Root of e Preview

Alister added to one of my tuning survey pieces and out popped an electro piece using the 13th root of e tuning. This piece uses a GR-20 relay re-tuned to 13th root of e which is e^(1/13) per step.

Download
http://notonlymusic.com/board/download/file.php?id=266

online listen
http://notonlymusic.com/board/viewtopic.php?f=23&t=289#p2000

--- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>
> Alister added to one of my tuning survey pieces and out popped an electro piece using the 13th root of e tuning. This piece uses a GR-20 relay re-tuned to 13th root of e which is e^(1/13) per step.

Since exp(9/13) is 1198.547 cents, this is a version of 9edo with flattened octaves. Some alternatives would be a single step of 27/25, so that the octave is 1199.138 cents, or an octave of 1199.737 cents, so that 12/7 is just, or an octave of 1200.919 cents, so that two steps are exactly 7/6. Or you could just leave the octave as 1200.0 cents.

Using e seems to me to be numerology, but what the heck; Margo ended up looking at some interesting stuff starting with numerology involving e. Charles Lucy has his numerology using pi instead, but I can't think of another pi example.

Now, I shall go listen.

--- On Thu, 7/22/10, christopherv <chrisvaisvil@...> wrote:

> Alister added to one of my tuning
> survey pieces and out popped an electro piece using the 13th
> root of e tuning. This piece uses a GR-20 relay re-tuned to
> 13th root of e which is e^(1/13) per step.
>
> Download
> http://notonlymusic.com/board/download/file.php?id=266
>
> online listen
> http://notonlymusic.com/board/viewtopic.php?f=23&t=289#p2000

Cool; I've been needing to do some more music with beats. Most of everything I've been doing for the past few years is of the "classical" variety.

About e as a tuning base: I tried to come up with an "unbiased" temperament using irrational bases like e and pi, the two constants in Euler's identity (now if I can only come up with a tuning using imaginary and complex numbers!). I never got far with with the experiment, but 76 equal divisions of e and 87 equal divisions of pi produce 53edo with about a 1207.3-cent octave. pi/e itself is 250.56 cents, or 11/53 of an octave and a little sharp of 15/13.

~D.

--- In tuning@yahoogroups.com, Danny Wier <dawiertx@...> wrote:

> About e as a tuning base: I tried to come up with an "unbiased" temperament using irrational bases like e and pi, the two constants in Euler's identity (now if I can only come up with a tuning using imaginary and complex numbers!).

Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
>

Could you provide an example tuning? I am intrigued by this prospect.

-Igs

This (post by Gene) is way, way over my head, but made me curious.

As a radical alternative to practicing a 13-limit JI scale, or as relief from it, some of these 'avoid JI' scales might be really interesting. I wish though, that I had something besides Pianotech to try them with. Even most the timbres in Logic produce harmonic spectra.

I've copied this scale of Danny's to my 'must try' file--necessary because there's so much information coming our way from this list and elsewhere all the time.

What might be some other scales to try?

1. 83.33 (22/21 or 21/20)
2. 150.00 (12/11)
3. 233.33 (8/7)
4. 300.00 (25/21)
5. 383.33 (5/4)
6. 450.00 (35/27)
7. 533.33 (15/11)
8. 616.67 (10/7) or 600.00 (99/70)
9. 683.33 (40/27)
10. 766.67 (14/9)
11. 833.33 (81/50)
12. 916.67 (56/33)
13. 983.33 (44/25)
14. 1066.67 (50/27)
15. 1133.33 (77/40 or 27/14)
16. 1216.67 (81/40)

Or, what might be some Scala files to try of scales made this (Gene's) way, that contained around 10 to 24 notes per 2-ish to 1-ish?

Caleb

On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:

>
>
> --- In tuning@yahoogroups.com, Danny Wier <dawiertx@...> wrote:
>
> > About e as a tuning base: I tried to come up with an "unbiased" temperament using irrational bases like e and pi, the two constants in Euler's identity (now if I can only come up with a tuning using imaginary and complex numbers!).
>
> Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
>
>

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

> Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
>

And if you really want to get serious, pick a zero where |Z'(1/2+i*t)| is relatively small.

seconded (no need to post my previous attempt to say the same thing)
On Jul 22, 2010, at 4:21 PM, cityoftheasleep wrote:

> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
> >
>
> Could you provide an example tuning? I am intrigued by this prospect.
>
> -Igs
>
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
> >
>
> Could you provide an example tuning? I am intrigued by this prospect.

