Suggestion for an EDO?

Ok, Experimental Musical Instruments quickly sent me fret wire and a fret saw. I have a miter box. Plus I decided to take advantage of a decent $50 used dreadnought guitar at Guitar Center today. A Woods by Samick DW-15

So, if anyone has any suggestion as to a first EDO to try as a re-fret I'd like to solicit your opinion. My fret wire looks mighty close to what is on the guitar already so 24 edo is quite tempting.

A picture of the guitar is here:
http://micro.soonlabel.com/various/IMG00066.jpg

or on my FB profile.

On Fri, Mar 25, 2011 at 9:10 PM, christopherv <chrisvaisvil@...> wrote:
>
> Ok, Experimental Musical Instruments quickly sent me fret wire and a fret saw. I have a miter box. Plus I decided to take advantage of a decent $50 used dreadnought guitar at Guitar Center today. A Woods by Samick DW-15
>
> So, if anyone has any suggestion as to a first EDO to try as a re-fret I'd like to solicit your opinion. My fret wire looks mighty close to what is on the guitar already so 24 edo is quite tempting.
>
> A picture of the guitar is here:
> http://micro.soonlabel.com/various/IMG00066.jpg
>
> or on my FB profile.

What acoustics do you already have?

-Mike

I only have 12 edo acoustics. classical, 6 string, 12 string, mandolin (2
actually but one is being cannibalized for parts).

On Fri, Mar 25, 2011 at 9:11 PM, Mike Battaglia <battaglia01@...>wrote:

>
>
> On Fri, Mar 25, 2011 at 9:10 PM, christopherv <chrisvaisvil@...>
> wrote:
> >
> > Ok, Experimental Musical Instruments quickly sent me fret wire and a fret
> saw. I have a miter box. Plus I decided to take advantage of a decent $50
> used dreadnought guitar at Guitar Center today. A Woods by Samick DW-15
> >
> > So, if anyone has any suggestion as to a first EDO to try as a re-fret
> I'd like to solicit your opinion. My fret wire looks mighty close to what is
> on the guitar already so 24 edo is quite tempting.
> >
> > A picture of the guitar is here:
> > http://micro.soonlabel.com/various/IMG00066.jpg
> >
> > or on my FB profile.
>
> What acoustics do you already have?
>
> -Mike
>
>

On Fri, Mar 25, 2011 at 9:20 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I only have 12 edo acoustics. classical, 6 string, 12 string, mandolin (2 actually but one is being cannibalized for parts).

I say 19-EDO then.

-Mike

It may look close in size but is probably very slightly different, even a very small difference will create extreme fretbuzz problems. Also a used guitar will have fretwear which will alter the height of the frets and create a varying height across each fret. Essential to have all the frets as new ones.

Also, the higher the EDO the more precise the fretting has to be, close frets are very prone to fretbuzz, so I recommend a low EDO.

MatC

--- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>My fret wire looks mighty close to what is on the guitar already so >24 edo is quite tempting.

I think you have a good point here about the fret wear. Upon close
inspection and indeed that is the case.
About 19 edo - I have an Ibenez electric guitar being re-fretted to 19 by
Brad. I should have that shortly.

Does anyone have strong feelings against BP? It looks easy to do - only 14
frets it looks like.

Chris

On Fri, Mar 25, 2011 at 9:31 PM, ixlramp <ixlramp@yahoo.co.uk> wrote:

>
>
> It may look close in size but is probably very slightly different, even a
> very small difference will create extreme fretbuzz problems. Also a used
> guitar will have fretwear which will alter the height of the frets and
> create a varying height across each fret. Essential to have all the frets as
> new ones.
>
> Also, the higher the EDO the more precise the fretting has to be, close
> frets are very prone to fretbuzz, so I recommend a low EDO.
>
> MatC
>
>
> --- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
> >My fret wire looks mighty close to what is on the guitar already so >24
> edo is quite tempting.
>
>
>

Chris,

here is my dyadic analysis of EDOs 4 to 24. 23EDO has more good dyads (within 6.776 cents (256/255) accuracy) than any other EDO from 4 to 24 so I would recommend 23EDO.

