Tuning Assitance?

Hello,

Since pretty much everything that can be tried has been tried by members of this list I am looking for advice.

When I looked at this Ron Sword BP guitar video Mike B. sent me
http://www.youtube.com/watch?v=lfC1zRLte_s
it occurred to me that a normal 13 notes per tritave Bohlen-Pierce guitar just didn't have enough notes for me.

The obvious thing to do is to double up BP and do 26 notes per tritave. No doubt someone here has tried that - and I'm wondering if the result was good - and if a better alternative exists.

Thanks,

Chris

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

> The obvious thing to do is to double up BP and do 26 notes per tritave. No doubt someone here has tried that - and I'm wondering if the result was good - and if a better alternative exists.

I've got a better idea: be the first person to use bohpier temperament. It's got a 25 note MOS which should do just fine, and someone needs to take the pioneering role.

Bohpier temperament is not a nonoctave tuning, but it is very closely related to Bohlen-Pierce, and in fact includes it as a generator chain.
You can use 5/41 as the generator. The wedgie is <<13 19 23 0 0 0|| and the mapping pair [<1 0 0 0|, <0 13 19 23|]. In terms of steps of 41, the 25 note MOS goes 3113113113113113113113111, and the Bohlen-Pierce scale is in there.

Hi Gene,

I'm a novice at this still.

Would this be the correct tuning scheme for your suggestion?

0: 1/1 C B unison, perfect prime
1: 76.078 cents
2: 152.156 cents C#\ D\
3: 228.235 cents D
4: 304.313 cents
5: 380.391 cents D#\ E\
6: 456.469 cents F E
7: 532.547 cents F) Gb)
8: 608.626 cents F#\ G\
9: 684.704 cents F#( G(
10: 760.782 cents G) Ab)
11: 836.860 cents
12: 912.938 cents G#( A(
13: 989.017 cents
14: 1065.095 cents A/ Cb/
15: 1141.173 cents A#( C(
16: 1217.251 cents C B
17: 1293.329 cents C/ Db/
18: 1369.408 cents
19: 1445.486 cents D
20: 1521.564 cents D/ Eb/
21: 1597.642 cents D#\ E\
22: 1673.720 cents F E
23: 1749.799 cents
24: 1825.877 cents F#\ G\
25: 3/1 perfect 12th

On Thu, Jun 10, 2010 at 2:21 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, "christopherv"
> <chrisvaisvil@...> wrote:
>
> > The obvious thing to do is to double up BP and do 26 notes per tritave.
> No doubt someone here has tried that - and I'm wondering if the result was
> good - and if a better alternative exists.
>
> I've got a better idea: be the first person to use bohpier temperament.
> It's got a 25 note MOS which should do just fine, and someone needs to take
> the pioneering role.
>
> Bohpier temperament is not a nonoctave tuning, but it is very closely
> related to Bohlen-Pierce, and in fact includes it as a generator chain.
> You can use 5/41 as the generator. The wedgie is <<13 19 23 0 0 0|| and the
> mapping pair [<1 0 0 0|, <0 13 19 23|]. In terms of steps of 41, the 25 note
> MOS goes 3113113113113113113113111, and the Bohlen-Pierce scale is in there.
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Gene,
>
> I'm a novice at this still.
>
> Would this be the correct tuning scheme for your suggestion?

Nope, sorry. Here you go:

! bohpier25.scl
Bohpier[25] in 41-et tuning
25
!
87.804878048780487805
117.07317073170731707
146.34146341463414634
234.14634146341463415
263.41463414634146341
292.68292682926829268
380.48780487804878049
409.75609756097560976
439.02439024390243902
526.82926829268292683
556.09756097560975610
585.36585365853658537
673.17073170731707317
702.43902439024390244
731.70731707317073171
819.51219512195121951
848.78048780487804878
878.04878048780487805
965.85365853658536585
995.12195121951219512
1024.3902439024390244
1112.1951219512195122
1141.4634146341463415
1170.7317073170731707
1200.0000000000000000

Once again, thank you Gene!

It is on the list for tonight with the Roland GR-20

On Thu, Jun 10, 2010 at 3:36 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > Hi Gene,
> >
> > I'm a novice at this still.
> >
> > Would this be the correct tuning scheme for your suggestion?
>
> Nope, sorry. Here you go:
>
> ! bohpier25.scl
> Bohpier[25] in 41-et tuning
> 25
> !
> 87.804878048780487805
> 117.07317073170731707
> 146.34146341463414634
> 234.14634146341463415
> 263.41463414634146341
> 292.68292682926829268
> 380.48780487804878049
> 409.75609756097560976
> 439.02439024390243902
> 526.82926829268292683
> 556.09756097560975610
> 585.36585365853658537
> 673.17073170731707317
> 702.43902439024390244
> 731.70731707317073171
> 819.51219512195121951
> 848.78048780487804878
> 878.04878048780487805
> 965.85365853658536585
> 995.12195121951219512
> 1024.3902439024390244
> 1112.1951219512195122
> 1141.4634146341463415
> 1170.7317073170731707
> 1200.0000000000000000
>
>
>

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

> The obvious thing to do is to double up BP and do 26 notes per tritave. No doubt someone here has tried that - and I'm wondering if the result was good - and if a better alternative exists.
>
> Thanks,
>
> Chris

A "triple BP" has been suggested by Paul Erlich, and used by Ron himself. Roughly, one step of it is 48.77¢ (calculated off of a 1:3 of 1902¢ because I'm lazy), dividing the tritave into 39 equal parts. However, the "triple BP" lets one get around the "point" of BP as it can function in a variety of different "modalities". Double BP has not been much spoken of...at around 73.15¢ a step, it's close to both 16-EDO and 17-EDO at first but gets pretty far from either of them very quickly. I think it could be great, and doesn't allow one to "cheat" on the basic premise of BP so easily.

But the thing with BP is that, because it's meant to treat the tritave as an octave, it sort of NEEDS to have wide steps, elsewise you'll end up with scales that have a huge number of steps. My feeling is that if you're gonna buy into BP, you should buy the whole package: 3:5:7 and 5:7:9 as the primary consonances, 3:1 as the "repeat period", and really "stretched-out" scales. If you can't get down with those principles, why do BP at all? There are other non-octave systems out there that would probably suit you better, like the Wendy Carlos Alpha or Beta scales, 88-cent Equal Temperament, 5th root of 7/5 (116.502-cent Equal Temperament)...or, geez, just go here:

http://www.nonoctave.com/tuning/twelfth.html

Click links in the sidebar to see other equal divisions of rational intervals.

The question you've really gotta ask yourself is, "what do I want in a tuning"? I'm surprised that first you were talking about 17, 19, and 22, and now suddenly you're looking at BP. BP has pretty much nothing in common with any of those...no fifths, no octaves, no hope of compatibility with common-practice music. Any sort of BP would be a rough place to start, I would think, unless you were really into the principle behind it.

