A strange 11-limit temperament

Hi again.

I don't know what this should be called, I don't know if someone has already mentioned this, I just know that this is not a linear temperament but it certainly is a temperament. It has two one-step interval sizes, the larger of which is 166.015 cents and the smaller one is 73.985 cents. If you stack 5L + 5S, you get an octave. But we definitely don't want to get two 5-EDO chains in this case so the pattern of LSLSLSLSLS is probably not the best choice. Instead, we can make a good 11-limit temperament if we know that:
A) 3L approximates 4/3,
B) 1L + 2S approximates 6/5,
C) 1L + 3S approximates 5/4,
D) 2L + 3S approximates 11/8.
In order to have at least one approximation of 4/3 in the scale, it is necessary to have three L sizes in a row somewhere. So, for example, we can do it like LLLSSLSLSS, which makes the scale symmetrical from the fourth degree (supposing the 1/1 is the first degree(. I tried to demonstrate the nice properties of the scale in this small recording. For the time being, it's not a serious composition, so you can expect more from me later: http://download.yousendit.com/A7E3DC8D722CC6BD

Petr

--- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:
>
> Hi again.
>
> I don't know what this should be called, I don't know if someone
> has already mentioned this, I just know that this is not a linear
> temperament but it certainly is a temperament.
//
> http://download.yousendit.com/A7E3DC8D722CC6BD
>
> Petr
>

I like that timbre. What is it?

-Carl

--- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:
>
> Hi again.
>
> I don't know what this should be called, I don't know if someone
has already
> mentioned this, I just know that this is not a linear temperament
but it
> certainly is a temperament. It has two one-step interval sizes, the
larger
> of which is 166.015 cents and the smaller one is 73.985 cents. If
you stack
> 5L + 5S, you get an octave. But we definitely don't want to get two
5-EDO
> chains in this case so the pattern of LSLSLSLSLS is probably not
the best
> choice. Instead, we can make a good 11-limit temperament if we know
that:
> A) 3L approximates 4/3,
> B) 1L + 2S approximates 6/5,
> C) 1L + 3S approximates 5/4,
> D) 2L + 3S approximates 11/8.
> In order to have at least one approximation of 4/3 in the scale, it
is
> necessary to have three L sizes in a row somewhere. So, for
example, we can
> do it like LLLSSLSLSS, which makes the scale symmetrical from the
fourth
> degree (supposing the 1/1 is the first degree(. I tried to
demonstrate the
> nice properties of the scale in this small recording. For the time
being,
> it's not a serious composition, so you can expect more from me
later:
> http://download.yousendit.com/A7E3DC8D722CC6BD
>
> Petr

It's very close to a subset of 65-EDO.

--George

Carl wrote:

> I like that timbre. What is it?

Two samples of a fender piano played in different dynamic levels, both mixed into one and sped up to make the timbre sharper.

Petr

George D. Secor wrote:
> --- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:
>> Hi again.
>>
>> I don't know what this should be called, I don't know if someone > has already >> mentioned this, I just know that this is not a linear temperament > but it >> certainly is a temperament. It has two one-step interval sizes, the > larger >> of which is 166.015 cents and the smaller one is 73.985 cents.
> > It's very close to a subset of 65-EDO.
> > --George

It could be described as a scale (mode?) of a regular temperament with a period of 240.0 cents and a generator of 73.985 cents. A partial generator mapping can be deduced (there isn't a very good approximation of 7/1).

[<5, 7, 11, *, 17], <0, 3, 2, *, 1]>

Or you could use your large and small steps of 166.015 cents and 73.985 cents as generators. The generator mapping then looks like this:

[<5, 7, 11, *, 17], <5, 10, 13, *, 18]>

If you do want to include the 7/1, there are a couple of 11-limit temperaments that fit this pattern. As far as I know these don't have names. The 15&50 does match George Secor's observation of this being close to 65-EDO.