EDO4...none

EDO5...none

EDO6...9/8,

EDO7...none

EDO8...11/6,

EDO9...7/6, 12/7, 13/7,

EDO10...none

EDO11...9/7, 11/8,

EDO12...9/8, 4/3, 3/2,

EDO13...11/8, 9/5,

EDO14...9/7,

EDO15...6/5, 5/3,

EDO16...8/7, 7/4, 11/6,

EDO17...4/3, 3/2, 11/7,

EDO18...9/8, 7/6, 12/7, 13/7,

EDO19...6/5, 5/3, 13/7,

EDO20...11/7, 9/5,

EDO21...8/7, 7/4,

EDO22...7/6, 5/4, 9/7, 11/8, 8/5, 12/7,

EDO23...9/8, 7/6, 6/5, 11/7, 5/3, 12/7, 11/6,

EDO24...9/8, 4/3, 11/8, 3/2, 11/6,

--- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>
> Ok, Experimental Musical Instruments quickly sent me fret wire and a fret saw. I have a miter box. Plus I decided to take advantage of a decent $50 used dreadnought guitar at Guitar Center today. A Woods by Samick DW-15
>
> So, if anyone has any suggestion as to a first EDO to try as a re-fret I'd like to solicit your opinion. My fret wire looks mighty close to what is on the guitar already so 24 edo is quite tempting.
>
> A picture of the guitar is here:
> http://micro.soonlabel.com/various/IMG00066.jpg
>
> or on my FB profile.
>

I'd suggest 15, 18, or 24, because these will cut down on the number of new slots you have to cut (you can re-use existing 12-TET slots). Probably 18 will be the most rewarding.

-Igs

--- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
>
> Ok, Experimental Musical Instruments quickly sent me fret wire and a fret saw. I have a miter box. Plus I decided to take advantage of a decent $50 used dreadnought guitar at Guitar Center today. A Woods by Samick DW-15
>
> So, if anyone has any suggestion as to a first EDO to try as a re-fret I'd like to solicit your opinion. My fret wire looks mighty close to what is on the guitar already so 24 edo is quite tempting.
>
> A picture of the guitar is here:
> http://micro.soonlabel.com/various/IMG00066.jpg
>
> or on my FB profile.
>

Chris,

I would probably choose 19, but I'm a little boring and still early in my experimentation. My gut says that 19 will sound too normal for you.

BP would make sense -- then you'd have to find someone with one of those BP clarinets and collaborate with them... :) The fretting might be a little wide, though, especially near the nut.

How about 22? The sharp fifths should still be usable and the major thirds are just shy of just, but there are lots of other wild and woolly intervals to play with. If you tune the usual way, to the 9th frets (the flattish fourth) to get the A, D, G, and high E strings, and tune to the 8th fret for the B string, your open Em chord becomes a septimal Em, or you can use your middle finger to choose between a 327-cent minor or a 382- or 436-cent major third. (You could tune the B one fret higher, of course, to get the 327-cent m3 instead.) You've got a seventh that's not far from harmonic, another that's not far from a 12-TET M7, and one that's just 55 cents off of the octave to provide a little extra color or tension. It seems like 22 could have a lot of familiarity to it that leads to easy playing, but more not-quite-normal possibilities than 19.

Practically speaking, it might be hell to try to cram in so many frets in the higher register of the instrument, especially if you're cutting close to other fret grooves. BP and 24 EDO sound really good when I think about that issue. :)

For what it's worth. Good luck!

Regards,
Jake

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> Chris,
>
> I would probably choose 19, but I'm a little boring and still early in
> my experimentation. My gut says that 19 will sound too normal for you.
>
> BP would make sense -- then you'd have to find someone with one of those
> BP clarinets and collaborate with them... :) The fretting might be a
> little wide, though, especially near the nut.

There are zillions of other subgroups aside from 3.5.7. I've collected a lot them here:

http://xenharmonic.wikispaces.com/Chromatic+pairs

Experimenting with these could mean boldly going where no man has gone before.

On Fri, Mar 25, 2011 at 11:03 PM, Jake Freivald <jdfreivald@...> wrote:
>
> How about 22? The sharp fifths should still be usable and the major
> thirds are just shy of just, but there are lots of other wild and woolly
> intervals to play with. If you tune the usual way, to the 9th frets (the
> flattish fourth) to get the A, D, G, and high E strings, and tune to the
> 8th fret for the B string, your open Em chord becomes a septimal Em, or
> you can use your middle finger to choose between a 327-cent minor or a
> 382- or 436-cent major third. (You could tune the B one fret higher, of
> course, to get the 327-cent m3 instead.) You've got a seventh that's not
> far from harmonic, another that's not far from a 12-TET M7, and one
> that's just 55 cents off of the octave to provide a little extra color
> or tension. It seems like 22 could have a lot of familiarity to it that
> leads to easy playing, but more not-quite-normal possibilities than 19.

And the 11-limit. Don't forget the 11-limit. And porcupine. But if
you're the kind of person who strongly needs some kind of element of
familiarity to what you're doing, 22 may easily throw you off. I think
that the reason that Chris liked 17-tet so much is partially because
it's a meantone (well, at least the way he was using it). 19 has the
same features, but doesn't come with 13-limit harmony - but it still
has plenty of stuff in it as well.