For the record, the temperament Gene suggested will be more difficult than an equal temperament to apply to a guitar. You *can* do it with straight, unbroken frets, but they will be unequally spaced and some frets on some strings will produce out-of-scale notes (or else there will be notes in the scale that don't appear in some positions on some strings). There may also be frets uncomfortably close together in some places, depending on how you want to tune the open strings. I'd only recommend it if you were really in love with the temperament, otherwise you may end up with a guitar you don't play because it requires too much "work". The problem with unequally-spaced frets is that every time you retune an open string, you change the "gamut" of notes available to you, and unless you tune in a "drone" tuning (i.e. something like DGDGGD), you'll have a hard time making a mental map of which notes are where on the fretboard.

That's what happened to me with the Catler 12-tone Ultra Plus, which adds JI frets in between 12-tET frets. I loved it to fool around with, and it sounded good, but it was too difficult to approach "systematically" and I lost interest in it very quickly. I got sick of being unable to play full scales on it, and having to wrack my brain to keep track of what JI chords were available to me in a given open-string tuning. I'm not trying to discourage you from using a linear temperament/subset of a high-numbered EDO, I'm just trying to make you aware of the difficulties they pose on guitar.

-Igs

>
> But the thing with BP is that, because it's meant to treat the tritave as an octave, it sort of NEEDS to have wide steps, elsewise you'll end up with scales that have a huge number of steps. My feeling is that if you're gonna buy into BP, you should buy the whole package: 3:5:7 and 5:7:9 as the primary consonances, 3:1 as the "repeat period", and really "stretched-out" scales. If you can't get down with those principles, why do BP at all? There are other non-octave systems out there that would probably suit you better, like the Wendy Carlos Alpha or Beta scales, 88-cent Equal Temperament, 5th root of 7/5 (116.502-cent Equal Temperament)...

But why would you think I could not still play those chords in BP with
a 26 / tritave guitar? I realize you talk a lot about scales - but
think of how you play in 12 - 12 chromatic notes are just the
framework - one can make subsets any which way. I intend to do the
same with my micro guitar. This is where I really disagree with
Michael S' idea - I want / need freedom. Sort of like Kirk telling
Sybok he needs his pain to be a whole person - so does a tuning. The
interesting stuff, for me, is at the edge of chaos. But I do agree
for me there is a limit to how many notes I can keep track of - which
I think I mentioned already. 26 is acceptable only because the tritave
is that much bigger.

"For the record, the temperament Gene suggested will be more difficult
than an equal temperament to apply to a guitar. You *can* do it with
straight, unbroken frets, but they will be unequally spaced and some
frets on some strings will produce out-of-scale notes "

first let me try it on my Roland GR-20. If I don't like how it sounds
all other points are moot.

or, geez, just go here:
>
> http://www.nonoctave.com/tuning/twelfth.html
>

My brain melted on first sight....

As for what do I want in a tuning - I haven't decided entirely yet -
except not something 12-ish. Perhaps not totally non-12 ish but
certainly Xen.

Honestly I see no conflict with looking all of these choices. I have
no preconceived notions and I'm doing this simply on musical merits
alone. Perhaps its the bliss of my ignorance of tuning theory? To me
each tuning will have its good and bad points. No way around that.
They are all just *different* - just like people, and for that matter,
composers :-)

I got my hands on some weed whacker filament. I start pulling frets tomorrow.

Thank you for your long and considered reply.

Chris

When viewing 13 equal divisions of the tritave as a tuning generated from a tempered 7:5 with a period of 3:1, the most similarly functioning scales are going to be 16-edt and 23-edt. They also will approximate the locations of consonance for odd harmonic spectra, unlike 26-edt which just fills in notes between those locations.

Think of it like comparing 12-edo to 31-, 17-, and 24-edo. 31- and 17-edo can function like 12-edo, whereas 24-edo, though at first intuitively similar, turns out to be functionally unrelated.

A little further away from 13-edt would be 10-edt and 19-edt, if you are feeling adventurous ;-)

John M

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> But why would you think I could not still play those chords in BP with
> a 26 / tritave guitar? I realize you talk a lot about scales - but
> think of how you play in 12 - 12 chromatic notes are just the
> framework - one can make subsets any which way. I intend to do the
> same with my micro guitar. This is where I really disagree with
> Michael S' idea - I want / need freedom. Sort of like Kirk telling
> Sybok he needs his pain to be a whole person - so does a tuning. The
> interesting stuff, for me, is at the edge of chaos. But I do agree
> for me there is a limit to how many notes I can keep track of - which
> I think I mentioned already. 26 is acceptable only because the tritave
> is that much bigger.

Oh, I really didn't mean to sound dismissive of the idea of a double BP. I just wasn't sure if you still actually *wanted* to do regular BP too. If you do want access to regular BP but more "tonal flexibility", then certainly a double-BP guitar might be worth your while. But if you're not interested in the regular BP approach, that's when I'd suggest checking out other tunings.

> My brain melted on first sight....

Yeah, it's a lot to take in. But it's a useful table for comparing, you can see all the cents-values for all the intervals in all these divisions right on top of each other, so you can see "well, THIS one has a decent fifth but no major third, THAT one has a near 8/7 major second...etc. etc."

> As for what do I want in a tuning - I haven't decided entirely yet -
> except not something 12-ish. Perhaps not totally non-12 ish but
> certainly Xen.
>
> Honestly I see no conflict with looking all of these choices. I have
> no preconceived notions and I'm doing this simply on musical merits
> alone. Perhaps its the bliss of my ignorance of tuning theory? To me
> each tuning will have its good and bad points. No way around that.
> They are all just *different* - just like people, and for that matter,
> composers :-)

Oh, there's no conflict at all, believe me, I'm as much of a "pantheist" as anyone here, maybe even more than some! I definitely espouse a "more is better" philosophy when it comes to microtunings, hence why I've damn near bankrupted myself with all these microtonal guitars (I've had guitars in every EDO from 15 to 22 except 19 and 21, so that also covers 5, 8, 9, 10, and 11, and I've also had a 31-tone and a Catler JI guitar, so I dare say I may have played guitar in more equal temperaments than anyone on this list!) I'm just used to people having really strong impressions of what they will accept or not. Usually the crowd that likes 22-EDO and 19-EDO isn't keen on BP, so I was just (pleasantly) surprised to see that you actually ARE open to tunings with no fifth or octave! Everything has its place. Trying to narrow it down to ONE is terribly difficult. For me, it took several tries to find the right direction, but I didn't have the luxury of a retunable guitar synth! Explore 'em all, man!

But for what it's worth, weren't YOU just lecturing ME about the necessity of theory awhile back?

-Igs

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> When viewing 13 equal divisions of the tritave as a tuning generated from a tempered 7:5 with a period of 3:1, the most similarly functioning scales are going to be 16-edt and 23-edt. They also will approximate the locations of consonance for odd harmonic spectra, unlike 26-edt which just fills in notes between those locations.
>

Actually, I don't see 16-ED3 and 23-ED3 looking that similar: they both have a good 5:7, but neither has a good 3:5, 5:9, or 7:9, making BP-like triads impossible.

OTOH, 22-ED3 looks passable, triad-wise. The 5:9 is a bit mistuned, but it's clearly relatable. Then 30-ED3 does a fine job, nearly as good 13-ED3, and has a step size of around 63 cents...wait, it's practically friggin' 19-ED2! Whoa, now that I think about it, you COULD totally use 19-EDO as a way to approximate BP...holy crap!! Someone inform the Internet!!!

