20

should anyone be interested, here are a few rough examples of this
tuning/temperament :

http://zebox.com/danstearns_2/

the first example is a little attempt to show that while 20-tone equal
temperament is not a particularly concordant temperament--it has
extremely rough maj 3rds or 5ths thereby making it a poor candidate for
orthodox tertian harmony,it can still be used to express tonality
without avoiding "pretty" sonorities.

the second example is a quick and dirty bit of funk /rock that plays
off the familiar 1/4th of an octave min 3rd .

the third example is a solo--note the faux bends that are
actually "chromatics" , and the slippery sense of "in" and "out" .

daniel

On 3/18/06, daniel_anthony_stearns <daniel_anthony_stearns@yahoo.com> wrote:
> should anyone be interested, here are a few rough examples of this
> tuning/temperament :
>
> http://zebox.com/danstearns_2/
[...]

Interesting. I never could understand why people used these "bad"
edos, but I admit it sounds better than I expected.

How did you make these? Don't tell me you actually built a 20-edo guitar?!

Keenan

>How did you make these? Don't tell me you actually built a 20-edo
>guitar?!

I'll leave that for Dan to answer (grin). But I do know of at
least one interesting scale in 20:

!
Balzano's 9-tone subset of 20-tet.
9
!
120.0 !....2
300.0 !....5
420.0 !....7
540.0 !....9
660.0 !...11
840.0 !...14
960.0 !...16
1080.0 !..18
2/1 !.....20
!

This was independently discovered by Dan, and its tuning in 31
was found by computer search by:

!
David Rothenberg and Connie Chan.
9
!
193.55 !....5
309.68 !....8
425.81 !...11
541.93 !...14
658.06 !...17
851.61 !...22
967.74 !...25
1083.87 !..28
2/1 !......31
!
! MOS (14/31), strictly proper, efficiency = 0.7407.

The 31 version is better-tuned for the 8ths, which enjoy a
diatonic-like pattern of 7:4 and 5:3. I don't think that's what
drew Dan to it, though. But for that reason, and the reasons
that drew Rothenberg to it, it ranks 3rd on my list of
generalized-diatonic scales, just behind the pentatonic and
diatonic scales in 12.

-Carl

--- In MakeMicroMusic@yahoogroups.com, "Keenan Pepper"
<keenanpepper@...> wrote:

> Interesting. I never could understand why people used these "bad"
> edos, but I admit it sounds better than I expected.

One way to treat it would be to say it has great 13s, good 19s and OK
7s, which gives you something to work with right there. Then add in
the fact that it's 14/11 third and its 11/7 minor sixth are fine, and
you are on your way.

yes, it's a 20edo guitar . I had it made back in the early 90s by
luthier/banjoist extrodinaire Glen Nelson :

http://www.mockingbirdmusic.com/

If you go to the bottom of this page:

http://kronoson.station185.com/kronosonic/contrib/dan.htm

there's a picture (the tune linked at the top is also a more extended
version of one of the examples, albiet with fretless and many other
tunings/instruments as well) .FWIW,one of the unique guitaristic
properties of this tuning is that i can tune it to 2/5ths of an
octave fourths which sits on the guitar in an all-fourths stack that
allows the two outside strings to still meet at E:

(E)420*, (A)900, (D)180, (G) 660, (B)1140, (E)420

And as far as as "bad edos" go, i also have a 13-tet tenor ukulele
which you can see in this forum's photo file!

thanks,daniel

--- In MakeMicroMusic@yahoogroups.com, "J.Smith" <jsmith9624@...>
wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Keenan Pepper"
> <keenanpepper@> wrote:
>
> > Interesting. I never could understand why people used these "bad"
> > edos, but I admit it sounds better than I expected.
> >
> > How did you make these? Don't tell me you actually built a 20-edo
> guitar?!
> >
> > Keenan
> >
>
> Yes, it was definitely different, though I thought it had
> coherent "harmonic" progressions -- they made sense.
>
> Was that an actual guitar, Dan?
>
> jls
>

On 3/19/06, daniel_anthony_stearns <daniel_anthony_stearns@yahoo.com> wrote:
> yes, it's a 20edo guitar . I had it made back in the early 90s by
> luthier/banjoist extrodinaire Glen Nelson :
>
> http://www.mockingbirdmusic.com/

Neat!

