World Harmony Project

Carl Lumma's Cosmolyra

Carl Lumma with the Cosmolyra that he built during his residency at the Southeast Just Intonation Center

Ivor Darreg, inventor of the Cosmolyra with three Megalyras (the big brothers of the Cosmolyra)

Denny Genovese playing his Cosmolyra (a collaboration between Denny, Ivor Darreg and Buzz Kimball) with Carl's Cosmolyra in foreground

Detail showing Tuning pins and Nut

Detail showing end piece with output jack, pickups and bridge

Detail showing pickups and bridge

Q & A


> I saw Your Cosmolyra on the Corporeal-Page and I would like to know more about the tuning.


The instrument is based on two scales.  One is a harmonic series 8-16.  In ratios, that looks like...


<A>  1/1, 9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2/1


The other scale is based on a "sub-harmonic series" (that is, a Partchian "utonality") 6-12:


<B>  1/1, 12/11, 6/5, 4/3, 3/2, 12/7, 2/1


> Please tell me the intervals and how You manage to find them.  I'm using a 6-string Monochord and found the Intervals of 3/2, 4/3, 7/4 and 2/1. The more complicated intervals are still a mystery for me.



By ear, I can tune the 2/1, 3/2, 5/4, and 7/4 very accurately.  The 9/8 and 15/8 I get by tuning a 3/2 on top of the 3/2 and 5/4 respectively.  I can tune the 6/5 by tuning a 5/4 below a 3/2, and a 4/3 by tuning a 3/2 down from a 2/1.  With the 11/8 and 13/8, 12/11 and 12/7 I am less accurate, but I check myself against the strobe tuner, and I can get pretty close by trying to get chords like 10:11:12 smooth by adjusting the 11 after I've

already set the 10 and 12.


> The Cosmolyra is the first electric Partch-like instrument I saw.  What do you need the strings on the bottom for?  Is it just reverb or do you play on these strings?


The instrument has two sides, with strings on both.  It sits on stands at either end, and the player simply turns the instrument over to access the different sides.  Or, it can stand on end between the player's legs, so that both sides are accessible.


Side 1 has 13 strings arranged in a single course, from lowest to highest. The lowest string plays the F# below A 220 on an normal piano.  On the Cosmolyra, this pitch is called "4" (as in "4/1").  The other strings on Side 1 are then 5, 6, 7, 8, 9, 10, 11... 16.  In other words, the strings are tuned to two octaves of a harmonic series, starting on the 4th harmonic. A very simple and effective tuning.


Side 2 has three courses of strings:


i) Six strings are tuned 4, 5, 6, 7, 9, 11.  This is Partch's otonal hexad.


ii) Six strings are tuned 48/11, 16/3, 48/7, 8, 48/5, 12.  This is a Partchian utonal hexad rooted on 12.


iii) Three strings are tuned to 16.  This course of unisons was intended for melodic playing.


On the body of the instrument, on both sides, two different scales are marked in Dymo tape, to guide the slide, as it were.  Scale <A> is marked in blue tape (with 1/1 at the nut), and scale <B> in red.


> Still have a few doubts about the completeness of my understanding.


> If possible, and if it won't inconvenience you too much, could you also send me an example or two of an 11-limit scale, and possibly a 13 within one octave; that is if they include octaves...  


Let's look at some chords first:


5-limit (odd limit)

1/1, 6/5, 3/2

1/1, 5/4, 3/2


5-limit (prime limit)

1/1, 6/5, 3/2

1/1, 5/4, 3/2

1/1, 9/8, 5/4

1/1, 3/2, 15/8


The Cosmolyra basically has two scales...


blue: 1/1, 9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8 (2/1)

red: 1/1, 12/11, 6/5, 4/3, 3/2, 12/7 (2/1)


The blue scale has odd limit 15, and prime-limit 13.  The red scale has odd-limit 11, and prime-limit 11.


> This may sound silly, but when I marked the fretboard of a guitar I'd de-fretted for just intonation, I simply took the harmonics between the octaves of harmonic 15 and 31 to make a scale of pitches which I repeated on all 6 strings.  I don't know what kind of sense it made.


Well, you can see that I did something very similar for the Cosmolyra.

 Introduction

The name Cosmolyra was suggested in the early 70's by Erv Wilson, and applied to, I believe, the entire class of amplified string instruments that Ivor Darreg was building at the time.  Later, somehow, the very large instruments took on the name "Megalyra", and Cosmolyra became associated with the treble side of the spectrum.  Sometimes the individual instruments had names, too.  The first Cosmolyra was called "The Hobnailed Newel Post", and was written up in Xenharmonikon 5 (available from Frog Peak music).  This happens to be the instrument that was on loan to the Southeast Just Intonation Center when I was doing my residency there, and it was the inspiration for the instrument I built.


