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Author Topic: A question about frets for just intonation  (Read 80369 times)

bigbadwolf

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A question about frets for just intonation
« on: September 03, 2011, 09:03:47 AM »

Hi. I’m new to this world of non-standard tunings (I’ve been vaguely interested in it for a little while but have never actually played in anything but 12-TET). I’ve been messing about with ratios on paper for the last few days and, though I’m not completely happy with it, I’ve come up with a tuning that somewhat appeals to me. However, what really doesn’t appeal to me is the way that JI guitars have those mini/broken frets or curved frets. I’m sort of beginning to accept that that’s just the way it is with JI but I don’t understand why that’s the case. All I know is it has something to do with string tension… maybe? If you can get the octave in tune with a regular straight fret, then why can’t you get the rest of the guitar in tune with straight frets?

So what I’d like to know is do the frets absolutely have to be like that? And, if so, why do they have to be like that? I've read some stuff about it but I still don't get it and this forum seems like it's probably the best place to ask. If any of you guys can help me get my head around this it would be much appreciated. I’m a bit of a technophobe and to be honest I’m not even really sure how guitars work (my best guess would be that some kind of magic is involved) so if you could put it in layman’s terms, as far as that’s possible, that would also be helpful.

Thanks.
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Mat

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Re: A question about frets for just intonation
« Reply #1 on: September 03, 2011, 11:39:52 AM »

Hi and welcome (Ah ... i see you are a fellow Englishman). Pitch is determined by the distance of a fret from the bridge. With the standard 12 equal temperament (12ET), there are 12 pitches equally spaced within an octave, which results in the familiar pattern of frets: smoothly and consistently getting closer together towards the bridge. In Just Intonation (JI) pitches are unequally spaced within an octave, which results in the random-looking spacings along a string. The guitar's open tuning then shifts these spacings around in a different way on each string so that they don't line up into straight frets. However, if you tune in octaves (crazy i know but i know someone who does this) then any JI system of ratios you choose results in straight frets.

Alternatively, tuning in alternating fifths and fourths (example CGCGCG or more precisely 1/1 - 3/2 - 2/1 - 2/1*3/2 - 4/1 - 4/1*3/2) can help achieve your desired JI system with straight frets, if there are lots of 3/2 intervals in that system. The Gs in CGCGCG can then be microtonally retuned (while maintaining the octaves between them) to achieve other JI systems. Many 'ethnic' lutes are tuned in alternating fifths and fourths, and have movable frets.

Essentially, once you choose your system of JI ratios, it may be possible to find an open tuning that results in straight frets, although this may also result in lots of fairly closely spaced frets.

Have you considered an alternative equal temperament such as 16EDO, 23EDO etc.? These are microtonal but always result in straight frets, such as the guitars Ron makes: http://www.swordguitars.com/PG.html

I recommend experimenting with the FretFInd2D microtonal fretboard visualiser: http://ninestring.org/index.php?topic=61.0
« Last Edit: September 03, 2011, 12:41:08 PM by matcooper »
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bigbadwolf

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Re: A question about frets for just intonation
« Reply #2 on: September 03, 2011, 06:09:08 PM »

Hi, Mat. Thanks for the welcome and for helping out.

I’ll start with the two questions at the end of your message. I tried the FretFind thing yesterday after reading about it here, actually. I couldn’t get it to work but I wasn’t on the site for very long so I’ll have another go with it at some point.

I’ve thought about other equal temperaments. I’m interested in them but I’m not sure if they’re for me. Obviously they all have their own flavours and could each be good in their own way. Lately I’ve been listening to bits and pieces in 5-TET and 7-TET (not exactly microtonal but they could be doubled to 10- and 14-TET or 20- and 28-TET for more notes) and I like the sound of them. I’ve written 12-TET wholetone scale stuff before, which is effectively 6-TET. I actually like the sound of 12-TET quite a lot (I don’t know how controversial that is round these parts). So I’m not against the concept of equal temperament. I think you could probably make good music with most equal temperaments if you knew what you were doing, and I appreciate the fact that you have more notes to choose from with things like 23-TET or 19-TET or whatever. The problem is you can’t just find a 23-TET guitar in a shop and try it out, and also I’m not sure if I could handle the theory behind it. I’d like to try something like that sometime but at the moment I can’t afford to buy a guitar like that when I have no idea if I’d ever have the brains to be able to grasp the theory and make it sound good. The other thing which is sort of drawing me away from those systems is one of the things that annoys me a bit with 12-TET, and that’s the intervals not being quite right. That’s really what I’m after at the moment. I know you can get close to having perfect intervals if you go up to the early thirties, but that’s too many frets for me. I don’t think I could fit my fingers between them at that point. I’m not ruling out other equal temperaments completely, it’s definitely an option but I’d have to listen to them more and study the theory for a few different ones before I’d feel good about splashing out on that kind of thing.