[<5, 7, 11, 14, 17], <0, 3, 2, 0, 1]> 15&35, 15&50, 35&50
TOP P = 240.285642, G = 72.410116
TOP-RMS P = 240.153941, G = 73.311021

[<5, 7, 11, 15, 17], <0, 3, 2, -3, 1]> 15&80, 15&95, 80&95
TOP P = 239.790292, G = 75.028284
TOP-RMS P = 239.734033, G = 74.857029

[<5, 7, 11, 11, 17], <0, 3, 2, 10, 1]> 50&115
TOP P = 240.133358, G = 73.061352
TOP-RMS P = 240.025618, G = 73.076177

Or you could just use it as a temperament without a 7/1 approximation.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Carl wrote:
>
> > I like that timbre. What is it?
>
> Two samples of a fender piano played in different dynamic levels,
> both mixed into one and sped up to make the timbre sharper.
>
> Petr

Killer. As for the temperament, it _sounds_ an awful lot
like Paul Erlich's piece "Glassic", which was in 22. According
to Paul, the beginning and end of that tune are in porcupine[7]
(as tuned in 22), but I don't hear a strong transition in
the piece to something different in the middle.

You should hear it if you haven't:
http://66.98.148.43/~xenharmo/mp3/erlich/glassic.mp3

-Carl

Hi Petr,

--- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:
>
> Hi again.
>
> I don't know what this should be called, I don't know if
> someone has already mentioned this, I just know that this
> is not a linear temperament but it certainly is a temperament.
> It has two one-step interval sizes, the larger of which is
> 166.015 cents and the smaller one is 73.985 cents. If you
> stack 5L + 5S, you get an octave. But we definitely don't
> want to get two 5-EDO chains in this case so the pattern
> of LSLSLSLSLS is probably not the best choice. Instead,
> we can make a good 11-limit temperament if we know that:
> A) 3L approximates 4/3,
> B) 1L + 2S approximates 6/5,
> C) 1L + 3S approximates 5/4,
> D) 2L + 3S approximates 11/8.
> In order to have at least one approximation of 4/3 in the
> scale, it is necessary to have three L sizes in a row
> somewhere. So, for example, we can do it like LLLSSLSLSS,
> which makes the scale symmetrical from the fourth degree
> (supposing the 1/1 is the first degree(. I tried to
> demonstrate the nice properties of the scale in this
> small recording. For the time being, it's not a serious
> composition, so you can expect more from me later:
> http://download.yousendit.com/A7E3DC8D722CC6BD

I really like this. Would you give me permission to
"orchestrate" a version of it in Tonescape?

What is the exact tuning you used?
What tools did you use to create it?
Is there a score of any kind?

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Monz wrote:

> I really like this. Would you give me permission to
"orchestrate" a version of it in Tonescape?
Oh, sure, I'm very glad to know you like something which I didn't even consider finished. :-D In fact, it was a cristal-clear improvisation.
> What is the exact tuning you used?

It's exactly as I describe it in my message, I just should have also said that the 1/1 is E. If something was unclear, please let me know.
> What tools did you use to create it?

My XG compatible Yamaha QS-300.

> Is there a score of any kind?
Oh, not at all, my friend. I made a link to the recording just a few minutes after playing the music.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Monz wrote:
>
> > I really like this. Would you give me permission to
> "orchestrate" a version of it in Tonescape?
>
> Oh, sure, I'm very glad to know you like something
> which I didn't even consider finished. :-D In fact,
> it was a cristal-clear improvisation.

Yes, well, umm ... i guess to me it doesn't sound very
finished either ... but it resembles in character a
scherzo that i started composing years ago but never
got very far with, and so it caught my imagination
right away. I'd like to score it for an ensemble
of traditional instrument timbres, like a small orchestra.

> > What is the exact tuning you used?
>
> It's exactly as I describe it in my message, I just
> should have also said that the 1/1 is E. If something
> was unclear, please let me know.

I would need to know exactly all of the notes you used.
Is it a 12-note tuning? etc.

