Yahoo Tuning Groups Ultimate Backup makemicromusic 14 edo and 28 edo.

I've dug out my old 14 edo guitar fingerboard and started playing it on stage again. 14 edo is a natural addition to the other intonations I play on stage (to audiences used to 12 edo) because 7 edo seems to be well received despite being regarded as xenharmonic. So far I have been mostly using 7 edo triad barre chords, but with the addition of another 7 possible root notes.

I am finding 14 edo much harder to play than pythagorean or quarter comma meantone (7 edo is the easiest to play fingerboard I use), but I may be able to make it easier by making a new fingerboard with wider string spacing at the nut. The problem I have is not being able to squeeze my fingers in to play chords like the open A chord (0, 6, 14, 20, 24, 28 in 14 edo steps).

I am also reminded of an incident in The Farthest Shore (by Ursula Leguinne and part of the Earthsea quartet), where the king who's secret name is lebanen (same as name of cedar tree) is trying to play a foreign lute-like instrument and says he can't get it out of the minor key. I am finding that the triad 0, 4, 8 sounds minor to me, but is much more harmonious to me than the triad 0,5,8. The 5 step interval is almost exactly equal to the wolf major third of quarter comma meantone, which is exactly 32/25.

I have found, however, that the chord 0,5,8,11 sounds quite harmonious to me despite using the 5 step interval.

I also find that the chord 0,3,8 sounds more harmonious to me than 0,5,8, which doesn't entirely surprise me since I find the minor third more flexible in exact tuning than the major third, though this may just be my personal taste.

I have reallised that 28 edo would give an almost exact rendition of the 5/4 just major third (less than a cent out and closer than the 31 edo version) whilst still giving all the 7 edo notes that would be found on a Thai xylophone (if my music history is correct). I am intrigued by the idea of such a combination. Has anyone here tried much in 28 edo and do you have recordings I could listen to if you have? (I did start making a 12 note an octave fingerboard a while ago that gives just 5/4 thirds with roots on E, F, G, G#, A#, B, C# and D and has all minor thirds equal to the 12 edo minor third, which is more or less a selection of 12 notes from 28 edo, but I didn't get round to finishing it)

I would also be interested to listen to people's recordings in 14 edo to give myself more ideas of what to do in that intonation.

🔗Herman Miller <hmiller@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Mark <mark.barnes3@...>

🔗Herman Miller <hmiller@...>

🔗cityoftheasleep <igliashon@...>

Hi Mark,
14 and 28-EDO are pretty awesome, IMO. I wrote a track in each one as part of my electro-pop survey album of EDOs 9-28, "Map of an Internal Landscape". The 14-EDO track, "Today the Wind Brought Regret", can be heard here:
http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/Today+the+Wind+Brought+Regret

The 28-EDO track, "The Bittersweet Orange Glow of Nostalgia", can be heard here:
http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/The+Bittersweet+Orange+Glow+of+Nostalgia

Some moment-of-symmetry scales I like in 28-EDO are LLLLLsLLLL, where L=3 steps and s=1 step (this one gives the most triads with the near-pure major third and the 7-EDO fifth). This scale is shared with 19-EDO as well. Also, LLLLsLLLLs where L=3 steps and s=2 steps (which I used in the Bittersweet Orange Glow of Nostalgia, though shuffled to give LLLsLLLLLs). This scale is shared loosely with 18-EDO and 26-EDO as well.

14-EDO I actually like a bit better than 28, as it has one of my very favorite scales: LsLsLsLsL, where L=2 steps and s=1. It's generated by the "hemifourth", aka the 14-EDO subminor third around 257 cents, also found in 19-EDO (though I like the 14-EDO version better, it has more "life" to it). "Today the Wind Brought Regret" is actually probably one of my favorites of all the microtonal pieces I've written...the way chord progressions work in that scale is just so COOL! Most of the chords are both major AND minor, but because the major and minor thirds are separated by a whole tone, you can often get away with using both in the same chord without causing too much dissonance. And for a 9-note scale, I think something like 7 of the triads are consonant, which is pretty good. It's tough to find scales of 10 notes or fewer that have as high a ratio of consonant chords to dissonant ones as the diatonic scale, and this one is one of the best!