OK, so about these frets…

“The guitar's open tuning then shifts these spacings around in a different way on each string so that they don't line up into straight frets.”

That’s the part that I wasn’t getting. I'm still not sure that I understand, but maybe I do. Are you saying that the reason the frets are like that is so that every note on every string is at a just interval from C (if C is the root or ‘main’ note, like in your example)? If that is what you’re saying then that’s very, very cool because that’s not what I want at all. I should probably just try to explain what I want with the tuning that I’m trying to come up with and then hopefully you'll be able say whether it would work with straight frets. I’m starting to think that ‘just intonation’ probably isn’t the correct term for what I want. What I want is just intervals but I want to be able to play in as many keys as possible, so some of the intervals between the open string or ‘fret zero’ and certain other frets will sound horrible but the notes on those frets would make just intervals with notes that are on different strings and frets. And since there could only be a finite amount of notes on the guitar, all you would have to do is remember which notes would work in which keys, and you could always play around with the ‘wrong’ intervals anyway if you wanted something dissonant. Would I need those mini-frets in that kind of tuning system? And also I’m wondering what those kinds of tuning systems are called.

Thanks.

P.S. Since you're English too, is there much microtonal stuff coming out of the UK? The impression I've got so far is that there isn't much at all.
« Last Edit: September 04, 2011, 08:20:07 PM by bigbadwolf »
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Mat

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Re: A question about frets for just intonation
« Reply #3 on: September 05, 2011, 11:04:20 AM »

I should probably just try to explain what I want with the tuning that I’m trying to come up with and then hopefully you'll be able say whether it would work with straight frets. I’m starting to think that ‘just intonation’ probably isn’t the correct term for what I want. What I want is just intervals but I want to be able to play in as many keys as possible, so some of the intervals between the open string or ‘fret zero’ and certain other frets will sound horrible but the notes on those frets would make just intervals with notes that are on different strings and frets. And since there could only be a finite amount of notes on the guitar, all you would have to do is remember which notes would work in which keys, and you could always play around with the ‘wrong’ intervals anyway if you wanted something dissonant. Would I need those mini-frets in that kind of tuning system? And also I’m wondering what those kinds of tuning systems are called.

Thanks.

P.S. Since you're English too, is there much microtonal stuff coming out of the UK? The impression I've got so far is that there isn't much at all.

Hmm okay ... it's very complex and mathematical and i'm not confident i can explain it. But anyway ... what you are after is indeed just intonation, but a carefully designed system that allows a few different keys to be played. Just intonation does limit the number of keys you can modulate to, it's a case of clever design without adding too many frets as to make the guitar unplayable. Jon Catler's guitar is like this: http://www.organicdesign.org/peterson/customers/catler_ji.html. However you can always play all the modes of the JI scales playable, by just moving the tonic to a different degree of the scale.

Tuning in octaves with such a system would help to line up the frets and create something that looks similar to this ...

"This is an experimental tuning system that provides some very interesting intervals. The frets represent Just Intonation intervals so each string acts like a tonic of it's own scale.  Tuning the strings differently yields a variety of tone palettes." From here: http://www.organicdesign.org/peterson/guitars/index.html.

While you ponder ... you may be interested in my tuning for conventionally fretted guitar which allows 24EDO and simple JI scales to be played just by buying a custom set of strings: http://www.sevenstring.org/forum/music-theory-lessons-techniques/161530-retune-play-quartertone-scales-microtonal-beginners-guide.html. The post in that thread about JI scales is here: http://www.sevenstring.org/forum/2530509-post6.html.

