Yahoo Tuning Groups Ultimate Backup makemicromusic A combination-product-set guitar (part 3)

Dear MMMers,

Here's part 3 (the final part) of the email conversation that Pete McRae and I had a year ago.

Part 1 is at
/makemicromusic/topicId_13042.html#13042

Part 2 is at
/makemicromusic/topicId_13048.html#13048

In part 3 (below) information is given to help set up the tuning on a pair of keyboards so you can get to hear it, and some practical matters of refretting are discussed. Also some realities of 11th harmonics on acoustic guitars.
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[Dave:]

Hi Pete,

A few more points:

1. If you want to tell me the nut to bridge length of that classical guitar I can figure out what nylon string gauges you'll need.

2. There may not be much point in using interchangeable fretboards for this, because of the need for different string gauges, (due to the neutral thirds tuning being significantly compressed relative to standard tuning).

I assume you're not going to want to change strings every time you change fretboards, and if you don't you'll get some strings so loose they rattle and some so tight they break.

It could still be worthwhile if you think you might do other fretboards that use an open thirds tuning. They don't have to all be neutral thirds, they could be alternating minor and major. And if there was no more than one fourth in there, you could still get away with the same strings, if we chose their gauges as a compromise.

3. Those complicated designations for the open strings (like Gb/ and Bbt) are due to the fact that the notes with simple names occur on the 1st and 2nd frets (and the middle frets of every group of four) to maximise playability of their 7th harmonics and 5th subharmonics.

With the lowest string tuned to Gb/, the notes on the 1st and 2nd frets are:

Gv Bb Dv F Av C

G Bv D F^ A C^ where "v" and "^" are semiflat and semisharp.

4. One quite reasonable point in the tradeoff continuum for tempering out the neutral-thirds kleisma (243/242) corresponds to a subset of 72-ET. This would allow 6 notes of the eikosany (and 4 non-eikosany notes) to be tuned the same as in 12-ET. Note that's 10 notes total over the two and three-quarter octaves, not 10 in every octave (in case you were worried we were getting too close to 12-ET). :-)

I gather this isn't a big priority, but it would make tuning-up more convenient, and give _some_ possibility of playing along with conventional instruments.

By the way, I've often thought about designing an electric guitar that could harmonise with highland bagpipes. Know anyone who plays them? :-)

5. Lest you think that by not using a 1.3.7.9.11.15 Eikosany we are somehow settling for a second-class citizen, I note that the only reason Erv chose to make an instrument for the 1.3.7.9.11.15 Eikosany (plus two) and thereby gave it a name ("Pascal") was because he only had enough material for a 22-tone instrument. You can read this in
http://www.anaphoria.com/dal.PDF starting on the last line of the first page.

He later went on to use the 1.3.5.7.9.11 Eikosany (that we are using an octave-specific version of) as the core of the 31 note tuning he calls "D'alessandro".

6. I believe Kraig came to the conclusion that eikosanies were not suited to guitars because
(a) he was looking at the wrong eikosany (Pascal isn't suited to guitars), and
(b) he was assuming repetition at the octave, and
(c) he doesn't realise just how tiny is the tempering I am proposing to use to straighten out the frets.

Now of course octave-repetition is a pretty reasonable thing to assume, and in a way we're cheating by violating it, but what counts is how it sounds. So we'll just have to try it and see.

7. If you really wanted to split those 232 cent gaps, then I think what makes most sense is to use them to introduce some true octaves. If we used the 72-ET version of the microtemperament we'd put these frets right in the middle of every 233 cent interval.

8. To facilitate you trying it out on synthesizers here are the pitches of all the notes available on the guitar, expressed as deviations from 12-ET. The 20 notes of the octave-specific 4.5.6.7.9.11 eikosany are given their product designations below. I've given the 72-ET version of the tuning as this is a lot simpler to deal with in relation to 12-ET-based synths. And of course you can lower the whole thing a fourth if you want.

