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Lumatone mapping for neutral thirds scales: Difference between revisions

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[[Neutral third scales]] could conceivably be mapped onto the [[Lumatone]] keyboard in different ways. The important intervals which could be mapped to adjacent hexagons in certain directions include the whole step, the [[diatonic semitone]], and the half-[[apotome]] which is half of a usual {{sharp}}/{{flat}} modifier. In this article the symbols ^ and v are used for half-sharp and half-flat (other symbols are sometimes available in different software).
[[Neutral third scales]] could conceivably be mapped onto the [[Lumatone]] keyboard in different ways. The important intervals which could be mapped to adjacent hexagons in certain directions include the whole step, the [[diatonic semitone]], and the half-[[apotome]] which is half of a usual {{sharp}}/{{flat}} modifier. In this article the symbols ^ and v are used for half-sharp and half-flat (other symbols are sometimes available in different software).


Here is one possible mapping of the neutral thirds system, which results in compact scales and the angle of the octave interval being fairly close to horizontal (perfect horizontal is impossible with this system):
=="Double-Bosanquet"==
This is called '''"Double-Bosanquet"''' since the diatonic scale is the same as in the [[Standard Lumatone mapping for Pythagorean|Bosanquet–Wilson layout]], except with rows of non-diatonic pitches inserted every other row. In other words it has exactly 2x as many pitches as Bosanquet, and if you removed all the half-sharps, half-flats etc. and slid the remaining rows together, it would become Bosanquet.


{{Lumatone mapping|
{{Lumatone key|x=0|y=0|label=D{{flat}}}}
{{Lumatone key|x=1|y=0|label=E{{flat}}}}
{{Lumatone key|x=1|y=1|label=E{{flat}}v|size=10px}}
{{Lumatone key|x=2|y=1|label=Fv}}
{{Lumatone key|x=3|y=1|label=Gv}}
{{Lumatone key|x=4|y=1|label=Av}}
{{Lumatone key|x=5|y=1|label=Bv}}
{{Lumatone key|x=1|y=2|label=E{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=2|y=2|label=F{{flat}}}}
{{Lumatone key|x=3|y=2|label=G{{flat}}}}
{{Lumatone key|x=4|y=2|label=A{{flat}}}}
{{Lumatone key|x=5|y=2|label=B{{flat}}}}
{{Lumatone key|x=6|y=2|label=C}}
{{Lumatone key|x=7|y=2|label=D}}
{{Lumatone key|x=8|y=2|label=E}}
{{Lumatone key|x=2|y=3|label=F{{flat}}v|size=10px}}
{{Lumatone key|x=3|y=3|label=G{{flat}}v|size=10px}}
{{Lumatone key|x=4|y=3|label=A{{flat}}v|size=10px}}
{{Lumatone key|x=5|y=3|label=B{{flat}}v|size=10px}}
{{Lumatone key|x=6|y=3|label=Cv}}
{{Lumatone key|x=7|y=3|label=Dv}}
{{Lumatone key|x=8|y=3|label=Ev}}
{{Lumatone key|x=9|y=3|label=F^}}
{{Lumatone key|x=10|y=3|label=G^}}
{{Lumatone key|x=11|y=3|label=A^}}
{{Lumatone key|x=12|y=3|label=B^}}
{{Lumatone key|x=2|y=4|label=F{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=3|y=4|label=G{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=4|y=4|label=A{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=5|y=4|label=B{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=6|y=4|label=C{{flat}}}}