SInce 3/2 = 7.02 semitones and 11/8 = 5.51 semitones, 24EDO very closely approximates a particular 15 tone JI system constructed from 3/2 and 11/8. Since 24EDO has 24 equally spaced pitches in an octave you can modulate freely, plus there are many different ways to tune the open strings. However you are then limited to one particular JI system, see the last 2 diagrams here: http://www.sevenstring.org/forum/2530117-post2.html.

UK microtonal music?
The bard of Cholsey, Mark Allan Barnes.

http://www.youtube.com/user/MarkAllanBarnes#p/a/u/0/mHyaW1fVWsg
14 EDO.

http://www.youtube.com/user/MarkAllanBarnes#p/u/5/c1PaBAwmUbs
Pythagorean scale.

http://www.myspace.com/markbarnes2
http://www.myspace.com/markbarnes2#!/markbarnes2/photos/albums/lyre-guitar/1222097
http://www.soundclick.com/bands/default.cfm?bandID=864909
« Last Edit: September 05, 2011, 07:33:49 PM by matcooper »
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bigbadwolf

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Re: A question about frets for just intonation
« Reply #4 on: September 05, 2011, 11:34:58 AM »

Yeah, that sounds like the sort of system I'm aiming for, and those frets look pretty damn straight. This line, though - "each string acts like a tonic of it's own scale.  Tuning the strings differently yields a variety of tone palettes." That's saying that you don't need to tune in octaves, right? So that (taking a random interval like major sixth) you could have a string tuned to E and then the major sixth fret would play the note that's a major sixth from E (some kind of C#), and then have a string tuned to A and the major sixth fret would play a note that's a major sixth from A (some kind of F#), right? And in theory the F# would be a perfect fourth above the C#? Or do you think the F# and C# would make some other interval that isn't quite a perfect fourth if you had straight frets? If it did work with straight frets then I'm pretty sure I could figure out a system to play in a few different keys, though whether it would sound any good is another matter.

Hmm. I'm guessing those JI modes would sound very different to the regular modes? Could be interesting...
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Mat

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Re: A question about frets for just intonation
« Reply #5 on: September 05, 2011, 11:54:53 AM »

This line, though - "each string acts like a tonic of it's own scale.  Tuning the strings differently yields a variety of tone palettes." That's saying that you don't need to tune in octaves, right?
Yep.
Tuning in octaves minimises the number of frets needed for a particular JI system. Any other open tuning can add more frets, and some frets may be very closely spaced, but careful choice of a non-octave open tuning minimises the additional frets. Essentially look for the most common interval in your desired JI system and incorporate it into the open tuning, this will minimise the number of frets. For example the JI major scale is mostly constructed from 3/2, so tune root, fifth, octave, octave plus fifth, 2 octaves, 2 octaves plus fifth.
« Last Edit: September 05, 2011, 07:39:09 PM by matcooper »
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bigbadwolf

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Re: A question about frets for just intonation
« Reply #6 on: September 05, 2011, 12:20:42 PM »

Haha, fair enough. Well, hopefully someone on here will know. Though it seems pretty quiet around these parts...

Thanks for the info anyway. I'm starting to feel a bit more optimistic about it, I'm more confident that it could work.
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Mat

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Re: A question about frets for just intonation
« Reply #7 on: September 05, 2011, 12:45:02 PM »

Just edited my last post ... what i meant was 'i can't be bothered to get my head around it' ;D
I recommend squared paper, a scientific calculator, a pen and lots of online study. With JI it really helps to visually map out a tone system as a tonal lattice.
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bigbadwolf

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Re: A question about frets for just intonation
« Reply #8 on: September 05, 2011, 01:34:42 PM »

Ahhh. Well, I've been using the calculator on my mobile phone. But to put what I said before another way, what I'm trying to figure out is this: Say you've got your E string and A string, they're obviously a perfect fourth apart, so if you hold down both strings on the first fret they should still be a perfect fourth apart from each other, and then if you hold both strings down on the second fret they should still be a perfect fourth apart... that's only if I'm right, though. If I'm wrong then something (maybe string tension or some other factor that I haven't considered) would stop it always being a perfect fourth. I've sort of got an understanding of how to work out what I need to work out with how the intervals and notes all relate to each other in my theoretical tuning system(though I don't know anything about lattices, so I should probably look into that), but if there's something preventing the intervals that I just talked about always being perfect fourths (or always being the same intervals depending on how the open strings are tuned) then my tuning idea probably won't work. It seems like Jon Catler was saying that it would work, and I think it would work.