I do feel your pain on 14-EDO guitar, though. I've mapped it out, thinking that I'd want a 14-EDO guitar one of these days, but I can't find a good open-string tuning that makes both chords and scales easy. Trying to play a subminor barre-chord in standard 7-EDO tuning looks to be pretty impossible, but dropping the "G" string down a half-step throws off the scale patterns. I should ask Ron Sword how he tunes...he's written a book on 14-EDO guitar scales, you should give him a shout too!

-Igs

--- In MakeMicroMusic@yahoogroups.com, "Mark" <mark.barnes3@...> wrote:
>
> I've dug out my old 14 edo guitar fingerboard and started playing it on stage again. 14 edo is a natural addition to the other intonations I play on stage (to audiences used to 12 edo) because 7 edo seems to be well received despite being regarded as xenharmonic. So far I have been mostly using 7 edo triad barre chords, but with the addition of another 7 possible root notes.
>
> I am finding 14 edo much harder to play than pythagorean or quarter comma meantone (7 edo is the easiest to play fingerboard I use), but I may be able to make it easier by making a new fingerboard with wider string spacing at the nut. The problem I have is not being able to squeeze my fingers in to play chords like the open A chord (0, 6, 14, 20, 24, 28 in 14 edo steps).
>
> I am also reminded of an incident in The Farthest Shore (by Ursula Leguinne and part of the Earthsea quartet), where the king who's secret name is lebanen (same as name of cedar tree) is trying to play a foreign lute-like instrument and says he can't get it out of the minor key. I am finding that the triad 0, 4, 8 sounds minor to me, but is much more harmonious to me than the triad 0,5,8. The 5 step interval is almost exactly equal to the wolf major third of quarter comma meantone, which is exactly 32/25.
>
> I have found, however, that the chord 0,5,8,11 sounds quite harmonious to me despite using the 5 step interval.
>
> I also find that the chord 0,3,8 sounds more harmonious to me than 0,5,8, which doesn't entirely surprise me since I find the minor third more flexible in exact tuning than the major third, though this may just be my personal taste.
>
> I have reallised that 28 edo would give an almost exact rendition of the 5/4 just major third (less than a cent out and closer than the 31 edo version) whilst still giving all the 7 edo notes that would be found on a Thai xylophone (if my music history is correct). I am intrigued by the idea of such a combination. Has anyone here tried much in 28 edo and do you have recordings I could listen to if you have? (I did start making a 12 note an octave fingerboard a while ago that gives just 5/4 thirds with roots on E, F, G, G#, A#, B, C# and D and has all minor thirds equal to the 12 edo minor third, which is more or less a selection of 12 notes from 28 edo, but I didn't get round to finishing it)
>
> I would also be interested to listen to people's recordings in 14 edo to give myself more ideas of what to do in that intonation.
>

🔗Mark <mark.barnes3@...>

Thank you very much for sharing those tracks and for your suggestions of scales and advice. I particularly enjoyed Today The Wind Brought Regret. I have had a similar problem with tuning a guitar to 9 edo. 9 edo gives both minor and major triads but to get the minor e shape barre chord you have to tune the g string to the minor third (from e) giving string tunings in 9 edo steps of 0, 4, 8, 11, 14, 18 which makes scales more difficult (for me) than 0, 4, 8, 12, 14, 18. I haven't used 9 edo on stage or recordings much because I think that the 5th is too flat for most of my audience at 666 and two thirds cents. With 14 edo I have the additional problem of the frets being much closer together, which makes it very hard for me to finger chords such as the open a chord which has the b, g and d strings all held down at the 2nd fret. My fingers are too wide to fit between the frets. Making the string spacing wider may solve this.

The 14 edo interval you and Herman Miller seem to be regarding as a major third I have had odd experiences with. It's basically the wolf major third of quarter comma meantone which is 32/25.