{{Lumatone key|x=7|y=4|label=D{{flat}}}}
{{Lumatone key|x=8|y=4|label=E{{flat}}}}
{{Lumatone key|x=9|y=4|label=F}}
{{Lumatone key|x=10|y=4|label=G}}
{{Lumatone key|x=11|y=4|label=A}}
{{Lumatone key|x=12|y=4|label=B}}
{{Lumatone key|x=13|y=4|label=C{{sharp}}}}
{{Lumatone key|x=14|y=4|label=D{{sharp}}}}
{{Lumatone key|x=15|y=4|label=E{{sharp}}}}
{{Lumatone key|x=3|y=5|label=G{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=4|y=5|label=A{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=5|y=5|label=B{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=6|y=5|label=C{{flat}}v|size=10px}}
{{Lumatone key|x=7|y=5|label=D{{flat}}v|size=10px}}
{{Lumatone key|x=8|y=5|label=E{{flat}}v|size=10px}}
{{Lumatone key|x=9|y=5|label=Fv}}
{{Lumatone key|x=10|y=5|label=Gv}}
{{Lumatone key|x=11|y=5|label=Av}}
{{Lumatone key|x=12|y=5|label=Bv}}
{{Lumatone key|x=13|y=5|label=C^}}
{{Lumatone key|x=14|y=5|label=D^}}
{{Lumatone key|x=15|y=5|label=E^}}
{{Lumatone key|x=16|y=5|label=F{{sharp}}^|size=10px}}
{{Lumatone key|x=17|y=5|label=G{{sharp}}^|size=10px}}
{{Lumatone key|x=18|y=5|label=A{{sharp}}^|size=10px}}
{{Lumatone key|x=19|y=5|label=B{{sharp}}^|size=10px}}
{{Lumatone key|x=3|y=6|label=G{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=4|y=6|label=A{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=5|y=6|label=B{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=6|y=6|label=C{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=7|y=6|label=D{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=8|y=6|label=E{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=9|y=6|label=F{{flat}}}}
{{Lumatone key|x=10|y=6|label=G{{flat}}}}
{{Lumatone key|x=11|y=6|label=A{{flat}}}}
{{Lumatone key|x=12|y=6|label=B{{flat}}}}
{{Lumatone key|x=13|y=6|label=C}}
{{Lumatone key|x=14|y=6|label=D}}
{{Lumatone key|x=15|y=6|label=E}}
{{Lumatone key|x=16|y=6|label=F{{sharp}}}}
{{Lumatone key|x=17|y=6|label=G{{sharp}}}}
{{Lumatone key|x=18|y=6|label=A{{sharp}}}}
{{Lumatone key|x=19|y=6|label=B{{sharp}}}}
{{Lumatone key|x=20|y=6|label=C{{sharp2}}}}
{{Lumatone key|x=21|y=6|label=D{{sharp2}}}}
{{Lumatone key|x=22|y=6|label=E{{sharp2}}}}
{{Lumatone key|x=6|y=7|label=C{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=7|y=7|label=D{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=8|y=7|label=E{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=9|y=7|label=F{{flat}}v|size=10px}}
{{Lumatone key|x=10|y=7|label=G{{flat}}v|size=10px}}
{{Lumatone key|x=11|y=7|label=A{{flat}}v|size=10px}}
{{Lumatone key|x=12|y=7|label=B{{flat}}v|size=10px}}
{{Lumatone key|x=13|y=7|label=Cv}}
{{Lumatone key|x=14|y=7|label=Dv}}
{{Lumatone key|x=15|y=7|label=Ev}}
{{Lumatone key|x=16|y=7|label=F^}}
{{Lumatone key|x=17|y=7|label=G^}}
{{Lumatone key|x=18|y=7|label=A^}}
{{Lumatone key|x=19|y=7|label=B^}}
{{Lumatone key|x=20|y=7|label=C{{sharp}}^|size=10px}}
{{Lumatone key|x=21|y=7|label=D{{sharp}}^|size=10px}}
{{Lumatone key|x=22|y=7|label=E{{sharp}}^|size=10px}}
{{Lumatone key|x=23|y=7|label=F{{sharp2}}^|size=10px}}
{{Lumatone key|x=24|y=7|label=G{{sharp2}}^|size=10px}}
{{Lumatone key|x=25|y=7|label=A{{sharp2}}^|size=10px}}
