Lumatone mapping for 15edo: Difference between revisions

Line 5:

This makes fingerings for most simple chords awkward though. The mappings that organise its intervals that make it easy to find consonant chords, in order of increasing compression, are the ~~Porcupine~~, ~~Blackwood~~, and ~~Hanson~~ mappings.

This makes fingerings for most simple chords awkward though. The mappings that organise its intervals that make it easy to find consonant chords, in order of increasing compression, are the porcupine, blackwood, and hanson mappings.

== Porcupine ==

Line 11:

== Blackwood + ~~Augmented~~ (~~Augene~~) + ~~Kleismic~~ (~~Hanson~~/~~Keemun~~/~~Superkleismic~~) ==

== Blackwood + augmented (augene) + kleismic (hanson/keemun/superkleismic) ==

[[Blackwood]] avoids the [[contorsion]] problem of 15edo by dividing the octave into five sections. Dividing 15edo by 3 gets a 3L 3s scale on top of this. With a 3:2 step ratio, this also makes for easy division of the octave into three sections, as in [[~~Augmented#family~~|~~Augmented~~]], specifically [[~~Augmented_family#Augene|Augene~~]]. This also functions as a [[~~Kleismic~~]] ([[~~Kleismic_family#Kleismic_a.k.a._hanson|Hanson~~]]/[[~~Kleismic_family#Keemun|Keemun~~]]/[[~~Superkleismic~~]]) [[4L 3s]] (3:1 step ratio) mapping. The range is a bit under 6 octaves, and while octaves slope up as expected for Blackwood, they do so in a way such that the vertical repeated notes cause double octaves to be nearly level.

[[Blackwood]] avoids the [[contorsion]] problem of 15edo by dividing the octave into five sections. Dividing 15edo by 3 gets a 3L 3s scale on top of this. With a 3:2 step ratio, this also makes for easy division of the octave into three sections, as in [[augmented (temperament)|augmented]], specifically [[augene]]. This also functions as a [[kleismic]] ([[hanson]]/[[keemun]]/[[superkleismic]]) [[4L 3s]] (3:1 step ratio) mapping. The range is a bit under 6 octaves, and while octaves slope up as expected for Blackwood, they do so in a way such that the vertical repeated notes cause double octaves to be nearly level.

=== 3L 3s (right, down-right) and 4L 3s (right, up) ===

Line 23:

== Hanson ==

If ~~Hanson~~ is most of what is needed and ~~Augmented~~ and ~~Blackwood~~ are not a priority, it is possible to compress the layout to a [[3L 1s]] scale (4:3 step ratio) and increase the range to over eight octaves that are nearly level.

If hanson is most of what is needed and augmented and blackwood are not a priority, it is possible to compress the layout to a [[3L 1s]] scale (4:3 step ratio) and increase the range to over eight octaves that are nearly level.

@@ Line 5: / Line 5: @@
 {{Lumatone EDO mapping|n=15|start=12|xstep=1|ystep=4}}
-This makes fingerings for most simple chords awkward though. The mappings that organise its intervals that make it easy to find consonant chords, in order of increasing compression, are the Porcupine, Blackwood, and Hanson mappings.
+This makes fingerings for most simple chords awkward though. The mappings that organise its intervals that make it easy to find consonant chords, in order of increasing compression, are the porcupine, blackwood, and hanson mappings.
 == Porcupine ==
@@ Line 11: / Line 11: @@
 {{Lumatone EDO mapping|n=15|start=0|xstep=2|ystep=1}}
-== Blackwood + Augmented (Augene) + Kleismic (Hanson/Keemun/Superkleismic) ==
+== Blackwood + augmented (augene) + kleismic (hanson/keemun/superkleismic) ==
-[[Blackwood]] avoids the [[contorsion]] problem of 15edo by dividing the octave into five sections. Dividing 15edo by 3 gets a 3L&nbsp;3s scale on top of this. With a 3:2 step ratio, this also makes for easy division of the octave into three sections, as in [[Augmented#family|Augmented]], specifically [[Augmented_family#Augene|Augene]]. This also functions as a [[Kleismic]] ([[Kleismic_family#Kleismic_a.k.a._hanson|Hanson]]/[[Kleismic_family#Keemun|Keemun]]/[[Superkleismic]]) [[4L&nbsp;3s]] (3:1 step ratio) mapping. The range is a bit under 6 octaves, and while octaves slope up as expected for Blackwood, they do so in a way such that the vertical repeated notes cause double octaves to be nearly level.
+[[Blackwood]] avoids the [[contorsion]] problem of 15edo by dividing the octave into five sections. Dividing 15edo by 3 gets a 3L&nbsp;3s scale on top of this. With a 3:2 step ratio, this also makes for easy division of the octave into three sections, as in [[augmented (temperament)|augmented]], specifically [[augene]]. This also functions as a [[kleismic]] ([[hanson]]/[[keemun]]/[[superkleismic]]) [[4L&nbsp;3s]] (3:1 step ratio) mapping. The range is a bit under 6 octaves, and while octaves slope up as expected for Blackwood, they do so in a way such that the vertical repeated notes cause double octaves to be nearly level.
 === 3L&nbsp;3s (right, down-right) and 4L&nbsp;3s (right, up) ===
@@ Line 23: / Line 23: @@
 == Hanson ==
-If Hanson is most of what is needed and Augmented and Blackwood are not a priority, it is possible to compress the layout to a [[3L&nbsp;1s]] scale (4:3 step ratio) and increase the range to over eight octaves that are nearly level.
+If hanson is most of what is needed and augmented and blackwood are not a priority, it is possible to compress the layout to a [[3L&nbsp;1s]] scale (4:3 step ratio) and increase the range to over eight octaves that are nearly level.
 {{Lumatone EDO mapping|n=15|start=9|xstep=4|ystep=-1}}
 {{Navbox Lumatone}}