22-tet is probably the best system to handle higher-limit harmonies
after 15 and 17 and outperforms both of them in terms of accuracy, but
it also forces one into more unfamiliar areas of playing, which means
learning more theory (or in many cases, inventing theory to describe
what you think sounds good). 19 is a good mix of both.

19 also supports island temperament, which is one of the subgroups
that Gene just wrote about as I was typing this, and has excellent
melodic properties to boot. Island[9] is like, if diatonic[9] is
normal starburst, then island[9] is tropical starburst. That's the
best way I can describe it.

Cheers,
Mike

Me:
> > How about 22? The sharp fifths should still be usable and the major
> > thirds are just shy of just, but there are lots of other wild and woolly
> > intervals to play with. [snip]

Mike Battaglia:
> And the 11-limit. Don't forget the 11-limit. And porcupine. But if you're
> the kind of person who strongly needs some kind of element of
> familiarity to what you're doing, 22 may easily throw you off.

Well, okay, but I haven't played with porcupine yet, and the most I've done in a greater-than-seven-limit tuning was when I wrote a little bagatelle with the temperament of the canton scale (2.3.11/7.13/7) that Gene posted. I'm not talking about what I could theorize about or what tuning I could *compose* in, but what I could *play*.

When I was talking about familiarity, I was thinking more about where my fingers would be on the fretboard for some normal types of chords, along with what minor tweaking I could do to significantly change the sound; I really wasn't considering the 11-limit or accuracy or anything else. When I pick up an instrument (and guitar is the only one I ever gained semi-competency with), it helps a lot if my fingers automatically know where to go. After looking at the interval layout of the 22-EDO fretboard -- I made a little spreadsheet that helps me with that -- my fingers tell me I could quickly get music out of a 22-EDO guitar.

I could get music out of a 19-EDO guitar, too, and if your arguments make sense to Chris then more power to you both! 19 looks great to me in ways that, say, 14, 15, and 16 don't, but Chris recently created music from an 11-EDO piece of lumber, so I'm just going to voice ideas and let him pick. I'll be happy as long as Chris does something that makes him post more songs that I can put on my Blackberry for the morning commute. :)

Gene:
> There are zillions of other subgroups aside from 3.5.7. I've collected a lot them here:
>
> http://xenharmonic.wikispaces.com/Chromatic+pairs
>
> Experimenting with these could mean boldly going where no man has gone before.

It's interesting that there's only one chromatic pair listed with 22 EDO: Supra, from the 2.3.7.11 subgroup.

Regards,
Jake

On Sat, Mar 26, 2011 at 12:29 AM, Jake Freivald <jdfreivald@...> wrote:
>
> When I was talking about familiarity, I was thinking more about where my
> fingers would be on the fretboard for some normal types of chords, along
> with what minor tweaking I could do to significantly change the sound; I
> really wasn't considering the 11-limit or accuracy or anything else.
> When I pick up an instrument (and guitar is the only one I ever gained
> semi-competency with), it helps a lot if my fingers automatically know
> where to go. After looking at the interval layout of the 22-EDO
> fretboard -- I made a little spreadsheet that helps me with that -- my
> fingers tell me I could quickly get music out of a 22-EDO guitar.

Well more power to you if so. 22-equal is an excellent tuning and I
plan on getting a guitar tuned to it sometime soon, but I don't find
it as easy. The fact that 81/80 doesn't vanish makes for some
interesting musical quirks that are difficult to get around if you've
been accustomed to meantone your whole life. Certain chord
progressions just don't work anymore. That being said, if you want to
experiment with 22, it will probably be one of the most rewarding
tunings there is.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> The fact that 81/80 doesn't vanish makes for some
> interesting musical quirks that are difficult to get around if you've
> been accustomed to meantone your whole life.

It's worse than not vanishing--it grows to 2.5 times as large.

Hey Chris, you'll have to choose the EDO very carefully to make sure the new slots don't get very close to existing ones. Either use existing slots or stay a few mms away. 15 or 16 would work.
MatC

--- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
> So, if anyone has any suggestion as to a first EDO to try as a re-fret

Thank you all for the suggestions (even the few emailed directly to me) -
I've printed out the posts. There were some really good suggestions - I
need to sort them out.

Chris

On Sat, Mar 26, 2011 at 1:55 AM, ixlramp <ixlramp@...> wrote:

>
>
> Hey Chris, you'll have to choose the EDO very carefully to make sure the
> new slots don't get very close to existing ones. Either use existing slots
> or stay a few mms away. 15 or 16 would work.
> MatC
>
>
> --- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@...> wrote:
> > So, if anyone has any suggestion as to a first EDO to try as a re-fret
>
>
>

You can fill the slots with hard setting resin, when it sets you can cut new slots anywhere.