{{Lumatone key|x=26|y=7|label=B{{sharp2}}^|size=10px}}
{{Lumatone key|x=6|y=8|label=C{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=7|y=8|label=D{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=8|y=8|label=E{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=9|y=8|label=F{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=10|y=8|label=G{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=11|y=8|label=A{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=12|y=8|label=B{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=13|y=8|label=C{{flat}}}}
{{Lumatone key|x=14|y=8|label=D{{flat}}}}
{{Lumatone key|x=15|y=8|label=E{{flat}}}}
{{Lumatone key|x=16|y=8|label=F}}
{{Lumatone key|x=17|y=8|label=G}}
{{Lumatone key|x=18|y=8|label=A}}
{{Lumatone key|x=19|y=8|label=B}}
{{Lumatone key|x=20|y=8|label=C{{sharp}}}}
{{Lumatone key|x=21|y=8|label=D{{sharp}}}}
{{Lumatone key|x=22|y=8|label=E{{sharp}}}}
{{Lumatone key|x=23|y=8|label=F{{sharp2}}}}
{{Lumatone key|x=24|y=8|label=G{{sharp2}}}}
{{Lumatone key|x=25|y=8|label=A{{sharp2}}}}
{{Lumatone key|x=26|y=8|label=B{{sharp2}}}}
{{Lumatone key|x=27|y=8|label=C{{sharp2}}{{sharp}}}}
{{Lumatone key|x=28|y=8|label=D{{sharp2}}{{sharp}}}}
{{Lumatone key|x=29|y=8|label=E{{sharp2}}{{sharp}}}}
{{Lumatone key|x=9|y=9|label=F{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=10|y=9|label=G{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=11|y=9|label=A{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=12|y=9|label=B{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=13|y=9|label=C{{flat}}v|size=10px}}
{{Lumatone key|x=14|y=9|label=D{{flat}}v|size=10px}}
{{Lumatone key|x=15|y=9|label=E{{flat}}v|size=10px}}
{{Lumatone key|x=16|y=9|label=Fv}}
{{Lumatone key|x=17|y=9|label=Gv}}
{{Lumatone key|x=18|y=9|label=Av}}
{{Lumatone key|x=19|y=9|label=Bv}}
{{Lumatone key|x=20|y=9|label=C^}}
{{Lumatone key|x=21|y=9|label=D^}}
{{Lumatone key|x=22|y=9|label=E^}}
{{Lumatone key|x=23|y=9|label=F{{sharp}}^|size=10px}}
{{Lumatone key|x=24|y=9|label=G{{sharp}}^|size=10px}}
{{Lumatone key|x=25|y=9|label=A{{sharp}}^|size=10px}}
{{Lumatone key|x=26|y=9|label=B{{sharp}}^|size=10px}}
{{Lumatone key|x=27|y=9|label=C{{sharp2}}^|size=10px}}
{{Lumatone key|x=28|y=9|label=D{{sharp2}}^|size=10px}}
{{Lumatone key|x=29|y=9|label=E{{sharp2}}^|size=10px}}
{{Lumatone key|x=30|y=9|label=F{{sharp2}}{{sharp}}^|size=9px}}
{{Lumatone key|x=9|y=10|label=F{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=10|y=10|label=G{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=11|y=10|label=A{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=12|y=10|label=B{{flat}}{{flat}}{{flat}}|size=7px}}
{{Lumatone key|x=13|y=10|label=C{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=14|y=10|label=D{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=15|y=10|label=E{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=16|y=10|label=F{{flat}}}}
{{Lumatone key|x=17|y=10|label=G{{flat}}}}
{{Lumatone key|x=18|y=10|label=A{{flat}}}}
{{Lumatone key|x=19|y=10|label=B{{flat}}}}
{{Lumatone key|x=20|y=10|label=C}}
{{Lumatone key|x=21|y=10|label=D}}
