A few THE triads

Can anyone tell me the entropy, and the most probable JI basis triad, for
these three triads?

0-1200-300
0-1200-316

0-702-300
0-702-316

0-300-702
0-316-702

0-300-1002
0-316-1018

Would be much appreciated.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Can anyone tell me the entropy, and the most probable JI basis triad, for these three triads?

1200:300:5.7693:8/16/19:
1200:316:5.7534:5/10/12:
702:300:5.8670:14/21/25:
702:316:5.8601:10/15/18:
300:702:5.8465:5/6/9:
316:702:5.7881:5/6/9:
300:1002:5.8847:16/19/34:
316:1018:5.8987:20/24/43:

HTH,
Steve.

On Sat, Dec 18, 2010 at 5:00 AM, martinsj013 <martinsj@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > Can anyone tell me the entropy, and the most probable JI basis triad, for these three triads?
>
> 1200:300:5.7693:8/16/19:
> 1200:316:5.7534:5/10/12:
> 702:300:5.8670:14/21/25:
> 702:316:5.8601:10/15/18:
> 300:702:5.8465:5/6/9:
> 316:702:5.7881:5/6/9:
> 300:1002:5.8847:16/19/34:
> 316:1018:5.8987:20/24/43:
>
> HTH,
> Steve.

Thanks Steve... I think I messed these up bad though. Sometimes I was
using lower-upper notation, and sometimes I was using lower-outer
notation.

I'll try again, in lower-upper notation, since that's probably what
you're used to:

0-1200-300
0-1200-316

0-702-814
0-702-798

0-300-402
0-316-386

0-300-702
0-316-702

I think you handled the first and the last one, so it's only the
middle two I screwed up on.

Thanks for the help,
Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Thanks Steve... I think I messed these up bad though ... I'll try again, in lower-upper notation ...

Hi Mike,
OK, here are some results (below); are they all intended to be minor triads in root position with different spacing and sometimes omitting the 5th? I see the minor 7th in two of them so, in case that was a mistake, I included my "correction" as well.

1200:300:5.7693:8/16/19:
1200:316:5.7534:5/10/12:
702:814:5.8559:10/15/24:
702:798:5.8504:8/12/19:
300:402:5.8640:16/19/24:
316:386:5.8551:10/12/15:
300:702:5.8465:5/6/9:
316:702:5.7881:5/6/9:
300:900:5.8044:5/6/10:
316:884:5.7704:5/6/10:

Looks like the 300 is mostly (but not always) appearing as a 16:19.

If it helps, when I plotted the cross-section with outer=702cents, there was a local minimum at (316,386), but a much deeper one at (267,435) (and of course at (386,316) but it looks like you are not interested in that :-))

Steve M.

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:

> OK, here are some results (below); are they all intended to be minor triads in root position with different spacing and sometimes omitting the 5th?

I repeat: if the entropy gang would use standard notation for chords, the rest of us could be sure we knew what you were talking about and, evidently, you would not so often confuse each other. If you follow that logic, a minor triad in close root position should *always* look like some variation on 0-316-702-1200. Note I am not using colons, which is incorrect as the quantities are not ratios. If you don't like dashes as separators, use something else, but please not colons!

Why is standard notation not being used?

Gene wrote:

> Why is standard notation not being used?

I too had problems reading the latest. Aside from substituting
semicolons for colons to accommodate Excel (which I explained
several times), I've used standard notation throughout.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > Why is standard notation not being used?
>
> I too had problems reading the latest. Aside from substituting
> semicolons for colons to accommodate Excel (which I explained
> several times), I've used standard notation throughout.

I found that confusing also until you explained it. I still don't like it, but I'm biased as I hate spreadsheets for anything but computing grades.

> I found that confusing also until you explained it.

I explained it before I posted it.

-Carl

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> I repeat: if the entropy gang would use standard notation for chords, the rest of us could be sure we knew what you were talking about ... Why is standard notation not being used?

I have to admit there is no good reason, so here are the previous sets of results again in standard notation:

triad-cents, triadic-HE, most-prob-Tenney-member
0-1200-300, 5.7693, 8:16:19
0-1200-316, 5.7534, 5:10:12
0-702-300, 5.8670, 14:21:25
0-702-316, 5.8601, 10:15:18
0-300-702, 5.8465, 5:6:9
0-316-702, 5.7881, 5:6:9
0-300-1002, 5.8847, 16:19:34
0-316-1018, 5.8987, 20:24:43
0-1200-300, 5.7693, 8:16:19
0-1200-316, 5.7534, 5:10:12
0-702-814, 5.8559, 10:15:24
0-702-798, 5.8504, 8:12:19
0-300-402, 5.8640, 16:19:24
0-316-386, 5.8551, 10:12:15
0-300-702, 5.8465, 5:6:9
0-316-702, 5.7881, 5:6:9
0-300-900, 5.8044, 5:6:10
0-316-884, 5.7704, 5:6:10

Steve M.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > Why is standard notation not being used?
>
> I too had problems reading the latest. Aside from substituting
> semicolons for colons to accommodate Excel (which I explained
> several times), I've used standard notation throughout.

