Lumatone mapping for 49edo: Difference between revisions

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Since 49edo is a [[superpyth]] temperament, the classic major third ~[[5/4]] is mapped to the interval of an augmented second (e.g. a 5/4 above C is D♯); also, the Pythagorean major second ~[[9/8]] is mapped inconsistently to be the same as the septimal major second ~[[8/7]]. [[Cam Taylor]] demonstrates this mapping in [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023).

== Whitewood + Bohpier ==

Since [[49edo]] is a multiple of [[7edo]], and not too far beyond the highest non-diatonic multiple thereof, [[whitewood]] mappings are legitimate, as [[Bryan Deister]] demonstrates in [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026). The sevenths of octaves proceed right, and therefore the octaves slope upwards with this, yielding a range a bit over 4½ octaves. The generator apart from the octave division proceeds down-right; as 6\42, it functions as a somewhat flat Alpharabian tendoneutral second ~[[12/11]] (and if the 49f val is used, also as a rather sharp but still consistent tridecimal neutral second ~[[13/12]]), thus making this also a [[bohpier]] mapping, with a rotated [[1L 7s]] scale having a 7:6 step ratio. Three of these generators make a somewhat sharp septimal major third ~[[9/7]]; four of them make a somewhat sharp lesser septimal tritone ~[[7/5]]; six of them make a slightly flat classic major sixth ~[[5/3]]; and seven of them make a very sharp classic major seventh ~[[9/5]].

== Didacus ==

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== Archipelago + Catalan ==

The most efficient mapping for [[49edo]], having a range of 5¼ octaves (which slope down moderately) with no missed notes and no repeated notes, is [[Bryan Deister]]'s [[4L 3s]] (10:3 step ratio) mapping that functions for both a rank-2 or rank-3 [[archipelago]]-related temperament and [[catalan]] temperament, demonstrated in [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026). The rank-2 archipelago-related temperament (which is not currently on the archipelago page) uses one key right (10\49) as a slightly sharp tridecimal semifourth ~[[15/13]] (in the 49f val) for its generator; two of them make the fairly flat fourth ~[[4/3]]; four of them make the sharp septimal minor seventh ~[[7/4]]; six of them (after octave reduction) make a slightly sharp septimal minor third ~[[7/6]]; thirteen of them (after more octave reduction) make a near-just undecimal minor sixth ~[[11/7]]; and fourteen of them make a sharp classic minor seventh ~[[9/5]]. Although this is a respectable list of intervals, ~~by itself~~ the rank-2 version of the temperament does not make a very good [[MOS]] scale — instead it makes for scales in which the small interval is only 1\49. Therefore, for facility in making scales, including the aforementioned 4L 3s, a second generator is needed (thus elevating this to a rank-3 temperament that tempers out [[364/363]], [[540/539]], and [[847/845]]); that generator uses one key down-right (3\49) as the slightly sharp classic chromatic semitone ~[[25/24]], which 49edo ~~actually~~ uses as a diatonic semitone. Catalan uses one key right plus one key down-right (13\49) as a slightly sharp classic minor third for its generator; two of them make a very flat Axirabian paraminor fifth ~[[16/11]]; four of them (after octave reduction) make a ~~somewhat~~ sharp classic chromatic semitone ~[[25/24]]; five of them make a mildly sharp classic major third ~[[5/4]]; six of them make a sharp fifth ~[[3/2]]; seven of them make a sharp classic minor seventh ~[[9/5]]; eight of them (after more octave-reduction) make a mildly flat undecimal neutral second ~[[12/11]]; and ten of them make a near-just undecimal minor sixth ~[[11/7]]. Catalan does not need a second generator to produce usable MOS scales, including the aforementioned 4L 3s.

