Tuning-Math Archive Section 1: 475

Message: 475 - Contents - Hide Contents 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¢

Message: 476 - Contents - Hide Contents 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 - Type Ok * [with cont.] (Wayb.)>. 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

Message: 477 - Contents - Hide Contents 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: Internet Express - Quality, Affordable Dial Up... * [with cont.] (Wayb.) 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- * [with cont.] 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 * [with cont.] (Wayb.) "All roads lead to n^0"

Message: 478 - Contents - Hide Contents 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 * [with cont.]

> > 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- * [with cont.] 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 * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)

Message: 479 - Contents - Hide Contents 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- * [with cont.] > 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 * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)

Message: 480 - Contents - Hide Contents 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 * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)

Message: 484 - Contents - Hide Contents 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 * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)

Message: 485 - Contents - Hide Contents Date: Thu, 05 Jul 2001 00:21:55 Subject: Re: periodicity block definition From: Herman Miller On Wed, 4 Jul 2001 16:21:53 -0700, "monz" <joemonz@y...> wrote:

>= (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.

Hmm, I see that this is a unison vector in 25-TET, although the 5-step "whole tone" is quite large at 240 cents, and there's a better approximation of 9/8 at 192 cents. Of course this is also a unison vector in 31-TET. Along a line from 31-TET to 56-TET (31+25) there is a number of tempered scales that share this unison vector, and this line approaches very close to 5-limit just (closer even than the line between 31 and 22, which goes through 53!) I'm not sure what you can do with this, but it's a start. Look at the chart at http://www.io.com/~hmiller/png/et-scales.png - Type Ok * [with cont.] (Wayb.) and draw a line from 31 to 25: it looks like there could be some good scales there.

Message: 486 - Contents - Hide Contents 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 * [with cont.] (Wayb.)

Message: 487 - Contents - Hide Contents 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.

Message: 488 - Contents - Hide Contents 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?

Message: 489 - Contents - Hide Contents 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

Message: 490 - Contents - Hide Contents 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?

Message: 491 - Contents - Hide Contents Date: Thu, 05 Jul 2001 23:40:20 Subject: Re: periodicity block definition From: carl@l...

>> >r 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

Message: 492 - Contents - Hide Contents Date: Thu, 05 Jul 2001 20:16:37 Subject: Re: Naming intervals using Miracle From: Herman Miller 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).

Message: 493 - Contents - Hide Contents 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

Message: 498 - Contents - Hide Contents 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! Sound Systems& Equipment Crosby Sound, Lighting and Video: "Reasonable rates for rental of sound, lighting, technical support All major Credit cards accepeted" Office # (915) 544-5996 24 hour answering service (915) 534-8268 DU MOTION Audio-Visual-Video Inc. AudioVisual Sound systems Wireless Microphones Sound podiums Rentals, Sales 1601 Montana (915) 532-2760 Mesilla Valley Music Pro Sound & Lighting Toll Free Call 1-800-955-0251 Hotel Cliff Inn Hotel and Conference Center 1600 East Cliff Drive (915) 533-6700 $35.00 double bed-non-smoking 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