl

Cameron wrote:

> Yes, I found them a while ago when I did "compare scale" on one of my experiments and found that it was identical to one of yours, in a different key.

Really? That's cool. Which one was it?

PP

Petr Par�zek wrote:
> Cameron wrote:
> >> Yes, I found them a while ago when I did "compare scale" on one of my experiments and found that it was identical to one of yours, in a different key.
> > Really? That's cool. Which one was it?
> > PP

I had the same experience with one of my scales. "parizek_ji1.scl : equal in key 9".

The scale has one 112/75 fifth, which someone here on the list pointed out can be improved by tempering out 225/224. But either way it's a pretty nice scale.

Herman wrote:

> I had the same experience with one of my scales. "parizek_ji1.scl :

equal in key 9".

Amazing. How did you get to this scale? I found it by making some sort of an "improper" Euler-Fokker genus with initial factors of "3, 3, 5/3, 7/5".

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Cameron wrote:
>
> > Yes, I found them a while ago when I did "compare scale" on one
of my experiments and found that it was identical to one of yours,
in a different key.
>
> Really? That's cool. Which one was it?
>
> PP
>

First JI WT. Don't remember how I got it, I don't know how to use
Fokker blocks and such. I always start with the classics- a
monochord, real or virtual, superparticular intervals, tetrachords,
some tasty interval I found by accident (crunched over the fretless
guitar with a ruler...)

-Cameron Bobro

> > I had the same experience with one of my
> > scales. "parizek_ji1.scl :
>
> equal in key 9".
>
> Amazing. How did you get to this scale? I found it by making some
> sort of an "improper" Euler-Fokker genus with initial factors of
> "3, 3, 5/3, 7/5".
>
> Petr

Not so amazing -- there are only so many 12-tone convex sections
of the 7-limit lattice, and there are even fewer that don't
contain a 225/224. These sorts of scales come up again and
again, and are equivalent under miracle tempering.

-Carl

Petr Par�zek wrote:
> Herman wrote:
> >> I had the same experience with one of my scales. "parizek_ji1.scl : > > equal in key 9".
> > Amazing. How did you get to this scale? I found it by making some sort of an "improper" Euler-Fokker genus with initial factors of "3, 3, 5/3, 7/5".
> > Petr

I started by following the harmonic progression of "The Imperial March" from _The Empire Strikes Back_, when I realized that there weren't any comma pumps in it and I could tune it as JI (at least the first part of it, which stays around G minor). I noticed the partial symmetry and filled in the gaps.

> I started by following the harmonic progression of "The Imperial
> March" from _The Empire Strikes Back_, when I realized that
> there weren't any comma pumps in it and I could tune it as
> JI (at least the first part of it, which stays around G minor).
> I noticed the partial symmetry and filled in the gaps.

Great work!

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > I started by following the harmonic progression of "The Imperial
> > March" from _The Empire Strikes Back_, when I realized that
> > there weren't any comma pumps in it and I could tune it as
> > JI (at least the first part of it, which stays around G minor).
> > I noticed the partial symmetry and filled in the gaps.
>
> Great work!
>
> -Carl

Dang it, Carl, why do you always trim off the
"--- In tuning@yahoogroups.com, "xxx" <xxx@...> wrote:"

??????

It's only one stinking line, and leaving it in would
really help the reader of your posts to follow the
thread from whence it proceeds.

Thanks, if you'll reconsider. ;-)

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > > I started by following the harmonic progression of "The Imperial
> > > March" from _The Empire Strikes Back_, when I realized that
> > > there weren't any comma pumps in it and I could tune it as
> > > JI (at least the first part of it, which stays around G minor).
> > > I noticed the partial symmetry and filled in the gaps.
> >
> > Great work!
> >
> > -Carl
>
> Dang it, Carl, why do you always trim off the
> "--- In tuning@yahoogroups.com, "xxx" <xxx@> wrote:"
>
> ??????
>
> It's only one stinking line, and leaving it in would
> really help the reader of your posts to follow the
> thread from whence it proceeds.
>
> Thanks, if you'll reconsider. ;-)

If you're reading on the web, you can use the thread navigator
below the message. But I'll consider leaving it in the future.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> >
> > Dang it, Carl, why do you always trim off the
> > "--- In tuning@yahoogroups.com, "xxx" <xxx@> wrote:"
> >
> > ??????
> >
> > It's only one stinking line, and leaving it in would
> > really help the reader of your posts to follow the
> > thread from whence it proceeds.
> >
> > Thanks, if you'll reconsider. ;-)
>
> If you're reading on the web, you can use the thread
> navigator below the message.

Thanks for that, but yes, i know. But sometimes if i am
following a thread and already know the general progression
of posts, i still can't remember who wrote what you quote,
so it would be nice to just see that embedded without
having to go thru the trouble of consulting the navigator.

> But I'll consider leaving it in the future.

Thanks.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
> > Dang it, Carl, why do you always trim off the
> > "--- In tuning@yahoogroups.com, "xxx" <xxx@> wrote:"
> >
> > ??????
> >
> > It's only one stinking line, and leaving it in would
> > really help the reader of your posts to follow the
> > thread from whence it proceeds.
> >
> > Thanks, if you'll reconsider. ;-)
>
> If you're reading on the web, you can use the thread navigator
> below the message. But I'll consider leaving it in the future.

Not to mention, Carl, that many folks get email delivery, so wouldn't
have the web context to help them.

-A.