Yahoo Tuning Groups Ultimate Backup tuning just right ? or just not quite

> C C# D D# E F F# G G# A A#
B

>JUST 0 -29 4 16 -14 -2 -10 2 14 -16
-12
>Harmonic 0 5 4 -2 -14 -29 -49 2 41
6 -31 -12
>Werkm. 0 -8 -3 -3 -7
0 -9 -1 -6 -6 -1 -9
>1/4Comma0 -24 7 10 -14 3 -21 -3 14 -18
7 -17
>1/5Comma0 -16 -5 7 -9 2 -14 -2 9 -7
5 -12

The Harmonic is correct for harmonics 12 to 24 mode 9:
1/1 17/16 9/8 19/16 5/4 21/16 11/8 23/16 299/192 161/96 115/64 23/12
except it misses out 600+28.27 = 23/16 (for obvious reasons)

The just scale is correct, except that the -29 is closest to
54/49 = 200-31.79 cents
in the scala intnams.par list
which I imagine isn't the one intended.
Should be
0 cents 100+11.73 cents 200+3.91 cents 300+15.64 cents 400-13.69 cents
500-1.955 cents 600-9.776 cents 700+1.955 cents 800+13.69 cents 900-15.64
cents 1000+17.6 cents 1100-11.73 cents 1200 cents
for
1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1

The Werckmeister III is
0 cents 100-9.775 cents 200-7.82 cents 300-5.865 cents 400-9.775 cents
500-1.955 cents 600-11.73 cents 700-3.91 cents 800-7.82 cents 900-11.73
cents 1000-3.91 cents 1100-7.82 cents 1200 cents werck3.scl | Andreas
Werckmeister's temperament III (the most famous one, 1681)

I've done a file of all the 12 tone scales in the SCALA archive as cents
diffs from 12-tet
see
http://www.robertwalker.f9.co.uk/12_tone_scales_as_cents_diffs.lsc [140 Kb]

I've done it to only 4 sig figs to make it easier to read, and as you don't
need the extra sig. figs.

(N.B. if you have Fractal Tune Smithy, and have made the association with
.lsc files, clicking on the link will start TS with it as the drop list of
scales. In IE, rt click and choose save target as. In Netscape, rt click and
Save Link as)

There are some gamelan 12 tone ones there that have white notes as Pelog,
and black notes as Slendro. (Try searching the file for Pelog).

If you have Wind 95/98, next update of TS beta later today or tomorrow has
option to show cents diffs from 12 tet which I've just added in response to
your posting.

To use it, enter the scale as ratios or cents notation into the Scale box,
then go to File | Number Options and tick "Show cents" and the new tick box
"Show cents as diffs from 12-tet".

You can also show the Scale window by clicking on the Scale.. button (has
more space for entering the numbers)

You can make mean-tone scales in TS using Scale...|Select from | mean
tone... and enter amount of the comma and position of the wolf fifth.

Quarter comma with wolf fifth between F sharp and D flat is
0 cents 100+17.11 cents 200-6.843 cents 300+10.26 cents 400-13.69 cents
500+3.422 cents 600-20.53 cents 700-3.422 cents 800+13.69 cents 900-10.26
cents 1000+6.843 cents 1100-17.11 cents 1200 cents

Fifth comma with wolf fifth in same pos is
0 cents 100+11.73 cents 200-4.693 cents 300+7.039 cents 400-9.385 cents
500+2.346 cents 600-14.08 cents 700-2.346 cents 800+9.385 cents 900-7.039
cents 1000+4.693 cents 1100-11.73 cents 1200 cents

N.B. this has turned up a bug in the new TS feature to search the SCALA
archive by the desired number of notes (in the File | More Scales | Search
box)Because it does it by counting words, it counts the word "cent" as a
note - fixed in next beta which ignores the word cents.

Robert

-----Original Message-----
From: tuning@egroups.com <tuning@egroups.com>
To: tuning@egroups.com <tuning@egroups.com>
Date: Thursday, October 19, 2000 6:35 AM
Subject: [tuning] Digest Number 893

