Lumatone mapping for 82edo: Difference between revisions

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You can use the b val instead, but this is barely distinguishable from a circulating system of [[7edo]] and only covers about 2/3rds of the notes due to the size of the edo.

There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since that means all notes are available in at least some of the octaves, this may actually be advantageous.

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== Bischismic ==

The [[Bischismic]] mapping can cover the whole gamut, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to do so.

The [[Bischismic]] mapping can cover the whole gamut, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to do so.

~~== Other Mappings ==~~

~~To maximise your range, you can use the [[8L 2s]] mapping generated by 9/82 and a half octave period, but this is not particularly efficient at putting the best note combinations close to one-another.~~

~~{{Lumatone EDO mapping|n=82|start=79|xstep=9|ystep=-4}}~~

== Magic (Divination/Soothsaying) related Lumatone mappings ==

[[Bryan Deister]] has demonstrated a [[8L 6s]] mapping of [[82edo]]. Being even 82edo supports a [[semioctave]] period, with the diagassormisma ([[3042/3025]]) being tempered out in the [[patent val]] or the kalisma ([[9801/9800]]) being tempered out in the 82e val; this enables it to use the (somewhat sharp) septimal major third ~[[9/7]] (as 30\82) as a generator (which would be [[contorted]] down to [[41edo]] with a whole octave period), in a temperament like [[Magic family#Soothsaying|Soothsaying]] or [[Magic family#Divination|Divination]], but using the septimal major third as a generator instead of the classic major third ~[[5/4]]. (Since 82edo also supports actual Soothsaying in its patent val and actual Divination in its 82e val, it is also possible to use generator 26\82, the somewhat flat ~[[5/4]], although the resulting [[6L 4s]] scale is a bit more tricky to play using this layout.) The range is about 2¾ octaves with no missed notes, and the octaves slant down.

== Buzurgic/Dhanvantaric ==

To maximise your range, you can use the [[8L 2s]] mapping generated by 9/82 and a half octave period (achieving a range slightly over three octaves, with a moderate upwards slant), but this is not particularly efficient at putting the best note combinations close to one-another. Despite not being designed with any temperament in mind, this mapping supports Buzurgic/Dhanvantaric temperament, because the rightward generator is 9\82, and 82edo tempers out the buzurgisma/dhanvantarisma ([[169/168]]), which causes this generator to function as both ~[[14/13]] and ~[[13/12]]; two of them make a somewhat sharp septimal minor third (~[[7/6]]). An article dedicated to this temperament is not currently available, but an article about [[Buzurgismic chords]] is available. The choice of whether to use 4\82 (upwards generator) or 5\82 (down-right generator) as the second generator, or to use no second generator and downgrade the temperament to rank-2, depends upon what one wants to do with the 11th harmonic. The patent val of 82edo maps a mildly sharp al-Farabi quarter tone (~[[33/32]]) to the upwards generator 4\82; four of these make a slightly sharp ~[[8/7]]. Two rightward generators plus one or two upwards generators yield the classic minor and major thirds (~[[6/5]] and ~[[5/4]]), respectively; four rightward generators plus three upwards generators yield the near just perfect fifth (~[[3/2]]). The 82e val maps a rather flat pentacircle minor second (~[[22/21]]) to the down-right generator 5\82; four of them make a slightly flat tridecimal minor third (~[[13/11]], made fairly accurate by cancellation of the errors in the wart-modified 11th harmonic and the patent 13th harmonic, and which would otherwise have to be mapped as ~[[19/16]]). However, use of the down-right generator in combination with the rightwards generator to produce common chords tends to require going rightward extra steps and then subtract down-right generators to get the effect of the upwards generator, making this a less attractive choice of secondary generator.