> If you go to the bottom of this page:
>
> http://kronoson.station185.com/kronosonic/contrib/dan.htm
>
> there's a picture (the tune linked at the top is also a more extended
> version of one of the examples, albiet with fretless and many other
> tunings/instruments as well) .FWIW,one of the unique guitaristic
> properties of this tuning is that i can tune it to 2/5ths of an
> octave fourths which sits on the guitar in an all-fourths stack that
> allows the two outside strings to still meet at E:
>
> (E)420*, (A)900, (D)180, (G) 660, (B)1140, (E)420

You get that with any blackwood temperament, i.e. edos of small
multiples of 5. 15 is usually considered better than 20...

> And as far as as "bad edos" go, i also have a 13-tet tenor ukulele
> which you can see in this forum's photo file!

*shudders* Okay, I take it back. 20 is a GREAT edo! =P

Keenan

Carl Lumma wrote:
>>How did you make these? Don't tell me you actually built a 20-edo
>>guitar?!
> > > I'll leave that for Dan to answer (grin). But I do know of at
> least one interesting scale in 20:
> > !
> Balzano's 9-tone subset of 20-tet.
> 9
> !
> 120.0 !....2
> 300.0 !....5
> 420.0 !....7
> 540.0 !....9
> 660.0 !...11
> 840.0 !...14
> 960.0 !...16
> 1080.0 !..18
> 2/1 !.....20
> !

This sounds like a pretty interesting scale; I tried it out in Scala. Like a number of 9-note scales, you can also find a fairly decent pelog scale in this one, especially if you stretch the octaves.

I wonder if it would be useful to treat this as a regular temperament... Without going into the mathematical details, which would be more suitable for the tuning-math list, this seems to be related to negri temperament (if you omit every other step in the chain), which suggests it might be useful to check out tunings with slightly sharp octaves (around 1203 cents). Also, take any ET that's compatible with negri temperament (such as 19-ET) and double the number of steps per octave: here it is in 38-ET:

!
38-ET version of Balzano's 9-note 20-ET scale
9
!
126.31579 !....4
284.21053 !....9
410.52632 !...13
536.84211 !...17
663.15789 !...21
821.05263 !...26
947.36842 !...30
1073.68421 !..34
2/1 !.........38

If you take this out to 20 steps, you've got a 20-note MOS of 38-ET that includes the 38-ET equivalent of Balzano's 9 from 20-ET scale (in several transpositions) as well as Joe Negri's 9 from 19-ET scale!

On Sun, 19 Mar 2006 dan stearns wrote:
>
> should anyone be interested, here are a few rough examples of this
> tuning/temperament :
>
> http://zebox.com/danstearns_2/
>
> the first example is a little attempt to show that while 20-tone equal
> temperament is not a particularly concordant temperament--it has
> extremely rough maj 3rds or 5ths thereby making it a poor candidate for
> orthodox tertian harmony,it can still be used to express tonality
> without avoiding "pretty" sonorities.
>
> the second example is a quick and dirty bit of funk /rock that plays
> off the familiar 1/4th of an octave min 3rd .
>
> the third example is a solo--note the faux bends that are
> actually "chromatics" , and the slippery sense of "in" and "out" .

Dan,

Very, very cool! They work well, to my ears.
I'd like to hear longer versions.

and later:
> yes, it's a 20edo guitar . I had it made back in the early 90s by
> luthier/banjoist extrodinaire Glen Nelson :
>
> http://www.mockingbirdmusic.com/
>
> If you go to the bottom of this page:
>
> http://kronoson.station185.com/kronosonic/contrib/dan.htm
>
> there's a picture (the tune linked at the top is also a more extended
> version of one of the examples, albiet with fretless and many other
> tunings/instruments as well) .FWIW,one of the unique guitaristic
> properties of this tuning is that i can tune it to 2/5ths of an
> octave fourths which sits on the guitar in an all-fourths stack that
> allows the two outside strings to still meet at E:
>
> (E)420*, (A)900, (D)180, (G) 660, (B)1140, (E)420

Love it! Gets over the G-B discontinuity in transferring
the same fingering from one string to the next, which
has always bugged me when playing the guitar - there
are enough technicalities going on that removing just one
of them would lead to smoother flow when improvising.
I think I'm going to have to make myself one ...