--- In tuning@yahoogroups.com, "ixlramp" <ixlramp@...> wrote:
>
> Hey Chris, you'll have to choose the EDO very carefully to make sure the new slots don't get very close to existing ones. Either use existing slots or stay a few mms away. 15 or 16 would work.
> MatC
>
> --- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@> wrote:
> > So, if anyone has any suggestion as to a first EDO to try as a re-fret
>

Oh cool, thanks John.

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
> You can fill the slots with hard setting resin, when it sets you can cut new slots anywhere.

Something else to consider ... Nut intonation.
Fret calculators provide distances from the mathematical position of the nut. However most guitars have a compensated nut which is offset very roughly 1mm towards the bridge to compensate for the tendency of the open string note being flat relative to the fretted notes. See here:

http://www.doolinguitars.com/intonation/intonation4.html

So you need to find and mark the mathematical position of the nut and measure your fret distances from there. If you know the exact scale length of the guitar, measure half the scale length from the 12th fret and mark that point on the nut. You could always double check the mathematical nut position by running your fret calculator for 12EDO and checking the fret distances.
MatC

On 3/26/2011 1:23 AM, genewardsmith wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia<battaglia01@...> wrote:
>
>> The fact that 81/80 doesn't vanish makes for some
>> interesting musical quirks that are difficult to get around if you've
>> been accustomed to meantone your whole life.
>
> It's worse than not vanishing--it grows to 2.5 times as large.

That's not necessarily worse. It's large enough to sound like a deliberate step if you're careful with it.

On Sat, Mar 26, 2011 at 1:56 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Thank you all for the suggestions (even the few emailed directly to me) - I've printed out the posts.  There were some really good suggestions - I need to sort them out.

Right, so, as you can see, everyone is pretty much unanimously
advocating for 19-equal. I'd go with that then!

:)

-Mike

Mike

I have an ibenez electric being converted to 19 by Brad Smith. I guess I should have mentioned that. Thought I had.

Chris
-----Original Message-----
From: Mike Battaglia <battaglia01@gmail.com>
Sender: tuning@yahoogroups.com
Date: Sat, 26 Mar 2011 18:16:02
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: Re: [tuning] Re: Suggestion for an EDO?

On Sat, Mar 26, 2011 at 1:56 PM, Chris Vaisvil <chrisvaisvil@gmail.com> wrote:
>
> Thank you all for the suggestions (even the few emailed directly to me) - I've printed out the posts.  There were some really good suggestions - I need to sort them out.

Right, so, as you can see, everyone is pretty much unanimously
advocating for 19-equal. I'd go with that then!

:)

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Mar 26, 2011 at 1:56 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Thank you all for the suggestions (even the few emailed directly to me) - I've printed out the posts.  There were some really good suggestions - I need to sort them out.
>
> Right, so, as you can see, everyone is pretty much unanimously
> advocating for 19-equal. I'd go with that then!

LOL, if by everyone you mean like 2 people. 18 would be an easier job, and Chris has done some good work in 18 already.

-Igs

Your list of "good dyads" seems to be based only on your personal taste- you leave out 11:9 for example, which is a bad idea if you're looking for rational reference points in interval systems.

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Chris,
>
> here is my dyadic analysis of EDOs 4 to 24. 23EDO has more good dyads (within 6.776 cents (256/255) accuracy) than any other EDO from 4 to 24 so I would recommend 23EDO.
>
> EDO4...none
>
> EDO5...none
>
> EDO6...9/8,
>
> EDO7...none
>
> EDO8...11/6,
>
> EDO9...7/6, 12/7, 13/7,
>
> EDO10...none
>
> EDO11...9/7, 11/8,
>
> EDO12...9/8, 4/3, 3/2,
>
> EDO13...11/8, 9/5,
>
> EDO14...9/7,
>
> EDO15...6/5, 5/3,
>
> EDO16...8/7, 7/4, 11/6,
>
> EDO17...4/3, 3/2, 11/7,
>
> EDO18...9/8, 7/6, 12/7, 13/7,
>
> EDO19...6/5, 5/3, 13/7,
>
> EDO20...11/7, 9/5,
>
> EDO21...8/7, 7/4,
>
> EDO22...7/6, 5/4, 9/7, 11/8, 8/5, 12/7,
>
> EDO23...9/8, 7/6, 6/5, 11/7, 5/3, 12/7, 11/6,
>
> EDO24...9/8, 4/3, 11/8, 3/2, 11/6,
>
>
>
> --- In tuning@yahoogroups.com, "christopherv" <chrisvaisvil@> wrote:
> >
> > Ok, Experimental Musical Instruments quickly sent me fret wire and a fret saw. I have a miter box. Plus I decided to take advantage of a decent $50 used dreadnought guitar at Guitar Center today. A Woods by Samick DW-15
> >
> > So, if anyone has any suggestion as to a first EDO to try as a re-fret I'd like to solicit your opinion. My fret wire looks mighty close to what is on the guitar already so 24 edo is quite tempting.
> >
> > A picture of the guitar is here:
> > http://micro.soonlabel.com/various/IMG00066.jpg
> >
> > or on my FB profile.
> >
>

Sorry, Chris, I didn't see your reply as it was addressed to Mat Cooper.