The most efficient mapping for [[49edo]], having a range of 5¼ octaves (which slope down moderately) with no missed notes and no repeated notes, is [[Bryan Deister]]'s [[4L 3s]] (10:3 step ratio) mapping that functions for both a rank-2 or rank-3 [[archipelago]]-related temperament and [[catalan]] temperament, demonstrated in [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026). The rank-2 archipelago-related temperament (which is not currently on the archipelago page) uses one key right (10\49) as a slightly sharp tridecimal semifourth ~[[15/13]] (in the 49f val) for its generator; two of them make the fairly flat fourth ~[[4/3]]; four of them make the sharp septimal minor seventh ~[[7/4]]; six of them (after octave reduction) make a slightly sharp septimal minor third ~[[7/6]]; thirteen of them (after more octave reduction) make a near-just undecimal minor sixth ~[[11/7]]; and fourteen of them make a sharp classic minor seventh ~[[9/5]]. Although this is a respectable list of intervals, the unmodified rank-2 version of the temperament does not make a very good [[MOS]] scale — instead it makes for scales in which the small interval is only 1\49. Therefore, for facility in making scales, including the aforementioned 4L 3s, a second generator is needed (thus elevating this to a rank-3 temperament that tempers out [[364/363]], [[540/539]], and [[847/845]]); that generator uses one key down-right (3\49) as the slightly sharp classic chromatic semitone ~[[25/24]], which 49edo uses here more like a diatonic semitone (although the actual 49edo diatonic semitone is only 2\49). Catalan uses one key right plus one key down-right (13\49) as a slightly sharp classic minor third for its generator; two of them make a very flat Axirabian paraminor fifth ~[[16/11]]; four of them (after octave reduction) make a slightly sharp classic chromatic semitone ~[[25/24]]; five of them make a mildly sharp classic major third ~[[5/4]]; six of them make a sharp fifth ~[[3/2]]; seven of them make a sharp classic minor seventh ~[[9/5]]; eight of them (after more octave-reduction) make a mildly flat undecimal neutral second ~[[12/11]]; and ten of them make a near-just undecimal minor sixth ~[[11/7]]. Catalan does not need a second generator to produce usable MOS scales, including the aforementioned 4L 3s.

==== Reverse chroma version ====

It is possible to make a reverse chroma version of the above mapping. The range is considerably less, at a bit over 3⅓ octaves, with considerable regions of non-contiguous notes in the upper left and lower right corners, and the octaves slope down, incurring a vertical wraparound; on the other hand, a considerable number of repeated notes are available in each complete octave to mitigate vertical wraparounds. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026), although with note 0 set to where note 38 is here.

== Machine ==

It is possible to get closer to level octaves for [[49edo]] with a slight gain in practical efficiency (having three repeated notes in each octave, but no non-contiguous notes in the lower left and upper right corners compared to the the archipelago + catalan mapping) with a machine scale ([[5L 1s]], with a 9:4 step ratio). [[Bryan Deister]] has demonstrated this in [[Bryan Deister]]'s [https://www.youtube.com/shorts/_yNrDI6nS1I ''49edo riff''] (2026). This mapping has a contiguous range of 5⅓ octaves; and the repeated notes may provide a bit of assistance with mitigation of vertical wraparounds. This mapping uses 9\49 (one key right) as its generator, which functions as a very flat septimal major second ~[[8/7]], a very sharp (and inconsistently-mapped) Pythagorean major second ~[[9/8]], and (much more accurately) a near-just undecimal acute whole tone ~[[25/22]] (both the Archytas comma [[64/63]] and the valinorsma [[176/175]] are tempered out). Two of them make a somewhat sharp septimal major third ~[[9/7]]; four of them make a slightly sharp classic major sixth ~[[5/3]]; seven of them (after octave reduction) make a somewhat flat undecimal neutral third ~[[11/9]]; eight of them make a very sharp undecimal major fourth ~[[11/8]]; and nine of them make a near-just undecimal minor sixth ~[[11/7]]. Thus, this mapping favors mostly xenharmonic intervals.

== Infraorwell ==

The septimal minor third ~[[7/6]] (11\49) of [[49edo]] is near-just, which suggests its use as a generator, as in [[Orwell]]; however, it is too close to just for actual Orwell eemperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]] — hence [[Orwellismic_temperaments#Infraorwell|infraorwell]]. It is possible to produce a forward chroma [[4L 5s]] (gramitonic, 6:5 step ratio) infraorwell mapping for 49edo, as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023) and (very differently) in [https://www.youtube.com/shorts/V8t7MyP2Nuo ''microtonal improv in 49edo''] (2024). This mapping gets all notes in each octave and has a range of a bit over 4 octaves with repeated notes to mitigate vertical wraparounds; the octaves alternate between near/far and middle, with double octaves sloping slightly upwards.