When I first made a quarter comma meantone fingerboard (this was before I had Scala, so the only way for me to test a new intonation was to make a fingerboard for it) I heard the major chords with the normal major third (5/4) and the major chords with the wolf third (32/25) as different but equally beautiful. (incidentally, all the chords I am talking about had the same 5th interval, which is the fourth root of 5, which is about 696.578 cents). After having played with quarter comma for some months I found that I liked the chords with the 5/4 third much much more than 12 edo major chords, but felt that the 32/25 third chords were almost completely unusable because of their dissonance. I would use this to check the guitar was in tune by playing the 5/4 major chords and then the 32/25 major chords and comparing the sound. Since having listened to your 14 edo and 28 edo pieces and Herman Miller's 14 edo piece I have found that I no longer hear the 32/25 third major chords of quarter comma meantone as dissonant in the way that I did just a few weeks ago.

--- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> "Today the Wind Brought Regret", can be heard here:
> http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/Today+the+Wind+Brought+Regret
>
> The 28-EDO track, "The Bittersweet Orange Glow of Nostalgia", can be heard here:
> http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/The+Bittersweet+Orange+Glow+of+Nostalgia
>

🔗cityoftheasleep <igliashon@...>

Y'know, when I play in 9, it's on my 18-EDO guitar, and lemme tell you, barre chords are an absurdity on that thing! I hadn't even thought about the fact that I can't play a minor barre with a root on the low E. Of course, that's assuming I'm using 9-EDO standard...though 18-EDO standard is just as nonsensical, because the fifth is so wide I can hardly span it (I have small hands). I don't find the 666+2/3-cent fifth to be objectionable, though, I even prefer it to the 675-cent fifth of 16-EDO (much as I love 16-EDO)...perhaps because it is very near the 47th harmonic? I dunno. Either way, if you play 9-EDO on guitar with some effects processing (a little reverb and delay goes a long way), it sounds pretty good, very lush and psychedelic.

Isn't it weird how some EDOs just resist the guitar? Come to think of it, aside from 19-EDO, they all kind of do. I've tried 5, 8, 9, 10, 15, 16, 17, 18, 20, 22, and 31, and aside from 5 and 10, I've found them all to be very "un-ergonomic" when dealing with either scales or chords (or both!). Hence, I tend to rely very heavily on "open" or drone tunings. Maybe trying an open tuning in 14-EDO might help? At any rate, if 14-EDO puts the frets too close for you to play some chords, 28-EDO will be a real horror for you.

-Igs

--- In MakeMicroMusic@yahoogroups.com, "Mark" <mark.barnes3@...> wrote:
>
> Thank you very much for sharing those tracks and for your suggestions of scales and advice. I particularly enjoyed Today The Wind Brought Regret. I have had a similar problem with tuning a guitar to 9 edo. 9 edo gives both minor and major triads but to get the minor e shape barre chord you have to tune the g string to the minor third (from e) giving string tunings in 9 edo steps of 0, 4, 8, 11, 14, 18 which makes scales more difficult (for me) than 0, 4, 8, 12, 14, 18. I haven't used 9 edo on stage or recordings much because I think that the 5th is too flat for most of my audience at 666 and two thirds cents. With 14 edo I have the additional problem of the frets being much closer together, which makes it very hard for me to finger chords such as the open a chord which has the b, g and d strings all held down at the 2nd fret. My fingers are too wide to fit between the frets. Making the string spacing wider may solve this.
>
> The 14 edo interval you and Herman Miller seem to be regarding as a major third I have had odd experiences with. It's basically the wolf major third of quarter comma meantone which is 32/25.
>
> When I first made a quarter comma meantone fingerboard (this was before I had Scala, so the only way for me to test a new intonation was to make a fingerboard for it) I heard the major chords with the normal major third (5/4) and the major chords with the wolf third (32/25) as different but equally beautiful. (incidentally, all the chords I am talking about had the same 5th interval, which is the fourth root of 5, which is about 696.578 cents). After having played with quarter comma for some months I found that I liked the chords with the 5/4 third much much more than 12 edo major chords, but felt that the 32/25 third chords were almost completely unusable because of their dissonance. I would use this to check the guitar was in tune by playing the 5/4 major chords and then the 32/25 major chords and comparing the sound. Since having listened to your 14 edo and 28 edo pieces and Herman Miller's 14 edo piece I have found that I no longer hear the 32/25 third major chords of quarter comma meantone as dissonant in the way that I did just a few weeks ago.
>
> --- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > "Today the Wind Brought Regret", can be heard here:
> > http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/Today+the+Wind+Brought+Regret
> >
> > The 28-EDO track, "The Bittersweet Orange Glow of Nostalgia", can be heard here:
> > http://www.last.fm/music/City+Of+The+Asleep/Map+of+an+Internal+Landscape/The+Bittersweet+Orange+Glow+of+Nostalgia
> >
>