-Igs

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> When viewing 13 equal divisions of the tritave as a tuning generated from > a tempered 7:5 with a period of 3:1,

If I'm not mistaken, both Bohlen and Pierce suggested a 9_tone "BP diatonic" like SLSLSSLSL or LSLSSLSLS, which implies tempering out 245/243 and therefore using a generator which approximates 9/7 by itself and two of them approximate 5/3. This way, you get the highest number of target 1:3:5:7 approximations compared to any other generator used with a period of 3/1.

Petr

Between the lines

On Fri, Jun 11, 2010 at 3:36 AM, cityoftheasleep
<igliashon@...> wrote:
>

> Oh, I really didn't mean to sound dismissive of the idea of a double BP. I just wasn't sure if you still actually *wanted* to do regular BP too. If you do want access to regular BP but more "tonal flexibility", then certainly a double-BP guitar might be worth your while. But if you're not interested in the regular BP approach, that's when I'd suggest checking out other tunings.

The idea of 19 edo and 13 edt being fairly sets of each other is an
interesting idea. Since I'm going flexible right now, and that is
going to mean gluing pieces of weed whacker line to the fret board at
the moment, its not super critical what I choose because I can change
it. One aspect of this I'm curious to know is how it will change my
perspective when I have real micro fretting verses the remapping of a
12 edo guitar.

>
> > My brain melted on first sight....
>
> Yeah, it's a lot to take in. But it's a useful table for comparing, you can see all the cents-values for all the intervals in all these divisions right on top of each other, so you can see "well, THIS one has a decent fifth but no major third, THAT one has a near 8/7 major second...etc. etc."

I don't think I'm to the point of choosing intervals that consciously

> > They are all just *different* - just like people, and for that matter,
> > composers :-)
>
Oh, there's no conflict at all, believe me, I'm as much of a
"pantheist" as anyone here, maybe even more than some! For me, it took
several tries to find the right direction, but I didn't have the
luxury of a retunable guitar synth! Explore 'em all, man!

You may want to consider a Roland GR-20 then. @$700 new, $500 used -
how many guitars is that worth?

>
> But for what it's worth, weren't YOU just lecturing ME about the necessity of theory awhile back?

Nope, I didn't say it was necessary, I said it is inescapable. And I'm
not *trying* to ignore tuning theory - I'm just ignorant of it. At the
same time I am trying to learn tuning theory. Thus I'm reading Doty's
JI Primer and everything on the net I can find. However, when you
started to toss out terms like MOS frankly I drew a blank. You see,
you have learned quite a bit of tuning theory and terms like Moment of
Symmetry has an innate meaning to you. It means means nothing to me.
Every field has its terminology that one needs to learn - essentially
another language. Chemistry, geology, music theory, medicine... etc.
etc.

Chris

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> The idea of 19 edo and 13 edt being fairly sets of each other is an
> interesting idea. Since I'm going flexible right now, and that is
> going to mean gluing pieces of weed whacker line to the fret board at
> the moment, its not super critical what I choose because I can change
> it. One aspect of this I'm curious to know is how it will change my
> perspective when I have real micro fretting verses the remapping of a
> 12 edo guitar.

True that.

> You may want to consider a Roland GR-20 then. @$700 new, $500 used -
> how many guitars is that worth?

Honestly, the thought never occurred to me that I could retune a GR-20 until you did it! Wish I had that idea five or six years ago, woulda saved me a ton. But I've got it narrowed down to a few favorites now, so my explorations are probably done for a while.

> Nope, I didn't say it was necessary, I said it is inescapable. And I'm
> not *trying* to ignore tuning theory - I'm just ignorant of it. At the
> same time I am trying to learn tuning theory. Thus I'm reading Doty's
> JI Primer and everything on the net I can find. However, when you
> started to toss out terms like MOS frankly I drew a blank. You see,
> you have learned quite a bit of tuning theory and terms like Moment of
> Symmetry has an innate meaning to you. It means means nothing to me.
> Every field has its terminology that one needs to learn - essentially
> another language. Chemistry, geology, music theory, medicine... etc.
> etc.

Ah, well, let me clarify: "moment of symmetry" is a concept of scale construction. The circle of fifths is a prime example of the moment of symmetry concept. Basically: pick any two intervals, one to be a "generator" and another to be a "period". You can make scales by adding the generators together in a series, and subtracting the period any time the sum of generators surpasses it. A "moment of symmetry" is a point wherein you have exactly two sizes of intervals between the consecutive notes in your scale. Think of the circle of fifths in 12-tET: when you have one fifth, F-C-F, you have your first MOS, a two-note scale of Large step--small step (Ls), where L = a fifth and s = a fourth. Add another fifth, G, and you have F-G-C-F. This is the next MOS, a scale of sLL, where s = a whole tone and L = a perfect fourth. Add another fifth, D, giving F-G-C-D-F: NOT a moment of symmetry, because there are three step sizes: a whole tone (F-G, C-D), a fourth (G-C), and a minor third (D-F). Basically, with an interval of a fifth of 12-tET and a period of an octave, you get moments of symmetry at 2, 3, 5, and 7 notes, hitting an "equal" scale at 12 notes.

Not all scales with only two step-sizes are MOS scales: consider the "melodic minor" in 12-tET of LsLLLLs: this scale cannot be produced by a series of fifths, or of any generator (to my knowledge); it is, rather, a permutation of the diatonic MOS scale. Similarly, Paul Erlich's "Pentachordal" scales in 22-EDO/Pajara are not MOS scales, but his "Symmetrical" scales are; the Pentachordal scales are permutations of the Symmetrical scales (his paper on "Tuning, Tonality, and Twenty-Two Tone Temperament" is a great read if you can gloss over the more abstract concepts in the beginning).

MOS scales are important because they serve to "unify" sets of equal temperaments. Just as 12, 17, 19, 22, 26, 27, 29, and 31-EDO have a diatonic scale (because they all have pretty good "fifths", which is the generator for the diatonic scale), other sets of EDOs have other scales in common (even as their harmonic properties may differ). Finding MOS scales that you like can help you evaluate various temperaments, and give some indication of a temperament's musical utility (especially when coupled with an assessment of its harmonic properties). This is why I like 23-EDO: it's got several of my favorite MOS scales, more so than any other equal temperament. Sadly, it's also a tad too many notes for my liking; I prefer one instrument for each of my favorite scales, really. But if I had to have only ONE microtonal instrument, it'd be in 23. But I'd never have known that about 23 if I'd only looked at it from a harmonic standpoint.

Hope that helps!

-Igs

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> However, when you
> started to toss out terms like MOS frankly I drew a blank. You see,
> you have learned quite a bit of tuning theory and terms like Moment of
> Symmetry has an innate meaning to you. It means means nothing to me.

It means the same as well-formed scale. :)

If that doesn't work as a definition, look at this:

http://xenharmonic.wikispaces.com/MOSScales

Thanks Gene!

By the way I tried that Bohpier 25 last night but it was a difficult tuning
to get a good handle on - and the fact that my roland gr-20 and fractal tune
smithy was fighting last night didn't help. I gave up at 1 am with nothing
to show. I will try it again.

I got the relay working fine again - and will be posting a BP piece in a
few.

