6ed7/3 - Revision history

BudjarnLambeth at 23:32, 25 September 2025

2025-09-25T23:32:48Z

← Older revision		Revision as of 23:32, 25 September 2025
Line 45:		Line 45:

	; 6ed7/3 on the x-steps		; 6ed7/3 on the x-steps
			{{Lumatone EDO mapping\|n=49\|start=0\|xstep=10\|ystep=7}}

			; 6ed7/3 on the x-steps (alt.)
	{{Lumatone EDO mapping\|n=49\|start=0\|xstep=10\|ystep=-7}}		{{Lumatone EDO mapping\|n=49\|start=0\|xstep=10\|ystep=-7}}

	; 6ed7/3 on the y-steps		; 6ed7/3 on the y-steps
			{{Lumatone EDO mapping\|n=49\|start=0\|xstep=7\|ystep=10}}

			; 6ed7/3 on the y-steps (alt.)
	{{Lumatone EDO mapping\|n=49\|start=0\|xstep=7\|ystep=-10}}		{{Lumatone EDO mapping\|n=49\|start=0\|xstep=7\|ystep=-10}}

			== See also ==
			* [[9ed7/3]]

BudjarnLambeth: /* 6ed7/3+7edo scale */

2025-09-25T23:19:01Z

6ed7/3+7edo scale

← Older revision		Revision as of 23:19, 25 September 2025
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	Within 49edo:		Within 49edo:
	• 6ed7/3 is the step pattern 10 10 10...		* 6ed7/3 is the step pattern 10 10 10...
	• 7edo is the step pattern 7 7 7...		* 7edo is the step pattern 7 7 7...
	Which means that both scales sync up every 70 steps of 49edo, at the interval 1714.286c.		Which means that both scales sync up every 70 steps of 49edo, at the interval 1714.286c.

BudjarnLambeth at 23:18, 25 September 2025

2025-09-25T23:18:24Z

← Older revision		Revision as of 23:18, 25 September 2025
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	{{Harmonics in equal\|6\|7\|3\|intervals=integer\|columns=11}}		{{Harmonics in equal\|6\|7\|3\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|6\|7\|3\|intervals=integer\|collapsed=1\|start=12\|columns=12}}		{{Harmonics in equal\|6\|7\|3\|intervals=integer\|collapsed=1\|start=12\|columns=12}}

			== Intervals ==
			{{Interval table}}

	== 6ed7/3+7edo scale ==		== 6ed7/3+7edo scale ==

BudjarnLambeth: /* Lumatone mappings */

2025-09-25T23:14:21Z

Lumatone mappings

← Older revision		Revision as of 23:14, 25 September 2025
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	=== Lumatone mappings ===		=== Lumatone mappings ===
	Mapping the 6ed7/3+7edo scale onto a 2D [[~~isomporhic~~ keyboard]] like the [[Lumatone]], one can use 7\49 for the x-steps and 10\49 for the y-steps or vice versa.		Mapping the 6ed7/3+7edo scale onto a 2D [[isomorphic keyboard]] like the [[Lumatone]], one can use 7\49 for the x-steps and 10\49 for the y-steps or vice versa.

	; 6ed7/3 on the x-steps		; 6ed7/3 on the x-steps

BudjarnLambeth: /* = Lumatone mappings */

2025-09-25T23:13:54Z

= Lumatone mappings

← Older revision		Revision as of 23:13, 25 September 2025
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	* 70\49 (period)		* 70\49 (period)

	=== Lumatone mappings ==		=== Lumatone mappings ===
	Mapping the 6ed7/3+7edo scale onto a 2D [[isomporhic keyboard]] like the [[Lumatone]], one can use 7\49 for the x-steps and 10\49 for the y-steps or vice versa.		Mapping the 6ed7/3+7edo scale onto a 2D [[isomporhic keyboard]] like the [[Lumatone]], one can use 7\49 for the x-steps and 10\49 for the y-steps or vice versa.

BudjarnLambeth: Created page with "{{Infobox ET}}{{ED intro}} == Theory == === Harmonics === {{Harmonics in equal|6|7|3|intervals=integer|columns=11}} {{Harmonics in equal|6|7|3|intervals=integer|collapsed=1|start=12|columns=12}} == 6ed7/3+7edo scale == On the Xenharmonic Alliance Discord in September 2025, Maeve Gutierrez noted that the notes of 3ed7/3 make for a nice chord when played simultaneously, and that 6ed7/3 is a good tuning for using said chord. Gutierrez also noted that playing..."

2025-09-25T23:13:37Z

Created page with "{{Infobox ET}}{{ED intro}} == Theory == === Harmonics === {{Harmonics in equal|6|7|3|intervals=integer|columns=11}} {{Harmonics in equal|6|7|3|intervals=integer|collapsed=1|start=12|columns=12}} == 6ed7/3+7edo scale == On the Xenharmonic Alliance Discord in September 2025, Maeve Gutierrez noted that the notes of 3ed7/3 make for a nice chord when played simultaneously, and that 6ed7/3 is a good tuning for using said chord. Gutierrez also noted that playing..."

New page

{{Infobox ET}}{{ED intro}}

== Theory ==
=== Harmonics ===
{{Harmonics in equal|6|7|3|intervals=integer|columns=11}}
{{Harmonics in equal|6|7|3|intervals=integer|collapsed=1|start=12|columns=12}}

== 6ed7/3+7edo scale ==
On the [[Xenharmonic Alliance]] Discord in September 2025, [[Maeve Gutierrez]] noted that the notes of [[3ed7/3]] make for a nice chord when played simultaneously, and that 6ed7/3 is a good tuning for using said chord.

Gutierrez also noted that playing 6ed7/3 on one instrument/track simultaneously with [[7edo]] on another (a [[polymicrotonal]] approach) makes for some useful effects: "6ed7/3+7edo together gives lots of shimmer to play with+2 different flavours of detuned perfect fifth and fourth".

[[Lériendil]] then noted that this 6ed7/3+7edo scale is very closely approximated by [[49edo]]. [[Budjarn Lambeth]] expanded on this idea, mentioning that after going 3 octaves up or 3 octaves down from the root note, the discrepancy between the two tunings (6ed7/3 and a stack of 7/3 from 49edo) will be no more than 6 [[cents]].

If one wished to use this 6ed7/3+7edo scale tempered to 49edo, then it would look as follows:

Within 49edo:
• 6ed7/3 is the step pattern 10 10 10...
• 7edo is the step pattern 7 7 7...
Which means that both scales sync up every 70 steps of 49edo, at the interval 1714.286c.

So (tempered to 49edo), the combined 6ed7/3 & 7edo scale is:
* 7\49
* 10\49
* 14\49
* 20\49
* 21\49
* 28\49
* 30\49
* 35\49
* 40\49
* 42\49
* 49\49
* 50\49
* 56\49
* 60\49
* 63\49
* 70\49 (period)

=== Lumatone mappings ==
Mapping the 6ed7/3+7edo scale onto a 2D [[isomporhic keyboard]] like the [[Lumatone]], one can use 7\49 for the x-steps and 10\49 for the y-steps or vice versa.

; 6ed7/3 on the x-steps
{{Lumatone EDO mapping|n=49|start=0|xstep=10|ystep=-7}}

; 6ed7/3 on the y-steps
{{Lumatone EDO mapping|n=49|start=0|xstep=7|ystep=-10}}