> > What tools did you use to create it?
>
> My XG compatible Yamaha QS-300.

Did you use Scala for the tuning?

> > Is there a score of any kind?
>
> Oh, not at all, my friend. I made a link to the
> recording just a few minutes after playing the music.

Yes, i get it: it's just an improvisation.

I think i remember seeing a score of a piece you wrote
that was done in microabc ... so since i'd like to
work out an arrangement of this piece, it would make
it easier if i had some type of score.

How did you record it? Is there a MIDI file?

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Monz wrote:

> Is it a 12-note tuning?
It's a 10-note tuning. As I have said, there are two interval sizes in the first class, the larger of which is 166.015 cents and the smaller one is 73.985 cents. Going from E upwards, the consecutive steps are LLLSSLSLSS.
> Did you use Scala for the tuning?
I used Scala in the sense that I chose "Mode/create 2 2 2 1 1 2 1 2 1 1" and then specified the interval sizes in cents as 73.985 and 166.015.
> I think i remember seeing a score of a piece you wrote that was done in microabc ...

I'm not sure what you mean. If someone made a score of my microtonal music, I don't know about it. And I have never made microtonal scores myself.

> How did you record it? Is there a MIDI file?
There isn't but I can make one if you wish -- though I don't see much of a point here in doing it.

Petr

I wrote:

> There isn't but I can make one if you wish -- though I don't see much of a point here in doing it.

Oh, sorry for that, Monz, I've misunderstood your suggestion. You will probably need a MIDI file to convert to the score, right? Okay, now I think I got you. Do you have any particular requirements which you'd like the MIDI file to meet -- as far as I am able to do that?

Petr

Carl wrote:

> like Paul Erlich's piece "Glassic", which was in 22. According

> to Paul, the beginning and end of that tune are in porcupine[7]

> (as tuned in 22), but I don't hear a strong transition in

> the piece to something different in the middle.

Neither do I. And I don't know anything about this piece using any other tunings than that.

Petr

Hi Petr,

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:

> Oh, sorry for that, Monz, I've misunderstood your
> suggestion. You will probably need a MIDI file to
> convert to the score, right? Okay, now I think I got you.
> Do you have any particular requirements which you'd like
> the MIDI file to meet -- as far as I am able to do that?

It would make it a lot easier for me to put the notes
into Tonescape if i already have something which tells
me what the notes and rhythms are, as opposed to having
to figure it all out by ear from the mp3.
That's all i'm talking about.

A MIDI-file of your improv would at least give me the
note listing with all the timing data.

If you have a better way of providing me with a note list
or score using the 10 specific notes you actually used,
that would be better. But the MIDI is fine.

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Monz wrote:
>
> > Is it a 12-note tuning?
> It's a 10-note tuning. As I have said, there are two interval
> sizes in the first class, the larger of which is 166.015 cents

That's very close to the porcupine generator in 22. Maybe
that's why I thought of glassic.

> > I think i remember seeing a score of a piece you wrote that
> > was done in microabc ...
>
> I'm not sure what you mean. If someone made a score of my
> microtonal music, I don't know about it. And I have never made
> microtonal scores myself.

Maybe monz is thinking of Hudson Lacerda's music?

-Carl

Hi Carl and Petr,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Petr Parízek <p.parizek@> wrote:
> >
> > Monz wrote:
>
> > > I think i remember seeing a score of a piece you wrote that
> > > was done in microabc ...
> >
> > I'm not sure what you mean. If someone made a score of my
> > microtonal music, I don't know about it. And I have never made
> > microtonal scores myself.
>
> Maybe monz is thinking of Hudson Lacerda's music?

Probably ... i just thought that i remembered Hudson at
one time posting a score to a small piece which Petr
composed. Or maybe Aaron Hunt has a piece by Petr which
he notated with Megascore? I think maybe that's what i'm
remembering (somewhat incorrectly).