Chris

On Fri, Jun 11, 2010 at 2:01 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
>
> > However, when you
> > started to toss out terms like MOS frankly I drew a blank. You see,
> > you have learned quite a bit of tuning theory and terms like Moment of
> > Symmetry has an innate meaning to you. It means means nothing to me.
>
> It means the same as well-formed scale. :)
>
> If that doesn't work as a definition, look at this:
>
> http://xenharmonic.wikispaces.com/MOSScales
>
>
>

On 11 June 2010 13:27, Petr Parízek <p.parizek@...> wrote:

> If I'm not mistaken, both Bohlen and Pierce suggested a 9_tone "BP diatonic"
> like SLSLSSLSL or LSLSSLSLS, which implies tempering out 245/243 and
> therefore using a generator which approximates 9/7 by itself and two of them
> approximate 5/3. This way, you get the highest number of target 1:3:5:7
> approximations compared to any other generator used with a period of 3/1.

http://x31eq.com/cgi-bin/rt.cgi?ets=9+13&limit=3.5.7

A real standout 3.5.7 temperament.

Graham

Graham wrote:

> http://x31eq.com/cgi-bin/rt.cgi?ets=9+13&limit=3.5.7

Couldn't say it better myself. :-)

Petr

great... but I don't understand this notation at all.

On Sat, Jun 12, 2010 at 2:38 AM, Graham Breed <gbreed@...> wrote:
>
>
>
> On 11 June 2010 13:27, Petr Parízek <p.parizek@...> wrote:
>

>
> http://x31eq.com/cgi-bin/rt.cgi?ets=9+13&limit=3.5.7
>
> A real standout 3.5.7 temperament.
>
> Graham
>

Chris wrote:

> great... but I don't understand this notation at all.

You mean, you don't understand the notation used on the webpage which appears after clicking the link Graham suggested? I think it's enough to understand at least a half of it to know how the temperament in question works. I don't get all of that either but, even though, I now know all three of us meant the same temperament.

There are the step approximations of the three target primes (3, 5, 7) in the two ETs (i.e. 9 and 13 equal divisions of 3/1, respectively);
then there's the period&generator mapping of the three primes in the 2D temperament which we've been discussing here (and which is the same in the two ETs mentioned above and therefore can be understood as a combination of them).
Then there are suggested interval sizes for the period and the generator.
And then there are a couple of other things listed which may help someone in understanding how much "mistuning" there is or in deciding how large a scale he/she wants to make out of this ... But the "core" is there on the top.

Petr

Let me put it another way.

Is there any resource that explains explicitly on how to take
information from the link Graham provided and convert to a scala file
I can use?

The vector-ish notation is not clear to me - and I really need a place
to go to refresh my memory each time I wish to translate to a form I
can use.

Eventually repetition would give me understanding - but I'm not there yet.

Thanks,

Chris

On Sat, Jun 12, 2010 at 12:22 PM, Petr Parízek <p.parizek@...> wrote:
>
>
>
> Chris wrote:
>
> > great... but I don't understand this notation at all.
>
> You mean, you don't understand the notation used on the webpage which
> appears after clicking the link Graham suggested? I think it's enough to
> understand at least a half of it to know how the temperament in question
> works. I don't get all of that either but, even though, I now know all three
> of us meant the same temperament.
>
> There are the step approximations of the three target primes (3, 5, 7) in
> the two ETs (i.e. 9 and 13 equal divisions of 3/1, respectively);
> then there's the period&generator mapping of the three primes in the 2D
> temperament which we've been discussing here (and which is the same in the
> two ETs mentioned above and therefore can be understood as a combination of
> them).
> Then there are suggested interval sizes for the period and the generator.
> And then there are a couple of other things listed which may help someone in
> understanding how much "mistuning" there is or in deciding how large a scale
> he/she wants to make out of this ... But the "core" is there on the top.
>
> Petr
>
>

Me, too, if it's any comfort.

Caleb

On Jun 12, 2010, at 12:44 PM, Chris Vaisvil wrote:

> Let me put it another way.
>
> Is there any resource that explains explicitly on how to take
> information from the link Graham provided and convert to a scala file
> I can use?
>
> The vector-ish notation is not clear to me - and I really need a place
> to go to refresh my memory each time I wish to translate to a form I
> can use.
>
> Eventually repetition would give me understanding - but I'm not there yet.
>
> Thanks,
>
> Chris
>
> On Sat, Jun 12, 2010 at 12:22 PM, Petr Parízek <p.parizek@chello.cz> wrote:
>>
>>
>>
>> Chris wrote:
>>
>>> great... but I don't understand this notation at all.
>>
>> You mean, you don't understand the notation used on the webpage which
>> appears after clicking the link Graham suggested? I think it's enough to
>> understand at least a half of it to know how the temperament in question
>> works. I don't get all of that either but, even though, I now know all three
>> of us meant the same temperament.
>>
>> There are the step approximations of the three target primes (3, 5, 7) in
>> the two ETs (i.e. 9 and 13 equal divisions of 3/1, respectively);
>> then there's the period&generator mapping of the three primes in the 2D
>> temperament which we've been discussing here (and which is the same in the
>> two ETs mentioned above and therefore can be understood as a combination of
>> them).
>> Then there are suggested interval sizes for the period and the generator.
>> And then there are a couple of other things listed which may help someone in
>> understanding how much "mistuning" there is or in deciding how large a scale
>> he/she wants to make out of this ... But the "core" is there on the top.
>>
>> Petr
>>
>>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@...m - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>

--- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:
>
> Graham wrote:
>
> > http://x31eq.com/cgi-bin/rt.cgi?ets=9+13&limit=3.5.7
>
> Couldn't say it better myself. :-)
>
> Petr

Graham, might I convince you to make the URLs more like this:

http://x31eq.com/temper/regular/
and
http://x31eq.com/temper/regular/rt.cgi?ets=9.13&limit=3.5.7

instead of like this:

http://x31eq.com/temper/pregular.html
and
http://x31eq.com/cgi-bin/rt.cgi?ets=9+13&limit=3.5.7

?

-Carl

Chris wrote:

> Is there any resource that explains explicitly on how to take
> information from the link Graham provided and convert to a scala file
> I can use?

#1. I'm not sure if something like this would be directly possible. For example, if you choose to make an octave-periodic temperament where 81/80 vanishes, the only information this gives you is the fact that 1 generator approximates 3/2 and 4 generators approximate 5/1 (or you may use fourths instead of fifths if you prefer). But whether you eventually make a 7-tone diatonic scale out of this (i.e. a chain of 6 generators) or a 12-tone chromatic scale (11 generators) or a 19-tone enharmonic scale (18 generators), it's completely up to you.

#2. People like Graham and Herman have been writing lots of pretty understandable articles/theses about this topic on the web and others, like Gene or Paul E., have contributed to the classification and introduction of many completely new temperaments within a systematic and logical "framework". The chance to examine the available materials is not hidden to you, anyone of us can do it -- so why should you still be deprived of knowing what things like "semisixths" or "tetracot" mean?

Petr

--- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
>
> Me, too, if it's any comfort.

I could write a Xenwiki article. Do you need anything beyond instructions as to how to convert it into a Scala scl file(s)?