By the way, what does entropy have to say about the Lumma Chord? This is the chord with intervals of approximately 7/5, 13/10 and 11/10 (or you could try permutations) making up an octave by tempering out 1001/1000. I'm calling it the Lumma Chord because you were picking on 1001/1000, which however unlike 101/100 is a comma which might actually get used. Can entropy say anything interesting about chords (of which this would be a typical example) when considered in isolation? Does it tell us if there is a local minimum in the region of the chord? If this isn't a good example, and I admit I picked it just to chaff you a bit, the same question for a triad. Can we select a triad and determine if it gives us a local minimum?

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:

> I have to admit there is no good reason, so here are the previous sets of results again in standard notation:
>
> triad-cents, triadic-HE, most-prob-Tenney-member

> 0-702-300, 5.8670, 14:21:25

> 0-300-702, 5.8465, 5:6:9

I'm still confused. What is the difference between these two chords?

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
If this isn't a good example, and I admit I picked it just to chaff you a bit, the same question for a triad.

Eh, what am I saying; it is a triad. The point was we got to an octave.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > 0-702-300, 5.8670, 14:21:25
> > 0-300-702, 5.8465, 5:6:9
> I'm still confused. What is the difference between these two chords?

Agh, sorry, I got that list badly wrong; below is correct:

triad-cents, triadic-HE, most-prob-Tenney-member
0-1200-1500, 5.7693, 8:16:19
0-1200-1516, 5.7534, 5:10:12
0-702-1002, 5.8670, 14:21:25
0-702-1018, 5.8601, 10:15:18
0-300-1002, 5.8465, 5:6:9
0-316-1018, 5.7881, 5:6:9
0-300-1302, 5.8847, 16:19:34
0-316-1334, 5.8987, 20:24:43

0-1200-1500, 5.7693, 8:16:19
0-1200-1516, 5.7534, 5:10:12
0-702-1516, 5.8559, 10:15:24
0-702-1500, 5.8504, 8:12:19
0-300-702, 5.8640, 16:19:24
0-316-702, 5.8551, 10:12:15
0-300-1002, 5.8465, 5:6:9
0-316-1018, 5.7881, 5:6:9
0-300-1200, 5.8044, 5:6:10
0-316-1200, 5.7704, 5:6:10

S.

Gene wrote:

>> If this isn't a good example, and I admit I picked it just to
>> chaff you a bit, the same question for a triad.
>
> Eh, what am I saying; it is a triad. The point was we got to
> an octave.

Try standard notation - I still don't know what chord you're
talking about.

[snip]
>> 0-702-300, 5.8670, 14:21:25
>> 0-300-702, 5.8465, 5:6:9
>
> I'm still confused. What is the difference between these
> two chords?

This still isn't standard notation. That would be

0-702-1002
0-300-1002

unless I'm mistaken. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Try standard notation - I still don't know what chord you're
> talking about.

A 1001/1000-comma tempered version of 1-7/5-20/11. If I use the POTE (pure octaves Tenney-Euclidean) tuning, that would be 0-582.027-1035.595. Compare 0-582.512-1034.996. I'm trying to ask if entropy sorts the "interesting" chords from the "uninteresting" ones by the presence or absence of a local minimum.

Gene wrote,

> A 1001/1000-comma tempered version of 1-7/5-20/11. If I use
> the POTE (pure octaves Tenney-Euclidean) tuning, that would be
> 0-582.027-1035.595. Compare 0-582.512-1034.996. I'm trying to
> ask if entropy sorts the "interesting" chords from the
> "uninteresting" ones by the presence or absence of a
> local minimum.

There's nothing about octaves in the thing, so maybe just TE
would be better. We've got a dyadic resolution of one cent
(except in a few cases where Steve looked more closely at cross
sections), so the chords are l=582,u=454 and l=583,u=452.

All the minima are in the file I provided before... nope,
neither chord is listed, nor anything close.

