Tuning-Math messages 475 - 499

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Message: 475

Date: Mon, 02 Jul 2001 18:55:12

Subject: Re: Hypothesis revisited

From: Paul Erlich

--- In tuning-math@y..., "monz" <joemonz@y...> wrote:
> 
> > From: Paul Erlich <paul@s...>
> > To: <tuning-math@y...>
> > Sent: Saturday, June 30, 2001 7:00 PM
> > Subject: [tuning-math] Re: Hypothesis revisited
> >
> 
> > I think so. The LucyTuning "major third" is 2^(1/pi).
> > Add two octaves to form the "major seventeenth": 2^(2+1/pi).
> > Take the fourth root (since it's a meantone, the fifth
> > will be the fourth root of the major seventeenth):
> > 2^(1/2 + 1/(4*pi)). Is that right?
> 
> 
> Thanks for this great explanation, Paul.
> 
> Your answer is slightly different from the one Ed Borasky
> calculated with Derive:
> 
>   2^( (2*pi) + 1 / (4*pi) )
> 
It's completely different.

2^( (2*pi) + 1 / (4*pi) ) = 82.2967 = 7635.3¢

2^(1/2 + 1/(4*pi)) = 1.4944 = 695.49¢


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Message: 476

Date: 2 Jul 2001 17:58:59 -0700

Subject: 17-tone PB and Justin White's question

From: paul@s...

Forwarded is a question from Justin White.

He refers to <http://www.anaphoria.com/genus.PDF - Ok *>. On the bottoms of pages
15, 19, 20, and 23, there is a lattice of Wilson's famous 17-tone scale,
which is clearly a periodicity block with unison vectors schisma and
chromatic semitone; i.e.,

[8 1]

and

[-1 2].


Anyone like to tackle Justin's question below? Justin, if you're reading
this, you might like to join tuning-math to see what responses this
generates!


-----Original Message-----
From: Justin White [mailto:justin.white@d...] 
Sent: Monday, May 14, 2001 3:53 AM
To: Paul H. Erlich
Subject: Re: adaptive tuning. Can a computer pick a melody from the
harmony ?





Hello Paul, Thanks for your offer of assistance with this one. Have you read
Erv
Wilsons paper "Some Basic Patterns Underlying Genus 12 & 17"?

--- In tuning@y..., "Justin White" <justin.white@d...> wrote:
>>
>> Yes I was attracted to this scale. I thought of creating a scale in
the smae
>> manner using a septimal tetrachord...I haven't found a tetrachord
that will give
>> me the tetrad s I want yet.

>Can you explain what you're trying to do? Maybe I can help.


What I want to do is use the same methodology to create a [septimal] subset
of
the scale I have posted below.


0.  1/1
1   25/24
2.  135/128
3.  35/32
4.  9/8
5.  7/6
6.  75/64
7.  1215/1024
8.  6/5
9.  315/256
10. 5/4
11. 81/64
12. 21/16
13. 675/512
14. 4/3
15. 7/5
16. 45/32
17. 35/24
18. 189/128
19. 3/2
20. 25/16
21. 405/256
22. 8/5
23. 105/64
24. 5/3
25. 27/16
26. 7/4
27. 225/128
28. 9/5
29. 945/512
30. 15/8
31. 243/128
32. 63/32
33. 2/1

Note how Wilsons genus 17 [see below] contains mostly notes from the above
superset [B&C's blue melodic reference]

0.  1/1
1.  135/128
2.  10/9
3.  9/8
4.  1215
5.  5/4
6.  81/80
7.  4/3
8.  45/32.
9.  729/512
10 .3/2
11. 405/256
12. 5/3
13. 27/16
14. 3645/2048
15. 15/8
16. 243/128
17. 2/1

The columns below are to indicate what ratios are more important than
others.
The notes in the left hand column should be used before the  notes in the
right
hand column.  [This is to do with th e chain of reference used in that
scale.]