>
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>
>------------------------------------------------------------------------
>
>There are 25 messages in this issue.
>
>Topics in this digest:
>
> 1. 31-tET guitar (was: thoughts on tuning)
> From: " Monz" <MONZ@JUNO.COM>
> 2. Re: the sound of a ?distant? horn...
> From: AMiltonF@aol.com
> 3. RE: the sound of a ?distant? horn...
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
> 4. Re: Re: thoughts on tuning
> From: David Beardsley <xouoxno@virtulink.com>
> 5. Re: Minors chords one example (BIS)
> From: "John A. deLaubenfels" <jdl@adaptune.com>
> 6. Re: Re: thoughts on tuning
> From: Afmmjr@aol.com
> 7. Re: the sound of a ?distant? horn...
> From: AMiltonF@aol.com
> 8. Webern the microtempoist
> From: "Joseph Pehrson" <josephpehrson@compuserve.com>
> 9. Re: the sound of a ?distant? horn...
> From: "Joseph Pehrson" <josephpehrson@compuserve.com>
> 10. Re: Re: the sound of a ?distant? horn...
> From: AMiltonF@aol.com
> 11. Re: the apical BP "Lambda scales"
> From: Kraig Grady <kraiggrady@anaphoria.com>
> 12. just right ? or just not quite
> From: "Buddhi Wilcox" <buddhi@paradise.net.nz>
> 13. RE: the sound of a ?distant? horn...
> From: "M. Edward Borasky" <znmeb@teleport.com>
> 14. Re: Tuning with Phi as interval ratio
> From: "M. Schulter" <MSCHULTER@VALUE.NET>
> 15. Re: Re: the sound of a distant acoustic horn...
> From: Kraig Grady <kraiggrady@anaphoria.com>
> 16. RE: Re: the sound of a ?distant? horn...
> From: "M. Edward Borasky" <znmeb@teleport.com>
> 17. RE: Re: the sound of a distant acoustic horn...
> From: "M. Edward Borasky" <znmeb@teleport.com>
> 18. Re: thoughts on tuning
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
> 19. Re: the sound of a ?distant? horn...
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
> 20. Re: the sound of a ?distant? horn...
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
> 21. Re: just right ? or just not quite
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
> 22. Re: the sound of a ?distant? horn...
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
> 23. One eikosany donut please
> From: David C Keenan <D.KEENAN@UQ.NET.AU>
> 24. RE: Re: the sound of a ?distant? horn...
> From: "M. Edward Borasky" <znmeb@teleport.com>
> 25. Re: One eikosany donut please
> From: Kraig Grady <kraiggrady@anaphoria.com>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 1
> Date: Wed, 18 Oct 2000 22:47:14 -0000
> From: " Monz" <MONZ@JUNO.COM>
>Subject: 31-tET guitar (was: thoughts on tuning)
>
>
>--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>> http://www.egroups.com/message/tuning/14595
>>
>> Dante -- I guess I was hoping for more of a reaction of how much
>> of a pain it is for you to get in between those frets on your
>> guitar, since you said:
>>
>> > I must say that frets too close to
>> > each other are a pain to play
>>
>> and also because I've been contemplating making a 31-tET guitar
>> my next one for some time now.
>
>
>Hey Dante and Paul, I just thought I'd toss this in since I have
>been playing around with one of Ivor's 31-tET guitars lately.
>
>At first, it was very difficult to navigate because of the small
>fret distances. But I find that the more I play it, the easier
>it gets. (And note my usual disclaimer: I am *not* a guitarist!)
>
>I still can't get my fingers to do much beyond the 12th fret,
>which gives the approximation to the '4th' (and the pitches for
>four of the strings in the 'normal' A-E-D-G-B-E tuning).
>
>But working below that fret-limit, there are lots and lots of
>new chords and scales to be found!
>
>I hope to get a fretboard diagram of this guitar up on my site soon.
>
>
>-monz
>http://www.ixpres.com/interval/monzo/homepage.html
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 2
> Date: Wed, 18 Oct 2000 19:14:15 EDT
> From: AMiltonF@aol.com
>Subject: Re: the sound of a ?distant? horn...
>
>PERLICH@ACADIAN-ASSET.COM writes:
>
>> >What if composers could go beyond the implementation problems and use
any
>> >pitch in the audible range whenever they wanted to? No tunings needed.
>>
>> Many people on this list (Johnny Reinhard, John deLaubenfels)
effectively
>> have this freedom, and yet they are not freed from issues like the
>> consonance of chords, the intelligibility of melodies (which leads
concepts
>> of scales), etc. These are tuning issues, aren't they?
>
>
> I should have been more specific by typing "fixed tunings." That is
what
>I meant in response to the "future of music" thread and if Johnny Reinhard
>and John deLaubenfels are the only two on the list with the said freedom
then
>what are the rest of you doing? I hear a lot of talk about how a new scale
>is superior to 12et and reduces pain across the board or makes a great
>picture but in reality you're just wasting time. The truth of the matter
is
>if you're going to limit yourself to a fixed tuning in the age of the
>integrated circuit then your'e going to be way behind in your tonal
>vocabulary when that age gives way to processors that blow the IC away.
When
>the new age dawns it will strip old rules from their foundations and music
>will have to be explored from the ground up on a composer by composer
basis.
>The only "rule" that will apply will be the one that started it all -- If
it
>sounds good, It is good.
> As for all of you who bag "computer music" your complaints are valid at
>this point in time, but what are you going to be saying in 10 years?
You're
>going to be kicking yourself for not learning everything you could have
about
>it. The computer is the most powerful tool on the planet. When recording
>was invented composers were given a "canvas" to work with a kind of stone
to
>be carved. The computer will let us do that with ease.
> And for those of you who prefer live performance over "dead" - you
should
>wake up, too. If you're going to achieve higher art, you're going to have
to
>sculpt it just like you heard it. People are going to want to hear it
>exactly like you did in your head.
>
>Andrew F.
>
>note: this was intended to incite backlash - steel sharpening steel!
>
>
>
>it
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 3
> Date: Wed, 18 Oct 2000 19:07:15 -0400
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
>Subject: RE: the sound of a ?distant? horn...
>
>>I hear a lot of talk about how a new scale
>>is superior to 12et and reduces pain across the board or makes a great
>>picture but in reality you're just wasting time. The truth of the matter
>is
>>if you're going to limit yourself to a fixed tuning in the age of the
>>integrated circuit then your'e going to be way behind in your tonal
>>vocabulary when that age gives way to processors that blow the IC away.
>
>Assuming that all significant music is going to be computer music -- and I
>think we're very far from that time.
>
>>As for all of you who bag "computer music" your complaints are valid at
>>this point in time, but what are you going to be saying in 10 years?
>
>I might be making a lot of computer music, but I still might believe in the
>magic of live performance.
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 4
> Date: Wed, 18 Oct 2000 19:31:51 -0700
> From: David Beardsley <xouoxno@virtulink.com>
>Subject: Re: Re: thoughts on tuning
>
>Rosati wrote:
>
>> On my guitar there are some frets that are nice and wide and a few, that
you
>> mentioned, that are obnoxiously close together. While none are impossible
to
>> play, getting a nice clear sound out of the narrow frets is tricky. Since
I
