Using the temperament finder-now making scales!

http://x31eq.com/temper/net.html

The "magic box" now generates a Scala file!

Why it does what it does remains somewhat mysterious to me.

However, on the whole I'm really happy to have another way to generate scales.

(I'm still trying to build a large collection of 46-pitch scales.)

Another thing I still don't understand is how Rodan can be Rodan if there are
two versions of it, one with a normal fifth, one with a very high fifth.

How are they the "same"?

Caleb

(This is second attempt at post--no need to post first version if you post this,
and vice-versa.)

--- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:

> Another thing I still don't understand is how Rodan can be Rodan if there are
> two versions of it, one with a normal fifth, one with a very high fifth.
>
> How are they the "same"?

Obviously, they aren't. I don't know where the second kind comes from.

With all due respect - how do I get it to generate a scala file?

Chris

On Sat, Nov 6, 2010 at 10:00 AM, Caleb Morgan <calebmrgn@...> wrote:

>
>
> http://x31eq.com/temper/net.html
>
>
> The "magic box" now generates a Scala file!
>
>
> *Why* it does what it does remains somewhat mysterious to me.
>
>
> However, on the whole I'm really happy to have another way to generate
> scales.
>
> (I'm still trying to build a large collection of 46-pitch scales.)
>
>
> Another thing I still don't understand is how Rodan can be Rodan if there
> are two versions of it, one with a normal fifth, one with a very high fifth.
>
> How are they the "same"?
>
> Caleb
>
> (This is second attempt at post--no need to post first version if you post
> this, and vice-versa.)
>
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> With all due respect - how do I get it to generate a scala file?

Click on the link.

Hi Gene, I did not see a link for generating a scala file - I did see same
data entry as before.

Is the link in the original post in this thread correct?

Chris

On Mon, Nov 8, 2010 at 6:27 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > With all due respect - how do I get it to generate a scala file?
>
> Click on the link.
>
>
>

________________________________
http://x31eq.com/temper/

Here's the link. (Sorry about this bold font--not sure how that happened.)

Put two or three numbers in the upper box, and the prime limit in the lower box.

The highest number you enter in the top box should be the number of pitches you
want to end up with.

The Scala file will come up when you click on the corresponding number (of
pitches) at the bottom of the form.

So, for example, I'm looking for 48-pitch scales, so I enter 46 and some other N
in the top box (other several other N's) and in the lower box I enter something
between 3 and 19.

As for my participation on the list--I can't mooch off my neighbor's broadband
connection anymore (justice, finally) --so please, no one should be insulted if
my responses are a little slow and sporadic and I'm not listening to people's
music these days...

Caleb

From: Chris Vaisvil <chrisvaisvil@...>
To: tuning@yahoogroups.com
Sent: Tue, November 9, 2010 6:43:48 AM
Subject: Re: [tuning] Re: Using the temperament finder-now making scales!

Hi Gene, I did not see a link for generating a scala file - I did see same data
entry as before.

Is the link in the original post in this thread correct?

Chris

On Mon, Nov 8, 2010 at 6:27 PM, genewardsmith <genewardsmith@...>
wrote:

>
>
>--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>>
>> With all due respect - how do I get it to generate a scala file?
>
>
Click on the link.
>
>

oops, make that 46-pitch scales in previous post.

________________________________
From: Chris Vaisvil <chrisvaisvil@...>
To: tuning@yahoogroups.com
Sent: Tue, November 9, 2010 6:43:48 AM
Subject: Re: [tuning] Re: Using the temperament finder-now making scales!

Hi Gene, I did not see a link for generating a scala file - I did see same data
entry as before.

Is the link in the original post in this thread correct?

Chris

On Mon, Nov 8, 2010 at 6:27 PM, genewardsmith <genewardsmith@...>
wrote:

>
>
>--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>>
>> With all due respect - how do I get it to generate a scala file?
>
>
Click on the link.
>
>

On 9 November 2010 15:43, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Gene, I did not see a link for generating a scala file - I did see same data entry as before.
>
> Is the link in the original post in this thread correct?

Right, you submit the data, and the resulting page should have links
near the bottom for Scala files.

Graham

I'm sure that the subtleties of the process I'm attempting to work out have been
thoroughly explored by others older wiser and brighter than me. So, I welcome
(non-discouraging) thoughts.

1) It's possible to simply add together a few EDOs to make a scale with more
notes.

2) For example, 46 pitches could be created by adding together 12, 17, and 19
pitches. This wouldn't add up to 48 as you might think, because they could each
share a common pitch--0 cents.