I just noticed your edit about UK music and your own tuning system. Some mates have just arrived so I probably won't be able to look at that stuff properly tonight. If I can't then I'll definitely check it out tomorrow.

Cheers.
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Mat

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Re: A question about frets for just intonation
« Reply #9 on: September 05, 2011, 01:52:01 PM »

But to put what I said before another way, what I'm trying to figure out is this: Say you've got your E string and A string, they're obviously a perfect fourth apart, so if you hold down both strings on the first fret they should still be a perfect fourth apart from each other, and then if you hold both strings down on the second fret they should still be a perfect fourth apart...

Ah i see. Yes for sure. Across any straight fret the intervals are the same as the open string intervals.

What you want is possible, it's just a case of how many different scales/keys will be playable, it may only be a few, but then there are all the modes of each of those.
For example the JI chromatic scale: 1/1  16/15  9/8  6/5  5/4  4/3  45/32  3/2  8/5  5/3  9/5  15/8  2/1 on a tonic of C has 12 tones per octave and contains JI C major, JI C minor, JI C phrygian etc. and then all the modes of each of those. it's just a case of choosing your scale out of the 12 tones. The difficult bit is doing this with straight frets and a non-octave open tuning.

The only reason i recommended a scientific calculator is for the LOG function, for converting ratios to cents. See this introduction to JI: http://www.kylegann.com/tuning.html. The rest of the math is simple.
« Last Edit: September 05, 2011, 07:40:23 PM by matcooper »
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Mat

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Re: A question about frets for just intonation
« Reply #10 on: September 05, 2011, 07:52:14 PM »

I'm thinking look into an 'standby' open tuning of all-tritones. This can then be easily retuned to alternating 5ths and 4ths, or 4ths and 5ths, or 3rds and 6ths etc. creating a variety of JI systems. Having the open tuning repeat at the octave every 2 strings means you are dealing with designing only a 2 string system, it then automatically repeats in octaves on the other strings due to the straight frets.
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Ron

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Re: A question about frets for just intonation
« Reply #11 on: September 06, 2011, 04:19:43 AM »

Hi. I’m new to this world of non-standard tunings (I’ve been vaguely interested in it for a little while but have never actually played in anything but 12-TET). I’ve been messing about with ratios on paper for the last few days and, though I’m not completely happy with it, I’ve come up with a tuning that somewhat appeals to me. However, what really doesn’t appeal to me is the way that JI guitars have those mini/broken frets or curved frets. I’m sort of beginning to accept that that’s just the way it is with JI but I don’t understand why that’s the case. All I know is it has something to do with string tension… maybe? If you can get the octave in tune with a regular straight fret, then why can’t you get the rest of the guitar in tune with straight frets?

So what I’d like to know is do the frets absolutely have to be like that? And, if so, why do they have to be like that? I've read some stuff about it but I still don't get it and this forum seems like it's probably the best place to ask. If any of you guys can help me get my head around this it would be much appreciated. I’m a bit of a technophobe and to be honest I’m not even really sure how guitars work (my best guess would be that some kind of magic is involved) so if you could put it in layman’s terms, as far as that’s possible, that would also be helpful.

Thanks.

The frets for just intonation are just that- pure intonation based on string divisions. equal temperaments can be viewd as subsets of the harmonic series or just intonation. So some people like to look at 12-tet like 2.3.5 subgroup based on those harmonics, while 16-tone could be a 2.5.7 subgroup, and so forth. some of them get pretty wacky, like 13-tet which has a neat 2.5.9.11.13.... or Triple Bohlen Pierce - 39-tone equal 3/1 (no octaves with steps near quartertone) with 3.5.7.9.11.13.15.19.21, which is pretty insane. For just intonation sonorities, you don't necessarily "need" JI frettings is my point here.

I haven't had much time lately to be on this site but I have been picking up my 9 string again, so keep my chops for my new 9. I'll make some vids today, I've been churning out guitars, I just made a 25-tet which is like a Rothenburg proper / Chromatic version of Mavila..  really sick, because you can tune it to mavila fourths, 11th fret, or blackwood fourths, tenth fret. So you have 2 diff fifths...The crazy thing is that in Blackwood string tuning is symmetrical so you end up with 10th fret tuning straight up all the strings of the guitar (because you're using 5-tet), and this works in 5,10,15,20,25,30-tet etc...so in multiples of five the arpeggios and chord fingerings don't change from 6th to 5th strings like a normal guitar. The learning curve is much more gentle in that way. It's like having a harmonic board with strings.