>> compose mostly by improvising, I have to admit that my tendency is to use
>> the wider frets more often and avoid the narrow ones.
>
>Me too. ;)
>
>> The one piece that I
>> wrote using a predetermined scale (Archytas enharmonic- hopfully soon to
be
>> an mp3 file) requires using many narrow frets and there I just had to get
>> used to it. So they're not impossible, just a pain in the butt. Also it
>> might be less of an issue on an electric guitar? where the metal strings
>> make it easier to get a clear sound?
>
>It doesn't seem to be a problem for Jon Catler. I have a bit of a
>problem
>with the narrow frets, but there are a few tight frets I've gotten used
>to.
>He has a technique of just laying a finger behind a higher fret that
>works.
>You don't have to push down and the note just sounds. I should note
>that we have jumbo size frets on these guitars.
>
>--
>* D a v i d B e a r d s l e y
>* 49/32 R a d i o "all microtonal, all the time"
>* http://www.virtulink.com/immp/lookhere.htm
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 5
> Date: Wed, 18 Oct 2000 17:56:33 -0600
> From: "John A. deLaubenfels" <jdl@adaptune.com>
>Subject: Re: Minors chords one example (BIS)
>
>[Paul E:]
>>>>But wouldn't playing, say, a major scale in JI, with alternating 9:8
>>>>and 10:9 whole tones, have an even more uneven sound than most of
>>>>your COFT tunings?
>
>[JdL:]
>>>I haven't tracked this down with numbers yet, but I suspect that COFT-
>>>induced deviations are sometimes more extreme than 81/80.
>
>[Paul:]
>>I'll bet the contents of my wallet that _all_ of your COFTs have
>>melodic whole tone sizes (that actually appear in the piece) within a
>>range _smaller_ than 81:80. Especially for the Scarlatti, where you
>>essentially got meantone, all the melodic whole tones would be about
>>equal -- thus a high degree of melodic smoothness.
>
>How big is your wallet, Paul? ;-> Actually, at the moment, I'm trying
>to recall which piece seemed to whap me in the face with this. I'll get
>back to you when possible; you can keep the contents of your wallet.
>
>[JdL:]
>>>So, for example, a 7-limit otonal tuning file would start by
>>>specifying that C is unchanged from 12-tET, E is about -14 cents from
>>>12-tET, G is about +2 cents from 12-tET, and Bb is about -31 cents
>>>from 12-tET (the program will separately "center" the deviations given
>>>it). In order to capture minor chords, the file tunes A at about -16
>>>cents from 12-tET. I think I also tune Eb at +16, allowing a good
>>>C,Eb,G as well as A,C,E; they will give the same tuning results.
>
>>>The program understands that each tuning file can be applied in 12
>>>keys.
>
>[Paul:]
>>uhh . . . right . . . .
>
>What's with the "uhh"? This seems so intuitive to me; how am I failing
>to convey the idea(s) here?
>
>[JdL:]
>>>To steer a given set of notes into a particular tuning vs. another,
>>>the tuning file rates each of the 66 intervals it forms; thus the
>>>above file would rate the 386 cent interval from C to E as very
>>>desirable, etc. The backside major third, from E to G#, is
>>>approximately 428 cents and is given very low desirability. The 7:9
>>>third from Bb to D, approx 435 cents, is given fairly high
>>>desirability so that a dom 7 will align to it, but not so high that a
>>>bare major third sticks to it instead of to 5:4.
>
>(I meant dom 9, not dom 7)
>
>>>The numbers I use for interval desirability are completely seat of the
>>>pants; when the program makes a bad choice, often the problem can be
>>>fixed by changing interval desirability in one or more tuning files to
>>>steer the tuning some other way than it was going.
>
>[Paul:]
>>I'm not sure you explained what interval desirability does. Does the
>>program determine which tuning file maximizes the desirability at each
>>moment of the piece, and use that tuning file?
>
>Yes. By summing the weighted "goodness" of all the dyadic intervals,
>much as your dyadic harmonic entropy calculations do.
>
>[Paul:]
>>>And what about your recent development to allow the intervallic
>>>springs to compete with one another in the case of a stack-of-fifths
>>>chord, etc.? Does that do away with tuning files?
>
>Partially; it jumps in ONLY when the previous logic has specified
>12-tET.
>
>[JdL:]
>>>The process starts by assigning a best tuning to each small period of
>>>time with a consistent set of notes.
>
>[Paul:]
>>That sounds like a yes to my question above. But what exactly is a
>>"small period of time"?
>
>A period when there are no notes on or notes off. However, in what I
>consider to be a very important refinement possible only with "leisure"
>retuning, I do create "pseudo-simultaneous events" (PSE's) which for
>the purposes of modelling compress small transition times together,
>times when typically some notes end and others begin.
>
>[Paul:]
>>Now in the tuning file you mention above, I can't see why you would
>>want to have Eb at +16. The tuning file will evidently be applied only
>>in dominant situations, using 4:5:6:7 for a C dominant seventh chord;
>>so shouldn't the Eb be a 7/3 or -33?
>
>Perhaps it should. I haven't thought about that permutation. It's true
>that redundancy in the provision for minor chords is not necessary.
>
>[Paul:]
>>Maybe if we think through this we can figure out a way to eliminate
>>tuning files altogether.
>
>Yes, we might! And, as I've said before, the continuous function
>represented by your harmonic entropy graphs is appealing to me as a
>tool to move toward that goal. The problem is the "traps": the
>question of how to get past local minima that hide better minima nearby.
>My current methods, messy though they are, have a rough-and-ready
>approach for dealing with this challenge, and it may take a fair number
>of new techniques to navigate a consistently better path. Better
>solutions will undoubtedly come in time. It's wide open.
>
>JdL
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 6
> Date: Wed, 18 Oct 2000 20:19:11 EDT
> From: Afmmjr@aol.com
>Subject: Re: Re: thoughts on tuning
>
>In a message dated 10/18/00 6:04:53 PM Eastern Daylight Time,
>jdl@adaptune.com writes:
>
>> And hooray for your efforts! Does the fact that this is your very
>> helpful focus negate other interpretations? Must there be one "winner"
>> rather than a multiplicity of offshoots?
>
>Just as we could use modern genetics to mix just about everything (e.g.,
>tomato with a frog) there are restraints. Moving to far away from nature
>distorts things about the integrity of a phenomenon which we cannot always
be
>prepared for. Sure, anyone can research or create anything. If a composer
>could be specifically tied to a single tuning, then that tuning is the
>"winner" as far as I am concerned.
>
>> [Johnny:]
>> >Granted, we have modern ears (and imaginations, and tolerances), but it
>> >does not negate what the appropriate tuning offers the music. Just as
>> >12-TET music is heard best in 12-TET, so each composer will achieve
>> >something that is inherent in its specific aesthetic.
>>
>> Again the absolute expression. And the word "appropriate". I would
>> much rather hear of "beauty", good or bad.
>
>I am not writing for your rathers. I began this as a stated disagreement.
>Beauty is in the ears of the beholder. "Appropriate" is taken to be the
>specific tuning in a sea of generalities.
>
>
>> [Johnny:]
>> >It is simply too easy for ignorance to light the way.
>>
>> Would you please explain what you mean by this?
>
>Not knowing something is not the same as never knowing. Ignorance of a