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 You can use the b&nbsp;val instead, but this is barely distinguishable from a circulating system of [[7edo]] and only covers about 2/3rds of the notes due to the size of the edo.
 {{Lumatone EDO mapping|n=82|start=62|xstep=12|ystep=-1}}
 There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since that means all notes are available in at least some of the octaves, this may actually be advantageous.
@@ Line 9: / Line 10: @@
 == Bischismic ==
-The [[Bischismic]] mapping can cover the whole gamut, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to do so.
+The [[Bischismic]] mapping can cover the whole gamut, although it needs to be expanded from [[2L&nbsp;8s]] to [[10L&nbsp;2s]] to do so.
 {{Lumatone EDO mapping|n=82|start=25|xstep=7|ystep=6}}
 {{Lumatone EDO mapping|n=82|start=67|xstep=7|ystep=-1}}
-== Other Mappings ==
-To maximise your range, you can use the [[8L 2s]] mapping generated by 9/82 and a half octave period, but this is not particularly efficient at putting the best note combinations close to one-another.
-{{Lumatone EDO mapping|n=82|start=79|xstep=9|ystep=-4}}
+== Magic (Divination/Soothsaying) related Lumatone mappings ==
+[[Bryan Deister]] has demonstrated a [[8L&nbsp;6s]] mapping of [[82edo]]. Being even 82edo supports a [[semioctave]] period, with the diagassormisma ([[3042/3025]]) being tempered out in the [[patent val]] or the kalisma ([[9801/9800]]) being tempered out in the 82e val; this enables it to use the (somewhat sharp) septimal major third ~[[9/7]] (as 30\82) as a generator (which would be [[contorted]] down to [[41edo]] with a whole octave period), in a temperament like [[Magic family#Soothsaying|Soothsaying]] or [[Magic family#Divination|Divination]], but using the septimal major third as a generator instead of the classic major third ~[[5/4]].  (Since 82edo also supports actual Soothsaying in its patent val and actual Divination in its 82e val, it is also possible to use generator 26\82, the somewhat flat ~[[5/4]], although the resulting [[6L&nbsp;4s]] scale is a bit more tricky to play using this layout.) The range is about 2¾ octaves with no missed notes, and the octaves slant down.
+{{Lumatone EDO mapping|n=82|start=4|xstep=8|ystep=-5}}
+== Buzurgic/Dhanvantaric ==
+To maximise your range, you can use the [[8L&nbsp;2s]] mapping generated by 9/82 and a half octave period (achieving a range slightly over three octaves, with a moderate upwards slant), but this is not particularly efficient at putting the best note combinations close to one-another. Despite not being designed with any temperament in mind, this mapping supports Buzurgic/Dhanvantaric temperament, because the rightward generator is 9\82, and 82edo tempers out the buzurgisma/dhanvantarisma ([[169/168]]), which causes this generator to function as both ~[[14/13]] and ~[[13/12]]; two of them make a somewhat sharp septimal minor third (~[[7/6]]). An article dedicated to this temperament is not currently available, but an article about [[Buzurgismic chords]] is available. The choice of whether to use 4\82 (upwards generator) or 5\82 (down-right generator) as the second generator, or to use no second generator and downgrade the temperament to rank-2, depends upon what one wants to do with the 11th harmonic. The patent val of 82edo maps a mildly sharp al-Farabi quarter tone (~[[33/32]]) to the upwards generator 4\82; four of these make a slightly sharp ~[[8/7]]. Two rightward generators plus one or two upwards generators yield the classic minor and major thirds (~[[6/5]] and ~[[5/4]]), respectively; four rightward generators plus three upwards generators yield the near just perfect fifth (~[[3/2]]). The 82e val maps a rather flat pentacircle minor second (~[[22/21]]) to the down-right generator 5\82; four of them make a slightly flat tridecimal minor third (~[[13/11]], made fairly accurate by cancellation of the errors in the wart-modified 11th harmonic and the patent 13th harmonic, and which would otherwise have to be mapped as ~[[19/16]]). However, use of the down-right generator in combination with the rightwards generator to produce common chords tends to require going rightward extra steps and then subtract down-right generators to get the effect of the upwards generator, making this a less attractive choice of secondary generator.
+{{Lumatone EDO mapping|n=82|start=79|xstep=9|ystep=-4}}
 {{Navbox Lumatone}}