About how big do you want the step to be?

why not use modplug tracker?

it can easily handle rank 1 (I think I have that right) tunings and you can
use any sample - like a pure sinewave.

Since you are friends with Michael S. I'm sure he can tell you the details
on doing it. It isn't hard once you see it.

chris

On Thu, Jul 22, 2010 at 4:29 PM, caleb morgan <calebmrgn@...> wrote:

>
>
> This (post by Gene) is way, way over my head, but made me curious.
>
> As a radical alternative to practicing a 13-limit JI scale, or as relief
> from it, some of these 'avoid JI' scales might be really interesting. I
> wish though, that I had something besides Pianotech to try them with. Even
> most the timbres in Logic produce harmonic spectra.
>
> I've copied this scale of Danny's to my 'must try' file--necessary because
> there's so much information coming our way from this list and elsewhere all
> the time.
>
> What might be some other scales to try?
>
> 1. 83.33 (22/21 or 21/20)
> 2. 150.00 (12/11)
> 3. 233.33 (8/7)
> 4. 300.00 (25/21)
> 5. 383.33 (5/4)
> 6. 450.00 (35/27)
> 7. 533.33 (15/11)
> 8. 616.67 (10/7) or 600.00 (99/70)
> 9. 683.33 (40/27)
> 10. 766.67 (14/9)
> 11. 833.33 (81/50)
> 12. 916.67 (56/33)
> 13. 983.33 (44/25)
> 14. 1066.67 (50/27)
> 15. 1133.33 (77/40 or 27/14)
> 16. 1216.67 (81/40)
>
>
> Or, what might be some Scala files to try of scales made this (Gene's) way,
> that contained around 10 to 24 notes per 2-ish to 1-ish?
>
> Caleb
>
>
>
> On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:
>
>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Danny Wier
> <dawiertx@...> wrote:
>
> > About e as a tuning base: I tried to come up with an "unbiased"
> temperament using irrational bases like e and pi, the two constants in
> Euler's identity (now if I can only come up with a tuning using imaginary
> and complex numbers!).
>
> Actually, a much better way of getting a tuning which makes some attempt to
> avoid JI does use complex numbers. Take a zero of the Riemann zeta function
> along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0
> (these have been extensively tabulated.) Now your "unbiased" equal tuning
> uses exp(2pi/t) as a step.
>
>
>
>

err, Chris, I'm not sure you're talking to me, but I Googled Modplug Tracker:

http://www.modplug.com/

And it appears to be PC only, and alas, i'm using a Mac.

Must get a PC one of these days.

But perhaps you were talking to someone else?

Caleb

On Jul 22, 2010, at 5:06 PM, Chris Vaisvil wrote:

> why not use modplug tracker?
>
> it can easily handle rank 1 (I think I have that right) tunings and you can use any sample - like a pure sinewave.
>
> Since you are friends with Michael S. I'm sure he can tell you the details on doing it. It isn't hard once you see it.
>
> chris
>
>
> On Thu, Jul 22, 2010 at 4:29 PM, caleb morgan <calebmrgn@...> wrote:
>
> This (post by Gene) is way, way over my head, but made me curious.
>
>
> As a radical alternative to practicing a 13-limit JI scale, or as relief from it, some of these 'avoid JI' scales might be really interesting. I wish though, that I had something besides Pianotech to try them with. Even most the timbres in Logic produce harmonic spectra.
>
> I've copied this scale of Danny's to my 'must try' file--necessary because there's so much information coming our way from this list and elsewhere all the time.
>
> What might be some other scales to try?
>
> 1. 83.33 (22/21 or 21/20)
> 2. 150.00 (12/11)
> 3. 233.33 (8/7)
> 4. 300.00 (25/21)
> 5. 383.33 (5/4)
> 6. 450.00 (35/27)
> 7. 533.33 (15/11)
> 8. 616.67 (10/7) or 600.00 (99/70)
> 9. 683.33 (40/27)
> 10. 766.67 (14/9)
> 11. 833.33 (81/50)
> 12. 916.67 (56/33)
> 13. 983.33 (44/25)
> 14. 1066.67 (50/27)
> 15. 1133.33 (77/40 or 27/14)
> 16. 1216.67 (81/40)
>
>
> Or, what might be some Scala files to try of scales made this (Gene's) way, that contained around 10 to 24 notes per 2-ish to 1-ish?
>
> Caleb
>
>
>
> On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:
>
>>
>>
>>
>> --- In tuning@yahoogroups.com, Danny Wier <dawiertx@...> wrote:
>>
>> > About e as a tuning base: I tried to come up with an "unbiased" temperament using irrational bases like e and pi, the two constants in Euler's identity (now if I can only come up with a tuning using imaginary and complex numbers!).
>>
>> Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
>>
>
>
>
>

then I suggest installing linux and WINE - it works like that too.