Regards,
Yahya

On Sat, 18 Mar 2006 Carl Lumma wrote:
>
> >How did you make these? Don't tell me you actually built a 20-edo
> >guitar?!
>
> I'll leave that for Dan to answer (grin). But I do know of at
> least one interesting scale in 20:
>
> !
> Balzano's 9-tone subset of 20-tet.
> 9
> !
> 120.0 !....2
> 300.0 !....5
> 420.0 !....7
> 540.0 !....9
> 660.0 !...11
> 840.0 !...14
> 960.0 !...16
> 1080.0 !..18
> 2/1 !.....20
> !
>
> This was independently discovered by Dan, and its tuning in 31
> was found by computer search by:
>
> !
> David Rothenberg and Connie Chan.
> 9
> !
> 193.55 !....5
> 309.68 !....8
> 425.81 !...11
> 541.93 !...14
> 658.06 !...17
> 851.61 !...22
> 967.74 !...25
> 1083.87 !..28
> 2/1 !......31
> !
> ! MOS (14/31), strictly proper, efficiency = 0.7407.
>
> The 31 version is better-tuned for the 8ths, which enjoy a
> diatonic-like pattern of 7:4 and 5:3. I don't think that's what
> drew Dan to it, though. But for that reason, and the reasons
> that drew Rothenberg to it, it ranks 3rd on my list of
> generalized-diatonic scales, just behind the pentatonic and
> diatonic scales in 12.

Carl,

The 31-EDO version also has its first note on 193,
approximating 180 rather than 120, ie 3 steps of
20-EDO. So the pattern of the first:
s l s s s l s s s

becomes:
l s s s s l s s s

which we have to rotate four scale degrees to get:
s l s s s l s s s

again. IOW, the 31-EDO tuning is the fifth mode
of the 20-EDO tuning.

You probably knew that, but I thought I'd point it
out in case anyone else didn't get it.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.385 / Virus Database: 268.2.5/284 - Release Date: 17/3/06

At 05:18 PM 3/19/2006, you wrote:
>
>On Sat, 18 Mar 2006 Carl Lumma wrote:
>>
>> >How did you make these? Don't tell me you actually built a 20-edo
>> >guitar?!
>>
>> I'll leave that for Dan to answer (grin). But I do know of at
>> least one interesting scale in 20:
>>
>> !
>> Balzano's 9-tone subset of 20-tet.
>> 9
>> !
>> 120.0 !....2
>> 300.0 !....5
>> 420.0 !....7
>> 540.0 !....9
>> 660.0 !...11
>> 840.0 !...14
>> 960.0 !...16
>> 1080.0 !..18
>> 2/1 !.....20
>> !
>>
>> This was independently discovered by Dan, and its tuning in 31
>> was found by computer search by:
>>
>> !
>> David Rothenberg and Connie Chan.
>> 9
>> !
>> 193.55 !....5
>> 309.68 !....8
>> 425.81 !...11
>> 541.93 !...14
>> 658.06 !...17
>> 851.61 !...22
>> 967.74 !...25
>> 1083.87 !..28
>> 2/1 !......31
>> !
>> ! MOS (14/31), strictly proper, efficiency = 0.7407.
>>
>> The 31 version is better-tuned for the 8ths, which enjoy a
>> diatonic-like pattern of 7:4 and 5:3. I don't think that's what
>> drew Dan to it, though. But for that reason, and the reasons
>> that drew Rothenberg to it, it ranks 3rd on my list of
>> generalized-diatonic scales, just behind the pentatonic and
>> diatonic scales in 12.
>
>
>Carl,
>
>The 31-EDO version also has its first note on 193,
>approximating 180 rather than 120, ie 3 steps of
>20-EDO. So the pattern of the first:
>s l s s s l s s s
>
>becomes:
>l s s s s l s s s
>
>which we have to rotate four scale degrees to get:
>s l s s s l s s s
>
>again. IOW, the 31-EDO tuning is the fifth mode
>of the 20-EDO tuning.
>
>You probably knew that, but I thought I'd point it
>out in case anyone else didn't get it.
>
>Regards,
>Yahya

Thanks Yahya. Yeah, I often don't bother to select any particular
mode of a scale in Scala. In this case, I believe I entered them
as they were given by Balzano and Rothenberg.