1/1
9/8            45/32           135/128           405/256
1215/1024
7/6            35/24
6/5
5/4            25/16             75/64              225/128
675/256
4/3
7/5                                     21/16               63/32
189/128
3/2            15/8
8/5            25/24
5/3
7/4            35/32           105/64              315/256
945/512
9/5                                     27/16                81/64
243/128


I'd be interested to see what you make of it all.



Best wishes,

Justin White


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Message: 477

Date: Tue, 03 Jul 2001 04:40:18

Subject: 17-tone PB and Justin White's question

From: monz

Hello all.  I was just working on my paper on John Dowland's
Lute Fretting (to be delivered in Italy on September 13,
Wim Hoogewerf performing).

See my old webpage on this, which I'm using as a basis
for expansion:
John Dowland's Lute Fretting  (c)1998 by Joe Monzo *

I made a graph of the entire set of intervals available
between any two pitches on Dowland's fretboard, which I've
posted here:

Yahoo groups: /tuning- *
math/files/monz/dowland_lute_fretting.xls

(copy/paste the broken link, remove break, copy/paste into
browser)


I created minor gridlines along the y-axis to represent
1/8-tones, because I was struck by the way nearly all the
intervals cluster between +/- ~25 cents from each 12-EDO
pitch-_gestalt_.

I'd appreciate some mathematical formalizations of this.
I'm very intrigued by this observation.  Any ideas?



-monz
Yahoo! GeoCities *
"All roads lead to n^0"


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Message: 478

Date: Mon, 2 Jul 2001 21:45:13

Subject: Re: interval set of Dowland's tuning

From: monz

--- In tuning-math@y..., "monz" <joemonz@y...> wrote:

Yahoo groups: /tuning-math/message/477 *

>  
> Hello all.  I was just working on my paper on John Dowland's
> Lute Fretting (to be delivered in Italy on September 13,
> Wim Hoogewerf performing).


Oops... totally my bad.  First of all, I didn't have a
subject line on that post.


> I made a graph of the entire set of intervals available
> between any two pitches on Dowland's fretboard, which I've
> posted here:
>
Yahoo groups: /tuning- *
math/files/monz/dowland_lute_fretting.xls


Secondly, as you can see by the file extension, this is
not simply a .gif graphic of the chart, but rather the
entire Excel spreadsheet.

I thought that would make things easier for you math-heads
to get right to work on it!  :)



-monz
Yahoo! GeoCities *
"All roads lead to n^0"


 


_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at Yahoo! Mail Setup *


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Message: 479

Date: Mon, 2 Jul 2001 21:48:44

Subject: Re: interval set of Dowland's tuning

From: monz

> From: monz <joemonz@y...>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Monday, July 02, 2001 9:40 PM
>
>
> 
> 
> Yahoo groups: /tuning- *
> math/files/monz/dowland_lute_fretting.xls
> 
> (copy/paste the broken link, remove break, copy/paste into
> browser)
> 
> 
> I created minor gridlines along the y-axis to represent
> 1/8-tones, because I was struck by the way nearly all the
> intervals cluster between +/- ~25 cents from each 12-EDO
> pitch-_gestalt_.


Oops... my bad yet again.  Of course, I meant "=/- ~25 cents
from each 12-EDO *interval*-_gestalt_.



-monz
Yahoo! GeoCities *
"All roads lead to n^0"


 


_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at Yahoo! Mail Setup *


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Message: 480

Date: Mon, 2 Jul 2001 22:00:30

Subject: Re: Lucytuning "5th" (was: Re Hypothesis revisited)

From: monz

> From: Paul Erlich <paul@s...>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Monday, July 02, 2001 11:55 AM
> Subject: [tuning-math] Re: Hypothesis revisited
>
>
> It's completely different.
>
> 2^( (2*pi) + 1 / (4*pi) ) = 82.2967 = 7635.3¢
>
> 2^(1/2 + 1/(4*pi)) = 1.4944 = 695.49¢


Hmmm... oddly enough, Paul, when I plugged
both of these formulas into Excel they gave the
same result!  (the latter of your two)

My choice of additional parentheses must have made
the difference.  Here are the exact Excel formulas,
which require PI to have an empty argument: PI() .