Gb/ F#2 +17c open string
Gv F#2 +50c
G G2
Gf G2 +33c 4.5.6

Bbt Bb2 -33c open string
Bb Bb2 4.5.7
Bv B2 -50c
B\ B2 -17c

Db/ C#3 +17c 4.6.7 open string
Dv C#3 +50c
D D3
Df D3 +33c 4.5.9

Ft F3 -33c open string
F F3 5.6.7
F^ F#3 -50c 4.6.9
F#\ F#3 -17c 4.5.11

Ab/ G#3 +17c 4.7.9 open string
Av G#3 +50c
A A3 4.6.11
Af A3 +33c 5.6.9
Note the reflective symmetry about this point.
Ct C4 -33c 4.7.11 open string
C C4 5.7.9
C^ C#4 -50c
C#\ C#4 -17c 5.6.11

Eb/ Eb4 +17c 6.7.9
Ev Eb4 +50c 5.7.11
E E4 4.9.11
Ef E4 +33c

Gt G4 -33c 6.7.11
G G4
G^ G#4 -50c
G#\ G#4 -17c 5.9.11

Bb/ Bb4 +17c
Bv Bb4 +50c
B B4 6.9.11
Bf B4 +33c

Dt D5 -33c 7.9.11
D D5
D^ Eb5 -50c
D#\ Eb5 -17c

We can map it to two keyboards in two different ways. We could either put every other note on the other keyboard, or we could put the top and bottom notes of each group of four on one keyboard (so we get a proper scale on that keyboard), and then put the middle notes of each group on the other keyboard.

In either case, you'll need to mark certain keys as "do not play", or just put stickers on all the keys that _are_ notes of the guitar.

Good luck.

[Pete:]

Dave,

My Yamaha synth is fully tunable over its whole range, in 1.17 cent increments. What's been my problem is getting my soft-synths that accept .tun and .scl files to line up with my old (more-than-12-tone?) tunings, some of which were done with a Scalatron [and] to match Kraig's actual ensemble. I've had some success, but it's not as easy as I think it should be.

Lately I've noticed I like 432Hz (A is 27/16) as a reference frequency, and C=256Hz for some things, but to my ear, its 426.6 (where A is 5/3) is actually too low. I'm still trying to decide how to manage all that. Some of my earliest attempts were to Partch's G=392Hz, and I still use them, too. I've been moving the Eikosany guitar I have around lately, in terms of A=440Hz or something else, and string guages. Right now, I like a .012-.052 "medium gauge" set tuned a little loose, which makes it pretty "light". We'll see. My instruments have been very forgiving in that sense.

I haven't had a lot of trouble with strings being too tight or too floppy, just with having to intonate the guitar when I change gauges. On an electric with adjustable bridges this isn't a big deal. On an acoustic it will be more crucial to set an acceptable range of tension and string-gauges, because the bridge is usually compensated for "normal" set-ups, if it's not just a straight line, ie uncompensated.

In any case, your data is a welcome consideration and help!

I'll probably get it fired up tomorrow, and hopefully my luthier pal will decide he's got time for me and my wackiness, around the same time.

[Pete:]

Dave,

I've pretty much decided to go with a simple refret, assuming that would be less prone to 'anomalies', but it may require a more 'ambitious' luthier, I'm afraid.

Apparently, the cost of a new strat neck has become somewhat prohibitive, but I'm still trying to decide what would be the highest quality/(relatively) low-cost solution. I think the Takoma budget acoustics have bolt-on necks, and sound quite good. I know a brilliant guy who'd love to do a _really_ nice guitar in xenharmonics, but that's another budget!

In any case, the fellow I had in mind is still backlogged. I'll keep you alerted.

Hopes you're well,

[Dave:]

Gidday Pete,

At 02:40 AM 16/03/2005, you wrote:
>I've pretty much decided to go with a simple refret, assuming that would be less prone to 'anomalies', but it may require a more 'ambitious' luthier, I'm afraid.

And Mark Rankin's kit is fairly expensive. Especially if you only end up doing one fretboard with it. That's why I balked at it.

One way to reduce anomalies with Mark's kit is to have a zero fret on the removable fretboard instead of relying on the nut and its relative position to the fretboard.

>Apparently, the cost of a new strat neck has become somewhat prohibitive, but I'm still trying to decide what would be the highest quality/(relatively) low-cost solution. I think the Takoma budget acoustics have bolt-on necks, and sound quite good.

Is it important that it have a bolt-on neck? Sure it will make it easier to work on, but it's not impossible otherwise.

I think most cheap guitars sound fine. A lot of the time you're just paying for a name. And with the smaller range of this tuning, you won't be asking for too much from it at the low and high ends where the problems are usually most evident (unless you go for the Db/ low string instead of the Gb/).

On the subject of anomalies: If you're going for an acoustic then you can't have a bridge with individual adjustments for each string because it would have too much mass and affect the acoustics. So it is very important to have the right gauge strings for the open tuning so that the tension of all the strings is similar and the frets can work accurately for all the strings.