@@ Line 4: / Line 4: @@
 Since 49edo is a [[superpyth]] temperament, the classic major third ~[[5/4]] is mapped to the interval of an augmented second (e.g. a 5/4 above C is D♯); also, the Pythagorean major second ~[[9/8]] is mapped inconsistently to be the same as the septimal major second ~[[8/7]]. [[Cam Taylor]] demonstrates this mapping in [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023).
 {{Lumatone EDO mapping|n=49|start=10|xstep=9|ystep=-7}}
+== Whitewood + Bohpier ==
+Since [[49edo]] is a multiple of [[7edo]], and not too far beyond the highest non-diatonic multiple thereof, [[whitewood]] mappings are legitimate, as [[Bryan Deister]] demonstrates in [https://www.youtube.com/shorts/BcBtD3nuEQs ''49edo groove''] (2026). The sevenths of octaves proceed right, and therefore the octaves slope upwards with this, yielding a range a bit over 4½ octaves. The generator apart from the octave division proceeds down-right; as 6\42, it functions as a somewhat flat Alpharabian tendoneutral second ~[[12/11]] (and if the 49f val is used, also as a rather sharp but still consistent tridecimal neutral second ~[[13/12]]), thus making this also a [[bohpier]] mapping, with a rotated [[1L&nbsp;7s]] scale having a 7:6 step ratio. Three of these generators make a somewhat sharp septimal major third ~[[9/7]]; four of them make a somewhat sharp lesser septimal tritone ~[[7/5]]; six of them make a slightly flat classic major sixth ~[[5/3]]; and seven of them make a very sharp classic major seventh ~[[9/5]].
+{{Lumatone EDO mapping|n=49|start=34|xstep=7|ystep=-1}}
 == Didacus ==
@@ Line 17: / Line 21: @@
 == Archipelago + Catalan ==
-The most efficient mapping for [[49edo]], having a range of 5¼ octaves (which slope down moderately) with no missed notes and no repeated notes, is [[Bryan Deister]]'s [[4L&nbsp;3s]] (10:3 step ratio) mapping that functions for both a rank-2 or rank-3 [[archipelago]]-related temperament and [[catalan]] temperament, demonstrated in [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026). The rank-2 archipelago-related temperament (which is not currently on the archipelago page) uses one key right (10\49) as a slightly sharp tridecimal semifourth ~[[15/13]] (in the 49f val) for its generator; two of them make the fairly flat fourth ~[[4/3]]; four of them make the sharp septimal minor seventh ~[[7/4]]; six of them (after octave reduction) make a slightly sharp septimal minor third ~[[7/6]]; thirteen of them (after more octave reduction) make a near-just undecimal minor sixth ~[[11/7]]; and fourteen of them make a sharp classic minor seventh ~[[9/5]]. Although this is a respectable list of intervals, by itself the rank-2 version of the temperament does not make a very good [[MOS]] scale &mdash; instead it makes for scales in which the small interval is only 1\49. Therefore, for facility in making scales, including the aforementioned 4L&nbsp;3s, a second generator is needed (thus elevating this to a rank-3 temperament that tempers out [[364/363]], [[540/539]], and [[847/845]]); that generator uses one key down-right (3\49) as the slightly sharp classic chromatic semitone ~[[25/24]], which 49edo actually uses as a diatonic semitone. Catalan uses one key right plus one key down-right (13\49) as a slightly sharp classic minor third for its generator; two of them make a very flat Axirabian paraminor fifth ~[[16/11]]; four of them (after octave reduction) make a somewhat sharp classic chromatic semitone ~[[25/24]]; five of them make a mildly sharp classic major third ~[[5/4]]; six of them make a sharp fifth ~[[3/2]]; seven of them make a sharp classic minor seventh ~[[9/5]]; eight of them (after more octave-reduction) make a mildly flat undecimal neutral second ~[[12/11]]; and ten of them make a near-just undecimal minor sixth ~[[11/7]]. Catalan does not need a second generator to produce usable MOS scales, including the aforementioned 4L&nbsp;3s.
+The most efficient mapping for [[49edo]], having a range of 5¼ octaves (which slope down moderately) with no missed notes and no repeated notes, is [[Bryan Deister]]'s [[4L&nbsp;3s]] (10:3 step ratio) mapping that functions for both a rank-2 or rank-3 [[archipelago]]-related temperament and [[catalan]] temperament, demonstrated in [https://www.youtube.com/shorts/34w7euOF-Ss ''49edo improv''] (2026). The rank-2 archipelago-related temperament (which is not currently on the archipelago page) uses one key right (10\49) as a slightly sharp tridecimal semifourth ~[[15/13]] (in the 49f val) for its generator; two of them make the fairly flat fourth ~[[4/3]]; four of them make the sharp septimal minor seventh ~[[7/4]]; six of them (after octave reduction) make a slightly sharp septimal minor