Overthink: /* Phicordial */ It's the octave, not the generator, that's indivisible because of 103 being prime. "Hemimiracle" is an alternative extension to 11 that splits the generator into two ~33/32's.

2026-05-16T04:27:17Z

Phicordial: It's the octave, not the generator, that's indivisible because of 103 being prime. "Hemimiracle" is an alternative extension to 11 that splits the generator into two ~33/32's.

← Older revision		Revision as of 04:27, 16 May 2026
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	{{Lumatone EDO mapping\|n=103\|start=0\|xstep=7\|ystep=-4}}		{{Lumatone EDO mapping\|n=103\|start=0\|xstep=7\|ystep=-4}}
	=== Phicordial ===		=== Phicordial ===
	Since 103 is a prime edo, it does not support ~~hemimiracle~~, but dividing the inverse generator in three gives you the [[10L 3s]] [[Phicordial]] mapping, which covers the whole gamut about as efficiently as possible and keeps octaves close to horizontal.		Since 103 is a prime edo, it does not support semimiracle, but dividing the inverse generator in three gives you the [[10L 3s]] [[Phicordial]] mapping, which covers the whole gamut about as efficiently as possible and keeps octaves close to horizontal.
	{{Lumatone EDO mapping\|n=103\|start=15\|xstep=10\|ystep=-9}}		{{Lumatone EDO mapping\|n=103\|start=15\|xstep=10\|ystep=-9}}

	{{Navbox Lumatone}}		{{Navbox Lumatone}}

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2025-08-27T15:01:12Z

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{{Lumatone mapping intro}}
== Diatonic ==
{{Lumatone EDO mapping|n=103|start=101|xstep=17|ystep=-8}}
Due to the size of the edo, this will not cover all the notes unless expanded out from [[5L 2s]] to [[12L 7s]], reducing the range commensurately.
{{Lumatone EDO mapping|n=103|start=6|xstep=8|ystep=-7}}

== Miracle ==
The [[Miracle]] mapping is the most efficient way to put well-tuned intervals close to one-another, but the [[10L 1s]] mapping does not cover the whole gamut and the [[10L 11s]] mapping has a very limited range & strong downward slope.
=== 10L 1s ===
{{Lumatone EDO mapping|n=103|start=9|xstep=10|ystep=-7}}
=== 10L 11s ===
{{Lumatone EDO mapping|n=103|start=0|xstep=7|ystep=-4}}
=== Phicordial ===
Since 103 is a prime edo, it does not support hemimiracle, but dividing the inverse generator in three gives you the [[10L 3s]] [[Phicordial]] mapping, which covers the whole gamut about as efficiently as possible and keeps octaves close to horizontal.
{{Lumatone EDO mapping|n=103|start=15|xstep=10|ystep=-9}}

{{Navbox Lumatone}}

Lumatone mapping for 103edo - Revision history

Overthink: /* Phicordial */ It's the octave, not the generator, that's indivisible because of 103 being prime. "Hemimiracle" is an alternative extension to 11 that splits the generator into two ~33/32's.

Yourmusic Productions: Create Page.