=2^((2*PI()+1)/(4*PI()))

=2^((1/2)+(1/(4*PI())))


Is there any way to decide which of the two is
more elegant?  Does it matter at all?  Can you
explain why they work out to the same ratio?



-monz
Yahoo! GeoCities *
"All roads lead to n^0"





_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at Yahoo! Mail Setup *


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Message: 484

Date: Wed, 4 Jul 2001 16:21:53

Subject: Re: periodicity block definition

From: monz

I was playing around with an interval conversion calculator
I created in an Excel spreadsheet, and I happened to notice
that 5 enharmonic dieses [= (128/125)^5] are almost the
same size as a 9:8 whole-tone.

enharmonic diesis  = (2^7)*(5^-3) = ~41.05885841 cents

5 enharmonic dieses = (2^35)*(5^-15) =  ~205.294292 cents

9/8 = (2^-3)*(3^2) = ~203.9100017 cents


difference:  ((128/125)^5) / (9/8)  = 

   2^x 3^y 5^z

  | 35  0  -15|
- |- 3  2    0|
  -------------
  | 38 -2  -15|

= (2^38)*(3^-2)*(5^-15) = ~1.384290297 cents = ~1&3/8 cents.


Has anyone ever noticed this before, or used it as a unison-vector?
Any comments?  I'd like to see a periodicity-block derived from it.


-monz
Yahoo! GeoCities *
"All roads lead to n^0"


 


_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at Yahoo! Mail Setup *


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Message: 486

Date: Wed, 04 Jul 2001 22:13:19

Subject: Naming intervals using Miracle

From: David C Keenan

The Miracle temperament gives us a logical way of further extending the
Fokker extended-diatonic interval-names from 31-EDO to Miracle chains, and
hence to 41-EDO, 72-EDO and 11-limit JI.

Previously there was no obvious way of deciding which of a pair of nearby
intervals (such as the neutral seconds 10:11 and 11:12 or the minor
sevenths 5:9 and 9:16) should be called "wide" or "narrow", and which
should be unmodified. Now the answer is obvious. The unmodified one is the
one that is represented within a chain of +-15 Miracle generators. i.e. The
intervals available in Miracle-31 should be named the same as in 31-EDO,
without using "wide" or "narrow".

The table below shows how this scheme names the intervals of 72-EDO.

Legend for interval names:

1 unison
2 second
3 third
4 fourth
5 fifth
6 sixth
7 seventh
8 octave

m = minor
N = neutral
M = major

d = diminished
P = perfect
A = augmented

s = sub
S = super

n = narrow
W = wide

Legend for note names:

A,B,C,D,E,F,G,#,b as for 12-tET
] = quarter-tone up   (+50 c)
> = sixth-tone   up   (+33 c)
^ = twelfth-tone up   (+17 c)
v = twelfth-tone down (-17 c)
< = sixth-tone   down (-33 c)
[ = quarter-tone down (-50 c)