I used to wish people posting here would take the time
to check the facts and not be so vague ... and now *i*
don't have the time to do it anymore! Aarrgh.

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Hi Petr,

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:

> It would make it a lot easier for me to put the notes
> into Tonescape if i already have something which tells
> me what the notes and rhythms are, as opposed to having
> to figure it all out by ear from the mp3.
> That's all i'm talking about.
>
> A MIDI-file of your improv would at least give me the
> note listing with all the timing data.
>
> If you have a better way of providing me with a note list
> or score using the 10 specific notes you actually used,
> that would be better. But the MIDI is fine.

And perhaps most importantly, for getting the Tonescape
file correct, i would appreciate as much information as
you can give me about the time-signatures.

I already started the Tonescape file, by figuring out
your improv by ear. It sounds to me like the time-signature
is mostly a polymetrical 3/4 and 6/8 on top of each other.
Yes?

But near the beginning, after the first entry of the left
hand, it sounds like you put in a 2/4 measure. Knowing
exactly how you played this kind of thing, in detail,
will really help me with my version.

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Hi Monz.

Nice to see your new message a few minutes after I've just started making the MIDI file. :-D

Well, it's about 11:50 PM in the Czech Republic right now (wandering what time it could be there at yours) so I'll get it ready tomorrow, I hope.

Petr

Hi Petr,

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Hi Monz.
>
> Nice to see your new message a few minutes after I've
> just started making the MIDI file. :-D
>
> Well, it's about 11:50 PM in the Czech Republic right
> now (wandering what time it could be there at yours)
> so I'll get it ready tomorrow, I hope.

It was 2:50 pm here. So if you get it done by Saturday
night, i'll be receiving when i come home from work
on Saturday, and it will already be past your bedtime.
So i'll work on it while you sleep, and hopefully i'll
have the Tonescape translation of it (using only a
piano timbre) ready when you wake up on Sunday morning.

:)

As for my "orchestration" of it, that will take a
little more time ...

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Hi Petr and everyone,

--- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:

/tuning/topicId_74791.html#74791

> http://download.yousendit.com/A7E3DC8D722CC6BD

I've made two versions of it in Tonescape, using for the
time being only a plain piano timbre. They can both be
found in this folder:

/tuning/files/monz/parizek/11-limit/

One version uses Petr's original temperament, and the
other is my "best fit" 3,5,11-space JI version, whose
ratios are very close to his temperament. Here are the
cents errors of Petr's temperament from my JI version:

---------- cents ------------
ratio 2,3,5,11-monzo 3,5,11-JI Petr temp error

48:25 [ 4 1, -2 0> 1129.328 1126.015 - 3.313
11:6 [-1 -1, 0 1> 1049.363 1052.030 + 2.667
5:3 [ 0 -1, 1 0> 884.359 886.015 + 1.656
8:5 [ 3 0, -1 0> 813.686 812.030 - 1.656
16:11 [ 4 0, 0 -1> 648.682 646.015 - 2.667
25:18 [-1 -2, 2 0> 568.717 572.030 + 3.313
4:3 [ 2 -1, 0 0> 498.045 498.045 0
40:33 [ 3 -1, 1 -1> 333.041 332.030 - 1.011
11:10 [-1 0, -1 1> 165.004 166.015 + 1.011
1:1 [ 0 0, 0 0> 0.000 0.000 0

(use the link for "Option|Use Fixed Width Font" if
viewing in the stupid Yahoo web interface)

It's really fun to watch the Lattice of the
JI version. The best Lattice notation to use for
that version is, naturally, "Ratio" ... but if
you want to see it with letter names, the best
letter notation Tonescape can offer so far for
this JI tuning (since it still lacks sagittal
and HEWM) is "Meantone, 1/3-comma, E"; that's
not surprising, given that 19-edo (which is
nearly identical to 1/3-comma meantone) is such
a nice fit to this tuning.