third ~[[7/6]]; thirteen of them (after more octave reduction) make a near-just undecimal minor sixth ~[[11/7]]; and fourteen of them make a sharp classic minor seventh ~[[9/5]]. Although this is a respectable list of intervals, the unmodified rank-2 version of the temperament does not make a very good [[MOS]] scale &mdash; instead it makes for scales in which the small interval is only 1\49. Therefore, for facility in making scales, including the aforementioned 4L&nbsp;3s, a second generator is needed (thus elevating this to a rank-3 temperament that tempers out [[364/363]], [[540/539]], and [[847/845]]); that generator uses one key down-right (3\49) as the slightly sharp classic chromatic semitone ~[[25/24]], which 49edo uses here more like a diatonic semitone (although the actual 49edo diatonic semitone is only 2\49). Catalan uses one key right plus one key down-right (13\49) as a slightly sharp classic minor third for its generator; two of them make a very flat Axirabian paraminor fifth ~[[16/11]]; four of them (after octave reduction) make a slightly sharp classic chromatic semitone ~[[25/24]]; five of them make a mildly sharp classic major third ~[[5/4]]; six of them make a sharp fifth ~[[3/2]]; seven of them make a sharp classic minor seventh ~[[9/5]]; eight of them (after more octave-reduction) make a mildly flat undecimal neutral second ~[[12/11]]; and ten of them make a near-just undecimal minor sixth ~[[11/7]]. Catalan does not need a second generator to produce usable MOS scales, including the aforementioned 4L&nbsp;3s.
 {{Lumatone EDO mapping|n=49|start=4|xstep=10|ystep=-7}}
+==== Reverse chroma version ====
+It is possible to make a reverse chroma version of the above mapping. The range is considerably less, at a bit over 3⅓ octaves, with considerable regions of non-contiguous notes in the upper left and lower right corners, and the octaves slope down, incurring a vertical wraparound; on the other hand, a considerable number of repeated notes are available in each complete octave to mitigate vertical wraparounds. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/VmUIxWb8NCY ''49edo prelude''] (2026), although with note 0 set to where note 38 is here.
+{{Lumatone EDO mapping|n=49|start=6|xstep=3|ystep=7}}
+== Machine ==
+It is possible to get closer to level octaves for [[49edo]] with a slight gain in practical efficiency (having three repeated notes in each octave, but no non-contiguous notes in the lower left and upper right corners compared to the the archipelago + catalan mapping) with a machine scale ([[5L&nbsp;1s]], with a 9:4 step ratio). [[Bryan Deister]] has demonstrated this in [[Bryan Deister]]'s [https://www.youtube.com/shorts/_yNrDI6nS1I ''49edo riff''] (2026). This mapping has a contiguous range of 5⅓ octaves; and the repeated notes may provide a bit of assistance with mitigation of vertical wraparounds. This mapping uses 9\49 (one key right) as its generator, which functions as a very flat septimal major second ~[[8/7]], a very sharp (and inconsistently-mapped) Pythagorean major second ~[[9/8]], and (much more accurately) a near-just undecimal acute whole tone ~[[25/22]] (both the Archytas comma [[64/63]] and the valinorsma [[176/175]] are tempered out). Two of them make a somewhat sharp septimal major third ~[[9/7]]; four of them make a slightly sharp classic major sixth ~[[5/3]]; seven of them (after octave reduction) make a somewhat flat undecimal neutral third ~[[11/9]]; eight of them make a very sharp undecimal major fourth ~[[11/8]]; and nine of them make a near-just undecimal minor sixth ~[[11/7]]. Thus, this mapping favors mostly xenharmonic intervals.
+{{Lumatone EDO mapping|n=49|start=4|xstep=9|ystep=-5}}
+== Infraorwell ==
+The septimal minor third ~[[7/6]] (11\49) of [[49edo]] is near-just, which suggests its use as a generator, as in [[Orwell]]; however, it is too close to just for actual Orwell eemperament, and so a stack of it manages to miss all of the intervals characteristic of Orwell, other than a fairly flat classic minor sixth ~[[8/5]] &mdash; hence [[Orwellismic_temperaments#Infraorwell|infraorwell]]. It is possible to produce a forward chroma [[4L&nbsp;5s]] (gramitonic, 6:5 step ratio) infraorwell mapping for 49edo, as demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023) and (very differently) in [https://www.youtube.com/shorts/V8t7MyP2Nuo ''microtonal improv in 49edo''] (2024). This mapping gets all notes in each octave and has a range of a bit over 4 octaves with repeated notes to mitigate vertical wraparounds; the octaves alternate between near/far and middle, with double octaves sloping slightly upwards.
+{{Lumatone EDO mapping|n=49|start=33|xstep=6|ystep=-1}}
 {{Navbox Lumatone}}