3) If the EDOs are even-numbered, they could be aligned to share 2 notes--0 and
600 cents. So another pitch would need to be added in the case of each even
EDO.

So far, so good--I imagine that the number of partitions of 46 with all the
unusable combinations removed to be in the hundreds. There's a lot of "pruning
of the trees"--many combinations don't work.

However, the problem is potentially much more subtle and complicated, because
the "starting pitch" of any of the EDOs could be something other than 0 cents.

This makes the number of combinations potentially much bigger, and my mind
boggles. (Not so hard to make my little mind boggle.)

The resulting scales would be gnarly and far from JI I imagine, in most cases,
but they would at least fill up the space of a 2:1 with 46 pitches, and so far,
the right pitches have been falling close enough to the right keys for these to
be useful. (So far, so useful.) It should be possible to
get the "sound" or personality of any given EDO but in a 46-pitch framework.

For all I know, Graham and Gene and Carl have already thought this problem
through and are at some higher level with it.

Thoughts?

MARKETPLACE
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.

It seems the idea of combined scales might be fruitful if you had different timbres that accented each. otherwise one can always look at two tunings as a combination of a larger set which they are, especially if there is a common tone. for instance 12 and 31 would be subsets of a 372 tone scale. It resembles Xenakis sieve method of combining patterns as a way of generating scales.

--- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
>
> I'm sure that the subtleties of the process I'm attempting to work out have been
> thoroughly explored by others older wiser and brighter than me. So, I welcome
> (non-discouraging) thoughts.
>
> 1) It's possible to simply add together a few EDOs to make a scale with more
> notes.
>
> 2) For example, 46 pitches could be created by adding together 12, 17, and 19
> pitches. This wouldn't add up to 48 as you might think, because they could each
> share a common pitch--0 cents.
>
> 3) If the EDOs are even-numbered, they could be aligned to share 2 notes--0 and
> 600 cents. So another pitch would need to be added in the case of each even
> EDO.
>
> So far, so good--I imagine that the number of partitions of 46 with all the
> unusable combinations removed to be in the hundreds. There's a lot of "pruning
> of the trees"--many combinations don't work.
>
> However, the problem is potentially much more subtle and complicated, because
> the "starting pitch" of any of the EDOs could be something other than 0 cents.
>
> This makes the number of combinations potentially much bigger, and my mind
> boggles. (Not so hard to make my little mind boggle.)
>
> The resulting scales would be gnarly and far from JI I imagine, in most cases,
> but they would at least fill up the space of a 2:1 with 46 pitches, and so far,
> the right pitches have been falling close enough to the right keys for these to
> be useful. (So far, so useful.) It should be possible to
> get the "sound" or personality of any given EDO but in a 46-pitch framework.
>
> For all I know, Graham and Gene and Carl have already thought this problem
> through and are at some higher level with it.
>
> Thoughts?
>
>
>
>
>
>
> MARKETPLACE
> Hobbies & Activities Zone: Find others who share your passions! Explore new
> interests.
>
>
> ________________________________
>
> Stay on top of your group activity without leaving the page you're on - Get the
> Yahoo! Toolbar now.
>
>
> ________________________________
>
> Get great advice about dogs and cats. Visit the Dog & Cat Answers Center.
>
> Switch to: Text-Only, Daily Digest • Unsubscribe • Terms of Use
> .
>

Interesting, thanks, I'll check out Xenakis approach--there was even some software somewhere (Athena?) maybe, that did Xenakis sieves. I'm only vaguely familiar with it.

On second glance, more combinations are possible than I first thought--if you allow either: counting two 0 cent notes as legitimate, or removing very-near misses to lower the total number of pitches, that triples the number of possible combinations with only two EDOs.

-c

On Nov 9, 2010, at 6:17 PM, Brofessor wrote:

> It seems the idea of combined scales might be fruitful if you had different timbres that accented each. otherwise one can always look at two tunings as a combination of a larger set which they are, especially if there is a common tone. for instance 12 and 31 would be subsets of a 372 tone scale. It resembles Xenakis sieve method of combining patterns as a way of generating scales.
>
> --- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
> >
> > I'm sure that the subtleties of the process I'm attempting to work out have been
> > thoroughly explored by others older wiser and brighter than me. So, I welcome
> > (non-discouraging) thoughts.
> >
> > 1) It's possible to simply add together a few EDOs to make a scale with more
> > notes.
> >
> > 2) For example, 46 pitches could be created by adding together 12, 17, and 19
> > pitches. This wouldn't add up to 48 as you might think, because they could each
> > share a common pitch--0 cents.
> >
> > 3) If the EDOs are even-numbered, they could be aligned to share 2 notes--0 and
> > 600 cents. So another pitch would need to be added in the case of each even
> > EDO.
> >
> > So far, so good--I imagine that the number of partitions of 46 with all the
> > unusable combinations removed to be in the hundreds. There's a lot of "pruning
> > of the trees"--many combinations don't work.
> >
> > However, the problem is potentially much more subtle and complicated, because
> > the "starting pitch" of any of the EDOs could be something other than 0 cents.
> >
> > This makes the number of combinations potentially much bigger, and my mind
> > boggles. (Not so hard to make my little mind boggle.)
> >
> > The resulting scales would be gnarly and far from JI I imagine, in most cases,
> > but they would at least fill up the space of a 2:1 with 46 pitches, and so far,
> > the right pitches have been falling close enough to the right keys for these to
> > be useful. (So far, so useful.) It should be possible to
> > get the "sound" or personality of any given EDO but in a 46-pitch framework.
> >
> > For all I know, Graham and Gene and Carl have already thought this problem
> > through and are at some higher level with it.
> >
> > Thoughts?
> >
> >
> >
> >
> >
> >
> > MARKETPLACE
> > Hobbies & Activities Zone: Find others who share your passions! Explore new
> > interests.
> >
> >
> > ________________________________
> >
> > Stay on top of your group activity without leaving the page you're on - Get the
> > Yahoo! Toolbar now.
> >
> >
> > ________________________________
> >
> > Get great advice about dogs and cats. Visit the Dog & Cat Answers Center.
> >
> > Switch to: Text-Only, Daily Digest • Unsubscribe • Terms of Use
> > .
> >
>
>

Here's an example of what I'm talking about--it turns out you can easily add together 31EDO pitches and 17EDO pitches to get 46 pitches. I simply removed 776.471 cents, which came very close to 774.194 cents, so was redundant. This makes another odd but not unusable 46-pitch scale.

(Cent values in second column are 46 EDO pitches for guidance. Header is just something slugged in.)

! irregular.scl
!
46 note scale from 31 & 17
! 46
! not Generated by
46
!
!0.
38.71
70.588
77.419
116.129 !104.348
141.176 !130.435
154.839 !156.522
193.548 !182.609
211.765 !208.696
232.258 !234.783
270.968 !260.87
282.353 !286.957
309.677 !313.043
348.387 !339.13
352.941 !365.217
387.097 !391.304
423.529 !417.391
425.806 ! !443.478
464.516 !469.565
494.118 ! !495.652
503.226 !521.739
541.935 !547.826
564.706 !573.913
580.645 !600.0
619.355 !626.087
635.294 !652.174
658.065 !678.261
696.774 ! !704.348
705.882 ! !730.435
735.484 !756.522
774.194 !782.609
812.903 !808.696
847.059 !834.783
851.613 !860.87
890.323 !886.957
917.647 !913.043
929.032 !939.13
967.742 !965.217
988.235 !991.304
1006.452 !1017.391
1045.161 !1043.478
1058.824 !1069.565
1083.871 !1095.652
1122.581 !1121.739
1129.412 !1147.826
1161.29 !1173.913
1200.0 !1200.00

On Nov 10, 2010, at 8:43 AM, caleb morgan wrote:

> Interesting, thanks, I'll check out Xenakis approach--there was even some software somewhere (Athena?) maybe, that did Xenakis sieves. I'm only vaguely familiar with it.
>
>
> On second glance, more combinations are possible than I first thought--if you allow either: counting two 0 cent notes as legitimate, or removing very-near misses to lower the total number of pitches, that triples the number of possible combinations with only two EDOs.
>
> -c
>
> On Nov 9, 2010, at 6:17 PM, Brofessor wrote:
>
>>
>> It seems the idea of combined scales might be fruitful if you had different timbres that accented each. otherwise one can always look at two tunings as a combination of a larger set which they are, especially if there is a common tone. for instance 12 and 31 would be subsets of a 372 tone scale. It resembles Xenakis sieve method of combining patterns as a way of generating scales.
>>
>> --- In tuning@yahoogroups.com, Caleb Morgan <calebmrgn@...> wrote:
>> >
>> > I'm sure that the subtleties of the process I'm attempting to work out have been
>> > thoroughly explored by others older wiser and brighter than me. So, I welcome
>> > (non-discouraging) thoughts.
>> >
>> > 1) It's possible to simply add together a few EDOs to make a scale with more
>> > notes.
>> >
>> > 2) For example, 46 pitches could be created by adding together 12, 17, and 19
>> > pitches. This wouldn't add up to 48 as you might think, because they could each
>> > share a common pitch--0 cents.
>> >
>> > 3) If the EDOs are even-numbered, they could be aligned to share 2 notes--0 and
>> > 600 cents. So another pitch would need to be added in the case of each even
>> > EDO.
>> >
>> > So far, so good--I imagine that the number of partitions of 46 with all the
>> > unusable combinations removed to be in the hundreds. There's a lot of "pruning
>> > of the trees"--many combinations don't work.
>> >
>> > However, the problem is potentially much more subtle and complicated, because
>> > the "starting pitch" of any of the EDOs could be something other than 0 cents.
>> >
>> > This makes the number of combinations potentially much bigger, and my mind
>> > boggles. (Not so hard to make my little mind boggle.)
>> >
>> > The resulting scales would be gnarly and far from JI I imagine, in most cases,
>> > but they would at least fill up the space of a 2:1 with 46 pitches, and so far,
>> > the right pitches have been falling close enough to the right keys for these to
>> > be useful. (So far, so useful.) It should be possible to
>> > get the "sound" or personality of any given EDO but in a 46-pitch framework.
>> >
>> > For all I know, Graham and Gene and Carl have already thought this problem
>> > through and are at some higher level with it.
>> >
>> > Thoughts?
>> >
>> >
>> >
>> >
>> >
>> >
>> > MARKETPLACE
>> > Hobbies & Activities Zone: Find others who share your passions! Explore new
>> > interests.
>> >
>> >
>> > ________________________________
>> >
>> > Stay on top of your group activity without leaving the page you're on - Get the
>> > Yahoo! Toolbar now.
>> >
>> >
>> > ________________________________
>> >
>> > Get great advice about dogs and cats. Visit the Dog & Cat Answers Center.
>> >
>> > Switch to: Text-Only, Daily Digest • Unsubscribe • Terms of Use
>> > .
>> >
>>
>
>
>

Caleb Morgan <calebmrgn@...> wrote:
> I'm sure that the subtleties of the process I'm
> attempting to work out have been thoroughly explored by
> others older wiser and brighter than me. So, I welcome
> (non-discouraging) thoughts.
>
> 1) It's possible to simply add together a few EDOs to
> make a scale with more notes.

Yes, but I'm not sure what your "simply add together" means.

> 2) For example, 46 pitches could be created by adding
> together 12, 17, and 19 pitches. This wouldn't add up to
> 48 as you might think, because they could each share a
> common pitch--0 cents.

Yes.

> 3) If the EDOs are even-numbered, they could be aligned
> to share 2 notes--0 and 600 cents. So another pitch
> would need to be added in the case of each even EDO.

You can always get the right number of notes by "cross
fading" from one equal temperament to another.

> So far, so good--I imagine that the number of partitions
> of 46 with all the unusable combinations removed to be in
> the hundreds. There's a lot of "pruning of the
> trees"--many combinations don't work.

It depends on what you count as working.

> However, the problem is potentially much more subtle and
> complicated, because the "starting pitch" of any of the
> EDOs could be something other than 0 cents.
>
> This makes the number of combinations potentially much
> bigger, and my mind boggles. (Not so hard to make my
> little mind boggle.)

It's much simpler if 46 is one of the equal temperaments
you start with. There's only one way of choosing 46 notes
from 46.

> The resulting scales would be gnarly and far from JI I
> imagine, in most cases, but they would at least fill up
> the space of a 2:1 with 46 pitches, and so far, the right
> pitches have been falling close enough to the right keys
> for these to be useful. (So far, so useful.) It should
> be possible to get the "sound" or personality of any
> given EDO but in a 46-pitch framework.

You can choose any EDO and pair it with 46 to get a regular
temperament. Then change the generator to get as close to
the EDO for the personality to come through.

> For all I know, Graham and Gene and Carl have already
> thought this problem through and are at some higher level
> with it.

There was a long discussion about taking scales on
tuning-math that isn't really resolved because I haven't
attended to it. What I did for the website essentially
follows Paul Erlich's recipe for Fokker blocks, which is
trying to reverse-engineer what Fokker is doing:

http://sonic-arts.org/td/erlich/intropblock3.htm

As you've noticed, it depends on the choice of unison
vectors, which correspond to the equal temperaments you
choose. Gene and Carl have more sensible ways of choosing
them.