Hi Petr,

With all due respect I'm here mostly as a composer, not someone who
wishes to make new tunings.
Given limited time I simply can't digest everything out there - given
my main interest is not tuning creation this means I can't read most
everything on tuning.

I can understand that in your field (of tuning creation) specialized
notation makes life much easier - chemistry has the same thing.
However, if you wish for these tunings to be actually used by people
beyond the tuning specialist there is a need for ways to make these
inventions accessible.

Chris

On Sat, Jun 12, 2010 at 1:19 PM, Petr Parízek <p.parizek@...> wrote:
> Chris wrote:
>
>> Is there any resource that explains explicitly on how to take
>> information from the link Graham provided and convert to a scala file
>> I can use?
>
>
> #2. People like Graham and Herman have been writing lots of pretty
> understandable articles/theses about this topic on the web and others, like
> Gene or Paul E., have contributed to the classification and introduction of
> many completely new temperaments within a systematic and logical
> "framework". The chance to examine the available materials is not hidden to
> you, anyone of us can do it -- so why should you still be deprived of
> knowing what things like "semisixths" or "tetracot" mean?
>
> Petr

For my part no,

And that would be wonderful Gene!!

Chris

On Sat, Jun 12, 2010 at 1:38 PM, genewardsmith
<genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
> >
> > Me, too, if it's any comfort.
>
> I could write a Xenwiki article. Do you need anything beyond instructions as to how to convert it into a Scala scl file(s)?
>

I wrote:

> #2. People like Graham and Herman have been writing lots of pretty > understandable articles/theses about this topic on the web and others, > like Gene or Paul E., have contributed to the classification and > introduction of many completely new temperaments within a systematic and > logical "framework". The chance to examine the available materials is not > hidden to you,

IOW, as long as you don't get the idea, you can hardly be "musically inventive" with it. I know what I'm saying, I've experienced it myself. There are chord progressions which I would never *ever* have thought of if I hadn't understood other 2D tunings than Pythagorean or meantone. These are chord progressions which are absolutely impossible to convert to standard notation -- not that one particular chord couldn't be notated, but rather that the first and last chord sound the same in the particular temperament but not in meantone and therefore would end up higher or lower in the notation. It's like trying to play "C major, A minor, D minor, G major, C major" in hanson, for example -- it's the opposite, the first and last chord sound different but are notated the same because our notation is meantone-based.

Or, yet another view ... If I offered you 34-EDO without giving you any suggestions, what would you do with it?

Petr

Chris wrote:

> With all due respect I'm here mostly as a composer, not someone who
> wishes to make new tunings.

My goodness, Chris, you've completely misunderstood my point. It's not about tuning creation at all, it's about compositional inventiveness.
As I've said earlier (if my last message manages to get through), there are lots of chord progressions which I would never ever have thought of, if I hadn't understood the proper "meaning" of other 2D tunings than Pythagorean or meantone. Now I'm happy that I could have used them in my music because I've discovered a completely new harmonic "dimmension" that way. And, I dare to say, you probably won't start thinking of them either -- until you break this "barrier". BTW: This is one of the topics discussed in the RTF document which I stored in the Tuning Files folder some months ago.

In case my last message gets stuck somewhere, I'm asking once again: If I offered you 34-EDO without giving you any suggestions, what would you do with it?

Petr

Hi Petr,

Are you talking to me?

If so, then I would add 34 edo to my tuning survey, of course.

So far I have been working mostly by ear. Over time I imagine I will
start to grasp the issues you discuss below.
However, asking me to wait until I grasp all of the subtleties of
tuning theory is a bit... unrealistic.

Chris

On Sat, Jun 12, 2010 at 1:41 PM, Petr Parízek <p.parizek@...> wrote:
> I wrote:
>
>> #2. People like Graham and Herman have been writing lots of pretty
>> understandable articles/theses about this topic on the web and others,
>> like Gene or Paul E., have contributed to the classification and
>> introduction of many completely new temperaments within a systematic and
>> logical "framework". The chance to examine the available materials is not
>> hidden to you,
>
> IOW, as long as you don't get the idea, you can hardly be "musically
> inventive" with it. I know what I'm saying, I've experienced it myself.
> There are chord progressions which I would never *ever* have thought of if I
> hadn't understood other 2D tunings than Pythagorean or meantone. These are
> chord progressions which are absolutely impossible to convert to standard
> notation -- not that one particular chord couldn't be notated, but rather
> that the first and last chord sound the same in the particular temperament
> but not in meantone and therefore would end up higher or lower in the
> notation. It's like trying to play "C major, A minor, D minor, G major, C
> major" in hanson, for example -- it's the opposite, the first and last chord
> sound different but are notated the same because our notation is
> meantone-based.
>
> Or, yet another view ... If I offered you 34-EDO without giving you any
> suggestions, what would you do with it?
>
> Petr
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
>  tuning-subscribe@yahoogroups.com - join the tuning group.
>  tuning-unsubscribe@yahoogroups.com - leave the group.
>  tuning-nomail@yahoogroups.com - turn off mail from the group.
>  tuning-digest@yahoogroups.com - set group to send daily digests.
>  tuning-normal@yahoogroups.com - set group to send individual emails.
>  tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

I'm with Chris all the way here.

One 'gets the idea' by a combination of playing by ear and concrete examples.

I'll go back to lurking. I give up.

Too bad, community is hard to find.

Good luck to all.

Caleb

On Jun 12, 2010, at 2:07 PM, Chris Vaisvil wrote:

> Hi Petr,
>
> Are you talking to me?
>
> If so, then I would add 34 edo to my tuning survey, of course.
>
> So far I have been working mostly by ear. Over time I imagine I will
> start to grasp the issues you discuss below.
> However, asking me to wait until I grasp all of the subtleties of
> tuning theory is a bit... unrealistic.
>
> Chris
>
> On Sat, Jun 12, 2010 at 1:41 PM, Petr Parízek <p.parizek@...> wrote:
> > I wrote:
> >
> >> #2. People like Graham and Herman have been writing lots of pretty
> >> understandable articles/theses about this topic on the web and others,
> >> like Gene or Paul E., have contributed to the classification and
> >> introduction of many completely new temperaments within a systematic and
> >> logical "framework". The chance to examine the available materials is not
> >> hidden to you,
> >
> > IOW, as long as you don't get the idea, you can hardly be "musically
> > inventive" with it. I know what I'm saying, I've experienced it myself.
> > There are chord progressions which I would never *ever* have thought of if I
> > hadn't understood other 2D tunings than Pythagorean or meantone. These are
> > chord progressions which are absolutely impossible to convert to standard
> > notation -- not that one particular chord couldn't be notated, but rather
> > that the first and last chord sound the same in the particular temperament
> > but not in meantone and therefore would end up higher or lower in the
> > notation. It's like trying to play "C major, A minor, D minor, G major, C
> > major" in hanson, for example -- it's the opposite, the first and last chord
> > sound different but are notated the same because our notation is
> > meantone-based.
> >
> > Or, yet another view ... If I offered you 34-EDO without giving you any
> > suggestions, what would you do with it?
> >
> > Petr
> >
> >
> >
> >
> > ------------------------------------
> >
> > You can configure your subscription by sending an empty email to one
> > of these addresses (from the address at which you receive the list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> >
> >
> >
> >
>

Hi Caleb -

Don't bail!