🔗Mark <mark.barnes3@...>

--- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Y'know, when I play in 9, it's on my 18-EDO guitar, and lemme tell you, barre chords are an absurdity on that thing! I hadn't even thought about the fact that I can't play a minor barre with a root on the low E. Of course, that's assuming I'm using 9-EDO standard...though 18-EDO standard is just as nonsensical, because the fifth is so wide I can hardly span it (I have small hands).

Mark: After trying 14 edo (the second microtonal fingerboard I made) and finding it too difficult I tried some edos with less than 12 notes in an octave. I rather like 9 edo. It's the only edo on my (first) microtonal album, but only as a lead riff intro with drone bass. Having less frets makes it easier to stretch to reach notes and easier to play generally. 9 edo has easy major barre chords (The E and A shape major chords are open 1st fret 1st fret open open open and open open 1st fret 1st fret 2nd fret open open in the tuning I use). And one easy minor barre chord (the open a minor form is open open 1st fret 1st fret 1st fret open).

City Of The Asleep: I don't find the 666+2/3-cent fifth to be objectionable, though, I even prefer it to the 675-cent fifth of 16-EDO (much as I love 16-EDO)...perhaps because it is very near the 47th harmonic? I dunno. Either way, if you play 9-EDO on guitar with some effects processing (a little reverb and delay goes a long way), it sounds pretty good, very lush and psychedelic.

Mark: I have sometimes had 9 edo well received by listeners and sometimes badly. For example, I once played a 9 edo version of House of The Rising Sun (The Animals' Version) and that was well received on that occasion. I was cautious when recording my first microtonal album (It's almost all Pythagorean and Quarter Comma Meantone) and I have been a bit more cautious with live performances lately. The 2 step 9 edo interval is one of the closest approximations to a just interval that I know. It approximates 7/6 with an accuracy closer than 2 ninths of a cent. Two of these make the fourth, so a 9 edo fifth is basically 72/49.
>
>City Of The Asleep: Isn't it weird how some EDOs just resist the guitar? Come to think of it, aside from 19-EDO, they all kind of do. I've tried 5, 8, 9, 10, 15, 16, 17, 18, 20, 22, and 31, and aside from 5 and 10, I've found them all to be very "un-ergonomic" when dealing with either scales or chords (or both!). Hence, I tend to rely very heavily on "open" or drone tunings. Maybe trying an open tuning in 14-EDO might help? At any rate, if 14-EDO puts the frets too close for you to play some chords, 28-EDO will be a real horror for you.

Mark: I recommend 7 edo. I find it much easier on guitar than 12 edo. Much of the chord shapes are like 12 edo, but easier.
I keep thinking that I should use a fretted instrument with a completely different tuning or a different number of strings to make more intonations easy. 12 edo resists the guitar a lot too. Try playing a six note version of a diminished triad (no 7th) or an augmented 5th triad. Have you tried using a Chapman stick? I haven't tried it myself, but it has been suggested that it might be more suitable for microtonal music than a guitar.
>