If someone could figure out how i can derive
Petr's temperament from this JI lattice (that is,
tell me which unison-vectors to temper out), then
i could make a Tonescape file which uses my Lattice
but has Petr's actual tuning.

Thanks to Petr for sending me a MIDI-file of the
keyboard mappings, which made it much easier to
create the Tonescape files.

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

> ---------- cents ------------
> ratio 2,3,5,11-monzo 3,5,11-JI Petr temp error
>
> 48:25 [ 4 1, -2 0> 1129.328 1126.015 - 3.313
> 11:6 [-1 -1, 0 1> 1049.363 1052.030 + 2.667
> 5:3 [ 0 -1, 1 0> 884.359 886.015 + 1.656
> 8:5 [ 3 0, -1 0> 813.686 812.030 - 1.656
> 16:11 [ 4 0, 0 -1> 648.682 646.015 - 2.667
> 25:18 [-1 -2, 2 0> 568.717 572.030 + 3.313
> 4:3 [ 2 -1, 0 0> 498.045 498.045 0
> 40:33 [ 3 -1, 1 -1> 333.041 332.030 - 1.011

> 11:10 [-1 0, -1 1> 165.004 166.015 + 1.011
> 1:1 [ 0 0, 0 0> 0.000 0.000 0
>
> (use the link for "Option|Use Fixed Width Font" if
> viewing in the stupid Yahoo web interface)

It still came out mangled (thanks, Yahoo).
With the leading quote mark, this one should look OK.
(my fingers are crossed)

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> Hi Petr and everyone,
>
>
> --- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@> wrote:
>
> /tuning/topicId_74791.html#74791
>
> > http://download.yousendit.com/A7E3DC8D722CC6BD
>
>
> I've made two versions of it in Tonescape, using for the
> time being only a plain piano timbre. They can both be
> found in this folder:
>
> /tuning/files/monz/parizek/11-limit/
>
> One version uses Petr's original temperament, and the
> other is my "best fit" 3,5,11-space JI version, whose
> ratios are very close to his temperament.

I also made a .gif graphic of the Tonescape Lattice window
of the JI tuning, and uploaded it to that same folder.

I'm still planning to "orchestrate" the Tonescape files!
(hopefully soon)

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Monz wrote:

> /tuning/files/monz/parizek/11-limit/

Thanks a lot, Monz. Could you please make a separate link for me? I don't
know how to get to the tuning files folder.

> If someone could figure out how i can derive
> Petr's temperament from this JI lattice (that is,
> tell me which unison-vectors to temper out), then
> i could make a Tonescape file which uses my Lattice
> but has Petr's actual tuning.

I'm realizing I should have told you how I made the temperament. It can be
all described using four basic factors:
11/10, 12500/11979, 4000/3993, and (this one better as a PSC -- or, as you
say, "monzo") "-7 6 -13 0 8" (the 0 meaning no 7s).
The last two are commas that I chose to temper out. What this means is that,
for example, 2/1 is then mapped to these as "5 5 2 2", 3/2 is "2 5 1 2", 5/4
is "1 3 0 1" and 11/8 is "2 3 0 1".

Petr

Hi Petr,

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Monz wrote:
>
> >
/tuning/files/monz/parizek/11-
limit/
>
> Thanks a lot, Monz. Could you please make a separate link
> for me? I don't know how to get to the tuning files folder.

The link will probably be broken in the quote above, but in
the post in which i originally put the link, you should be
able to click on it or paste it into a web browser, and go
directly to the folder. All members of this list have access
to its "Files" section.

I also sent you all three files as attachments in a private
email ... i guess you haven't checked.

Anyway, to make things easy, and since i plan to do more
work on this myself, i decided to just make a webpage
about it:

http://tonalsoft.com/monzo/parizek/parizek_11-limit-temperament.aspx

And what's nice about that is that i was able to use the
very long filenames of which i'm so fond (... yahoo forced
me to shorten them).

Bookmark that page, because i'll be adding more to it.

-monz

email: joemonz(AT)yahoo.com
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software