Gene is writing up a article for implementing the tuning notation and
Petr is quite a nice guy.

I believe Petr is saying that greater understanding gives you more
options - which is how I look at conventional music theory.

Chris

On Sat, Jun 12, 2010 at 2:13 PM, caleb morgan <calebmrgn@...> wrote:
>
>
>
> I'm with Chris all the way here.
> One 'gets the idea' by a combination of playing by ear and concrete examples.
> I'll go back to lurking.  I give up.
> Too bad, community is hard to find.
> Good luck to all.
> Caleb
>
>
>
> On Jun 12, 2010, at 2:07 PM, Chris Vaisvil wrote:
>
>
>
> Hi Petr,
>
> Are you talking to me?
>
> If so, then I would add 34 edo to my tuning survey, of course.
>
> So far I have been working mostly by ear. Over time I imagine I will
> start to grasp the issues you discuss below.
> However, asking me to wait until I grasp all of the subtleties of
> tuning theory is a bit... unrealistic.
>
> Chris
>
> On Sat, Jun 12, 2010 at 1:41 PM, Petr Parízek <p.parizek@...> wrote:
> > I wrote:
> >
> >> #2. People like Graham and Herman have been writing lots of pretty
> >> understandable articles/theses about this topic on the web and others,
> >> like Gene or Paul E., have contributed to the classification and
> >> introduction of many completely new temperaments within a systematic and
> >> logical "framework". The chance to examine the available materials is not
> >> hidden to you,
> >
> > IOW, as long as you don't get the idea, you can hardly be "musically
> > inventive" with it. I know what I'm saying, I've experienced it myself.
> > There are chord progressions which I would never *ever* have thought of if I
> > hadn't understood other 2D tunings than Pythagorean or meantone. These are
> > chord progressions which are absolutely impossible to convert to standard
> > notation -- not that one particular chord couldn't be notated, but rather
> > that the first and last chord sound the same in the particular temperament
> > but not in meantone and therefore would end up higher or lower in the
> > notation. It's like trying to play "C major, A minor, D minor, G major, C
> > major" in hanson, for example -- it's the opposite, the first and last chord
> > sound different but are notated the same because our notation is
> > meantone-based.
> >
> > Or, yet another view ... If I offered you 34-EDO without giving you any
> > suggestions, what would you do with it?
> >
> > Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> IOW, as long as you don't get the idea, you can hardly be
> "musically inventive" with it.

In another universe, somebody could survey scales and blow
right by 12-ET, if they weren't careful. In this universe, we
certainly wound up with 12-ET through a long process of
evolution and understanding. You can't throw out 1,000 years
of music theory and expect to breeze by on unicorn farts.

That said, there's certainly a balance, and the potential for
collaboration between folks who do more of one or the other.
And a need to make regular mapping more accessible.

-Carl

Carl,

Can you expand on what you mean by this?

In another universe, somebody could survey scales and blow
right by 12-ET, if they weren't careful. In this universe, we
certainly wound up with 12-ET through a long process of
evolution and understanding. You can't throw out 1,000 years
of music theory and expect to breeze by on unicorn farts.

Thanks,

Chris

On Sat, Jun 12, 2010 at 2:33 PM, Carl Lumma <carl@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
> >
> > IOW, as long as you don't get the idea, you can hardly be
> > "musically inventive" with it.
>
> In another universe, somebody could survey scales and blow
> right by 12-ET, if they weren't careful. In this universe, we
> certainly wound up with 12-ET through a long process of
> evolution and understanding. You can't throw out 1,000 years
> of music theory and expect to breeze by on unicorn farts.
>
> That said, there's certainly a balance, and the potential for
> collaboration between folks who do more of one or the other.
> And a need to make regular mapping more accessible.
>
> -Carl
>
>

Chris wrote:

> However, asking me to wait until I grasp all of the subtleties of
> tuning theory is a bit... unrealistic.

Here we weren't talking about "grasping all of it" but rather about understanding one particular idea, namely what "period&generator mapping" means. It's not difficult to get this and it's also very useful to understand for the sake of compositional possibilities, so I think it's worth it.

In meantone, for example, the period is the octave (since the scale steps repeat after spanning one octave) and the generator is a tempered fifth or fourth (some people prefer fourths as generators but that's another story, let's go with fifths). So 2/1 is one octave, 3/1 is approximated by one octave and a fifth, and 5/1 is approximated by 4 fifths. So if the first number of every pair means the number of periods and the second number means the number of generators needed for one particular approximation, then it's "1, 0" for 2/1, "1, 1" for 3/1, and "0, 4" for 5/1.
Obviously, if you used fourths as generators instead of fifths, the mapping would then be different. That's why it's always necessary to know not only the period&generator mapping but also the size (either in cents or as a ratio) of the period and the generator.

In contrast, in hanson, for example, the generator is a slightly wider minor third. So 2/1 is represented by one octave, 3/1 is represented by 6 "wider minor thirds", and 5/1 is represented by 5 minor thirds + one octave. So the mapping for hanson is "1, 0" for 2/1, "0, 6" for 3/1, and "1, 5" for 5/1.

For some reason, many people prefer listing the mapping vertically -- i.e. you have to read one particular column, not one line, to know the mapping for one particular interval.

That's it. :-)

Petr

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> For my part no,
>
> And that would be wonderful Gene!!

Thinking about such an article, it seems to me it would depend too heavily on what kind of language you had to program in. A far better solution would be a pair of online gadgets, and so I hope someone with asperations to be helpful by creating such a thing will do it. What's need are two things:

(1) Something which takes a generator and an interval of equivalence, both given in cents, and the number of scale steps, and returns a Scala scl file.

(2) Not really necessary but nice to have: something which takes a generator and period, given in cents, and returns the number of notes in corresponding MOS up to some limit.

Any volunteers?

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

> Any volunteers?

By the way, you may be asking why I want volunteers instead of explaining how to do it from within Scala. The answer is, I can't figure out how to get Scala to do this sort of thing. If someone does know, I would be interested to learn myself.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Carl,
>
> Can you expand on what you mean by this?

I'll let Petr speak for me. -Carl

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > Any volunteers?
>
> By the way, you may be asking why I want volunteers instead of
> explaining how to do it from within Scala. The answer is, I can't
> figure out how to get Scala to do this sort of thing. If someone
> does know, I would be interested to learn myself.

Graham gives optimal generators:
http://x31eq.com/cgi-bin/rt.cgi?ets=9+13&limit=3.5.7

Those can be plugged into Scala with the "lineartemp" command.
What more do you want?

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> With all due respect I'm here mostly as a composer, not someone who
> wishes to make new tunings.
> Given limited time I simply can't digest everything out there - given
> my main interest is not tuning creation this means I can't read most
> everything on tuning.

But you are a composer who wants to TRY new tunings. In actuality, tunings are not made, they are "found", since they are all based on mathematics which is universal and transcendent and perhaps even absolute. To "find" tunings, it helps to know where to look, what you're looking for, and HOW to look.