>composer's preferred tuning does not give license to willy-nilly use
anything
>you want when you are truly representing a composer's music in concert.
>
>John, I have no difficulty with your view and your expressions (though I
must
>admit I haven't had the opportunity to hear your musical examples...people
>seem to love it.) My only beef is with the necessary honesty of presenting
>composer's as ideally as possible. The concept of "beauty" is only
relative,
>while cultural context is integral to any music, way beyond tuning itself.
>
>Johnny Reinhard
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 7
> Date: Wed, 18 Oct 2000 21:11:35 EDT
> From: AMiltonF@aol.com
>Subject: Re: the sound of a ?distant? horn...
>
>In a message dated 10/18/00 11:20:29 PM !!!First Boot!!!,
>PERLICH@ACADIAN-ASSET.COM writes:
>
>> >if you're going to limit yourself to a fixed tuning in the age of the
>> >integrated circuit then your'e going to be way behind in your tonal
>> >vocabulary when that age gives way to processors that blow the IC away.
>>
>> Assuming that all significant music is going to be computer music -- and
I
>> think we're very far from that time.
>
>Why do you think it's so far off?
>
>> >As for all of you who bag "computer music" your complaints are valid at
>> >this point in time, but what are you going to be saying in 10 years?
>>
>> I might be making a lot of computer music, but I still might believe in
the
>> magic of live performance.
>
>There is only one original "Starry Night" as Van Gogh saw it.
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 8
> Date: Thu, 19 Oct 2000 01:28:32 -0000
> From: "Joseph Pehrson" <josephpehrson@compuserve.com>
>Subject: Webern the microtempoist
>
>--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
>http://www.egroups.com/message/tuning/14615
>
>Congratulations, Joe, on your recent work with the Webern Piano
>Variations... I believe Webern is VERY much "on topic" for this
>list, since we recently were considering rhythmic ratios, and
>rhythmic constructs that were related to just intonation PITCH
>ratios, only just a "tad" slower :)
>
>I was particularly intrigued by your comments concerning Webern's
>relationship to Mahler... something that I had, regrettably, never
>thought about. They certainly were in the same camp.
>
>Hmmm. Well maybe "camp" isn't the right word for it...
>
>It seemed to me too, in Weberns Chamber Concerto of 1934... which I
>actually tried to conduct for a conducting class and messed up, if I
>recall... had VERY arbitrary barlines. The barlines have NOTHING to
>do with the music.
>
>I guess the point was to keep the meter simple... the music was SO
>new at that time that a constantly changing time sig. would "freak
>out" anybody trying to do the works.
>
>However, I think you are right... Webern is after something here that
>is NOT congruent with his bar lines... and your version seems to well
>take this into account!
>
>Oh. By the way... I can't see your music pages in Netscape. I had
>to open my Internet Explorer (Bill Gates would be proud).
>
>I wonder why it works only in Explorer (??)
>
>Anyway, congrats, again and I'm sure we will figure out how Webern
>fits into microtonal tuning discussion. If not, I will personally
>make something up...
>
>Joe
>__________ _____ __ _
>Joseph Pehrson
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 9
> Date: Thu, 19 Oct 2000 01:34:50 -0000
> From: "Joseph Pehrson" <josephpehrson@compuserve.com>
>Subject: Re: the sound of a ?distant? horn...
>
>--- In tuning@egroups.com, AMiltonF@a... wrote:
>
>http://www.egroups.com/message/tuning/14620
>
>Well, I'm not particularly interested in adding to the "flames"
>here... but I do have one comment.
>
>Within the last year I have TOTALLY stopped writing music at the
>piano and am only working at a MIDI keyboard with the computer in
>front of me... so I guess I'm getting affected by this process to
>some
>degree as well...
>__________ ____ __ _ _
>Joseph Pehrson
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 10
> Date: Wed, 18 Oct 2000 21:45:46 EDT
> From: AMiltonF@aol.com
>Subject: Re: Re: the sound of a ?distant? horn...
>
>In a message dated 10/19/00 1:35:45 AM !!!First Boot!!!,
>josephpehrson@compuserve.com writes:
>
>> Within the last year I have TOTALLY stopped writing music at the
>> piano and am only working at a MIDI keyboard with the computer in
>> front of me... so I guess I'm getting affected by this process to
>> some
>> degree as well...
>
>This is exactly what I'm talking about. The old ways are severely
outdated,
>the notation system sucks and we're trying to adapt an adaptation just to
>hear something which was there from the start. What would happen if a
>programmer set out to code a music composition application and just said to
>hell with backward compatability? How would the composition process be
>implemented? What kind of music would be heard?
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 11
> Date: Wed, 18 Oct 2000 18:44:00 -0700
> From: Kraig Grady <kraiggrady@anaphoria.com>
>Subject: Re: the apical BP "Lambda scales"
>
>Dan!
> This shows this same scale as an intersection of the 3-5-7 and the
5-7-9 both which
>generates the same pitches. It shows also that if you wanted to use a
3-5-7-9 diamond the 3
>and the 9 being the same pitch you would end up with triads? how very
uninteresting.
>
>http://www.anaphoria.com/images/BPdia2.gif
>
>Why the golden lambda generates fifth and octaves is strange (if not
suspicious) and I don't
>understand why.
>
>"D.Stearns" wrote:
>
>> Kraig Grady wrote,
>>
>> > I knew this structure was a just a diamond at the 3/1, but it took
>> me till now to figure out how to map it. By the same method one could
>> produce all types of diamonds that repeat at other intervals than the
>> 2/1
>> >
>> > http://www.anaphoria.com/images/BPdiamond.gif
>>
>> Neat. Note the he actually uses an "odd-numbered tetraktys" to
>> essentially do the same thing, see:
>>
>> <http://members.aol.com/bpsite/scales.html#anchor48667>
>>
>> What do you make of the "Golden Lambda scale" with its just octaves
>> and fifths? I thought it was pretty interesting...
>>
>> --d.stearns
>
>-- Kraig Grady
>North American Embassy of Anaphoria island
>www.anaphoria.com
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 12
> Date: Thu, 19 Oct 2000 15:17:01 +1300
> From: "Buddhi Wilcox" <buddhi@paradise.net.nz>
>Subject: just right ? or just not quite
>
>Trying to understand the mathematics of different tunings has been
>difficult for me to follow and appreciate without hearing them.
>To this end I decided to enter an area of my synth's hard drive
>that I had not visited before. I knew that the synth had some
>facility to be able to alter tunings but had no idea why,how, or to what
degree.
>
>As it turns out , it has 18 pre - programmed tunings , which are fully
editable
>(each note is editable up to +/- 9999 cents ! ) . However , it is still
based on a
>12 note octave so it unable to create a 19 note or 31 note octave. It also
has
>facility to create and store as many other tunings as you desire.
>
>Anyway , I would like your learned opinions on the pre-programmed tunings
>as whether they are accurate. I think some of the 18 tunings are
speculations
>with no great musical application , but some entitled JUST , and 1/4
COMMA,
>and WERKMEISTER might be accurate and I would like to know if these
tunings are actually
>true to their names.
>
>If you think that adjustments are needed please let me know.
>
>So here they are. All figures are cents from ET.