Basically, the fretting has to assume a particular string tension and if you change the open tuning by more than about 50 cents then you should change string gauges to keep the tension the same.

> I know a brilliant guy who'd love to do a _really_ nice guitar in xenharmonics, but that's another budget!
>
>In any case, the fellow I had in mind is still backlogged.

Have you thought about doing it yourself? Have you seen John Starret's detailed instructions?
http://infohost.nmt.edu/~jstarret/guitar.html

If you use the 72-ET version, you can leave the existing 7th and 14th frets in place. But I think I still prefer the version with the strictly just 9-limit. Here's why:

While I don't think it's true that guitars can't do eikosanies, I think there may be a sense in which guitars (particularly acoustics) can't really do 11-limit JI. When you get to a ratio as complex as 9:11, you need fairly special conditions to actually _hear_ its justness (or unjustness).

First, you need a timbre that actually contains significant amounts of 9th and 11th harmonics (the plain strings of an acoustic guitar only do so during the initial attack and the wound strings only when they are very new).

Second, it needs to be sustained, in order to notice any slow beats or the absence thereof. Try actually playing an 11th harmonic by lightly damping a string about halfway between the first and second (12-ET) frets. If you can find it at all, you'll find it is very short lived.

Third, it needs to be tuned _very_ accurately. Consider a 4:5:9:11 tetrad. If a 2.5 cent error is barely tolerable in the 4:5 due to its beat rate then only a fifth of that error (0.5 cent) will be tolerable in the 9:11 (since it will produce the same beat rate). (9*11)/(4*5) ~= 5.

Reproducible 0.5 cent accuracy is impossible on a guitar, except by using sustained audible feedback to adjust finger tension and cancel beats. But with a 9:11 (or any ratio of 11) there is no such sustained audible beating.

So, once you're 0.5 cent away from the 9:11, any justness (in the sense of locking-in of partials) is lost and "a miss is as good as a mile" so the 3.6 cent error of our tuning will make no further significant audible difference. The approximate ratios of 11 will still have their affect as "neutral intervals" about halfway between major and minor.

To test this, I tried tuning the open strings on my (12-ET) acoustic guitar to 4:5:6:7:9:11, G B\ D Ft A C^.

I could tune all but the top string by ear. I could only tune the 9 by ear because it is a 2:3 from the 6 (I couldn't tune it against the 4, 5 or 7 strings). But I just could not find any obvious sweet spot for the 11, nor could I tune it by harmonics. I could tell when I was getting closer to it being a 10 or 12 than an 11 (+-25 cents), but there was no great audible difference in the general vicinity of 11, so I can't see how anyone is ever going to hear a 3.6 cent error in it. I recommend you try this for yourself.

>I'll keep you alerted.

Thanks. I'd appreciate that.

> Hopes you're well,

Yes. And the same to you. I'm going to be away for the next two and a half weeks. Going camping with the family, in Tasmania (I live in Brisbane Australia in case you didn't know). I may or may not have email during that time.

[Pete:]

Howdy, Dave,

> And Mark Rankin's kit is fairly expensive. Especially if you only end up
> doing one fretboard with it. That's why I balked at it.

My only interest is/was in the possibility of doing two or more with it, allowing for mistakes, tweaks, and chances to try other things, like a dekany?, or a more conservative JI for the luthier guy to have fun with.

I had one very fine luthier refuse to do my guitar, because, he said, for his effort he didn't like the sound of it (and all I asked for was "JI"). I thought THAT was interesting, and I had to respect it, because he was so damned talented! He did a wonderful refret on another one for me.

> Is it important that it have a bolt-on neck? Sure it will make it easier
> to work on, but it's not impossible otherwise.

The consideration there is that the guy who did the one I have has a CNC machine to cut the fret slots to max precision...but the jig is only for Fender-style necks.

I may just have the fellow here pull my frets for me and level the 'board. Then I'll play around with ligatures until I get something I really want done more solidly.

> Going camping with the family, in Tasmania

Sounds cool to me! (But I have NO idea what Tasmania might be like...)

Best,

Pete

[The end]

A combination-product-set guitar (part 3)

🔗Dave Keenan <d.keenan@...>

🔗Carl Lumma <ekin@...>

🔗Dave Keenan <d.keenan@...>

🔗Carl Lumma <ekin@...>