I use the Mavila tuning on my 25 right now because I'm so used to it in 16-tet, but Blackwood [10] is amazing. It's a 10-note MOS scale similar to half whole, but 1212121212 in 15-tet, 2323232323 in 25-tet yields symmetrical major and minor chords intertwining instead of dominant and diminished in 12-tone half whole scales.

For pure JI - you can have straight frets or broken frets, depending on how you want your open strings. Sorry if I'm being redundant by talking about things you already covered here..
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bigbadwolf

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Re: A question about frets for just intonation
« Reply #12 on: September 06, 2011, 09:33:18 AM »

Quote
While you ponder ... you may be interested in my tuning for conventionally fretted guitar which allows 24EDO and simple JI scales to be played just by buying a custom set of strings

I checked it out and that’s some great work you’ve done there. I’ve tried to think of tunings that would allow quarter tones before but it never worked very well. I found it hard to find the right balance between chords and melody so I gave up. This is actually a really practical way of doing it. I’ll have to try it out sometime, for sure. I bet you could write some good stuff with that tuning. Good job, man.

Quote
UK microtonal music?
The bard of Cholsey, Mark Allan Barnes

I like Welcome to Cholsey quite a bit. Actually, it’s quite refreshing to hear someone writing sort of ‘regular’ songs in these tunings. That’s probably what I’d end up trying to do with my tuning system.

I was looking at the xenharmonic wiki and the only microtonal guitarists listed on there who are from the UK are Charles Lucy and Damian Laws. I’ve read some stuff about Lucy tuning but I think it went over my head a bit, something to do with pi and then… ummmmm…*head explodes*. Unfortunately I can’t find anything much from Damian Law. So not much from the UK then, I guess. Well, hopefully people will catch on at some point.

Quote
What you want is possible, it's just a case of how many different scales/keys will be playable, it may only be a few, but then there are all the modes of each of those.
For example the JI chromatic scale: 1/1  16/15  9/8  6/5  5/4  4/3  45/32  3/2  8/5  5/3  9/5  15/8  2/1 on a tonic of C has 12 tones per octave and contains JI C major, JI C minor, JI C phrygian etc. and then all the modes of each of those. it's just a case of choosing your scale out of the 12 tones. The difficult bit is doing this with straight frets and a non-octave open tuning.

Cool. So, rather than there being 7 modes of the diatonic scale (major, minor, phrygian, etc.), in JI there would be 7 modes of the JI major scale, 7 modes of the JI minor scale, 7 modes of the JI phrygian scale, and so on. I never really thought about that. The way this is going it’s possible that I’m going to be able to play hundreds of different scales! Sweet. At the moment, I’ve got it so that you could play more than 10 major scales and quite a few other scales in some of the sus2/sus4 tunings that I’ll write a little bit about further down this post. I could probably fit more scales in but there are certain scales that I really want and I’d have to sacrifice some of those to do it.


Quote
The only reason i recommended a scientific calculator is for the LOG function, for converting ratios to cents

Ah, OK, gotcha. That seemed like a lot of hard work to me so I looked around and found a thing that does all of that for you - http://www.sengpielaudio.com/calculator-centsratio.htm

It’s pretty smart. The box on the top right is the one you need for that. There are some other converters on there that you might want to mess about with.

Quote
I'm thinking look into an 'standby' open tuning of all-tritones. This can then be easily retuned to alternating 5ths and 4ths, or 4ths and 5ths, or 3rds and 6ths etc. creating a variety of JI systems. Having the open tuning repeat at the octave every 2 strings means you are dealing with designing only a 2 string system, it then automatically repeats in octaves on the other strings due to the straight frets.