>
> C C# D D# E F F# G G# A A#
B
>
>JUST 0 -29 4 16 -14 -2 -10 2 14 -16
-12
>Harmonic 0 5 4 -2 -14 -29 -49 2 41
6 -31 -12
>Werkm. 0 -8 -3 -3 -7
0 -9 -1 -6 -6 -1 -9
>1/4Comma0 -24 7 10 -14 3 -21 -3 14 -18
7 -17
>1/5Comma0 -16 -5 7 -9 2 -14 -2 9 -7
5 -12
>
>There are some others like ARABIC : 0,30,-20,-50,-45,2,23,6,-14,-43,-70,10
>and BALI JAVA : 0,27,-58,-42,-123,-130,-126,-211,24,-61,-57,-142
>and others but I think they are speculations.
>
>If it is easier , or more accessible tuning group protocol that the
>figures are presented in total cents rather than deviation from ET
>then let me knwo and I'll do this. Don't ask me to present them in
>ratios tho ! I'll go mad. (NOTE : If someone wanted to show me how
>to convert one of the above tunings into ratios I would be grateful.
>(As long as it is relatively simple to follow) )
>
>Buddhi
>
>
>
>[This message contained attachments]
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 13
> Date: Wed, 18 Oct 2000 19:34:20 -0700
> From: "M. Edward Borasky" <znmeb@teleport.com>
>Subject: RE: the sound of a ?distant? horn...
>
>> -----Original Message-----
>> From: AMiltonF@aol.com [mailto:AMiltonF@aol.com]
>> Sent: Wednesday, October 18, 2000 4:14 PM
>> To: tuning@egroups.com
>> Subject: Re: [tuning] the sound of a ?distant? horn...
>>
>> The truth of
>> the matter is
>> if you're going to limit yourself to a fixed tuning in the age of the
>> integrated circuit then your'e going to be way behind in your tonal
>> vocabulary when that age gives way to processors that blow the IC
>> away. When
>> the new age dawns it will strip old rules from their foundations
>> and music
>> will have to be explored from the ground up on a composer by
>> composer basis.
>> The only "rule" that will apply will be the one that started it
>> all -- If it
>> sounds good, It is good.
>
>Composers are still writing tonal 12-TET music for conventional
instruments.
>I listen to their music, I don't think it will ever die -- I certainly hope
>it doesn't! I don't happen to write that kind of music because I have
>neither the skill set nor the patience to do so. But I am not willing to
>discard the efforts, talents, and creations of those who do.
>
>> As for all of you who bag "computer music" your complaints
>> are valid at
>> this point in time, but what are you going to be saying in 10
>> years? You're
>> going to be kicking yourself for not learning everything you
>> could have about
>> it. The computer is the most powerful tool on the planet.
>
>I first got interested in computer music in the 1960s when I was an
>undergraduate at the University of Illinois. Both Lejaren Hiller, the first
>person I know of to compose music by an algorithm, and Harry Partch, whose
>memory is revered here, were on the faculty. The first program I ever wrote
>and the first program I got paid to write were written for the same ILLIAC
I
>where Hiller's "ILLIAC Suite" was composed. I still have the programmer's
>manual for ILLIAC I. :-)
>
>That was almost 40 years ago, and "the most powerful tool on the planet"
has
>replaced neither the composer nor the conventional musical instrument in
all
>that time. In that time I have "learned everything I could have about it"
>and make my living in computer science and applied mathematics to this day.
>I am currently getting back into computer music after a long (18 year)
>absence from it. In short, I have no complaints about today's tools;
>computer-synthesized music is my chosen form and I welcome as much help as
>can be obtained from algorithmic composition.
>
>> And for those of you who prefer live performance over "dead"
>> - you should
>> wake up, too. If you're going to achieve higher art, you're
>> going to have to
>> sculpt it just like you heard it. People are going to want to hear it
>> exactly like you did in your head.
>
>Here I have to disagree. Music is a social phenomenon; not all music is
>written by a solitary composer in a room with pen and music paper. A fairly
>large effort by some major talents, for example, Barry Vercoe, is being
>invested in real-time computer music and making the computer an instrument
>that can participate in live performances played by a performer just like a
>clarinet, piano or violin. Will there ever be a "concerto for computer and
>orchestra?" Will there ever be scholarships to prestigious conservatories
>for young computer virtuosi? Maybe ... certainly if a piece of music comes
>along that is *recognized* as good that happens to be for computer and
>orchestra, it could happen.
>
>I don't think there is the widespread discrimination against computer music
>there was in, say, Hiller's day. The simple fact is that, while a quite a
>number of halfway decent computer-only pieces do exist, and some pieces for
>conventional instruments accompanied by computers also exist, *nothing* has
>been written for computer and orchestra that has caught the fancy of a
major
>musical institution, and I'm not holding my breath waiting for a composer
to
>write such a piece. Nor am I attempting to create one myself. It's just too
>big a job for an amateur like me.
>--
>M. Edward Borasky
>mailto:znmeb@teleport.com
>http://www.borasky-research.com
>
>Cold leftover pizza: it's not just for breakfast any more!
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 14
> Date: Wed, 18 Oct 2000 19:35:16 -0700 (PDT)
> From: "M. Schulter" <MSCHULTER@VALUE.NET>
>Subject: Re: Tuning with Phi as interval ratio
>
>Hello, there, this is just a note on a neo-Gothic tuning based on Phi
>as an _interval ratio_, in contrast to various tuning systems such as
>those of Thorwald Kornerup, Keenan Pepper, and Dan Stearns where a
>Phi-based function is applied to logarithmic divisions of the octave,
>or to ratios between logarithmic sizes of intervals (as measured, for
>example, in cents).
>
>This tuning is defined as the regular tuning having Phi as its
>augmented fifth, an interval of ~1.61803398874989484820459:1 or
>approximately 833.090 cents, a kind of "superminor sixth" quite close
>to 34:21 (~834.175 cents).
>
>Since an augmented fifth is made up of precisely four whole-tones --
>and is thus termed a _tetratonus_ by Jacobus of Liege (c. 1325) --
>this gives us a regular major second of ~208.273 cents. From here we
>can determine the rest of the tuning, with a fifth of ~704.136 cents.
>
>Does this look at all familiar? Curiously, Keenan Pepper's "Noble
>Fifth" tuning based on the Phi-based mediant between 4/7-octave and
>3/5-octave (weighted toward the latter) yields a fifth of ~704.096
>cents.
>
>In discussing the "Noble Fifth" temperament, devised as Keenan Pepper
>has emphasized from the viewpoint of a theoretical "noble generator"
>rather than specifically as a neo-Gothic temperament, I noted the very
>close approximation of Phi for the augmented fifth.
>
>Thus these two tunings, derived from Phi in radically different ways,
>curiously are almost identical.
>
>Again, I'd like to emphasize that these distinct methods of using Phi
>should _not_ be confused or equated; here, for whatever reason, they
>happen to produce these similar results.
>
>Most respectfully,
>
>Margo Schulter
>mschulter@value.net
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 15
> Date: Wed, 18 Oct 2000 19:26:42 -0700
> From: Kraig Grady <kraiggrady@anaphoria.com>
>Subject: Re: Re: the sound of a distant acoustic horn...
>
>AMiltonF!
> One of the problems of doing music on a computer is that one will not
develop skills like
>one does on an instrument unless you see typing 80 words a minute a