-Mike

On Sat, Mar 26, 2011 at 7:34 PM, <chrisvaisvil@...> wrote:
>
> Mike
>
> I have an ibenez electric being converted to 19 by Brad Smith. I guess I should have mentioned that. Thought I had.
>
> Chris

On Sat, Mar 26, 2011 at 9:43 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Right, so, as you can see, everyone is pretty much unanimously
> > advocating for 19-equal. I'd go with that then!
>
> LOL, if by everyone you mean like 2 people. 18 would be an easier job, and Chris has done some good work in 18 already.
>
> -Igs

Haha, sorry, just being facetious. I just think that Chris would do
amazing things with 19-equal, that's all. Call it a hunch. I'll stop
mentioning it.

Out of curiosity, because I don't think I've ever asked before - what
exactly do you like about 18-equal? The fact that it's a father
temperament? Just the fact that it has a certain ineffable sound?
What?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Out of curiosity, because I don't think I've ever asked before - what
> exactly do you like about 18-equal? The fact that it's a father
> temperament? Just the fact that it has a certain ineffable sound?
> What?

It's not really a Father temperament, because its best 5/4 is 400 cents (a different interval than 4/3). The scale in it that looks like Father is the 2.9.21 subgroup I call "A-Team", and yes, it's one of my faves for its feeling of "expectant floatiness".

More to the point, it's the smallest ET that gives you both a 7/6 and a 6/5, and together they span 600 cents, making for a swell temperament for 5:6:7 triads that has a 1/2 octave period (which functions as both 7/5 and 10/7) and a generator of the 333-cent minor 3rd, such that you get either 5:6:7 or 1/(5:6:7) on every root in the scale. You can do this in 22 and 26-ET, too, but 18 has the pure 7/6's, and that seems to help.

Also, there's some cool augmented-type stuff you can do with 18, and I'll admit I find that it does have a "certain ineffable sound". There is something about the way intervals beat in 18 that just sounds really good to me, compared to something like 14 or 15. 18 has a stability to it that I can't really explain. Maybe it's due to the fact that the two 4ths are both very close to rational intervals (21/16 and 15/11), intervals which are not Just but have a certain subliminal regularity to them nonetheless.

I just find 18 to be very xenharmonic but very pleasant at the same time, and it's been very under-explored.

-Igs

18 is pretty compelling. I really did enjoy playing in it.

http://chrisvaisvil.com/?p=3

Right now I'm torn between 18, 23, and 24.

And Gene - I looked at your link to the xenwiki listing and I'm a bit
confused by it all. So many options and I'm not sure in every case what I'm
looking at. Could I ask you to narrow done the choices a little to your
favorite alternatives?

Perhaps I should go really obscure and figure out how to fret for the 12th
root of Phi. I really liked that tuning but I think I'm the only person on
the planet that did.

http://micro.soonlabel.com/12th-root-phi/

Chris

On Sun, Mar 27, 2011 at 3:20 PM, cityoftheasleep <igliashon@...>wrote:

>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > Out of curiosity, because I don't think I've ever asked before - what
> > exactly do you like about 18-equal? The fact that it's a father
> > temperament? Just the fact that it has a certain ineffable sound?
> > What?
>
> It's not really a Father temperament, because its best 5/4 is 400 cents (a
> different interval than 4/3). The scale in it that looks like Father is the
> 2.9.21 subgroup I call "A-Team", and yes, it's one of my faves for its
> feeling of "expectant floatiness".
>
> More to the point, it's the smallest ET that gives you both a 7/6 and a
> 6/5, and together they span 600 cents, making for a swell temperament for
> 5:6:7 triads that has a 1/2 octave period (which functions as both 7/5 and
> 10/7) and a generator of the 333-cent minor 3rd, such that you get either
> 5:6:7 or 1/(5:6:7) on every root in the scale. You can do this in 22 and
> 26-ET, too, but 18 has the pure 7/6's, and that seems to help.
>
> Also, there's some cool augmented-type stuff you can do with 18, and I'll
> admit I find that it does have a "certain ineffable sound". There is
> something about the way intervals beat in 18 that just sounds really good to
> me, compared to something like 14 or 15. 18 has a stability to it that I
> can't really explain. Maybe it's due to the fact that the two 4ths are both
> very close to rational intervals (21/16 and 15/11), intervals which are not
> Just but have a certain subliminal regularity to them nonetheless.
>
> I just find 18 to be very xenharmonic but very pleasant at the same time,
> and it's been very under-explored.
>
> -Igs
>
>
>

