Lumatone mapping for 26edo: Difference between revisions

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== Diatonic ==

Being in the [[flattone]] part of [[meantone]], and indeed at the flat end of flattone itself, 26edo requires some adjustment to convert [[common practice]] music to sound right, and what is technically a diatonic layout (although fairly extreme in its softness) may require different usage than in a more middle-of-the-road diatonic tuning. [[YoVariable]] demonstrates this mapping in [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025) and explains the harmonic characteristics of 26edo (with demonstrations of chord shapes on this layout) in [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone''] ~~by [[YoVariable]] (2026)~~.

Being in the [[flattone]] part of [[meantone]], and indeed at the flat end of [[flattone]] itself, 26edo requires some adjustment to convert common practice music to sound right, and what is technically a diatonic layout (although fairly extreme in its softness) may require different usage than in a more middle-of-the-road diatonic tuning. [[YoVariable]] demonstrates this mapping in [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025) and explains the harmonic characteristics of 26edo (with demonstrations of chord shapes on this layout) in [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone'']. However, being at the flat end of flattone, 26edo does not have very accurate 5-limit approximations, so other options are probably preferable.

== Orgone ==

== Orgone + Superkleismic ==

~~However, 26edo is a [[flattone]] system that does not have very accurate 5-limit approximations, so other options are probably preferable.~~ If you want to ~~maximise~~ the playable range and put the best consonances close to each other, the [[orgone]] mapping is the clear winner.

If you want to maximize the playable range and put the best consonances close to each other, the [[orgone]] + [[superkleismic]] mapping is the clear winner. These temperaments meet at 26edo; they use a sharp classic minor third ~[[6/5]] (as 7\26) as their generator, which can also be mapped with greater accuracy but much greater complexity as a slightly flat doublewide minor third ~[[35/29]]. Either way, the generator chain is accessed very simply by moving right one key at a time. Two keys right yields a slightly flat undecimal minor fifth ~[[16/11]]; three keys right yields a near-just septimal minor seventh ~[[7/4]]; nine keys right with two octave-reductions (which translates into two keys up and one key right) gives the sharp fourth ~[[4/3]]; and another key right from this gives the very sharp classic minor sixth ~[[8/5]].

== ~~Other mappings~~ ==

== Lemba ==

The [[~~Lemba~~]] ~~and [[Hendec]] mappings also work particularly~~ well in 26edo.

The [[lemba]] mapping works well in 26edo, as [[Bryan Deister]] has demonstrated in [https://www.youtube.com/shorts/Gw9Fu5MAozs ''Waltz in 26edo''] (2025); he explains that right (which is a near-just septimal major second ~[[8/7]]) and up yields the sharp classic minor third ~[[6/5]] and right three times yields the flat fifth ~[[3/2]] (bypassing the semioctave-reduction). The range is just under six octaves, with a gentle downward slope.

~~=== Lemba ===~~

[[Bryan Deister]] has demonstrated ~~this mapping~~ in [https://www.youtube.com/shorts/Gw9Fu5MAozs ''Waltz in 26edo''] (2025)~~, and~~ explains that right and up yields the minor third (~[[6/5]]~~, fairly sharp)~~ and right three times yields the fifth (~[[3/2]], ~~fairly flat)~~.

=== Hendec ===

== Hendec ==

For those who favor stacking major rather than minor thirds, 26edo offers a good option with [[hendec]], which uses a slightly flat undecimal (pentacircle) major third ~[[14/11]] as its generator, which at 9\26, is reached simply by moving one key right plus one key down-right. Two of these generators make the very sharp classic minor sixth ~[[8/5]]. Five of these generators after octave-reduction (which translates to one key right plus four keys down-right) yields the flat classic major sixth ~[[5/3]]. The octaves still slope downwards gently, with a range a bit less than that of lemba, but in exchange, the diatonic scale is also easily accessible in a way reminiscent of neutral thirds mappings.

== Fifive ==

With the fifth ~[[3/2]] being divisible by 5 (going from 15\26 down to 3\26, which is a near-just lesser tridecimal neutral second ~[[13/12]]), [[26edo]] supports [[fifive]] temperament, as shown in [[Bryan Deister]]'s [https://www.youtube.com/shorts/WvnJb5VNGj4 ''<nowiki>Caprice in 26edo [short clip]</nowiki>''] (2026). This uses 3\26 as the (rightward) generator, and splits the octave in half. Two of these make a sharp septimal minor third ~[[7/6]] which also functions as a flat tridecimal minor third ~[[13/11]], or a mildly flat diatismic minor third ~[[20/17]]; three of these make a very flat septimal major third ~[[9/7]] or a slightly flat undecimal (pentacircle) major third ~[[14/11]]; four of these make a slightly sharp undecimal major fourth ~[[11/8]]; five of these make a very flat fifth ~3/2 if bypassing the semioctave-reduction, or a very flat al-Farabi quarter tone ~[[33/32]] with the semioctave-reduction. The range is about 4¾ octaves, and the octaves slope upwards so gently that it is tempting to move the note 0 position and use the generous allotment of repeated notes to split this mapping into two manuals.