technique. Waiting for
>computers to catch up and surpass corporeal instruments is like waiting for
the second coming.
>First you have to convince me that electronic music is "improving": do
modern
>synth./computers sound better than old moogs? many would say no and they
are the youngest.
>Electronic music changes and offers more control , but what you have to do
to your brain to
>control more is think about things that are already a given on an acoustic
instrument. More
>choices are not necessarily a good thing. If i go into a market maybe i
really don't want to
>have to decide between 17 type of canned corn. The computer is indeed a
powerful tool but
>power has little to do with poetic statements unless you are the type that
thinks music is
>just the "interaction of formal relations".
>f..k this damn thing......go ahead and worship it . I am turning it off
right now!!!!!!!!
>I have more f..king power than any of these things :-)
>
>AMiltonF@aol.com wrote:
>
>>
>> This is exactly what I'm talking about. The old ways are severely
outdated,
>> the notation system sucks and we're trying to adapt an adaptation just to
>> hear something which was there from the start. What would happen if a
>> programmer set out to code a music composition application and just said
to
>> hell with backward compatability? How would the composition process be
>> implemented? What kind of music would be heard?
>
>-- Kraig Grady
>North American Embassy of Anaphoria island
>www.anaphoria.com
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 16
> Date: Wed, 18 Oct 2000 20:07:26 -0700
> From: "M. Edward Borasky" <znmeb@teleport.com>
>Subject: RE: Re: the sound of a ?distant? horn...
>
>> -----Original Message-----
>> From: AMiltonF@aol.com [mailto:AMiltonF@aol.com]
>> Sent: Wednesday, October 18, 2000 6:46 PM
>> To: tuning@egroups.com
>> Subject: Re: [tuning] Re: the sound of a ?distant? horn...
>>
>>
>> In a message dated 10/19/00 1:35:45 AM !!!First Boot!!!,
>> josephpehrson@compuserve.com writes:
>>
>> > Within the last year I have TOTALLY stopped writing music at the
>> > piano and am only working at a MIDI keyboard with the computer in
>> > front of me... so I guess I'm getting affected by this process to
>> > some
>> > degree as well...
>>
>> This is exactly what I'm talking about. The old ways are
>> severely outdated,
>> the notation system sucks and we're trying to adapt an adaptation just to
>> hear something which was there from the start. What would happen if a
>> programmer set out to code a music composition application and
>> just said to
>> hell with backward compatability? How would the composition process be
>> implemented? What kind of music would be heard?
>
>It would depend on how good the programmer was, what his or her musical
>interests and expertise were, and so on. I have to disagree with you about
>"the old ways". Just intonation, for example, is one of those "old ways"
>that's been around in some form or another since ancient Greece! The
>notation system is nothing more than a communication tool ... without
>agreed-upon tools you don't have "co-mmunication", just "munication". :-)
>
>I've seen some pretty impressive music tools in the past few months that
>I've been getting back into computer music. One that stands out in my
>estimation is Michael Gogin's "Silence", a Java wrapper around CSound that
>is designed for algorithmic composition. "Silence" features an
>11-dimensional musical space. Another is Phil Burk's "JSyn", also written
in
>Java, which is descended from something called HMSL (Hierarchical Music
>Specification Language), another algorithmic composition tool. For
composers
>with a "musique concrete" bent, there is the "Composer's Desktop Project".
>
>I prefer building my own tools, and both "Silence" and "JSyn" require the
>Java 2 Release 1.3 System Development Kit, which unfortunately occupies far
>more disk space than I am willing to give up for the pretty GUIs and the
>pseudo-portability that the current bloated Java offers. I mostly use the
>emerging MPEG-4 Structured Audio standard for synthesis, and for
algorithmic
>work I use either the Derive math package, the Perl scripting language or
>the SwiftForth Windows development environment, depending on the nature of
>the task that needs to be done. The only tools I use that actually cost
real
>money are Derive, SwiftForth and CoolEdit; everything else is freeware
>downloaded from the web.
>
>And what kind of music do I write with these tools? Well ... the past few
>weeks I have mostly been experimenting with John deLaubenfels' retuned MIDI
>files, getting them to play with a piano emulation "instrument" from the
>MPEG-4 Structured Audio examples. My next project is something I call the
>"Setharophone" ... a computer sound generator that uses additive synthesis
>and can actually compute the Sethares dissonance score as it plays. Once I
>get that built, I'll be posting some sounds on my web site.
>--
>M. Edward Borasky
>mailto:znmeb@teleport.com
>http://www.borasky-research.com
>
>Cold leftover pizza: it's not just for breakfast any more!
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 17
> Date: Wed, 18 Oct 2000 20:32:45 -0700
> From: "M. Edward Borasky" <znmeb@teleport.com>
>Subject: RE: Re: the sound of a distant acoustic horn...
>
>
>> -----Original Message-----
>> From: Kraig Grady [mailto:kraiggrady@anaphoria.com]
>> Sent: Wednesday, October 18, 2000 7:27 PM
>> To: tuning@egroups.com
>> Subject: Re: [tuning] Re: the sound of a distant acoustic horn...
>>
>>
>> AMiltonF!
>> One of the problems of doing music on a computer is that one
>> will not develop skills like
>> one does on an instrument unless you see typing 80 words a
>> minute a technique. Waiting for
>> computers to catch up and surpass corporeal instruments is like
>> waiting for the second coming.
>> First you have to convince me that electronic music is
>> "improving": do modern
>> synth./computers sound better than old moogs? many would say no
>> and they are the youngest.
>> Electronic music changes and offers more control , but what you
>> have to do to your brain to
>> control more is think about things that are already a given on an
>> acoustic instrument. More
>> choices are not necessarily a good thing. If i go into a market
>> maybe i really don't want to
>> have to decide between 17 type of canned corn. The computer is
>> indeed a powerful tool but
>> power has little to do with poetic statements unless you are the
>> type that thinks music is
>> just the "interaction of formal relations".
>> f..k this damn thing......go ahead and worship it . I am turning
>> it off right now!!!!!!!!
>> I have more f..king power than any of these things :-)
>
>Thanks, Kraig!! I knew there was something I liked about you besides your
>music. :-) Seriously, though, I am totally incompetent as a performer on
>conventional instruments. Even when I was younger and practiced an hour or
>so a day, I was never competitive as a flute player, although I enjoyed
>playing in the band and playing jazz. It's been over ten years since I even
>tried to play the thing; about the only performing I do these days is
>karaoke, at least until the smoke in the karaoke bar gets to me and I have
>to leave. If I am to make music at all, I need a computer. :-)
>
>And you're right about most computer music not sounding appreciably better
>than the old Moogs. I can tell you why that is. The paradigm used in
>computer music programs is a lot like the paradigm of the Moog --