On Thu, Jul 22, 2010 at 5:46 PM, caleb morgan <calebmrgn@...> wrote:

>
>
> err, Chris, I'm not sure you're talking to me, but I Googled Modplug
> Tracker:
>
> http://www.modplug.com/
>
> And it appears to be PC only, and alas, i'm using a Mac.
>
> Must get a PC one of these days.
>
> But perhaps you were talking to someone else?
>
> Caleb
>
>
>
>
>
> On Jul 22, 2010, at 5:06 PM, Chris Vaisvil wrote:
>
>
>
> why not use modplug tracker?
>
> it can easily handle rank 1 (I think I have that right) tunings and you can
> use any sample - like a pure sinewave.
>
> Since you are friends with Michael S. I'm sure he can tell you the details
> on doing it. It isn't hard once you see it.
>
> chris
>
> On Thu, Jul 22, 2010 at 4:29 PM, caleb morgan <calebmrgn@...> wrote:
>
>>
>>
>> This (post by Gene) is way, way over my head, but made me curious.
>>
>> As a radical alternative to practicing a 13-limit JI scale, or as relief
>> from it, some of these 'avoid JI' scales might be really interesting. I
>> wish though, that I had something besides Pianotech to try them with. Even
>> most the timbres in Logic produce harmonic spectra.
>>
>> I've copied this scale of Danny's to my 'must try' file--necessary because
>> there's so much information coming our way from this list and elsewhere all
>> the time.
>>
>> What might be some other scales to try?
>>
>> 1. 83.33 (22/21 or 21/20)
>> 2. 150.00 (12/11)
>> 3. 233.33 (8/7)
>> 4. 300.00 (25/21)
>> 5. 383.33 (5/4)
>> 6. 450.00 (35/27)
>> 7. 533.33 (15/11)
>> 8. 616.67 (10/7) or 600.00 (99/70)
>> 9. 683.33 (40/27)
>> 10. 766.67 (14/9)
>> 11. 833.33 (81/50)
>> 12. 916.67 (56/33)
>> 13. 983.33 (44/25)
>> 14. 1066.67 (50/27)
>> 15. 1133.33 (77/40 or 27/14)
>> 16. 1216.67 (81/40)
>>
>>
>> Or, what might be some Scala files to try of scales made this (Gene's)
>> way, that contained around 10 to 24 notes per 2-ish to 1-ish?
>>
>> Caleb
>>
>>
>>
>> On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:
>>
>>
>>
>>
>>
>> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Danny Wier
>> <dawiertx@...> wrote:
>>
>> > About e as a tuning base: I tried to come up with an "unbiased"
>> temperament using irrational bases like e and pi, the two constants in
>> Euler's identity (now if I can only come up with a tuning using imaginary
>> and complex numbers!).
>>
>> Actually, a much better way of getting a tuning which makes some attempt
>> to avoid JI does use complex numbers. Take a zero of the Riemann zeta
>> function along the critical line, meaning find a place where Zeta(1/2 + i*t)
>> = 0 (these have been extensively tabulated.) Now your "unbiased" equal
>> tuning uses exp(2pi/t) as a step.
>>
>>
>>
>
>
>
>

Thanks, I'll look into it. The rest of your message also confused me, but I won't pursue it.