We looked for other 'tempered better than just' chords and
couldn't find any. See the thread ending here:
/tuning/topicId_93392.html#94911

However, when we insist that the lower and upper intervals
be multiples of some generator, then we get the rank 2
temperaments we know and love out of the minima of the
resulting cross-section... very good tunings for their
generators in fact, as I think you saw.

-Carl

On Sat, Dec 18, 2010 at 3:28 PM, martinsj013 <martinsj@...> wrote:
>
> Agh, sorry, I got that list badly wrong; below is correct:

Thanks for the help, Steve. Some interesting things to note here...

> triad-cents, triadic-HE, most-prob-Tenney-member
> 0-1200-1500, 5.7693, 8:16:19
> 0-1200-1516, 5.7534, 5:10:12

Are 8:16:18 and 5:10:12 both the top 2 contributing JI triads for both
of these? What are the top 5 for both of them?

> 0-300-1002, 5.8465, 5:6:9
> 0-316-1018, 5.7881, 5:6:9

Same here. The fact that 0-316-1018 is of lower entropy than 0-316-702
is interesting. I'm not sure that it's really less dissonant. It's
also a good triad to use as a tonic for Locrian.

Can you give two more a whirl? Let's try these two:

0-2400-2700
0-2400-2716

and

0-4800-5100
0-4800-5116

It would be much appreciated. It would also be very helpful if you
could post the relative strength of the 19-limit vs the 5-limit
contributions to the final triad, if possible...

-Mike

Gene> ... 0-582.027-1035.595. Compare 0-582.512-1034.996. ...
Carl> ... the chords are l=582,u=454 and l=583,u=452. All the minima are in the file I provided before... nope, neither chord is listed, nor anything close.

FWIW, the nearest minima are at
l=583, u=435, 19 cents distant, (5:7:9 most prob)
l=618, u=455, 36 cents distant, (7:10:13 most prob)

Steve.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Are 8:16:18 and 5:10:12 both the top 2 contributing JI triads for both
> of these? What are the top 5 for both of them?

Here's the list again but with the top 2 JI's and the prob for each (some are close, some are not). Top 5 would be a bit more work.

Triad, THE, Pmax, PmaxJI, Prob2, Prob2JI,
0-702-1516, 5.8559, 0.0303, 10:15:24, 0.0183, 12:18:29,
0-702-1500, 5.8504, 0.0374, 8:12:19, 0.0170, 10:15:24,
0-300-702, 5.8640, 0.0238, 16:19:24, 0.0217, 10:12:15,
0-316-702, 5.8551, 0.0384, 10:12:15, 0.0116, 24:29:36,
0-300-1002, 5.8465, 0.0406, 5:6:9, 0.0125, 22:26:39,
0-316-1018, 5.7881, 0.0719, 5:6:9, 0.0076, 29:35:52,
0-300-1200, 5.8044, 0.0389, 5:6:10, 0.0240, 11:13:22,
0-316-1200, 5.7704, 0.0693, 5:6:10, 0.0109, 19:23:38,

> Can you give two more a whirl? Let's try these two:
> 0-2400-2700
> 0-2400-2716
> 0-4800-5100
> 0-4800-5116

At the moment my list of JI triads does not go that far from the origin.

> ... the relative strength of the 19-limit vs the 5-limit
> contributions to the final triad, if possible...

Do you mean a further generalisation of the top 2 or 5 as above?

Steve M.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > 0-300-1002, 5.8465, 5:6:9
> > 0-316-1018, 5.7881, 5:6:9
>
> Same here. The fact that 0-316-1018 is of lower entropy than
> 0-316-702 is interesting.

5*6*9 < 10*12*15 so that's as expected. Steve, can you plot
the entropy of the Tenney members with Tenney height < 1000?
Or maybe just < 100?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> ... Steve, can you plot the entropy of the Tenney members with Tenney height < 1000? Or maybe just < 100?

I had thought of doing this but not got around to it - will do. Please chase if you don't see it within a reasonable time :-)

> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > ... Steve, can you plot the entropy of the Tenney members with Tenney height < 1000? Or maybe just < 100?

Or < 256 ... please see:
/tuning/files/SteveMartin/ratlist.csv

Steve.

Steve wrote:

> > > ... Steve, can you plot the entropy of the Tenney members
> > > with Tenney height < 1000? Or maybe just < 100?
>
> Or < 256 ... please see:
> /tuning/files/SteveMartin
> /ratlist.csv

OK great, I'm getting a good linear trend by plotting
log2(a*b*c) vs EXP(THE).

-Carl