I thought about going with an all-tritones tuning for a while. First of all I was thinking all fifths and fourths would be the best way, and after I scrapped that idea I looked into all tritones, but in the end I decided that 3 notes on the open strings would be the perfect number for me. (I also looked into 4 but it just got silly. 3 is a lot more manageable.) So, with the way I’ve got it now, there would automatically be a few scales you can use with 3 different tonics. I don’t really want to be limited to having to stick with one tuning all the way, though. I like to be able to change tunings on a regular guitar, and I’ll probably feel the same way with this system, though that would switch all the intervals around so it might get confusing. At the moment I’m thinking of tuning to sus2/sus4 chords. I’m mostly thinking of tunings like DADGAD and EADEAD. Each tuning would remove some options but hopefully add some different ones to play with. I expect some tunings would be more usable than others but any tuning like that should work up to a point. Tunings like DADEAD, EABEBE, CGDGCD, anything like that should be OK, and open major or minor chords might be OK too. All of those kinds of tunings are made up of notes that are just intervals from each other. (So for the sus2/sus4 tunings it would be like D to E is 9/8, D to A is 3/2, E to A is 4/3, E to D is 16/9, A to D is 4/3 and A to E is 3/2 – I just think it’ll be less confusing that way.) All fifths and fourths would still work but I might have gone beyond the point where all tritones could work (though it might still work as a more experimental tuning). Nothing’s set in stone yet, so I could still change it all around. One thing which I’m a bit worried about is that a lot of the frets are going to be very close together. The system needs fine-tuning, for sure, maybe even a complete overhaul.
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bigbadwolf

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Re: A question about frets for just intonation
« Reply #13 on: September 06, 2011, 09:45:28 AM »

The frets for just intonation are just that- pure intonation based on string divisions. equal temperaments can be viewd as subsets of the harmonic series or just intonation. So some people like to look at 12-tet like 2.3.5 subgroup based on those harmonics, while 16-tone could be a 2.5.7 subgroup, and so forth. some of them get pretty wacky, like 13-tet which has a neat 2.5.9.11.13.... or Triple Bohlen Pierce - 39-tone equal 3/1 (no octaves with steps near quartertone) with 3.5.7.9.11.13.15.19.21, which is pretty insane. For just intonation sonorities, you don't necessarily "need" JI frettings is my point here.

I haven't had much time lately to be on this site but I have been picking up my 9 string again, so keep my chops for my new 9. I'll make some vids today, I've been churning out guitars, I just made a 25-tet which is like a Rothenburg proper / Chromatic version of Mavila..  really sick, because you can tune it to mavila fourths, 11th fret, or blackwood fourths, tenth fret. So you have 2 diff fifths...The crazy thing is that in Blackwood string tuning is symmetrical so you end up with 10th fret tuning straight up all the strings of the guitar (because you're using 5-tet), and this works in 5,10,15,20,25,30-tet etc...so in multiples of five the arpeggios and chord fingerings don't change from 6th to 5th strings like a normal guitar. The learning curve is much more gentle in that way. It's like having a harmonic board with strings.

I use the Mavila tuning on my 25 right now because I'm so used to it in 16-tet, but Blackwood [10] is amazing. It's a 10-note MOS scale similar to half whole, but 1212121212 in 15-tet, 2323232323 in 25-tet yields symmetrical major and minor chords intertwining instead of dominant and diminished in 12-tone half whole scales.

For pure JI - you can have straight frets or broken frets, depending on how you want your open strings. Sorry if I'm being redundant by talking about things you already covered here..
Hi, Ron.

In short: *head explodes*! Haha. I'm assuming that the numbers you're referring to (2.3.5, etc.) are the numbers of the harmonic series. Is that right? I really am pretty new to all of this! If that's right then why would 12-TET be 2.3.5 and another system be 2.3.7? Doesn't 12-TET get closer to the seventh harmonic than it does to the fifth? Or do those numbers mean something else?

Cheers.
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Mat

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Re: A question about frets for just intonation
« Reply #14 on: September 06, 2011, 12:14:46 PM »

Quote
I'm thinking look into an 'standby' open tuning of all-tritones.
I thought about going with an all-tritones tuning for a while.
What i mean by a 'standby' tuning is that all-tritones is never used, but is the average of all possible future retunings (it's the average of 5ths and 4ths, 4ths and 5ths etc.). Gauges are chosen to have all strings at equal tension in tritones tuning, this then gives the widest choice of retunings while avoiding overly tight or slack strings. Then you can tune 3/2 4/3 ... or 4/3 3/2 ... or 11/8 16/11 ... or 16/11 11/8 ... etc. etc.
;)
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