On Jul 22, 2010, at 6:21 PM, Chris Vaisvil wrote:

> then I suggest installing linux and WINE - it works like that too.
>
>
>
>
> On Thu, Jul 22, 2010 at 5:46 PM, caleb morgan <calebmrgn@...> wrote:
>
> err, Chris, I'm not sure you're talking to me, but I Googled Modplug Tracker:
>
>
> http://www.modplug.com/
>
> And it appears to be PC only, and alas, i'm using a Mac.
>
> Must get a PC one of these days.
>
> But perhaps you were talking to someone else?
>
> Caleb
>
>
>
>
>
> On Jul 22, 2010, at 5:06 PM, Chris Vaisvil wrote:
>
>>
>> why not use modplug tracker?
>>
>> it can easily handle rank 1 (I think I have that right) tunings and you can use any sample - like a pure sinewave.
>>
>> Since you are friends with Michael S. I'm sure he can tell you the details on doing it. It isn't hard once you see it.
>>
>> chris
>>
>>
>> On Thu, Jul 22, 2010 at 4:29 PM, caleb morgan <calebmrgn@...> wrote:
>>
>> This (post by Gene) is way, way over my head, but made me curious.
>>
>>
>> As a radical alternative to practicing a 13-limit JI scale, or as relief from it, some of these 'avoid JI' scales might be really interesting. I wish though, that I had something besides Pianotech to try them with. Even most the timbres in Logic produce harmonic spectra.
>>
>> I've copied this scale of Danny's to my 'must try' file--necessary because there's so much information coming our way from this list and elsewhere all the time.
>>
>> What might be some other scales to try?
>>
>> 1. 83.33 (22/21 or 21/20)
>> 2. 150.00 (12/11)
>> 3. 233.33 (8/7)
>> 4. 300.00 (25/21)
>> 5. 383.33 (5/4)
>> 6. 450.00 (35/27)
>> 7. 533.33 (15/11)
>> 8. 616.67 (10/7) or 600.00 (99/70)
>> 9. 683.33 (40/27)
>> 10. 766.67 (14/9)
>> 11. 833.33 (81/50)
>> 12. 916.67 (56/33)
>> 13. 983.33 (44/25)
>> 14. 1066.67 (50/27)
>> 15. 1133.33 (77/40 or 27/14)
>> 16. 1216.67 (81/40)
>>
>>
>> Or, what might be some Scala files to try of scales made this (Gene's) way, that contained around 10 to 24 notes per 2-ish to 1-ish?
>>
>> Caleb
>>
>>
>>
>> On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:
>>
>>>
>>>
>>>
>>> --- In tuning@yahoogroups.com, Danny Wier <dawiertx@...> wrote:
>>>
>>> > About e as a tuning base: I tried to come up with an "unbiased" temperament using irrational bases like e and pi, the two constants in Euler's identity (now if I can only come up with a tuning using imaginary and complex numbers!).
>>>
>>> Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
>>>
>>
>>
>>
>
>
>
>

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

>
> About how big do you want the step to be?
>

Something between 100 and 50 cents, maybe?

-Igs

I'm sure Michael can explain it to you..

chris

On Thu, Jul 22, 2010 at 6:47 PM, caleb morgan <calebmrgn@...> wrote:

>
>
> Thanks, I'll look into it. The rest of your message also confused me, but
> I won't pursue it.
>
>
> On Jul 22, 2010, at 6:21 PM, Chris Vaisvil wrote:
>
>
>
> then I suggest installing linux and WINE - it works like that too.
>
>
>
> On Thu, Jul 22, 2010 at 5:46 PM, caleb morgan <calebmrgn@...> wrote:
>
>>
>>
>> err, Chris, I'm not sure you're talking to me, but I Googled Modplug
>> Tracker:
>>
>> http://www.modplug.com/
>>
>> And it appears to be PC only, and alas, i'm using a Mac.
>>
>> Must get a PC one of these days.
>>
>> But perhaps you were talking to someone else?
>>
>> Caleb
>>
>>
>>
>>
>>
>> On Jul 22, 2010, at 5:06 PM, Chris Vaisvil wrote:
>>
>>
>>
>> why not use modplug tracker?
>>
>> it can easily handle rank 1 (I think I have that right) tunings and you
>> can use any sample - like a pure sinewave.
>>
>> Since you are friends with Michael S. I'm sure he can tell you the details
>> on doing it. It isn't hard once you see it.
>>
>> chris
>>
>> On Thu, Jul 22, 2010 at 4:29 PM, caleb morgan <calebmrgn@...>wrote:
>>
>>>
>>>
>>> This (post by Gene) is way, way over my head, but made me curious.
>>>
>>> As a radical alternative to practicing a 13-limit JI scale, or as relief
>>> from it, some of these 'avoid JI' scales might be really interesting. I
>>> wish though, that I had something besides Pianotech to try them with. Even
>>> most the timbres in Logic produce harmonic spectra.
>>>
>>> I've copied this scale of Danny's to my 'must try' file--necessary
>>> because there's so much information coming our way from this list and
>>> elsewhere all the time.
>>>
>>> What might be some other scales to try?
>>>
>>> 1. 83.33 (22/21 or 21/20)
>>> 2. 150.00 (12/11)
>>> 3. 233.33 (8/7)
>>> 4. 300.00 (25/21)
>>> 5. 383.33 (5/4)
>>> 6. 450.00 (35/27)
>>> 7. 533.33 (15/11)
>>> 8. 616.67 (10/7) or 600.00 (99/70)
>>> 9. 683.33 (40/27)
>>> 10. 766.67 (14/9)
>>> 11. 833.33 (81/50)
>>> 12. 916.67 (56/33)
>>> 13. 983.33 (44/25)
>>> 14. 1066.67 (50/27)
>>> 15. 1133.33 (77/40 or 27/14)
>>> 16. 1216.67 (81/40)
>>>
>>>
>>> Or, what might be some Scala files to try of scales made this (Gene's)
>>> way, that contained around 10 to 24 notes per 2-ish to 1-ish?
>>>
>>> Caleb
>>>
>>>
>>>
>>> On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:
>>>
>>>
>>>
>>>
>>>
>>> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Danny Wier
>>> <dawiertx@...> wrote:
>>>
>>> > About e as a tuning base: I tried to come up with an "unbiased"
>>> temperament using irrational bases like e and pi, the two constants in
>>> Euler's identity (now if I can only come up with a tuning using imaginary
>>> and complex numbers!).
>>>
>>> Actually, a much better way of getting a tuning which makes some attempt
>>> to avoid JI does use complex numbers. Take a zero of the Riemann zeta
>>> function along the critical line, meaning find a place where Zeta(1/2 + i*t)
>>> = 0 (these have been extensively tabulated.) Now your "unbiased" equal
>>> tuning uses exp(2pi/t) as a step.
>>>
>>>
>>>
>>
>>
>>
>
>
>
>

You have me confused with someone else, or you're baiting me for no apparent reason.

Aside from admiring a few people here, I don't really have an opinion.

My interest is in large JI scales; I'm practicing one currently with 48 notes per octave. My background is jazz and modern classical, and I'm middle-aged.