No.	Cents	Intvl	Note	11-limit
gens          name	frm C	Ratio
---------------------------------
0	0	  P1	C	1:1
31	17	  W1	C^	
-10	33	  S1	C>	
21	50	 WS1	C]	
-20	67	nsm2	C#<	
11	83	 sm2	C#v	
-30	100	 nm2	C#	
1	117	  m2	C#^	
32	133	 Wm2	C#>	
-9	150	  N2	D[	11:12
22	167	 WN2	D<	10:11
-19	183	 nM2	Dv	9:10
12	200	  M2	D	8:9
-29	217	nSM2	D^	
2	233	 SM2	D>	7:8
33	250	WSM2	D]	
-8	267	 sm3	Eb<	6:7
23	283	Wsm3	Ebv	
-18	300	 nm3	Eb	
13	317	  m3	Eb^	5:6
-28	333	 nN3	Eb>	
3	350	  N3	E[	9:11
34	367	 WN3	E<	
-7	383	  M3	E	4:5
24	400	 WM3	E	
-17	417	nSM3	E^	11:14
14	433	 SM3	E>	7:9
-27	450	 ns4	F[	
4	467	  s4	F<	
35	483	 Ws4	Fv	
-6	500	  P4	F	3:4
25	517	 WP4	F^	
-16	533	 nS4	F>	
15	550	  S4	F]	8:11
-26	567	 nA4	F#<	
5	583	  A4	F#v	5:7
+-36	600  WA4/nd5  F#	
-5	617	  d5	F#^	7:10
26	633	 Wd5	F#>	
-15	650	  s5	G[	11:16
16	667	 Ws5	G<	
-25	683	 nP5	Gv	
6	700	  P5	G	2:3
-35	717	 nS5	G^	
-4	733	  S5	G>	
27	750	 WS5	G]	
-14	767	 sm6	G#<	9:14
17	783	Wsm6	G#v	7:11
-24	800	 nm6	G#	
7	817	  m6	G#^	5:8
-34	833	 nN6	G#>	
-3	850	  N6	A[	11:18
28	867	 WN6	A<	
-13	883	  M6	Av	3:5
18	900	 WM6	A	
-23	917	nSM6	A^	
8	933	 SM6	A>	7:12
-33	950	nsm7	A]	
-2	967	 sm7	Bb<	4:7
29	983	Wsm7	Bbv	
-12	1000	  m7	Bb	9:16
19	1017	 Wm7	Bb^	5:9
-22	1033	 nN7	Bb>	11:20
9	1050	  N7	B[	6:11
-32	1067	 nM7	B<	
-1	1083	  M7	Bv	
30	1100	 WM7	B	
-11	1117	 SM7	B^	
20	1133	WSM7	B>	
-21	1150	 ns8	C[	
10	1167	  s8	C<	
-31	1183	  n8	Cv	

Does anyone feel that any of these names are somehow wrong?

Does this conflict with any existing use of "wide" and "narrow"? e.g. Scala.

Regards,
-- Dave Keenan
Brisbane, Australia
Dave Keenan's Home Page *


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Message: 487

Date: Thu, 05 Jul 2001 18:04:40

Subject: Re: periodicity block definition

From: Paul Erlich

--- In tuning-math@y..., carl@l... wrote:

> () How are the above affected by the decision to
> temper out some or all of the unison vectors?  For
> example, what happens when there are commatic unison
> vectors larger than any chromatic ones?

Nothing too special, if you're tempering out the commatic ones. You 
might call such a scale "artificial", if you believe all scales 
should start out in JI and then evolve into a tempered form.

If the chromatic unison vector is larger than one of the scale steps, 
you get an improper scale.


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Message: 488

Date: Thu, 05 Jul 2001 21:29:17

Subject: Re: A septimal 22 tone scale subset of B&C matrix

From: Paul Erlich

--- In tuning-math@y..., "Justin White " <JUSTINTONATION@H...> wrote:
> 
> Is it a PB ?

No -- 135/128 would be two steps, not one, in a 22-tET PB or CS.

Before I start spouting out 22-tone 7-limit periodicity blocks that 
are very similar to this for you, can I ask you, why only 22 tones, 
given that you have intervals
as small as a syntonic comma (about 1/56 of an octave) in your scale 
(e.g., between 5/4 and 81/64)?

> If someone can suggest a tempered scale that would allow me to play 
> most [or all] of the the B&C blue reference scale with sufficient 
> accuracy

You'll have to specify what "sufficient accuracy" means for you. 
Presumably, each of the consonant intervals in the chains of 
reference need to be tuned correctly to within x cents. What is x? 
Presumably, you'd also rather have comma differences respected rather 
than tempered out/confuted -- yes?


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Message: 489

Date: Thu, 05 Jul 2001 22:28:12

Subject: Re: periodicity block definition

From: carl@l...

>> () How are the above affected by the decision to
>> temper out some or all of the unison vectors?  For
>> example, what happens when there are commatic unison
>> vectors larger than any chromatic ones?