 Build it!

It's a really simple project.  I did it for less than $150, in about 40 hours.  I had very little experience working with tools, let alone building one of these.  The following parts came from Lowe's hardware store:


1 pine 2x6" (or hard wood)

1 red oak 1x6 (or hard wood)

1 sheet of steel (about 1/16" thick)

1 flat bar of aluminum (about 3/4 x 1/8")

1 steel rod (about 1" diameter)

1 sheet Plexiglass (or Lexan)

3 large hobby magnets (see below)

18 wood screws

1 bottle wood glue (I didn't use it all)

1 can tung oil (ditto)

1 pack graduated sandpaper (I *did* used it all)

1 tube instant epoxy (ditto!)


The following came from my local electronics shop...


1 spool copper "magnet wire" (see below)

1 resistor (1K)

1 standard 1/4" phone plug jack


The following came from my local music store...


lots of guitar strings

(recommend "ground wound" such as GHS Brite Flats)


The following came from Staples office supply...


1 Dymo tape printer

1 spool red tape

1 spool blue tape


Lastly, I ordered the following parts from the fantastic piano supply company, www.pianoparts.com:


1 dozen nickel-plated zither tuning pins

1 L-style, star head, zither tuning hammer

1 Peterson strobe tuner (optional)


The tools I used were borrowed from friends...


table saw

hand-held circular saw

manual hack saw

drill press

hand drill with hole saw attachment

Dremel drill with cutting wheel attachment.


Okay, there's your 150 bucks.  


Now, the theory (assuming you know a little about just intonation).  The instrument is two-sided because...


1. It gives you twice as much to play in the same amount of space

2. The thing would curl up under the tension of the strings otherwise


It is designed for regular guitar strings, using a speaking length of 26".

On Side A we have 13 strings, spaced 5/16" apart, and tuned to 4, 5, 6, 7, 8, 9....16 times a certain fundamental frequency.  This fundamental is chosen so the range of notes 4-16 times it will fit the range of available guitars strings.  This is, unfortunately, guess work.  I had to buy more strings than I used, and I even broke two or three.  I wound up tuning the

"4" string to 92.5hz, which is two F#'s below middle C on a piano tuned at A=440.  On Side B, we have 15 strings in three groups:


a) 6 strings tuned 4, 5, 6, 7, 9, 11 (Partchian otonal hexad)

b) 6 strings tuned 1/4, 1/5, 1/6, 1/7, 1/9, 1/11 (Partchian utonal hexad)

c) 3 strings tuned 16, 16, 16 (chorused unisons for melodic playing)


[There is one important note about group "b".  The ratios I list are only relative -- they don't share the same fundamental as the rest of the ratios on the instrument.  That is, unlike the other ratios in this document, you can't use them to calculate frequencies.  The 1/4 of group "b" is tuned to the 12 of the rest of the instrument.  This arrangement works well, because

the 1/6 of the utonal hexad tends to be heard as the root, despite Partch's theory, and 1/6 here is 8 -- an octave duplicate of our fundamental.]


The strings are spaced 1/4" apart, and the groups are spaced 5/8" apart.


I started by cutting the pine 2x6 to length on the table saw.  Then, using the lowest settings on the hand-held circular saw, I routed out areas at either end of the instrument, on both sides, for the bridge and pin blocks.

I routed 1/8" for the bridge blocks, and 1/4" for the pin blocks.  I cut the red oak for these blocks on the table saw.  In the bridge blocks, I routed grooves 3/8" deep for the bridges with one pass of the circular saw.  I cut the aluminum bar into sections with the hack saw, and tapped them into these

grooves with a drop of glue.  Then I sanded everything, including the aluminum bridges.  I drilled out the pin blocks for 4 wood screws each.  I glued all the blocks in place, clamping the bridge blocks and screwing down the pin blocks.  I finished the thing off with three coats of Tung oil.  It really brings out the natural beauty of the wood! :)


Next, I made the steel tail.  I forget how I cut the sheet metal to size. Maybe I used my friend's jig saw, maybe I did it by hand with the hack.  I measured the thickness of the instrument at the tail, and made a paper template showing the hole positions.  You should be able to see in the photo that these holes catch the grommets on the strings.  I lined up the holes so they would barely clear the bridge blocks at the end of the instrument, so the strings would have some downbearing on the bridge (the 1/8" deeper route to the pin blocks would provide downbearing at the nut).  I taped the template to the steel, used a punch to put dimples where the holes would be,

and then used these dimples to guide the bit on the drill press.