My impression is that Michael is into something completely different.

I don't get it, and I suggest we drop it.

If you'd like to know more about my background, or what I'm interested in, I'd be happy to oblige.

My email is calebmrgn@...

caleb

On Jul 22, 2010, at 7:14 PM, Chris Vaisvil wrote:

> I'm sure Michael can explain it to you..
>
> chris
>
>
> On Thu, Jul 22, 2010 at 6:47 PM, caleb morgan <calebmrgn@...> wrote:
>
>
> Thanks, I'll look into it. The rest of your message also confused me, but I won't pursue it.
>
>
> On Jul 22, 2010, at 6:21 PM, Chris Vaisvil wrote:
>
>>
>> then I suggest installing linux and WINE - it works like that too.
>>
>>
>>
>>
>> On Thu, Jul 22, 2010 at 5:46 PM, caleb morgan <calebmrgn@...> wrote:
>>
>> err, Chris, I'm not sure you're talking to me, but I Googled Modplug Tracker:
>>
>>
>> http://www.modplug.com/
>>
>> And it appears to be PC only, and alas, i'm using a Mac.
>>
>> Must get a PC one of these days.
>>
>> But perhaps you were talking to someone else?
>>
>> Caleb
>>
>>
>>
>>
>>
>> On Jul 22, 2010, at 5:06 PM, Chris Vaisvil wrote:
>>
>>>
>>> why not use modplug tracker?
>>>
>>> it can easily handle rank 1 (I think I have that right) tunings and you can use any sample - like a pure sinewave.
>>>
>>> Since you are friends with Michael S. I'm sure he can tell you the details on doing it. It isn't hard once you see it.
>>>
>>> chris
>>>
>>>
>>> On Thu, Jul 22, 2010 at 4:29 PM, caleb morgan <calebmrgn@...> wrote:
>>>
>>> This (post by Gene) is way, way over my head, but made me curious.
>>>
>>>
>>> As a radical alternative to practicing a 13-limit JI scale, or as relief from it, some of these 'avoid JI' scales might be really interesting. I wish though, that I had something besides Pianotech to try them with. Even most the timbres in Logic produce harmonic spectra.
>>>
>>> I've copied this scale of Danny's to my 'must try' file--necessary because there's so much information coming our way from this list and elsewhere all the time.
>>>
>>> What might be some other scales to try?
>>>
>>> 1. 83.33 (22/21 or 21/20)
>>> 2. 150.00 (12/11)
>>> 3. 233.33 (8/7)
>>> 4. 300.00 (25/21)
>>> 5. 383.33 (5/4)
>>> 6. 450.00 (35/27)
>>> 7. 533.33 (15/11)
>>> 8. 616.67 (10/7) or 600.00 (99/70)
>>> 9. 683.33 (40/27)
>>> 10. 766.67 (14/9)
>>> 11. 833.33 (81/50)
>>> 12. 916.67 (56/33)
>>> 13. 983.33 (44/25)
>>> 14. 1066.67 (50/27)
>>> 15. 1133.33 (77/40 or 27/14)
>>> 16. 1216.67 (81/40)
>>>
>>>
>>> Or, what might be some Scala files to try of scales made this (Gene's) way, that contained around 10 to 24 notes per 2-ish to 1-ish?
>>>
>>> Caleb
>>>
>>>
>>>
>>> On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:
>>>
>>>>
>>>>
>>>>
>>>> --- In tuning@yahoogroups.com, Danny Wier <dawiertx@...> wrote:
>>>>
>>>> > About e as a tuning base: I tried to come up with an "unbiased" temperament using irrational bases like e and pi, the two constants in Euler's identity (now if I can only come up with a tuning using imaginary and complex numbers!).
>>>>
>>>> Actually, a much better way of getting a tuning which makes some attempt to avoid JI does use complex numbers. Take a zero of the Riemann zeta function along the critical line, meaning find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
>>>>
>>>
>>>
>>>
>>
>>
>>
>
>
>
>