> /../
>
> If the chromatic unison vector is larger than one of the scale
> steps, you get an improper scale.

If the scale is just, then the difference between a commatic
and chromatic unison vector is one of a naming only, right?
So would your statement here be better put, "If any unison
vector which is left untempered is larger than one of the scale
steps, you get an improper scale."?  Or does the difference
in naming actually affect propriety?

-Carl


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Message: 490

Date: Thu, 05 Jul 2001 22:32:46

Subject: Re: periodicity block definition

From: Paul Erlich

--- In tuning-math@y..., carl@l... wrote:
> >> () How are the above affected by the decision to
> >> temper out some or all of the unison vectors?  For
> >> example, what happens when there are commatic unison
> >> vectors larger than any chromatic ones?
> 
> > /../
> >
> > If the chromatic unison vector is larger than one of the scale
> > steps, you get an improper scale.
> 
> If the scale is just, then the difference between a commatic
> and chromatic unison vector is one of a naming only, right?

Right. But you said "temper out" above, so I was focusing on that 
case.

> So would your statement here be better put, "If any unison
> vector which is left untempered is larger than one of the scale
> steps, you get an improper scale."?

Yes I think that's right.

> Or does the difference
> in naming actually affect propriety?

Well it would be kind of perverse to call something a _commatic_ 
unison vector if it's larger than one of the scale steps and it's not 
tempered out . . . don't you think?


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Message: 491

Date: Thu, 05 Jul 2001 23:40:20

Subject: Re: periodicity block definition

From: carl@l...

>> Or does the difference
>> in naming actually affect propriety?
> 
>Well it would be kind of perverse to call something a _commatic_ 
>unison vector if it's larger than one of the scale steps and it's
>not tempered out . . . don't you think?

Yes.

-Carl


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Message: 493

Date: Sat, 07 Jul 2001 02:54:32

Subject: Re: Naming intervals using Miracle

From: Dave Keenan

--- In tuning-math@y..., Herman Miller <hmiller@I...> wrote:
> On Wed, 04 Jul 2001 22:13:19 -0700, David C Keenan <D.KEENAN@U...>
> wrote:
> 
> >35	483	 Ws4	Fv	
> >-6	500	  P4	F	3:4
> >25	517	 WP4	F^	
> 
> >-25	683	 nP5	Gv	
> >6	700	  P5	G	2:3
> >-35	717	 nS5	G^	
> 
> I like this scheme in general, but I don't see any reason to avoid 
"narrow
> perfect fourth" or "wide perfect fifth" (especially given that you 
have
> "WP4" and "nP5". These are slightly closer to just than the 5-TET 
fourths
> and fifths (which is about the limit of what I'd consider a good 
perfect
> fourth or fifth).

Good point. In 72-EDO, nP4 and Ws4 are indeed alternative names for 
the same interval. Ws4 is +35 generators and nP4 is -37 generators. 
The only time they might actually refer to different interval is on an 
open Miracle chain with 38 notes or more, or a closed one with more 
than 72 notes. So such distinctions are not really of any practical 
interest.

There are 21 (=3*31-72) intervals with alternative names like this in 
72-EDO. Then there are the alternative names allowed by the Fokker 
31-EDO system itself (like sd5 and A4 for 5:7). These carry over to 
the Miracle system as well.

Regards,
-- Dave Keenan


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Message: 498

Date: Thu, 12 Jul 2001 14:09:15

Subject: El Paso Microtonal Festival

From: John Chalmers

Erv Wilson and Jeniffer Stapher has asked me to circulate this notice
about the Microtone Conference in El Paso this November.


--John

Subject: RE: Please Reply to Confirm Your Participation!
Date: Sat, 30 Jun 2001 17:43:52 EDT
From: Microtonezone@a...
To: Microtonezone@a...
CC: stapherthomas@e...

Dear
      The purpose of this email is to inform you that indeed we have secured
the El Paso International Museum of Art  for  November 1 - through November
4, 2001. We hope you find this information helpful.
      This is a lengthy document and we recommend that you print it,
fill it

out, email info and snail mail the final portion.

