41edo Keyboards: Difference between revisions
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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. | 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: | There are various DIY options. Or these existing high-end instruments could be retuned to 41-edo: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! rowspan="3" |midi | ! colspan="2" | | ||
! # of notes | |||
! price (2021) | |||
|- | |||
! rowspan="3" | midi | |||
controllers | controllers | ||
! rowspan="2" |[https://www.rogerlinndesign.com/linnstrument Linnstrument] | ! rowspan="2" | [https://www.rogerlinndesign.com/linnstrument Linnstrument] | ||
|128 (8x16) | | 128 (8x16) | ||
|$1000 | | $1000 | ||
|- | |- | ||
|200 (8x25) | | 200 (8x25) | ||
|$1500 | | $1500 | ||
|- | |- | ||
![https://www.lumatone.io/ Lumatone] | ! [https://www.lumatone.io/ Lumatone] | ||
|280 hexagonal | | 280 hexagonal | ||
|$3600 | | $3600 | ||
|- | |- | ||
! rowspan="4" |string | ! rowspan="4" | string | ||
instruments | instruments | ||
![http://stick.com/ Chapman Stick] | ! [http://stick.com/ Chapman Stick] | ||
|various options | | various options | ||
|varies | | varies | ||
|- | |- | ||
! rowspan="3" |[https://www.marcodi.com/pages/harpejji-model-comparison Harpejji] | ! rowspan="3" | [https://www.marcodi.com/pages/harpejji-model-comparison Harpejji] | ||
|12 strings x 15 12-edo frets (25 or 26 41-edo) | | 12 strings x 15 12-edo frets (25 or 26 41-edo) | ||
|$2600 | | $2600 | ||
|- | |- | ||
|16 strings x 19 (32) frets | | 16 strings x 19 (32) frets | ||
|$4000 | | $4000 | ||
|- | |- | ||
|24 strings x 15 (25-26) frets | | 24 strings x 15 (25-26) frets | ||
|$6000 | | $6000 | ||
|} | |} | ||
The [https://www.striso.org/ Striso board] has potential, but currently it has only 61 keys. | The [https://www.striso.org/ Striso board] has potential, but currently it has only 61 keys. | ||
== Layouts == | == Layouts == | ||
=== Horizontal skip-key layout === | |||
===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.[[File:The Kite Tuning 3.png|none|thumb|879x879px]] | 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.[[File:The Kite Tuning 3.png|none|thumb|879x879px]] | ||
| Line 53: | Line 53: | ||
Here is a computer-keyboard and touch-screen playable [https://sevish.com/scaleworkshop/?name=41%20equal%20divisions%20of%202%2F1&data=29.26829268292683%0A58.53658536585366%0A87.8048780487805%0A117.07317073170732%0A146.34146341463415%0A175.609756097561%0A204.8780487804878%0A234.14634146341464%0A263.4146341463415%0A292.6829268292683%0A321.9512195121951%0A351.219512195122%0A380.4878048780488%0A409.7560975609756%0A439.0243902439025%0A468.2926829268293%0A497.5609756097561%0A526.829268292683%0A556.0975609756098%0A585.3658536585366%0A614.6341463414634%0A643.9024390243902%0A673.1707317073171%0A702.439024390244%0A731.7073170731708%0A760.9756097560976%0A790.2439024390244%0A819.5121951219512%0A848.7804878048781%0A878.048780487805%0A907.3170731707318%0A936.5853658536586%0A965.8536585365854%0A995.1219512195122%0A1024.3902439024391%0A1053.658536585366%0A1082.9268292682927%0A1112.1951219512196%0A1141.4634146341464%0A1170.7317073170732%0A1200.&freq=440.621&midi=69&vert=13&horiz=2&colors=&waveform=octaver&env=perc-medium horizontal 41edo skip-key layout in scale workshop]. | Here is a computer-keyboard and touch-screen playable [https://sevish.com/scaleworkshop/?name=41%20equal%20divisions%20of%202%2F1&data=29.26829268292683%0A58.53658536585366%0A87.8048780487805%0A117.07317073170732%0A146.34146341463415%0A175.609756097561%0A204.8780487804878%0A234.14634146341464%0A263.4146341463415%0A292.6829268292683%0A321.9512195121951%0A351.219512195122%0A380.4878048780488%0A409.7560975609756%0A439.0243902439025%0A468.2926829268293%0A497.5609756097561%0A526.829268292683%0A556.0975609756098%0A585.3658536585366%0A614.6341463414634%0A643.9024390243902%0A673.1707317073171%0A702.439024390244%0A731.7073170731708%0A760.9756097560976%0A790.2439024390244%0A819.5121951219512%0A848.7804878048781%0A878.048780487805%0A907.3170731707318%0A936.5853658536586%0A965.8536585365854%0A995.1219512195122%0A1024.3902439024391%0A1053.658536585366%0A1082.9268292682927%0A1112.1951219512196%0A1141.4634146341464%0A1170.7317073170732%0A1200.&freq=440.621&midi=69&vert=13&horiz=2&colors=&waveform=octaver&env=perc-medium horizontal 41edo skip-key layout in scale workshop]. | ||
===Vertical skip-key layout === | === 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. | 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. | 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. | ||
| Line 60: | Line 60: | ||
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. | 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=== | === 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 [https://hpi.zentral.zone/tonalplexus 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. | 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 [https://hpi.zentral.zone/tonalplexus 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. | ||
[[File:41edo keyboard layout.png|none|thumb|517x517px]] | [[File:41edo keyboard layout.png|none|thumb|517x517px]] | ||
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. | 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. | ||
[[File:41-edo keyboard 2.jpg|none|thumb|795x795px]] | [[File:41-edo keyboard 2.jpg|none|thumb|795x795px]] | ||
Various hexagonal Lumatone layouts are a possibility too, see below. | Various hexagonal Lumatone layouts are a possibility too, see below. | ||
=== Bosanquet layout === | === Bosanquet layout === | ||
A 7-column hexagonal layout. See the first lumatone link below. | A 7-column hexagonal layout. See the first lumatone link below. | ||
=== Multi-Halberstadt === | === 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. | 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 | For a layout that contains a 41-edo subset, see https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_73151.html#74155 | ||
== High-end Options== | == High-end Options == | ||
Linnstrument options are described above. | Linnstrument options are described above. | ||
=== Lumatone Options === | === Lumatone Options === | ||
[[Lumatone mapping for 41edo]] | [[Lumatone mapping for 41edo]] | ||
| Line 108: | Line 107: | ||
See also "Learning Lumatone: Ep. 27 - 41-Edo Basics": https://youtu.be/BfZVnktJZdw | See also "Learning Lumatone: Ep. 27 - 41-Edo Basics": https://youtu.be/BfZVnktJZdw | ||
===Harpejji Options=== | === 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. | 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. | ||
'''<u>12 strings</u>''' x 15 old frets (25 or 26 new) = $2600 | '''<u>12 strings</u>''' 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. | One rainbow zone has 3 octaves plus a 6th total range, 3 octaves tonic-to-tonic guaranteed in every key. | ||
| Line 117: | Line 116: | ||
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. | 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. | ||
'''<u>16 strings</u>''' x 19 old (32 new) = $4000 | '''<u>16 strings</u>''' 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. | 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. | ||
'''<u>24 strings</u>''' x 15 (25 or 26) = $6000 is probably overkill | '''<u>24 strings</u>''' 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. | 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== | == DIY Options == | ||
===Reed Organ=== | === 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. | 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. | 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. | ||