>oscillators, filters, noise generators, buses, reverb units and so on. To
>some extent, that is a necessary simplification to make computer music
>accessible at all to musicians ... the underlying mathematics of
>sampled-data systems and the mechanics of generating the sound samples are
>decidedly non-trivial and something like a "patch panel" is required to
>facilitate understanding.
>
>As I said earlier, I have been studying computer music for nearly 40 years,
>and I prefer to build my own tools. And I think a "music theory" for
>computer music *will* emerge; I've seen hints of it in Michael Gogins'
>"Silence", in the work on algorithmic composition since "ILLIAC Suite" and
>in the Audio Groups work at MIT that led to the MPEG-4 Structured Audio
>standard. But that's just me; I won't expect you to make computer music and
>hope that no one will expect me to learn to play the Diamond Marimba :-).
>--
>M. Edward Borasky
>mailto:znmeb@teleport.com
>http://www.borasky-research.com
>
>Cold leftover pizza: it's not just for breakfast any more!
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 18
> Date: Thu, 19 Oct 2000 04:03:02 -0000
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
>Subject: Re: thoughts on tuning
>
>--- In tuning@egroups.com, Afmmjr@a... wrote:
>
>> John, I have no difficulty with your view and your expressions
>(though I must
>> admit I haven't had the opportunity to hear your musical
>examples...people
>> seem to love it.) My only beef is with the necessary honesty of
>presenting
>> composer's as ideally as possible. The concept of "beauty" is only
>relative,
>> while cultural context is integral to any music, way beyond tuning
>itself.
>
>Johnny, I do wish you would listen to John's examples. I personally
>worked pretty hard to
>get John to listen to and accomodate my views about what is and is
>not appropriate for
>various composers. Although we have just begun along this path, I
>truly believe that
>many of the examples John has produced are both faithful to the
>composer's intentions,
>and ideal in terms of the tradeoff of harmonic and melodic
>considerations. Think of it as
>the way a wind, brass, or string ensemble would perform the piece if
>they had
>superhuman pitch control and sensitivity to prior and future events
>in the score.
>
>The idea of adaptive tuning goes back to Vicentino in 1555, who
>proposed the two chains
>of 1/4-comma meantone tuning a pure fifth (or equivalently, a pure
>minor third, or 1/4
>comma) apart. This proposal would never compromise the melodic
>integrity of the chain
>of identical (in this case, meantone) fifths by more than a
>melodically inaudible interval,
>1/4-comma, while attaining perfect vertical JI in all triads. To me,
>this amounts to audibly
>"perfect" tuning within the Renaissance theoretical ideal (as
>expressed by, say, Zarlino),
>and much of the subsequent repertoire well into the 18th century --
>until enharmonic
>equivalents began to be used. Though Vicentino's two-keyboard
>implementation was not
>practical at the time, with computers (or, perhaps, AFMM performers),
>we can acheive
>his goals, and even surpass him in cases where his proposal runs into
>difficulties.
>
>I would add a belated comment to John deLaubenfels -- in cases where
>a late 15th
>through early 18th century piece has more than 12 notated pitches,
>his program still
>leaves something to be desired relative to Vicentino's method -- as,
>if I recall correctly,
>he touched upon when considering 13-pitch schemes (John, what exactly
>did you look at
>as regards 13 notated pitches -- is it obsolete now)?
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 19
> Date: Thu, 19 Oct 2000 04:06:02 -0000
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
>Subject: Re: the sound of a ?distant? horn...
>
>--- In tuning@egroups.com, AMiltonF@a... wrote:
>
>> > Assuming that all significant music is going to be computer
>music -- and I
>> > think we're very far from that time.
>>
>> Why do you think it's so far off?
>
>Because there's still a lot of instrumental performance that's worth
>doing, and I can't
>imagine that changing before dramatic changes in our civilization
>take place.
>>
>> > >As for all of you who bag "computer music" your complaints are
>valid at
>> > >this point in time, but what are you going to be saying in 10
>years?
>> >
>> > I might be making a lot of computer music, but I still might
>believe in the
>> > magic of live performance.
>>
>> There is only one original "Starry Night" as Van Gogh saw it.
>
>I see live improv groups (such as the Fringe here in Cambridge, MA)
>regularly create new
>Van Goghs every time they play.
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 20
> Date: Thu, 19 Oct 2000 04:08:17 -0000
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
>Subject: Re: the sound of a ?distant? horn...
>
>--- In tuning@egroups.com, "Joseph Pehrson" <josephpehrson@c...>
>wrote:
>> --- In tuning@egroups.com, AMiltonF@a... wrote:
>>
>> http://www.egroups.com/message/tuning/14620
>>
>> Well, I'm not particularly interested in adding to the "flames"
>> here... but I do have one comment.
>>
>> Within the last year I have TOTALLY stopped writing music at the
>> piano and am only working at a MIDI keyboard with the computer in
>> front of me... so I guess I'm getting affected by this process to
>> some
>> degree as well...
>
>But working at a MIDI keyboard the way you do, you're still
>restricted to 12 pitches out of
>the infinity at a time, right?
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 21
> Date: Thu, 19 Oct 2000 04:15:00 -0000
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
>Subject: Re: just right ? or just not quite
>
>--- In tuning@egroups.com, "Buddhi Wilcox" <buddhi@p...> wrote:
>
>> As it turns out , it has 18 pre - programmed tunings , which are
>fully editable
>> (each note is editable up to +/- 9999 cents ! ) . However , it is
>still based on a
>> 12 note octave so it unable to create a 19 note or 31 note octave.
>
>With 9999 cents to play with, you can easily create a 19 or 31 note
>octave.
>
>> Anyway , I would like your learned opinions on the pre-programmed
>tunings
>> as whether they are accurate.
>
>I'll look at this tomorrow, if someone doesn't beat me to it. Which
>synth are you using?
>
>> don't ask me to present them in ratios, tho
>
>Only the Just and Harmonic (and Pythagorean, if you have that)
>tunings would be
>expressible as ratios. I'll explain how if you like.
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 22
> Date: Thu, 19 Oct 2000 04:22:19 -0000
> From: "Paul Erlich" <PERLICH@ACADIAN-ASSET.COM>
>Subject: Re: the sound of a ?distant? horn...
>
>--- In tuning@egroups.com, "M. Edward Borasky" <znmeb@t...> wrote:
>
>> My next project is something I call the
>> "Setharophone" ... a computer sound generator that uses additive
>synthesis
>> and can actually compute the Sethares dissonance score as it plays.
>
>How do you compute Sethares dissonance? In my latest discussions with
>Bill Sethares,
>he started off saying that the "amplitudes" in his formulas are not
>meant to be
>amplitudes at all but should be volumes in decibels, and then he
>ended up retracting
>that and seemed to suggest that psychoacoustic loudness was the right
>measure to plug
>in. I haven't heard from him for weeks (Bill?)
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 23
> Date: Wed, 18 Oct 2000 21:47:11 -0700
> From: David C Keenan <D.KEENAN@UQ.NET.AU>
>Subject: One eikosany donut please
>