Igs>"More to the point, it's the smallest ET that gives you both a 7/6 and a
6/5, and together they span 600 cents, making for a swell temperament
for 5:6:7 triads that has a 1/2 octave period (which functions as both
7/5 and 10/7) "

    Fascinating observations!  18 equal indeed has some interesting properties...and lots of stuff that seems both counter to many leading concordance theories and somewhat in common with how/why 12TET works with occasionally obscure errors relative to just intervals.  18 seems to be able to achieve a variety of chords much because it is so vaguely tied to just intervals in so many cases and can flip between different intervals as needed.
--------------
   There are a lot of ratios dead in-between strong ratios that can act as either.
   For example, 1.5874 can act as a 8/5 or an 11/7.  Also 1.414 can double between a 7/5 and 10/7 (as noted).  Note BOTH of these ratios and swaps are virtually the same as those already in 12TET (so perhaps you are already used to them?) :-D  Note 10/7 doesn't come up in HE as having a noticeable field of attraction...but, personally, I think it definitely should!

    Also to note...the "alternative to a perfect fifth" of 22/15 leans upward, away from the horrid tri-tone-ish sounding 16/11...and there is a flat neutral third that can be conned into acting "major or minor" when needed, plus it leans toward a .  As you said, there is also a 15/11, which can be connected fairly well with the 22/15 since 22/15 is near 16/11. 

  Perhaps some of the sense of "stability" is also because, although many notes are off pure...they tend to be about the same amount off pure (14 cents or so) so there are few unpredictable spikes of consonance of dissonance.  Also the 13/12-ish interval lends a decent option to diffuse the sort of root-tone critical band dissonance (AKA the type you get with sine waves) associated with the typical 17/16-ish semitone.

   I'd consider it a "predictable vague" tuning of sorts...it succeed because of the sheer vast number of intervals it can approximate rather than its Just-ness.  In fact 7/6 is just about the only thing I see in it that's disproportionately Just compared to everything else...the error is even evenly distributed, giving it a rather soft, if vague, feel.  You're not going to get razor-sharp Just triads but, instead, you get a large range of chords with a predictable level of consonance/dissonance...it seems.

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

> And Gene - I looked at your link to the xenwiki listing and I'm a bit
> confused by it all. So many options and I'm not sure in every case what I'm
> looking at. Could I ask you to narrow done the choices a little to your
> favorite alternatives?

I'm not sure what link you mean and don't really have a favorite edo, though lately I've been pushing 29 as I think it is under-explored. If 29 is too large, and you haven't yet done 19, that's sort of obligatory at some point.

Hi Gene,

I have an Ibenez electric that is being converted to 19 by Brad Smith.

As for the link

genewardsmith  to tuning
show details Mar 25 (2 days ago)

There are zillions of other subgroups aside from 3.5.7. I've collected
a lot them here:

http://xenharmonic.wikispaces.com/Chromatic+pairs

Experimenting with these could mean boldly going where no man has gone before.

filtering as to which of these you think has the most promise would be
great to know.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Right now I'm torn between 18, 23, and 24.

Funny, that's also the decision I'm trying to make about the next guitar (though I'm a long ways from another guitar...gotta spend some time with the ones I already have!!). 18 and 23 are very closely related, in terms of harmonies. Neither does common-practice harmonies at all, both approximate 5:6:7 and 16:18:21 very well, both have excellent 9/8's but not 3/2's. Both support the following DE scales: 5L+3s, 2L+5s, and 4L+3s.

On guitar, 18 and 23 can both be tuned either as a series of flat fourths with one sharp/augmented 4th:

0-466.7-933.3-200-733.3-0 cents in 18
vs.
0-469.6-939.1-208.7-730.4-0 cents in 23

Or, as a series of sharp 4ths with one 3rd:

0-533.3-1066.7-400-666.7-0 cents in 18
vs.
0-521.7-1043.5-365.2-678.2-0 cents in 23

So chord and scale shapes will be similar in both tunings.

In 23's favor, we have higher accuracy (as John as noted--it has the most nearest-to-Just intervals of any EDO below 24), neutral intervals, some reasonable 11 and 13-limit implications (sort of).

18, however, has simplicity and convenience on its side. It's an easy conversion to do because 1/3 of the fret-slots are already cut for you, it's got 5 fewer notes per octave, it contains 3-EDO, 6-EDO, and 9-EDO, and a lot of what you can do in 23 you can do in 18 with only a bit lower accuracy. Because it tempers out 50/49 to approximate 7/5 and 10/7 with the same 600-cent interval, it allows for simpler temperaments of 5:6:7 harmonies.

