41-edo Keyboards
Overview
This page discusses layouts for 41-equal keyboards and tapping instruments. Some of the layouts are skip-key layouts, analogous to the Kite Guitar.
The usual guitar vs. keyboard trade-off is that the keyboard has more range and polyphony and freedom of voicing, but the guitar is more expressive (bends, slides, vibrato etc.) Tapping instruments are included here with the keyboards as these have much the same trade-offs. This page discusses the design of an instrument that does what a 61-note 12-edo keyboard does. Instantly play in any key (or at least every other key) without using transpose buttons, and a 5 octave range, so 4 octaves low-tonic-to-high-tonic range is guaranteed in every key.
There are various DIY options. Or these existing high-end instruments could be retuned to 41-edo:
| # of notes | price (2021) | ||
|---|---|---|---|
| midi
controllers |
Linnstrument | 128 (8x16) | $1000 |
| 200 (8x25) | $1500 | ||
| Lumatone | 280 hexagonal | $3600 | |
| string
instruments |
Chapman Stick | various options | varies |
| Harpejji | 12 strings x 15 12-edo frets (25 or 26 41-edo) | $2600 | |
| 16 strings x 19 (32) frets | $4000 | ||
| 24 strings x 15 (25-26) frets | $6000 | ||
The Striso board has potential, but currently it has only 61 keys.
Layouts
Horizontal skip-key layout
Skipping every other key like the Kite guitar skips frets makes chord shapes twice as compact. Also it makes it easy to switch from Kite guitar to Kite keyboard. The obvious layout duplicates the Kite guitar exactly. The "strings" run horizontally. One hand plays in each rainbow zone. Most notes are duplicated, and you can roll on that note with both hands, good for rhythmically dense music.
This picture matches the 8x25 Linnstrument, if you omit the first column and add 1 row. But the Linnstrument would have only a 3 octave range. And it gives you 2 full rainbow zones in only 6 keys! These 6 tonics are found in the 2x3 rectangle in the bottom 3 rows, in the columns marked "-1" and "0".
30 columns makes a 7x3 rectangle = 21 keys. To get a 13x3 rectangle = 39 keys, we need 36 columns. If one ever needed to play in the other 2 keys, they would still work. One would just give up the high ^M6. Or go to 37 columns, or 40 or even 45 or 50 to let you play "I Will Survive" in any key. (This song "walks" all over the fretboard.) To get a full 5 octave range, more rows are needed. 14 rows makes 5 octaves. 14 x 30 = 420 keys and 14 x 40 = 560 keys.
Here is a computer-keyboard and touch-screen playable horizontal 41edo skip-key layout in scale workshop.
Vertical skip-key layout
You could rotate the layout 90 degrees so that one long rainbow zone runs sideways. "Strings" are now vertical columns, like the Harpejji. This is more like a piano layout, runs mainly left to right, not down to up.
The smaller Linnstrument's 16 columns would make 5 octaves. But the zone doesn't fit entirely on the 8 rows. 12 or more rows are needed for a single tonic's zone. To get a 3x13 rectangle of 39 tonics, 24 rows are needed. 24 rows by 16 columns = 384 keys.
Ideally a midi keyboard could switch between both layouts. Encompassing both 14x40 and 16x24 requires 16x40 = 640 keys. A 2x2 array of four Linnstruments makes 16x50. Total cost is $6000.
12-column layout
This layout has keys one edostep apart adjacent to each other, forming a column. The top of one column "jumps" to the bottom of the next column. It's like the Tonal Plexus layout, but omitting 80% of the keys to reduce 205-edo to 41-edo. Each column corresponds to a 12-edo note. The columns with white keys have 3 notes, and the columns with black keys have 4 notes. Most white keys have a black-key sharp to its upper right and a black-key flat to its lower left. This picture shows 2 octaves, with the white keys running C to C.
To avoid awkward reaches when playing near the upper or lower edge of the keyboard, some duplication of pitches might be desirable, analogous to a button accordion having 5 rows of buttons but only 3 rows of reeds. This picture shows a layout in which every note appears twice.
Various hexagonal Lumatone layouts are a possibility too, see below.
Bosanquet layout
A 7-column hexagonal layout. See the first lumatone link below.
Multi-Halberstadt
One can use several conventional 12-edo keyboards simultaneously. For example, there can be two keyboards, one set above the other. Each one is tuned skip-key, analogous to one string on a Kite guitar, so that the 5th spans 12 keys. One keyboard is tuned one edostep sharper than the other. This provides an isomorphic layout that contains all 41 notes without specialized hardware. But it takes two hands to do what one hand does in 12-edo, e.g. play a tetrad in close position.
For a layout that contains a 41-edo subset, see https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_73151.html#74155
High-end Options
Linnstrument options are described above.
Lumatone Options
terpstrakeyboard.com Bosanquet layout
terpstrakeyboard.com 12-column layout slanted
terpstrakeyboard.com 12-column layout not slanted
terpstrakeyboard.com horizontal skip-key layout slanted
terpstrakeyboard.com horizontal skip-key layout not slanted
terpstrakeyboard.com vertical skip-key layout slanted
terpstrakeyboard.com vertical skip-key layout not slanted
terpstrakeyboard.com vertical skip-key layout alternate slant and flipped rotation
See also these five 41edo layouts from Herman Miller https://www.youtube.com/watch?v=ZeUdl-54CrI
Zip file of these layouts: https://en.xen.wiki/images/b/b9/41edo_lumatone_layouts.zip
See also this facebook discussion https://www.facebook.com/groups/lumatone.keyboard/posts/4777542052354989/
See also "Learning Lumatone: Ep. 27 - 41-Edo Basics": https://youtu.be/BfZVnktJZdw
Harpejji Options
In the chart above, the rows are strings. The player is on the left, facing right. If the lowest string is on the player's left, all the guitar chord shapes would be flipped to their mirror image. Rather than having a luthier refret it, it's probably best to get Marcodi to do a custom fretting, better in the long run for later customers. Note that the intra-string interval changes from 2\12 to 13\41, so new string gauges are needed.
12 strings x 15 old frets (25 or 26 new) = $2600
One rainbow zone has 3 octaves plus a 6th total range, 3 octaves tonic-to-tonic guaranteed in every key.
15x3 rectangle of tonics = all 41 keys, but one can jump up a zone to get an extra 5th of range in only a few keys.
16 strings x 19 old (32 new) = $4000
One rainbow zone is 5 octaves wide. 4 octaves tonic-to-tonic is guaranteed in all 41 keys. One can get a 2nd zone in most keys.
24 strings x 15 (25 or 26) = $6000 is probably overkill
Assuming the 16-string model, and estimating $1000 setup costs and $500 increased parts and labor, the total cost would be $5500 for the first one, and $4500 for future orders.
DIY Options
Reed Organ
If it's acceptable to do without dynamics, one can make a giant reed organ instrument fairly cheaply. It would use reeds from accordions or harmonicas. Such reeds are not too hard to tune by hand. A 10-hole harmonica supplies 20 reeds. The keyboard could be modeled after an accordion's button keyboard. A foot pump or an electric motor would pump air.
The mechanism could be similar to an accordion. Inside an accordion, each reed is in a little wooden box. It's like a tiny room, a closet where the reed is the door of the room. Valves limit a reed to sound on either inhale or exhale, but valves wouldn't be needed in a reed organ. Air flows in/out thru a hole in the ceiling when the button on the roof is pressed.