I'm sorry,

I do think I owe you an apology.

Chris

On Thu, Jul 22, 2010 at 7:22 PM, caleb morgan <calebmrgn@...> wrote:

>
>
> You have me confused with someone else, or you're baiting me for no
> apparent reason.
>
> Aside from admiring a few people here, I don't really have an opinion.
>
> My interest is in large JI scales; I'm practicing one currently with 48
> notes per octave. My background is jazz and modern classical, and I'm
> middle-aged.
>
> My impression is that Michael is into something completely different.
>
> I don't get it, and I suggest we drop it.
>
> If you'd like to know more about my background, or what I'm interested in,
> I'd be happy to oblige.
>
> My email is calebmrgn@...
>
> caleb
>
>
>
> On Jul 22, 2010, at 7:14 PM, Chris Vaisvil wrote:
>
>
>
> I'm sure Michael can explain it to you..
>
> chris
>
> On Thu, Jul 22, 2010 at 6:47 PM, caleb morgan <calebmrgn@...> wrote:
>
>>
>>
>> Thanks, I'll look into it. The rest of your message also confused me, but
>> I won't pursue it.
>>
>>
>> On Jul 22, 2010, at 6:21 PM, Chris Vaisvil wrote:
>>
>>
>>
>> then I suggest installing linux and WINE - it works like that too.
>>
>>
>>
>> On Thu, Jul 22, 2010 at 5:46 PM, caleb morgan <calebmrgn@...>wrote:
>>
>>>
>>>
>>> err, Chris, I'm not sure you're talking to me, but I Googled Modplug
>>> Tracker:
>>>
>>> http://www.modplug.com/
>>>
>>> And it appears to be PC only, and alas, i'm using a Mac.
>>>
>>> Must get a PC one of these days.
>>>
>>> But perhaps you were talking to someone else?
>>>
>>> Caleb
>>>
>>>
>>>
>>>
>>>
>>> On Jul 22, 2010, at 5:06 PM, Chris Vaisvil wrote:
>>>
>>>
>>>
>>> why not use modplug tracker?
>>>
>>> it can easily handle rank 1 (I think I have that right) tunings and you
>>> can use any sample - like a pure sinewave.
>>>
>>> Since you are friends with Michael S. I'm sure he can tell you the
>>> details on doing it. It isn't hard once you see it.
>>>
>>> chris
>>>
>>> On Thu, Jul 22, 2010 at 4:29 PM, caleb morgan <calebmrgn@yahoo.com>wrote:
>>>
>>>>
>>>>
>>>> This (post by Gene) is way, way over my head, but made me curious.
>>>>
>>>> As a radical alternative to practicing a 13-limit JI scale, or as relief
>>>> from it, some of these 'avoid JI' scales might be really interesting. I
>>>> wish though, that I had something besides Pianotech to try them with. Even
>>>> most the timbres in Logic produce harmonic spectra.
>>>>
>>>> I've copied this scale of Danny's to my 'must try' file--necessary
>>>> because there's so much information coming our way from this list and
>>>> elsewhere all the time.
>>>>
>>>> What might be some other scales to try?
>>>>
>>>> 1. 83.33 (22/21 or 21/20)
>>>> 2. 150.00 (12/11)
>>>> 3. 233.33 (8/7)
>>>> 4. 300.00 (25/21)
>>>> 5. 383.33 (5/4)
>>>> 6. 450.00 (35/27)
>>>> 7. 533.33 (15/11)
>>>> 8. 616.67 (10/7) or 600.00 (99/70)
>>>> 9. 683.33 (40/27)
>>>> 10. 766.67 (14/9)
>>>> 11. 833.33 (81/50)
>>>> 12. 916.67 (56/33)
>>>> 13. 983.33 (44/25)
>>>> 14. 1066.67 (50/27)
>>>> 15. 1133.33 (77/40 or 27/14)
>>>> 16. 1216.67 (81/40)
>>>>
>>>>
>>>> Or, what might be some Scala files to try of scales made this (Gene's)
>>>> way, that contained around 10 to 24 notes per 2-ish to 1-ish?
>>>>
>>>> Caleb
>>>>
>>>>
>>>>
>>>> On Jul 22, 2010, at 3:39 PM, genewardsmith wrote:
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Danny Wier
>>>> <dawiertx@...> wrote:
>>>>
>>>> > About e as a tuning base: I tried to come up with an "unbiased"
>>>> temperament using irrational bases like e and pi, the two constants in
>>>> Euler's identity (now if I can only come up with a tuning using imaginary
>>>> and complex numbers!).
>>>>
>>>> Actually, a much better way of getting a tuning which makes some attempt
>>>> to avoid JI does use complex numbers. Take a zero of the Riemann zeta
>>>> function along the critical line, meaning find a place where Zeta(1/2 + i*t)
>>>> = 0 (these have been extensively tabulated.) Now your "unbiased" equal
>>>> tuning uses exp(2pi/t) as a step.
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>
>>
>>
>
>
>
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> >
> > About how big do you want the step to be?
> >
>
> Something between 100 and 50 cents, maybe?

97.2308 cents and 58.6085 cents both come with small Zeta derivatives.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...>

> 97.2308 cents and 58.6085 cents both come with small Zeta derivatives.

Interesting. The latter looks like about half a secor. The former is very cool, almost like 2 out of a very stretched 25-EDO. Though both seem to hit close to some JI intervals on more than a few occasions...I wonder if it's possible for any equal tuning to really not approximate (within 7 cents) any 13-or-lower-odd-limit JI intervals at all (including 2/1).

-Igs

Igs>"I wonder if it's possible for any equal tuning to really not approximate
(within 7 cents) any 13-or-lower-odd-limit JI intervals at all (including 2/1)."

Even in 13-limit (as in odd limit) I am pretty sure not. It seems there are
some pretty large gray areas in between 13-limit dyads.
In addition, many TET tunings temper out intervals greater than 14-cents (thus
making it impossible for every note to be with 7 cents of a 13-odd-limit
interval, if I have it right).

Here are just a few of them (nearest odd limit intervals with a difference of
over 14 cents for the nearest 2 13-or-less odd limit tones and therefore, no way
to be tempered within 7 cents of both intervals):

16/11 compared to 3/2
13/9 compared to 10/7
10/7 compared to 7/5
10/9 compared to 11/10
11/10 compared to 12/11
11/9 compared to 6/5
13/10 compared to 4/3
9/7 compared to 13/10
9/7 compared to 14/11
5/4 compared to 14/11
..............

In summary: I think finding any scale that hits the 13(odd)-limit or lower
within 7-cents in all or virtually all combinations of dyads is certainly not a
random occurrence and definitely not something you can just pull out of your,
well....

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Even in 13-limit (as in odd limit) I am pretty sure not.