24, OTOH, is very different. On the plus side, it'd be a cinch to refret because half the work is already done for you and you can practically eye-ball the new slots. You get excellent 10:13:15, 6:8:11, 6:9:11, and 8:11:12 chords, good neutral melodic intervals, two really good DE scales/"temperaments" (3L+4s "Mohajira", 5L+4s "Barbados"), subdivisions into 2, 3, 4, 6, and 8 equal parts, standard tuning, and access to a "large" existing repertoire of quarter-tone guitar music. On the minus side, well, you're stuck with all the 12-TET intervals, and there's not as much potential in 24 for doing really new and fresh-sounding stuff. Also most of the stuff that's been written in 24 kind of sucks, and it may prove to be the least rewarding.

> Perhaps I should go really obscure and figure out how to fret for the 12th
> root of Phi. I really liked that tuning but I think I'm the only person on
> the planet that did.
>
> http://micro.soonlabel.com/12th-root-phi/
>

Very interesting. Pretty much uncharted territory there if you're feeling like trail-blazing! Has some flavors of 18 but also a decent 3/2 and a decent 7/4. Not sure how you'd want to tune the open strings, might be a challenge to find good chords that span all 6 strings as well.

-Igs

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

> There are zillions of other subgroups aside from 3.5.7. I've collected
> a lot them here:
>
> http://xenharmonic.wikispaces.com/Chromatic+pairs
>
> Experimenting with these could mean boldly going where no man has gone before.
>
>
>
> filtering as to which of these you think has the most promise would be
> great to know.

I could give it a shot, but can you clue me in to what you are most interested in?

Far as chromatic pairs go......
Gene, I'd like to know which chromatic pair scales and tunings:

  A) Are strictly proper
  B) Use mostly a combination of 14/9, 3/2, or 22/15 as fifths or "alternatives to 5ths".
  C) If possible...have mostly evenly distributed "semitones" (IE anything less than 11/10 or so is maximally spaced across the scale...just like the semitone is in the diatonic scale)

A balance of harmony and melody I guess.

But my ears work funny. I found the 12th root of phi did that.

On Sun, Mar 27, 2011 at 10:33 PM, genewardsmith <genewardsmith@...
> wrote:

>
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
>
> > There are zillions of other subgroups aside from 3.5.7. I've collected
> > a lot them here:
> >
> > http://xenharmonic.wikispaces.com/Chromatic+pairs
> >
> > Experimenting with these could mean boldly going where no man has gone
> before.
> >
> >
> >
> > filtering as to which of these you think has the most promise would be
> > great to know.
>
> I could give it a shot, but can you clue me in to what you are most
> interested in?
>
>
>

and more than 12 notes, <= 24 notes per octave.

On Mon, Mar 28, 2011 at 6:51 AM, Chris Vaisvil <chrisvaisvil@...>wrote:

> A balance of harmony and melody I guess.
>
> But my ears work funny. I found the 12th root of phi did that.
>
>
> On Sun, Mar 27, 2011 at 10:33 PM, genewardsmith <
> genewardsmith@...> wrote:
>
>>
>>
>>
>>
>> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>> >
>>
>> > There are zillions of other subgroups aside from 3.5.7. I've collected
>> > a lot them here:
>> >
>> > http://xenharmonic.wikispaces.com/Chromatic+pairs
>> >
>> > Experimenting with these could mean boldly going where no man has gone
>> before.
>> >
>> >
>> >
>> > filtering as to which of these you think has the most promise would be
>> > great to know.
>>
>> I could give it a shot, but can you clue me in to what you are most
>> interested in?
>>
>>
>>
>
>

Though, I'm thinking I'll give 18 a shot because if not anything else
measuring the 12 equal slots will give me an idea of the compensation the
original manufacturer used.
Right now I'm in the dark on that - and unlike an electric guitar there is
nothing that can be adjusted easily.

Chris

On Mon, Mar 28, 2011 at 6:52 AM, Chris Vaisvil <chrisvaisvil@...>wrote:

> and more than 12 notes, <= 24 notes per octave.
>
>
> On Mon, Mar 28, 2011 at 6:51 AM, Chris Vaisvil <chrisvaisvil@...>wrote:
>
>> A balance of harmony and melody I guess.
>>
>> But my ears work funny. I found the 12th root of phi did that.
>>
>>
>> On Sun, Mar 27, 2011 at 10:33 PM, genewardsmith <
>> genewardsmith@...> wrote:
>>
>>>
>>>
>>>
>>>
>>> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>>> >
>>>
>>> > There are zillions of other subgroups aside from 3.5.7. I've collected
>>> > a lot them here:
>>> >
>>> > http://xenharmonic.wikispaces.com/Chromatic+pairs
>>> >
>>> > Experimenting with these could mean boldly going where no man has gone
>>> before.
>>> >
>>> >
>>> >
>>> > filtering as to which of these you think has the most promise would be
>>> > great to know.
>>>
>>> I could give it a shot, but can you clue me in to what you are most
>>> interested in?
>>>
>>>
>>>
>>
>>
>

Well, if you look at the calculations
http://windworld.com/features/tools-resources/exmis-fret-placement-calculator/

18 and 12 do not share frets to speak of.