@@ Line 2: / Line 2: @@
 == Diatonic ==
-Being in the [[flattone]] part of [[meantone]], and indeed at the flat end of flattone itself, 26edo requires some adjustment to convert [[common practice]] music to sound right, and what is technically a diatonic layout (although fairly extreme in its softness) may require different usage than in a more middle-of-the-road diatonic tuning. [[YoVariable]] demonstrates this mapping in [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025) and explains the harmonic characteristics of 26edo (with demonstrations of chord shapes on this layout) in [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone''] by [[YoVariable]] (2026).
+Being in the [[flattone]] part of [[meantone]], and indeed at the flat end of [[flattone]] itself, 26edo requires some adjustment to convert common practice music to sound right, and what is technically a diatonic layout (although fairly extreme in its softness) may require different usage than in a more middle-of-the-road diatonic tuning. [[YoVariable]] demonstrates this mapping in [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025) and explains the harmonic characteristics of 26edo (with demonstrations of chord shapes on this layout) in [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone'']. However, being at the flat end of flattone, 26edo does not have very accurate 5-limit approximations, so other options are probably preferable.
 {{Lumatone EDO mapping|n=26|start=-4|xstep=4|ystep=-1}}
-== Orgone ==
+== Orgone + Superkleismic ==
-However, 26edo is a [[flattone]] system that does not have very accurate 5-limit approximations, so other options are probably preferable. If you want to maximise the playable range and put the best consonances close to each other, the [[orgone]] mapping is the clear winner.
+If you want to maximize the playable range and put the best consonances close to each other, the [[orgone]] + [[superkleismic]] mapping is the clear winner. These temperaments meet at 26edo; they use a sharp classic minor third ~[[6/5]] (as 7\26) as their generator, which can also be mapped with greater accuracy but much greater complexity as a slightly flat doublewide minor third ~[[35/29]]. Either way, the generator chain is accessed very simply by moving right one key at a time. Two keys right yields a slightly flat undecimal minor fifth ~[[16/11]]; three keys right yields a near-just septimal minor seventh ~[[7/4]]; nine keys right with two octave-reductions (which translates into two keys up and one key right) gives the sharp fourth ~[[4/3]]; and another key right from this gives the very sharp classic minor sixth ~[[8/5]].
 {{Lumatone EDO mapping|n=26|start=17|xstep=7|ystep=-2}}
-== Other mappings ==
+== Lemba ==
-The [[Lemba]] and [[Hendec]] mappings also work particularly well in 26edo.
+The [[lemba]] mapping works well in 26edo, as [[Bryan Deister]] has demonstrated  in [https://www.youtube.com/shorts/Gw9Fu5MAozs ''Waltz in 26edo''] (2025); he explains that right (which is a near-just septimal major second ~[[8/7]]) and up yields the sharp classic minor third ~[[6/5]] and right three times yields the flat fifth ~[[3/2]] (bypassing the semioctave-reduction). The range is just under six octaves, with a gentle downward slope.
-=== Lemba ===
-[[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/Gw9Fu5MAozs ''Waltz in 26edo''] (2025), and explains that right and up yields the minor third (~[[6/5]], fairly sharp) and right three times yields the fifth (~[[3/2]], fairly flat).
 {{Lumatone EDO mapping|n=26|start=25|xstep=5|ystep=-2}}
-=== Hendec ===
+== Hendec ==
+For those who favor stacking major rather than minor thirds, 26edo offers a good option with [[hendec]], which uses a slightly flat undecimal (pentacircle) major third ~[[14/11]] as its generator, which at 9\26, is reached simply by moving one key right plus one key down-right. Two of these generators make the very sharp classic minor sixth ~[[8/5]]. Five of these generators after octave-reduction (which translates to one key right plus four keys down-right) yields the flat classic major sixth ~[[5/3]]. The octaves still slope downwards gently, with a range a bit less than that of lemba, but in exchange, the diatonic scale is also easily accessible in a way reminiscent of neutral thirds mappings.
 {{Lumatone EDO mapping|n=26|start=20|xstep=4|ystep=1}}
+== Fifive ==
+With the fifth ~[[3/2]] being divisible by 5 (going from 15\26 down to 3\26, which is a near-just lesser tridecimal neutral second ~[[13/12]]), [[26edo]] supports [[fifive]] temperament, as shown in [[Bryan Deister]]'s [https://www.youtube.com/shorts/WvnJb5VNGj4 ''<nowiki>Caprice in 26edo [short clip]</nowiki>''] (2026). This uses 3\26 as the (rightward) generator, and splits the octave in half. Two of these make a sharp septimal minor third ~[[7/6]] which also functions as a flat tridecimal minor third ~[[13/11]], or a mildly flat diatismic minor third ~[[20/17]]; three of these make a very flat septimal major third ~[[9/7]] or a slightly flat undecimal (pentacircle) major third ~[[14/11]]; four of these make a slightly sharp undecimal major fourth ~[[11/8]]; five of these make a very flat fifth ~3/2 if bypassing the semioctave-reduction, or a very flat al-Farabi quarter tone ~[[33/32]] with the semioctave-reduction. The range is about 4¾ octaves, and the octaves slope upwards so gently that it is tempting to move the note 0 position and use the generous allotment of repeated notes to split this mapping into two manuals.
+{{Lumatone EDO mapping|n=26|start=19|xstep=3|ystep=1}}
 {{Navbox Lumatone}}