Septimagic comma - Revision history

FloraC: Review. - data (addressed in the misc. page)

2026-01-18T09:37:02Z

Review. - data (addressed in the misc. page)

← Older revision		Revision as of 09:37, 18 January 2026
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	'''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a [[2.3.7 subgroup\|no-fives]] [[7-limit]] [[comma]] of measuring 20.7 [[cent]]s. It is the difference between five [[14/9]]s and ~~two~~ [[3/1]]s.		'''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a [[2.3.7 subgroup\|no-fives]] [[7-limit]] [[comma]] measuring 20.7 [[cent]]s. It is the difference between a stack of five [[14/9]]'s and [[9/1]].

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma gives the rank-3 ~~'''~~septimagic temperament~~'''~~ in the full 7-limit, and the ~~'''~~[[No-fives subgroup temperaments #Magi\|magi ~~temperament~~]]~~'''~~ in its minimal prime subgroup of 2.3.7. Magi is the no-five restriction of ~~the~~ [[~~Magic\|~~magic ~~temperament]].~~		[[Tempering out]] this comma gives the rank-3 [[septimagic]] temperament in the full 7-limit, and the [[No-fives subgroup temperaments #Magi\|magi]] temperament in its minimal prime subgroup of 2.3.7. Magi is the no-five restriction of [[magic]].

	~~=== Septimagic ===~~
	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 537824/531441~~

	~~{{Mapping\|legend=1\| 1 0 0 -1 \| 0 5 0 12 \| 0 0 1 0 }}~~
	~~: Mapping generators: ~2, ~243/196, ~5~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1199.822{{c}}, ~243/196 = 380.604{{c}}, ~5 = 2786.312{{c}}
	* [[CWE]]: ~2 = 1200.000{{c}}, ~243/196 = 380.638{{c}}, ~5 = 2786.523{{c}}

	~~{{Optimal ET sequence\|legend=1\| 19, 41, 104c, 126, 145, 167, 186 }}~~

	~~[[Badness~~]] ~~(Sintel): 11~~.~~758~~


	== Etymology ==		== Etymology ==
	~~The word ''septimagic'' is~~ a contraction of ''septimal magic'' into a single word.		This comma was named by [[Xenllium]] in 2026 as a contraction of ''septimal magic'' into a single word.

	== See also ==		== See also ==

Xenllium at 02:02, 18 January 2026

2026-01-18T02:02:44Z

@@ Line 9: / Line 9: @@
 == Temperaments ==
-Tempering out this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and the '''[[No-fives subgroup temperaments #Magi|magi temperament]]''' in its minimal prime subgroup of 2.3.7.
+[[Tempering out]] this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and the '''[[No-fives subgroup temperaments #Magi|magi temperament]]''' in its minimal prime subgroup of 2.3.7. Magi is the no-five restriction of the [[Magic|magic temperament]].
 == Etymology ==

Xenllium: Created page with "{{Infobox interval | Ratio = 537824/531441 | Name = septimagic comma, magi comma | Color name = sz⁵4, saquinzo 4th | Comma = yes }} '''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a no-fives 7-limit comma of measuring 20.7 cents. It is the difference between five 14/9s and two 3/1s. == Temperaments == Tempering out this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and..."

2026-01-18T01:49:40Z

Created page with "{{Infobox interval | Ratio = 537824/531441 | Name = septimagic comma, magi comma | Color name = sz<sup>5</sup>4, saquinzo 4th | Comma = yes }} '''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a no-fives 7-limit comma of measuring 20.7 cents. It is the difference between five 14/9s and two 3/1s. == Temperaments == Tempering out this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and..."

New page

{{Infobox interval
| Ratio = 537824/531441
| Name = septimagic comma, magi comma
| Color name = sz<sup>5</sup>4, saquinzo 4th
| Comma = yes
}}

'''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a [[2.3.7 subgroup|no-fives]] [[7-limit]] [[comma]] of measuring 20.7 [[cent]]s. It is the difference between five [[14/9]]s and two [[3/1]]s.

== Temperaments ==
Tempering out this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and the '''[[No-fives subgroup temperaments #Magi|magi temperament]]''' in its minimal prime subgroup of 2.3.7.

== Etymology ==
The word ''septimagic'' is a contraction of ''septimal magic'' into a single word.

== See also ==
* [[Septimagic clan]]

[[Category:Septimagic]]
[[Category:Commas named for their regular temperament properties]]