I did find out that the guitar is not compensated (as defined by the above
calculations) and this is taken care of by the bridge offset.

I have the guitar de-fretted. I'm going after the fretboard binding now.
I'll be posting pictures in a bit.

On Mon, Mar 28, 2011 at 6:54 AM, Chris Vaisvil <chrisvaisvil@...>wrote:

> Though, I'm thinking I'll give 18 a shot because if not anything else
> measuring the 12 equal slots will give me an idea of the compensation the
> original manufacturer used.
> Right now I'm in the dark on that - and unlike an electric guitar there is
> nothing that can be adjusted easily.
>
> Chris
>
>
> On Mon, Mar 28, 2011 at 6:52 AM, Chris Vaisvil <chrisvaisvil@...>wrote:
>
>> and more than 12 notes, <= 24 notes per octave.
>>
>>
>> On Mon, Mar 28, 2011 at 6:51 AM, Chris Vaisvil <chrisvaisvil@...>wrote:
>>
>>> A balance of harmony and melody I guess.
>>>
>>> But my ears work funny. I found the 12th root of phi did that.
>>>
>>>
>>> On Sun, Mar 27, 2011 at 10:33 PM, genewardsmith <
>>> genewardsmith@...> wrote:
>>>
>>>>
>>>>
>>>>
>>>>
>>>> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>>>> >
>>>>
>>>> > There are zillions of other subgroups aside from 3.5.7. I've collected
>>>> > a lot them here:
>>>> >
>>>> > http://xenharmonic.wikispaces.com/Chromatic+pairs
>>>> >
>>>> > Experimenting with these could mean boldly going where no man has gone
>>>> before.
>>>> >
>>>> >
>>>> >
>>>> > filtering as to which of these you think has the most promise would be
>>>> > great to know.
>>>>
>>>> I could give it a shot, but can you clue me in to what you are most
>>>> interested in?
>>>>
>>>>
>>>>
>>>
>>>
>>
>

Please let me take that back - they do share frets indeed. My bad. So, that
gets the nod - 18 edo it will be.

I can change to something else later.

Chris

On Tue, Mar 29, 2011 at 1:36 PM, Chris Vaisvil <chrisvaisvil@gmail.com>wrote:

> Well, if you look at the calculations
>
> http://windworld.com/features/tools-resources/exmis-fret-placement-calculator/
>
> 18 and 12 do not share frets to speak of.
>
> I did find out that the guitar is not compensated (as defined by the above
> calculations) and this is taken care of by the bridge offset.
>
> I have the guitar de-fretted. I'm going after the fretboard binding now.
> I'll be posting pictures in a bit.
>
>
> On Mon, Mar 28, 2011 at 6:54 AM, Chris Vaisvil <chrisvaisvil@...>wrote:
>
>> Though, I'm thinking I'll give 18 a shot because if not anything else
>> measuring the 12 equal slots will give me an idea of the compensation the
>> original manufacturer used.
>> Right now I'm in the dark on that - and unlike an electric guitar there is
>> nothing that can be adjusted easily.
>>
>> Chris
>>
>>
>> On Mon, Mar 28, 2011 at 6:52 AM, Chris Vaisvil <chrisvaisvil@...>wrote:
>>
>>> and more than 12 notes, <= 24 notes per octave.
>>>
>>>
>>> On Mon, Mar 28, 2011 at 6:51 AM, Chris Vaisvil <chrisvaisvil@...>wrote:
>>>
>>>> A balance of harmony and melody I guess.
>>>>
>>>> But my ears work funny. I found the 12th root of phi did that.
>>>>
>>>>
>>>> On Sun, Mar 27, 2011 at 10:33 PM, genewardsmith <
>>>> genewardsmith@sbcglobal.net> wrote:
>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>>>>> >
>>>>>
>>>>> > There are zillions of other subgroups aside from 3.5.7. I've
>>>>> collected
>>>>> > a lot them here:
>>>>> >
>>>>> > http://xenharmonic.wikispaces.com/Chromatic+pairs
>>>>> >
>>>>> > Experimenting with these could mean boldly going where no man has
>>>>> gone before.
>>>>> >
>>>>> >
>>>>> >
>>>>> > filtering as to which of these you think has the most promise would
>>>>> be
>>>>> > great to know.
>>>>>
>>>>> I could give it a shot, but can you clue me in to what you are most
>>>>> interested in?
>>>>>
>>>>>
>>>>>
>>>>
>>>>
>>>
>>
>