{{Lumatone key|x=22|y=10|label=E}}
{{Lumatone key|x=23|y=10|label=F{{sharp}}}}
{{Lumatone key|x=24|y=10|label=G{{sharp}}}}
{{Lumatone key|x=25|y=10|label=A{{sharp}}}}
{{Lumatone key|x=26|y=10|label=B{{sharp}}}}
{{Lumatone key|x=27|y=10|label=C{{sharp2}}}}
{{Lumatone key|x=28|y=10|label=D{{sharp2}}}}
{{Lumatone key|x=29|y=10|label=E{{sharp2}}}}
{{Lumatone key|x=30|y=10|label=F{{sharp2}}{{sharp}}}}
{{Lumatone key|x=31|y=10|label=G{{sharp2}}{{sharp}}}}
{{Lumatone key|x=14|y=11|label=D{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=15|y=11|label=E{{flat}}{{flat}}v|size=8px}}
{{Lumatone key|x=16|y=11|label=F{{flat}}v|size=10px}}
{{Lumatone key|x=17|y=11|label=G{{flat}}v|size=10px}}
{{Lumatone key|x=18|y=11|label=A{{flat}}v|size=10px}}
{{Lumatone key|x=19|y=11|label=B{{flat}}v|size=10px}}
{{Lumatone key|x=20|y=11|label=Cv}}
{{Lumatone key|x=21|y=11|label=Dv}}
{{Lumatone key|x=22|y=11|label=Ev}}
{{Lumatone key|x=23|y=11|label=F^}}
{{Lumatone key|x=24|y=11|label=G^}}
{{Lumatone key|x=25|y=11|label=A^}}
{{Lumatone key|x=26|y=11|label=B^}}
{{Lumatone key|x=27|y=11|label=C{{sharp}}^|size=10px}}
{{Lumatone key|x=28|y=11|label=D{{sharp}}^|size=10px}}
{{Lumatone key|x=29|y=11|label=E{{sharp}}^|size=10px}}
{{Lumatone key|x=30|y=11|label=F{{sharp2}}^|size=10px}}
{{Lumatone key|x=31|y=11|label=G{{sharp2}}^|size=10px}}
{{Lumatone key|x=32|y=11|label=A{{sharp2}}^|size=10px}}
{{Lumatone key|x=33|y=11|label=B{{sharp2}}^|size=10px}}
{{Lumatone key|x=34|y=11|label=C{{sharp2}}{{sharp}}^|size=9px}}
{{Lumatone key|x=16|y=12|label=F{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=17|y=12|label=G{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=18|y=12|label=A{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=19|y=12|label=B{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=20|y=12|label=C{{flat}}}}
{{Lumatone key|x=21|y=12|label=D{{flat}}}}
{{Lumatone key|x=22|y=12|label=E{{flat}}}}
{{Lumatone key|x=23|y=12|label=F}}
{{Lumatone key|x=24|y=12|label=G}}
{{Lumatone key|x=25|y=12|label=A}}
{{Lumatone key|x=26|y=12|label=B}}
{{Lumatone key|x=27|y=12|label=C{{sharp}}}}
{{Lumatone key|x=28|y=12|label=D{{sharp}}}}
{{Lumatone key|x=29|y=12|label=E{{sharp}}}}
{{Lumatone key|x=30|y=12|label=F{{sharp2}}}}
{{Lumatone key|x=31|y=12|label=G{{sharp2}}}}
{{Lumatone key|x=32|y=12|label=A{{sharp2}}}}
{{Lumatone key|x=33|y=12|label=B{{sharp2}}}}
{{Lumatone key|x=34|y=12|label=C{{sharp2}}{{sharp}}|size=10px}}
{{Lumatone key|x=20|y=13|label=C{{flat}}v|size=10px}}
{{Lumatone key|x=21|y=13|label=D{{flat}}v|size=10px}}
{{Lumatone key|x=22|y=13|label=E{{flat}}v|size=10px}}
{{Lumatone key|x=23|y=13|label=Fv}}
{{Lumatone key|x=24|y=13|label=Gv}}
{{Lumatone key|x=25|y=13|label=Av}}
{{Lumatone key|x=26|y=13|label=Bv}}
{{Lumatone key|x=27|y=13|label=C^}}
{{Lumatone key|x=28|y=13|label=D^}}
{{Lumatone key|x=29|y=13|label=E^}}
{{Lumatone key|x=30|y=13|label=F{{sharp}}^|size=10px}}
{{Lumatone key|x=31|y=13|label=G{{sharp}}^|size=10px}}
{{Lumatone key|x=32|y=13|label=A{{sharp}}^|size=10px}}
{{Lumatone key|x=33|y=13|label=B{{sharp}}^|size=10px}}
{{Lumatone key|x=34|y=13|label=C{{sharp2}}^|size=10px}}
{{Lumatone key|x=23|y=14|label=F{{flat}}}}