>Hey folks, I just understood the structure of the eikosany (and CPS in
>general) for the first time (pathetic I know). What an awesome thing. Major
>kudos to Erv Wilson.
>
>I have to say that neither Monz's dictionary entries nor Kraig's web pages
>did it for me, although they helped. It was Paul Erlich's simple
>explanation that made it click. My how easily something so simple in
>concept (but not in conception) can be obscured.
>
>The hard part for me was that I was looking for how one generates _ratios_
>for the pitches. But in fact one doesn't. One simply generates _integers_.
>And (in general) no note corresponds to 1. Of course these integers can
>become ratios by scaling them all by the same amount or by scaling them to
>the same octave.
>
>I couldn't help thinking, hey this eikosany thing is at least 4
>dimensional, assuming products of 3 at a time from {1,3,5,7,9,11}) so it
>sure suffers when mapped to 2 dimensions, whether in Wilson's
>10-star-inside-a-10-gon diagram or his bosanquet-style keyboard mapping.
>
>I want it mapped to the surface of a donut. One just large enough to get my
>fingers inside, with 20 buttons distributed over the surface. To see how to
>map it, just take the standard 10-star-inside-a-10-gon diagram and raise
>every second note of the star above the page while lowering the others. the
>outer decagon can get a bit zig-zaggy too.
>
>You can build this approximately in zometool but it's too big (with 10 long
>reds in the middle, 10 medium yellows around the outside and 10 short reds
>joining them).
>
>I would limit it to 20 notes, but not to one octave (about 2.5 octaves) as
>follows. Simply take products of 3 at a time from {4,5,6,7,9,11} and don't
>reduce them to the same octave. The "scale" would have no octave but it
>would be a brilliant toy to let people hear the maximum number of different
>types of 11-limit consonance with the fewest notes (?), even if it was just
>some cheesy battery operated thing that only did sawtooth waves with no
>dynamics.
>
>I've also looked at microtempering it (distributing the 224:225 and
>384:385). By my rough count this would add about 17 additional dyads to the
>already 96 (?). This may complete some pentads. Eikosanies are normally
>limited to tetrads (for complete pairwise consonance).
>
>This microtempering would avoid phase-locking and would only introduce
> 1.1 c errors in the 2:3's,
>max 3.2 c errors in ratios of 5,
>max 2.4 c errors in ratios of 7,
>max 2.1 c errors in ratios of 9,
>max 1.6 c errors in ratios of 11.
>
>Regards,
>
>-- Dave Keenan
>http://dkeenan.com
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 24
> Date: Wed, 18 Oct 2000 21:58:44 -0700
> From: "M. Edward Borasky" <znmeb@teleport.com>
>Subject: RE: Re: the sound of a ?distant? horn...
>
>> -----Original Message-----
>> From: Paul Erlich [mailto:PERLICH@ACADIAN-ASSET.COM]
>> Sent: Wednesday, October 18, 2000 9:22 PM
>> To: tuning@egroups.com
>> Subject: [tuning] Re: the sound of a ?distant? horn...
>>
>>
>> --- In tuning@egroups.com, "M. Edward Borasky" <znmeb@t...> wrote:
>>
>> > My next project is something I call the
>> > "Setharophone" ... a computer sound generator that uses additive
>> synthesis
>> > and can actually compute the Sethares dissonance score as it plays.
>>
>> How do you compute Sethares dissonance? In my latest discussions with
>> Bill Sethares,
>> he started off saying that the "amplitudes" in his formulas are not
>> meant to be
>> amplitudes at all but should be volumes in decibels, and then he
>> ended up retracting
>> that and seemed to suggest that psychoacoustic loudness was the right
>> measure to plug
>> in. I haven't heard from him for weeks (Bill?)
>
>Well, my plan was to use the formulas from the book. I think what's
>important is the location of the sharp mimima, not the amplitudes /
volumes.
>Actually, I think it makes more sense to display consonance peaks rather
>than dissonance mimima. In any event, I've got to do some math to get the
>computational complexity down. The consonance or dissonance calculations
>will be done at the "control rate", which is typically on the order of once
>every 1 to 10 milliseconds, so efficiency is important.
>--
>M. Edward Borasky
>mailto:znmeb@teleport.com
>http://www.borasky-research.com
>
>Cold leftover pizza: it's not just for breakfast any more!
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 25
> Date: Wed, 18 Oct 2000 22:24:51 -0700
> From: Kraig Grady <kraiggrady@anaphoria.com>
>Subject: Re: One eikosany donut please
>
>
>
>David C Keenan wrote:
>
>> I couldn't help thinking, hey this eikosany thing is at least 4
>> dimensional, assuming products of 3 at a time from {1,3,5,7,9,11}) so it
>> sure suffers when mapped to 2 dimensions, whether in Wilson's
>> 10-star-inside-a-10-gon diagram or his bosanquet-style keyboard mapping.
>
>Erv stated that it was 12 dimensional In that it should look like a donut
from 12 different
>directions
>
>> I would limit it to 20 notes, but not to one octave (about 2.5 octaves)
as
>> follows. Simply take products of 3 at a time from {4,5,6,7,9,11} and
don't
>> reduce them to the same octave. The "scale" would have no octave but it
>> would be a brilliant toy to let people hear the maximum number of
different
>> types of 11-limit consonance with the fewest notes (?), even if it was
just
>> some cheesy battery operated thing that only did sawtooth waves with no
>> dynamics.
>
>I used to have an instrument called the tree that used the 10 tone cycle as
the pattern to
>hang bars that I made. I explored quite a few lattices of this type. the
article in Xen XI
>(which ! should put up) shows another application of this type of spacing.
>
> http://www.anaphoria.com/images/xenXI-15.gif
>
>Here the idea was to place the entire 1-3-5-7-9-11 CPS (36 notes) on a 31
tone keyboard. On
>examination you have one note in one octave with the other possibility in
the other. Such a
>technique can be used in other ways to great advantage. here the tuning
spans 2 octaves and a
>"large whole tone"
>
>> I've also looked at microtempering it (distributing the 224:225 and
>> 384:385). By my rough count this would add about 17 additional dyads to
the
>> already 96 (?). This may complete some pentads. Eikosanies are normally
>> limited to tetrads (for complete pairwise consonance).
>
>Such things are possible and might seem advantageous, but as some one who
has used this tuning
>extensively, you would be undermining what the tuning does. Every tetrad
has a unique
>relationship to the whole and each pair of hexanies, in fact every scale
has a strongly
>defined relationship to the whole that becomes musically meaningful.
Inversions are always
>found at the most dissonant points, now if you get rid of these dissonance
you have undermined
>the meaning.
>
>> This microtempering would avoid phase-locking and would only introduce
>> 1.1 c errors in the 2:3's,
>> max 3.2 c errors in ratios of 5,
>> max 2.4 c errors in ratios of 7,
>> max 2.1 c errors in ratios of 9,
>> max 1.6 c errors in ratios of 11.
>>
>> Regards,
>>
>> -- Dave Keenan
>> http://dkeenan.com
>
>-- Kraig Grady
>North American Embassy of Anaphoria island
>www.anaphoria.com
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>
>
>

just right ? or just not quite

🔗Buddhi Wilcox <buddhi@paradise.net.nz>

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Robert Walker <robert_walker@rcwalker.freeserve.co.uk>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Buddhi Wilcox <buddhi@paradise.net.nz>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>