       Sonja  will be out of town on and off, so you will need to send your
                        info to me, Jeniffer Stapher
                               15308 Marburn
                         Horizon City, Texas 79928
                      Email- stapherthomas@e...
                        Phone Number- (915) 852-9315

                         Set Up and Take Down Times

Thursday-9:30 a.m. to 5:00 p.m.
Friday-9:30 a.m. to 12:30 p.m.
Saturday-9:30 a.m. to 11:30 p.m.
Saturday Afternoon-5:00 p.m. to 6:30 p.m.
Sunday-9:30 a.m. 2:00 p.m.

       Performance time blocks  are:
Thursday - Welcoming Night-7:00 p.m. - 10:00 p.m.
Friday Matinee-1:00 p.m. - 5:00 p.m.
Friday Evening - 7:00 p.m.-10:00 p.m.
Saturday Matinee-12 p.m. to 5 p.m.
Saturday Evening- 7:00 p.m.-10:00 p.m.

                                   Theater Info

     We have contracted to use the lower floor of the museum which includes
a small theater and several spacious galleries.

      The theater is vintage 1960s art deco revival and is in  near mint
condition, but has not been upgraded for new technology ! It has a small
lighted stage, a  booth, a ramp for truck access and 168 seats. Remember,
the
technology is of the 1960s, thus participants  must be responsible for
providing for their own equipment needs-outside of the basics!

                             Gallery Dimensions

#1- Front to Back- 25 feet
Side to Side- 18 feet

#2- Front to Back- 18 feet
Side to Side- 25 feet

#3- Front to Back- 29 feet
Side to Side- 30 feet

#4- Front to Back- 18 feet
Side to Side- 25 feet

#5- Teaching Space Across the Hall from the Theater
Front to Back- 33 feet
Side to Side- 29 feet

            Info We Need From You ASAP-Please email this data !
   If you have already provided this data, kindly do so again! Thank You!

Name
Address
Phone Number
Email Address
Field of Expertise
Bio or Web Site

                              Publicity MUSTS!
       Write a brief explanation of what microtonalism means to you!
    PR Photo- black & white or color- to be used for newspaper, magazine
                                 publicity

    Nature of Presentation (Lecture/Workshop/Demonstration/ Performance)
           Please let us know more about what you intend to do !

Theme of Presentation, instrument, theory, etc.!

Select Day(s) and Time(s) and Place (s) ( Refer to Schedule Performance Time

                 Blocks  and Theater / Gallery Info Above)

First Choice(s)-
Day(s)-
Time(s)-
Place(s)-
Second Choice(s)
Day(s)-
Time(s)-
Place(s)-
Alternate Choice (s)
Day(s)-
Time(s)-
Place(s)-

                       Confirming Your Participation

      In order to secure a place in this event you will need to send your
information by email or snail mail by August 1, 2001.

                                 Entry Fee
  An entry fee of $35.00 is due on or before September 14, 2001. Send your
             personal check, cashier's check or money order to
                               Sonja A. Wayne
                              3217 Suffolk Rd
                             El Paso, TX  79925
                                     or
                              Jeniffer Stapher

                    (Make checks out to Sonja A. Wayne)
 The purpose of the fee is to assist in covering the costs of the insurance,

             production and the publishing costs of this event.
                                 Questions?
                 You can call Sonja anytime (915) 591-3105
                     or email either Sonja or Jeniffer!
                                Thank You !
We thank you for your cooperation and look forward to future correspondence!



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Christi Villegas manager
cell phone # ((15) 252-9390

The Cliff Inn is located very near the International Museum of Art, and is
in the Medical District El Pasoan's call, "Pill Hill". As you can see, they
are offering a wonderful rate- if this does not fit your fancy, there are
many hotels near the airport- Hilton, Radisson, Marriott, La Quinta, Travel
Lodge, Howard Johnson's etc!!!! 
If you need more info please email me!

Car Rentals
www.carrentalselpaso.com


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