{{Lumatone key|x=24|y=14|label=G{{flat}}}}
{{Lumatone key|x=25|y=14|label=A{{flat}}}}
{{Lumatone key|x=26|y=14|label=B{{flat}}}}
{{Lumatone key|x=27|y=14|label=C}}
{{Lumatone key|x=28|y=14|label=D}}
{{Lumatone key|x=29|y=14|label=E}}
{{Lumatone key|x=30|y=14|label=F{{sharp}}}}
{{Lumatone key|x=31|y=14|label=G{{sharp}}}}
{{Lumatone key|x=32|y=14|label=A{{sharp}}}}
{{Lumatone key|x=33|y=14|label=B{{sharp}}}}
{{Lumatone key|x=34|y=14|label=C{{sharp2}}}}
{{Lumatone key|x=27|y=15|label=Cv}}
{{Lumatone key|x=28|y=15|label=Dv}}
{{Lumatone key|x=29|y=15|label=Ev}}
{{Lumatone key|x=30|y=15|label=F^}}
{{Lumatone key|x=31|y=15|label=G^}}
{{Lumatone key|x=32|y=15|label=A^}}
{{Lumatone key|x=33|y=15|label=B^}}
{{Lumatone key|x=34|y=15|label=C{{sharp}}^|size=10px}}
{{Lumatone key|x=35|y=15|label=D{{sharp}}^|size=10px}}
{{Lumatone key|x=36|y=15|label=E{{sharp}}^|size=10px}}
{{Lumatone key|x=37|y=15|label=F{{sharp2}}^|size=10px}}
{{Lumatone key|x=30|y=16|label=F}}
{{Lumatone key|x=31|y=16|label=G}}
{{Lumatone key|x=32|y=16|label=A}}
{{Lumatone key|x=33|y=16|label=B}}
{{Lumatone key|x=34|y=16|label=C{{sharp}}}}
{{Lumatone key|x=35|y=16|label=D{{sharp}}}}
{{Lumatone key|x=36|y=16|label=E{{sharp}}}}
{{Lumatone key|x=37|y=16|label=F{{sharp2}}}}
{{Lumatone key|x=34|y=17|label=C^}}
{{Lumatone key|x=35|y=17|label=D^}}
{{Lumatone key|x=36|y=17|label=E^}}
{{Lumatone key|x=37|y=17|label=F{{sharp}}^|size=10px}}
{{Lumatone key|x=38|y=17|label=G{{sharp}}^|size=10px}}
{{Lumatone key|x=37|y=18|label=F{{sharp}}}}
{{Lumatone key|x=38|y=18|label=G{{sharp}}}}
}}
Pros:
* Some familiarity to users of the standard Bosanquet layout, since major seconds have the same shape.
* Good ergonomics for major seconds.
Cons:
* Because of the angle of the octave direction (rising up away from the player toward the left and descending towards the player on the right), this doesn't even include 4 complete octaves of the diatonic scale. (With equal temperaments this is alleviated somewhat because octaves will be available in alternate, enharmonic locations. For example, in 31edo G{{flat}}{{flat}}v is the same as F, so an octave of F is available there.)
=="Anti-double-Bosanquet"==
Here is a reflected version of the above, which results in compact scales and the angle of the octave interval being fairly close to horizontal (perfect horizontal is impossible with this system):


{{Lumatone mapping|
{{Lumatone mapping|
Line 314: Line 607:
{{Lumatone key|x=35|y=11|label=C{{flat}}{{flat}}|size=9px}}
{{Lumatone key|x=35|y=11|label=C{{flat}}{{flat}}|size=9px}}
}}
}}
Pros:
* Over 5 complete octaves.
* Neutral seconds have good ergonomics, because they have the same shape that major seconds do in Bosanquet–Wilson.
Cons:
* Worse ergonomics for major seconds.
* May be unfamiliar or confusing to people familiar with normal Bosanquet.
* In particular the "sharp" direction is now down toward the player (not up away from the player as in normal Bosanquet), which may be confusing.


[[Category:Lumatone mappings]]
[[Category:Lumatone mappings]]
Retrieved from "https://en.xen.wiki/w/Lumatone_mapping_for_neutral_thirds_scales"