Like you, I tend to shy away from anything that suggest I have to learn and/or do math BEFORE I can make music. I am a musician, not a mathematician, and I resent being "seduced" into math for the purpose of making music. That said, the alternative tuning universe is vast and densely-populated. To set out to explore it without a map is dangerous, for you risk getting totally lost and never finding that for which you are seeking.

Now, there are a LOT of maps out there, and none of them really cover all of the terrain. The "regular mapping paradigm" (i.e. the one that produces the largest array of indecipherable specialist notation and esoteric jargon) is the most comprehensive map yet made, because it unifies JI theory with equal and unequal temperaments. It also unifies the idea of harmonies as JI-approximations with the melodic structure of moment-of-symmetry scales, allowing one to look at a given scale and know both its harmonic properties AND its melodic properties (assuming one has a good idea of what generators produce which shape of MOS scales). This paradigm even gives an "access point" for working with unmanageably-dense EDOs, like 271-EDO or 840-EDO, because you can break them down to smaller subsets which have the unified structure of familiar temperament classes. I.e. you could "manage" 55-EDO by treating it as "meantone" and using a 12-note meantone subset of it.

Basically, if you know how a given linear temperament class works (like meantone), and you know the generator "range" for that class (i.e. a fifth sharper than that of 7-EDO but flatter than that of 12-EDO), you can be sure any equal temperament that produces a generator *in that range* will function *as that linear temperament*, at least to a certain degree of accuracy. This effectively reduces the vast infinitude of equal temperaments to a manageable number of temperament classes, effectively reducing the amount of learning and exploration one must do to find "the good stuff".

Now, this paradigm has several flaws: one, it's got a steep learning curve, until someone can find a way to explain it (and its notation and jargon) in a concise and systematic way. Two, it's more cumbersome than necessary for people who have a narrowly-defined field of interest in the alternate-tuning universe (i.e. me, who is interested fairly exclusively in EDOs <36). Three, it's totally useless for other areas (non-Western historical/traditional tunings, strict JI, and scales based on irrational intervals not meant to approximate JI). Four, the distinction between two temperament classes is not always all that musically significant.

Aaand...five (this one deserves its own paragraph): the boundaries between temperament classes aren't always clear or well-defined (and in fact, the paradigm does not seem to offer any good tools for determining these boundaries). You can't always tell what the "mapping" will be from the generator, because two generators very close in size might produce different mappings (viz 350¢ and 355¢: the former is Mohajira, the latter Beatles). Also, there exist scales (many scales, in fact), which are at the "boundary" between two temperaments. 7-EDO, for instance, is both Meantone AND Mavila, in that prime 5 (the major third) maps both to 4 generators AND 13 generators. Likewise, 12-EDO is both Meantone and Superpyth. In fact--though I don't have a proof of this--any EDO can be seen as a "boundary" between two "related" temperaments.

The upshot of this is that if you extend the "regular mapping paradigm" to an arbitrarily-high level of exactitude in mapping primes, you have to divide a given temperament-class into an infinite amount of subclasses, as at some point the difference in size between two very similar generators will cause a deviation in the mapping of some prime, thus splitting the temperament class. The "classes" are only valid if you arbitrarily set a "limit" to the primes you wish to approximate (AND to the acceptable level of error for the approximation...22-EDO can be said to map prime 5 to 4 generators (and thus be a meantone) IF you can accept an error of 50¢ in the mapping). Thus "linear temperament classes" are essentially arbitrary, and not absolute, so there is room for debate on whether two similar temperaments are in fact distinct or not (like "Beatles" and "Mohajira" or "Bug" and "Beep", etc. etc.).

Bottom line is this: the "regular mapping" paradigm is powerful but also limited, and before deciding whether to learn it or dismiss it, it's good to know what its strengths and weaknesses are. I hope I've done an acceptable job of characterizing them here.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > > Any volunteers?
> >
> > By the way, you may be asking why I want volunteers instead of
> > explaining how to do it from within Scala. The answer is, I can't
> > figure out how to get Scala to do this sort of thing. If someone
> > does know, I would be interested to learn myself.
>
> Graham gives optimal generators:
> http://x31eq.com/cgi-bin/rt.cgi?ets=9+13&limit=3.5.7
>
> Those can be plugged into Scala with the "lineartemp" command.
> What more do you want?

I want to plug in a generator and an interval of repetition (not necessarily period) and number of steps, and have it give forth a Scala scl file.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> What more do you want?

Never mind, I see I can get it to do what's needed.

I'll look at scala

Hopefully I can figure it out with Petr's explanation.

Chris

On Sat, Jun 12, 2010 at 6:08 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, "Carl Lumma"
> <carl@...> wrote:
>
> > What more do you want?
>
> Never mind, I see I can get it to do what's needed.
>
>
>

Igs,

The issue was about getting help to interpret a tuning representation
into something I could use.

I actually want to *avoid* picking tunings by intervals and instead
pick them by my interpretation of musical merit for right now. What
good is it to say "neutral third" if I have no sound to correspond? My
method is to gather a collection of tunings I find inspiring and then
go back and analyze why I like them.

The other issue at hand was Petr's suggestion that I needed a deeper
understanding to use a tuning to its fullest. That is a valid point of
view.

Since I am reading Doty and the material available on the web I will
eventually grasp the meaning of the terminology enough to get a better
understanding of what is being discussed by the esteemed tune smiths
on this list and elsewhere.

Chris

On Sat, Jun 12, 2010 at 6:00 PM, cityoftheasleep
<igliashon@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> > With all due respect I'm here mostly as a composer, not someone who
> > wishes to make new tunings.
> > Given limited time I simply can't digest everything out there - given
> > my main interest is not tuning creation this means I can't read most
> > everything on tuning.
>
> But you are a composer who wants to TRY new tunings. In actuality, tunings are not made, they are "found", since they are all based on mathematics which is universal and transcendent and perhaps even absolute. To "find" tunings, it helps to know where to look, what you're looking for, and HOW to look.
>

On 13 June 2010 04:25, Chris Vaisvil <chrisvaisvil@...> wrote:

> The issue was about getting help to interpret a tuning representation
> into something I could use.

Carl explained how to do that with Scala. Is the issue resolved?

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Carl explained how to do that with Scala. Is the issue resolved?

One thing that's missing is that people may not know what the
MOS are. Surprisingly, it doesn't look like Scala does this.
Perhaps you could add it to your output.

By the way, did you change the text so both period and generator
are called generators now?

-Carl

On 13 June 2010 10:13, Carl Lumma <carl@...> wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>>
>> Carl explained how to do that with Scala.  Is the issue resolved?
>
> One thing that's missing is that people may not know what the
> MOS are.  Surprisingly, it doesn't look like Scala does this.
> Perhaps you could add it to your output.

There are two example equal temperaments.

What I could do is change the output to actually produce Scala files.
And I fully intend to do that, although I won't give a deadline.

> By the way, did you change the text so both period and generator
> are called generators now?

I think it's always been like that with this code. The template for
rank 2 temperaments is the same as for higher ranks. I'm not sure
that I ever released a version that was different. The code behind it
does special-case rank 2, though. The generator mapping is chosen to
give a generator between a unison and a period. For higher ranks it's
arbitrary, following the way I reduce the mappings, which may be
Hermite reduction.

