4ed5/2 - Revision history

FloraC: Oops that's not quite right

2026-05-27T13:46:11Z

Oops that's not quite right

← Older revision		Revision as of 13:46, 27 May 2026
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	== Theory ==		== Theory ==
	4ed5/2 is [[3edo]] with the [[2/1\|octave]] compressed by about 10 cents, or [[~~5ed5~~]] with the [[5/1\|5th harmonic]] compressed by the same amount. It therefore can be considered ~~more optimized for the~~ 2.5 subgroup ~~than either of above,~~ tempering out [[128/125]].		4ed5/2 is [[3edo]] with the [[2/1\|octave]] compressed by about 10 cents, or [[7ed5]] with the [[5/1\|5th harmonic]] compressed by the same amount. It therefore can be considered as an overcompressed 2.5-subgroup temperament tempering out [[128/125]].

	=== Harmonics ===		=== Harmonics ===

2026-05-27T13:39:58Z

Expand & unstub. Mark as mathematical interest

← Older revision		Revision as of 13:39, 27 May 2026
Line 1:		Line 1:
			{{Mathematical interest}}
	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

			== Theory ==
			4ed5/2 is [[3edo]] with the [[2/1\|octave]] compressed by about 10 cents, or [[5ed5]] with the [[5/1\|5th harmonic]] compressed by the same amount. It therefore can be considered more optimized for the 2.5 subgroup than either of above, tempering out [[128/125]].

			=== Harmonics ===
			{{Harmonics in equal\|4\|5\|2}}

			=== Subsets and supersets ===
			4ed5/2 is the first composite ed5/2, containing 2ed5/2 as the only nontrivial subset ed5/2.

	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable center-1 right-2"
	\|+		\|+
	!~~Steps~~		! #
	!Cents		! Cents
	!~~JI approximation (2.5.31)~~		! Approximated ratio
	\|-		\|-
	\|0		\| 0
	\|0		\| 0
	\|1/1		\| 1/1
	\|-		\|-
	\|1		\| 1
	\|~~396.58~~		\| 397
	\|5/4~~, 31/25~~		\| 5/4
	\|-		\|-
	\|2		\| 2
	\|793~~.15~~		\| 793
	\|8/5		\| 8/5
	\|-		\|-
	\|3		\| 3
	\|~~1189.74~~		\| 1190
	\|2/1		\| 2/1
	\|-		\|-
	\|4		\| 4
	\|1586~~.31~~		\| 1586
	\|5/2~~, 62/25~~		\| 5/2
	\|}		\|}

	~~==Harmonics==~~
	~~{{Harmonics in equal\|4\|5\|2\|intervals=prime}}~~


	~~{{stub}}~~

2024-12-16T17:04:10Z

Interval table

@@ Line 2: / Line 2: @@
 {{ED intro}}
-== Harmonics ==
+== Intervals ==
-{{Harmonics in equal|4|5|2}}
+{| class="wikitable"
 {{stub}}

2024-12-16T16:44:23Z

2024-12-16T16:44:13Z

Harmonics stub

2024-12-12T12:48:21Z

Created page with "{{Infobox ET}} {{ED intro}}"

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