-Carl

thanks yahya and everybody. I first tried 20 because I'm a bit of a
contrarian and it totally ignored12's major thirds and fifths--not
once, but twice! I also knew that it contained 5, which I was
interested in for its approximations in various world cultures;so i
guess i was hoping for something both "weird" and "exotic" . At first
it was quite a shock, because you really can't play anything from the
standard repertoire as you can in tunings like 19 and 31 (etc) ,and
it took me quite awhile to learn how to use the tuning and be
comfortable with its many stubborn obstinations and obstinate
stubbornations. But i'm not a one tuning guy at all, and 20 is NOT a
good utilitarian tuning.....but i'm not a utilitarian tuning guy
either So, i guess i wouldn't want to be stuck with only 20, but i
sure am glad i have it . For me, microtonality is like space
exploration and every tuning, of which there are a vast and never-
ending stock, is like some new planet......a fresh alien vista
calling out to me(and FWIW, 13 and 11, both tunings I've used quite a
bit, are quite sweet and pretty if you want them to be).
--- In MakeMicroMusic@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...>
wrote:
>
>
> On Sun, 19 Mar 2006 dan stearns wrote:
> >
> > should anyone be interested, here are a few rough examples of
this
> > tuning/temperament :
> >
> > http://zebox.com/danstearns_2/
> >
> > the first example is a little attempt to show that while 20-tone
equal
> > temperament is not a particularly concordant temperament--it has
> > extremely rough maj 3rds or 5ths thereby making it a poor
candidate for
> > orthodox tertian harmony,it can still be used to express tonality
> > without avoiding "pretty" sonorities.
> >
> > the second example is a quick and dirty bit of funk /rock that
plays
> > off the familiar 1/4th of an octave min 3rd .
> >
> > the third example is a solo--note the faux bends that are
> > actually "chromatics" , and the slippery sense of "in" and "out" .
>
> Dan,
>
> Very, very cool! They work well, to my ears.
> I'd like to hear longer versions.
>
>
> and later:
> > yes, it's a 20edo guitar . I had it made back in the early 90s by
> > luthier/banjoist extrodinaire Glen Nelson :
> >
> > http://www.mockingbirdmusic.com/
> >
> > If you go to the bottom of this page:
> >
> > http://kronoson.station185.com/kronosonic/contrib/dan.htm
> >
> > there's a picture (the tune linked at the top is also a more
extended
> > version of one of the examples, albiet with fretless and many
other
> > tunings/instruments as well) .FWIW,one of the unique guitaristic
> > properties of this tuning is that i can tune it to 2/5ths of an
> > octave fourths which sits on the guitar in an all-fourths stack
that
> > allows the two outside strings to still meet at E:
> >
> > (E)420*, (A)900, (D)180, (G) 660, (B)1140, (E)420
>
> Love it! Gets over the G-B discontinuity in transferring
> the same fingering from one string to the next, which
> has always bugged me when playing the guitar - there
> are enough technicalities going on that removing just one
> of them would lead to smoother flow when improvising.
> I think I'm going to have to make myself one ...
>
>
> Regards,
> Yahya
>

Dan,

Thanks, as always, for your particular take on the universe.

{you wrote...}
>I first tried 20 because I'm a bit of a contrarian and it totally ignored12's major thirds and fifths--not once, but twice! I also knew that it contained 5, which I was interested in for its approximations in various world cultures;so i
>guess i was hoping for something both "weird" and "exotic" . At first it was quite a shock, because you really can't play anything from the standard repertoire as you can in tunings like 19 and 31 (etc) ,and it took me quite awhile to learn how to use the tuning and be comfortable with its many stubborn obstinations and obstinate stubbornations.

Ah, yes, ladies and gentlemen, this is why it is so soulful to have Dan around - he has a poetic take not only on words but on tunings and music, and it is good to be reminded, from time to time, that these are communicative, malleable tools, to be used as you will.

Whatever that means.

Cheers,
Jon