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >
> > Carl explained how to do that with Scala. Is the issue resolved?
>
> One thing that's missing is that people may not know what the
> MOS are. Surprisingly, it doesn't look like Scala does this.
> Perhaps you could add it to your output.

You can use "convergents" from the drop-down menu under Tools, but it would take another article on Xenwiki to explain how to use it.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> What I could do is change the output to actually produce Scala files.
> And I fully intend to do that, although I won't give a deadline.

If you do that, it would be great if you allow the user to specify the size of the interval of equivalence.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> > >
> > > Carl explained how to do that with Scala. Is the issue resolved?
> >
> > One thing that's missing is that people may not know what the
> > MOS are. Surprisingly, it doesn't look like Scala does this.
> > Perhaps you could add it to your output.
>
> You can use "convergents" from the drop-down menu under Tools, but it would take another article on Xenwiki to explain how to use it.

Or you can use "lineartemps /wellformed" to get either a MOS or an equal temperament.

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

> Or you can use "lineartemps /wellformed" to get either a MOS or
> an equal temperament.

Wellfound! It seems that could be a sentence on the xenwiki page.

-Carl

> Actually, I don't see 16-ED3 and 23-ED3 looking that similar: they both have a good 5:7, but neither has a good 3:5, 5:9, or 7:9, making BP-like triads impossible.

26-edo can function diatonically, as can 22-edo, even though both exist far from ideal locations in the syntonic temperament for approximating just ratios like 3/2, 5/4, and 6/5. The point is that they can all support the same MOS scales like pentatonic (SSLSL), diatonic(LLSLLLLS), and so on, with harmonies of recognizable JI function.

That's the same way I'm relating 16-edt and 23-edt to 13-edt. They are most similar equal divisions (from a generator size perspective) that can function with the same MOS scales one might use in 13-edo with an approximate 7:5 generator while retaining recognizable JI functions, even if their consonance is not well approximated.

For example, 13-edt, 23-edt, and 16-edt can all host a 7 note MOS scale SLSLSLS and a ten note MOS scale LSSSLSSSLS, both of which function very similarly among the tunings, at least IMO.

Still speaking nonsense?

John M

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> > One thing that's missing is that people may not know what the
> > MOS are. Surprisingly, it doesn't look like Scala does this.
> > Perhaps you could add it to your output.
>
> There are two example equal temperaments.
>
> What I could do is change the output to actually produce
> Scala files. And I fully intend to do that, although I won't
> give a deadline.

That would be awesome, but even then, they'll want to see
the first several terms of the MOS series and then pick a
number of notes/octave. So the MOS readout would seem to be
a stepping stone.

-Carl

Hi Gene,

I'd guess you did not care for the improvisation I came up with. Is
there possibly something with the tuning I overlooked that you want me
to try or is it a moot issue?

Thanks,

Chris

On Thu, Jun 10, 2010 at 2:21 PM, genewardsmith
<genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>
> > The obvious thing to do is to double up BP and do 26 notes per tritave. No doubt someone here has tried that - and I'm wondering if the result was good - and if a better alternative exists.
>
> I've got a better idea: be the first person to use bohpier temperament. It's got a 25 note MOS which should do just fine, and someone needs to take the pioneering role.
>
> Bohpier temperament is not a nonoctave tuning, but it is very closely related to Bohlen-Pierce, and in fact includes it as a generator chain.
> You can use 5/41 as the generator. The wedgie is <<13 19 23 0 0 0|| and the mapping pair [<1 0 0 0|, <0 13 19 23|]. In terms of steps of 41, the 25 note MOS goes 3113113113113113113113111, and the Bohlen-Pierce scale is in there.
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Gene,
>
> I'd guess you did not care for the improvisation I came up with. Is
> there possibly something with the tuning I overlooked that you want me
> to try or is it a moot issue?

Sorry, Chris, I didn't know you wanted a comment. It certainly showed bohpier was capable of sounding xenharmonic, and that people looking for something exotic don't need to eschew octaves to get there. But really, the most interesting comments would be yours: how did the temperament finally shake out, in your view? Can it reasonably be suggested to people interested in Bohlen-Pierce as something to try? Why did you get such a xenharmonic sound--was it your choice, or did the temperament itself lead you there?

1. To play on guitar each string was "tuned" about half an octave from its
neighbor. Probably with a guitar fretted to this tuning this would not be as
big of an issue.

2. The chords I play are pretty much the most consonant sounding ones I
could find - not saying there are not more. Probably this tuning as a
chromatic set of pitches would be difficult on a "normal" keyboard.

3. I'm not sure I saw the relationship to 13 note BP. But then I'm not a BP
expert.

4. I will probably try it again.

Chris

On Fri, Jun 18, 2010 at 2:29 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > Hi Gene,
> >
> > I'd guess you did not care for the improvisation I came up with. Is
> > there possibly something with the tuning I overlooked that you want me
> > to try or is it a moot issue?
>
> Sorry, Chris, I didn't know you wanted a comment. It certainly showed
> bohpier was capable of sounding xenharmonic, and that people looking for
> something exotic don't need to eschew octaves to get there. But really, the
> most interesting comments would be yours: how did the temperament finally
> shake out, in your view? Can it reasonably be suggested to people interested
> in Bohlen-Pierce as something to try? Why did you get such a xenharmonic
> sound--was it your choice, or did the temperament itself lead you there?
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

> 2. The chords I play are pretty much the most consonant sounding ones I
> could find - not saying there are not more. Probably this tuning as a
> chromatic set of pitches would be difficult on a "normal" keyboard.

One of the things I like about your versions is that they bring out the differences between temperaments. I tend to iron them out.

Thanks - the differences is why I like microtonal music.

I feel the need to change direction a bit.
The playability of the fretless guitar is such a huge surprise I want
to explore that more in the near term.
And I'm kind of burnt out on Ethno.

However, this tuning, "normal" BP, 17, 22, and 24 edo  are my primary
(not only) targets right now. Along with finishing Doty's book.

Chris

On Fri, Jun 18, 2010 at 8:02 PM, genewardsmith
<genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > 2. The chords I play are pretty much the most consonant sounding ones I
> > could find - not saying there are not more. Probably this tuning as a
> > chromatic set of pitches would be difficult on a "normal" keyboard.
>
> One of the things I like about your versions is that they bring out the differences between temperaments. I tend to iron them out.
>

By the way.

If you want me to try a tuning I'm always up for that.

Chris

On Fri, Jun 18, 2010 at 8:02 PM, genewardsmith
<genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > 2. The chords I play are pretty much the most consonant sounding ones I
> > could find - not saying there are not more. Probably this tuning as a
> > chromatic set of pitches would be difficult on a "normal" keyboard.
>
> One of the things I like about your versions is that they bring out the differences between temperaments. I tend to iron them out.
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> By the way.
>
> If you want me to try a tuning I'm always up for that.

What's the range in notes per octave you find best?

5, 7, 9 to 18 - ish

But with the technique I developed for the bohpier25 I can deal with more or
less I suppose.

Chris

On Sun, Jun 20, 2010 at 2:19 PM, genewardsmith
<genewardsmith@...>wrote:

>
>
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > By the way.
> >
> > If you want me to try a tuning I'm always up for that.
>
> What's the range in notes per octave you find best?
>
>
>