Graham

For constant structures i find a keyboard mapping useful in that i can see what my options are.
I sense that one would not get at all the PB possible with the math as there are numerous way say one can map 11 limit structures into 31. I assume the math result would be the most compact and uniform.

say in 31ET the comma is gone but in a JI version one chooses between the two say a 9/8 or a 10/9 ( as only one example).

What would be useful if say one could plug in a harmonic structure, say a dekany like i did recently and be able to find the PB or the constant structure with the least amount of added tones. Here one might have to think of it not so much tuning out a comma as having an either/or fluctuation. or given a constant structure what would be the next largest one. One method is to use the scale tree to see what scales lie below it.
for instance one takes a 12 tone scale and maps it out on a 19 or 17 tone keyboard and fills in the blanks.
Brun's method captures many places inbetween those seen on the tree

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> There was a long discussion about taking scales on
> tuning-math that isn't really resolved because I haven't
> attended to it. What I did for the website essentially
> follows Paul Erlich's recipe for Fokker blocks, which is
> trying to reverse-engineer what Fokker is doing:
>
> http://sonic-arts.org/td/erlich/intropblock3.htm
>
> As you've noticed, it depends on the choice of unison
> vectors, which correspond to the equal temperaments you
> choose. Gene and Carl have more sensible ways of choosing
> them.
>
>
> Graham
>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> As you've noticed, it depends on the choice of unison
> vectors, which correspond to the equal temperaments you
> choose. Gene and Carl have more sensible ways of choosing
> them.

What happened to your idea of using TLLL reduction with the temperamental complexity quadratic form to choose them? That seemed sensible.

"genewardsmith" <genewardsmith@...> wrote:

> What happened to your idea of using TLLL reduction with
> the temperamental complexity quadratic form to choose
> them? That seemed sensible.

I think it gives the same unison vectors as Carl for the
example. I thought it was your idea but as I don't get the
same vectors as you maybe not. I'll explain more when I
have some time. Eid's coming up.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>Eid's coming up.

No it isn't, but Hajj is coming up.

Graham meant Eid al-Adha, which is coming up, not the Eid at the end of Ramadan. :-)

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >Eid's coming up.
>
> No it isn't, but Hajj is coming up.
>

We call it Kurban Bayrami (Festivity of the Sacrifice) in Turkish. But unless this is cause for celebration by tuning list colleagues, it has little to do with tuning... except the microtonal nature of Quranic/Islamic chants during the period.

Oz.

--

✩ ✩ ✩
www.ozanyarman.com

genewardsmith wrote:
>
> --- In tuning@yahoogroups.com, Graham Breed<gbreed@...> wrote:
>> Eid's coming up.
>
> No it isn't, but Hajj is coming up.
>
>

I think it just means that Graham is pressed for time as the holidays are coming up, as he lives in a country where this holiday is celebrated.

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> We call it Kurban Bayrami (Festivity of the Sacrifice) in Turkish. But
> unless this is cause for celebration by tuning list colleagues, it has
> little to do with tuning... except the microtonal nature of
> Quranic/Islamic chants during the period.
>
> Oz.
>
> --
>
> âo?=© âo?=© âo?=©
> www.ozanyarman.com
>
>
> genewardsmith wrote:
> >
> > --- In tuning@yahoogroups.com, Graham Breed<gbreed@> wrote:
> >> Eid's coming up.
> >
> > No it isn't, but Hajj is coming up.
> >
> >
>

On 13 November 2010 17:58, cameron <misterbobro@...> wrote:
> I think it just means that Graham is pressed for time as the holidays are coming up, as he lives in a country where this holiday is celebrated.

Yes, that's the point, but I didn't want to write a post solely about
it because it is off topic, but here I am. I have Monday to Wednesday
off, during which time I can study interval-complexity lattices, play
some music, and buy some internet time to discuss it. I'm not
teaching now because the students claimed an early holiday, but I
still have things I should be doing.

Graham

> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> We call it Kurban Bayrami (Festivity of the Sacrifice) in Turkish. But
>> unless this is cause for celebration by tuning list colleagues, it has
>> little to do with tuning... except the microtonal nature of
>> Quranic/Islamic chants during the period.
>>
>> Oz.
>>
>> --
>>
>> � � �
>> www.ozanyarman.com
>>
>>
>> genewardsmith wrote:
>> >
>> > --- In tuning@yahoogroups.com, Graham Breed<gbreed@>  wrote:
>> >> Eid's coming up.
>> >
>> > No it isn't, but Hajj is coming up.
>> >
>> >
>>
>
>
>
>
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