He's talking about not being close to JI, not about being close to it. And no assumption is being made that octaves are pure; quite the contrary, they shouldn't be. So even if 13/8 gets missed, you might get closer to 13/4, or 13/2, or 13. It's going to be pretty hard to miss everything.

Gene is correct, I'm talking about NOT hitting any ratios. Every EDO tuning above 6-EDO hits at least ONE 13-odd-limit ratio within 7 cents (or at least two, if you're counting inversions, and make that three if you're counting 2/1):
6-EDO: 9/8
7-EDO: 11/9
8-EDO: 12/11, 13/10
9-EDO: 7/6, 14/13
10-EDO: 16/13
11-EDO: 9/7, 11/8
12-EDO: 9/8, 4/3
13-EDO: 10/9, 11/8
14-EDO: 11/10, 11/9, 9/7
15-EDO: 11/10, 6/5
16-EDO: 12/11, 13/10, 8/7
17-EDO: 13/12, 13/11, 11/9, 4/3

Etc., etc. Extend the odd-limit to 15 or the tolerance to 10 or 11 cents, and the number goes up. So if you're trying to avoid anything JI, EDOs aren't the way to go. I'm thinking it's not just EDOs, either, but rather ALL equal divisions of anything. As Gene noted, when you try to miss the octave, you open up great possibilities of hitting JI ratios with smaller denominators, like 13/2 or 5/2 or 9/2 or whatever. Perhaps the only way to consistently avoid any JI approximations is to not use an equal temperament, but rather an inharmonic series? I have to wonder....

-Igs

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Igs>"I wonder if it's possible for any equal tuning to really not approximate
> (within 7 cents) any 13-or-lower-odd-limit JI intervals at all (including 2/1)."
>
> Even in 13-limit (as in odd limit) I am pretty sure not. It seems there are
> some pretty large gray areas in between 13-limit dyads.
> In addition, many TET tunings temper out intervals greater than 14-cents (thus
> making it impossible for every note to be with 7 cents of a 13-odd-limit
> interval, if I have it right).
>
>
> Here are just a few of them (nearest odd limit intervals with a difference of
> over 14 cents for the nearest 2 13-or-less odd limit tones and therefore, no way
> to be tempered within 7 cents of both intervals):
>
> 16/11 compared to 3/2
> 13/9 compared to 10/7
> 10/7 compared to 7/5
> 10/9 compared to 11/10
> 11/10 compared to 12/11
> 11/9 compared to 6/5
> 13/10 compared to 4/3
> 9/7 compared to 13/10
> 9/7 compared to 14/11
> 5/4 compared to 14/11
> ..............
>
> In summary: I think finding any scale that hits the 13(odd)-limit or lower
> within 7-cents in all or virtually all combinations of dyads is certainly not a
> random occurrence and definitely not something you can just pull out of your,
> well....
>

Gene,
I'm probably being dim, but in what sense is the tuning "unbiased", and (in simple terms, please!) why is it so?

Steve M.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > ... find a place where Zeta(1/2 + i*t) = 0 (these have been extensively tabulated.) Now your "unbiased" equal tuning uses exp(2pi/t) as a step.
> ... And if you really want to get serious, pick a zero where |Z'(1/2+i*t)| is relatively small.

--- On Fri, 7/23/10, martinsj013 <martinsj@...> wrote:
> Gene,
> I'm probably being dim, but in what sense is the tuning
> "unbiased", and (in simple terms, please!) why is it so?

It was I that said "unbiased", but what I meant is that I wanted a tuning that was based the least bit upon rational JI as possible, maximally atonal. I also had in mind a TOP tuning (I didn't know what one was then).

~D.

Ah ok you are right then...of course at least one dyad is almost certainly
going to be within 7-cents of a 13-limit JI ratio.

Igs>"So if you're trying to avoid anything JI, EDOs aren't the way to go."
I wouldn't be too sure of that considering if an EDO misses 13-limit-or-lower
JI on many if not most occasions.
If anything it seems to simply prove what you showed me earlier...that if you
try to get too dissonant far as scale's ratios you indirectly create consonant
ones (be they at multi-octave spans or what not).

>"Perhaps the only way to consistently avoid any JI approximations is to not use
>an equal temperament, but rather an inharmonic series? I have to wonder...."
It's quite a challenge...but I think you're right in that you'd have to use
different spacing on different periods to avoid further-apart ratios forming
JI-like patterns. Also non-clustered tones with low periodicity between them,
I'm guessing, is a good way to go.