Pickups are easy.  I cut 4 pieces of Plexiglass to size.  This was actually the hardest part.  That stuff is hell to cut (maybe I had Lexan, or are Lexan and Plexiglass the same?).  I used the Dremel to score it (actually, sort of melt it), and then I broke it.  Now, I list 3 hobby magnets.  You'd only need two, but I couldn't find ones long enough.  So I bought three, and broke one in half.  So each pickup uses 1.5 magnets.  The point is, you can use any number of magnets.  Using the epoxy, I made sandwiches with the Plexiglass and magnets.  Just leave enough room around the magnet for 200-

500 windings of magnet wire.  Magnet wire is just copper wire that's coated with shellac, so it can make a coil (won't conduct through its sides).  Make sure to leave the inside end hang out!  After winding, I coated the coil with epoxy.  This stuff is great.  I plan on building my next instrument entirely out of epoxy. :)


I spray-painted the pickups black, but you don't really need to do that. What you need to do is use the hole saw to cut a 1-2" hole thru the middle of your instrument, where you want the pickups, and then from the tail end to intersect the first hole.  Now, you've got a number of wiring options, none of which I really understand.  I wired the like ends of the pickups together, left one pair hang, and hooked the other pair to the phone jack with a 1K resistor in the way.  The resistor may be optional -- I've heard various things.  It helps to have a soldering iron here.  Okay, you need one - so I forgot to list it above!  There are many pickup options you might

want to look into, including split coil pickups, called "humbuckers" because of their excellent S/N ratio. The point is, all your wiring is internal.  Now, I sealed the entire

business shut with epoxy.  In retrospect, I should have made little platforms for the pickups, with screws at each corner so their distance from the strings could be adjusted.  And I shouldn't have sealed the thing shut, in case I ever needed to access the wiring.


Stands:  You'll need those.  I found an old piece of wood on top of my buddy's outdoor fridge, and cut it into two pieces.  I glued and screwed them to the ends of the instrument.  I was clever enough to screw the tail piece to the stand with the same screws.  Then, I drilled through the holes in the tail, making matching holes in the stand at that end.  So the strings go right through the stand.  The tail has a hole for the phone jack, and the strings are grounded through it by virtue of everything fitting together!  What a great design!


Next I drilled holes for the tuning pins in the pin block, and carefully turned them in.  Then I strung it up.  I tune it with my Peterson strobe tuner, but you can tune it by ear, or with a microtonal synth, or whatever. I made a slide, since I couldn't buy one long enough, by hacksawing the steel bar listed above to length.


I let things settle for a month before measuring out the scale on the body. I started by calculating lengths from ratios, and then I tested those lengths with the strobe tuner.  In reality, strings stretch and whatever, so small corrections were made.  I marked the final positions on the body with Dymo tape.  I was amazed to find that the tape could be removed and re-stuck without leaving so much as a scratch on the finish.  Two years later, it hasn't budged an inch.  The scale I used is due to Denny Genovese,


1/1, 12/11, 9/8, 6/5, 5/4, 4/3, 11/8, 3/2, 13/8, 12/7, 7/4, 15/8.


It is a harmonic series 8-16:


1/1, 9/8, 5/4, 11/8, 3/2, 13/8, 12/7, 7/4, 15/8


plus a subharmonic series 6-12:


1/1, 12/11, 6/5, 4/3, 3/2, 12/7


I marked the harmonic part of the scale with blue tape, and the sub-harmonic part with red tape.  The idea is, you can modulate harmonic chords by subharmonic roots, and subharmonic chords by harmonic roots, in order to

navigate a Partch-like tonality diamond.


I want to stress that this was very much an experiment, and it was only by luck that it turned out at all.  Please take this as an example, rather than a set of instructions.  The other point I want to make is: I'm not a guitarist!  I can't play the bloody thing to save my life.  I built it for fun, and so I could  demonstrate JI until I can get a suitable microtonal keyboard.  


I'm going to go over some of the design points:


1. Pine is not good.  The body is already starting to warp.  I only used it because I couldn't find 2" oak.  I thought of laminating two 1" strips of oak together, and indeed this would have been much better, but I opted not to do it for time and money reasons.


2. The strings are too close together for easy fingerpicking, or so I have been told.  Maybe the body should be 8" across.  Although John Starrett did fingerpick the living daylights out of the thing when I showed it to him in Denver in 1998.


3. The tuning stability is good, but not great (I tune it about once a week).  Pine is responsible, I am sure, for much of this.  But tuning pins should be considered an expedient solution only.  I had actually drafted a very cool tuning machine for the instrument, based on a design of John Starrett's, and obtained estimates on it from two local machine shops. Unfortunately, I couldn't afford them.  I can describe this design if you want.


I couldn't have done this without Denny Genovese, who owned the fridge I mentioned above, and came up with the scale I used.  He also was caretaker of the instrument that inspired this project -- Ivor Darreg's four-sided "Hobnailed Newel Post".  Which was built on far less a budget than my instrument, and was still making music at age 20!


That's all I can think of for now.  Good luck!