Septischismic family - Revision history

FloraC: Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

2026-09-30T17:44:18Z

Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

← Older revision		Revision as of 17:44, 30 September 2026
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	Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079		Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 -6 \| 0 1 0 -14 23 12 5 \| 0 0 1 0 0 -1 1 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 -6 \| 0 1 0 -14 23 12 5 \| 0 0 1 0 0 -1 1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 784/783, 1216/1215, 1540/1539, 1729/1728, 2080/2079		Comma list: 784/783, 1216/1215, 1540/1539, 1729/1728, 2080/2079

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 -6 23 \| 0 1 0 -14 23 12 5 -31 \| 0 0 1 0 0 -1 1 0 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 -6 23 \| 0 1 0 -14 23 12 5 -31 \| 0 0 1 0 0 -1 1 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 784/783, 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2233/2232		Comma list: 784/783, 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2233/2232

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 -6 23 19 \| 0 1 0 -14 23 12 5 -31 -24 \| 0 0 1 0 0 -1 1 0 0 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 -6 23 19 \| 0 1 0 -14 23 12 5 -31 -24 \| 0 0 1 0 0 -1 1 0 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 1216/1215, 1540/1539, 1625/1624, 1729/1728, 2080/2079		Comma list: 1216/1215, 1540/1539, 1625/1624, 1729/1728, 2080/2079

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 -6 -41 \| 0 1 0 -14 23 12 5 26 \| 0 0 1 0 0 -1 1 2 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 -6 -41 \| 0 1 0 -14 23 12 5 26 \| 0 0 1 0 0 -1 1 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 1216/1215, 1540/1539, 1625/1624, 1729/1728, 2080/2079, 2233/2232		Comma list: 1216/1215, 1540/1539, 1625/1624, 1729/1728, 2080/2079, 2233/2232

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 -6 -41 -52 \| 0 1 0 -14 23 12 5 26 33 \| 0 0 1 0 0 -1 1 2 2 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 -6 -41 -52 \| 0 1 0 -14 23 12 5 26 33 \| 0 0 1 0 0 -1 1 2 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 1225/1224, 2080/2079, 2431/2430, 4096/4095		Comma list: 1225/1224, 2080/2079, 2431/2430, 4096/4095

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 47 \| 0 1 0 -14 23 12 -30 \| 0 0 1 0 0 -1 2 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 47 \| 0 1 0 -14 23 12 -30 \| 0 0 1 0 0 -1 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 1216/1215, 1225/1224, 1540/1539, 1729/1728, 2080/2079		Comma list: 1216/1215, 1225/1224, 1540/1539, 1729/1728, 2080/2079

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 47 -6 \| 0 1 0 -14 23 12 -30 5 \| 0 0 1 0 0 -1 2 1 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 47 -6 \| 0 1 0 -14 23 12 -30 5 \| 0 0 1 0 0 -1 2 1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 2080/2079, 2500/2499, 4096/4095, 19712/19683		Comma list: 2080/2079, 2500/2499, 4096/4095, 19712/19683

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 -48 \| 0 1 0 -14 23 12 27 \| 0 0 1 0 0 -1 4 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 -48 \| 0 1 0 -14 23 12 27 \| 0 0 1 0 0 -1 4 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2500/2499		Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2500/2499

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 -48 -6 \| 0 1 0 -14 23 12 27 5 \| 0 0 1 0 0 -1 4 1 }}		{{Mapping\|legend=2\| 1 0 0 25 -33 -13 -48 -6 \| 0 1 0 -14 23 12 27 5 \| 0 0 1 0 0 -1 4 1 }}

	Optimal tunings:		Optimal tunings:

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:29Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 2080/2079, 4096/4095, 19712/19683		Comma list: 2080/2079, 4096/4095, 19712/19683

	~~Mapping:~~ {{~~mapping~~\| 1 0 0 25 -33 -13 \| 0 1 0 -14 23 12 \| 0 0 1 0 0 -1 }}		{{Mapping\|legend=0\| 1 0 0 25 -33 -13 \| 0 1 0 -14 23 12 \| 0 0 1 0 0 -1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 2080/2079, 10648/10647, 43904/43875		Comma list: 2080/2079, 10648/10647, 43904/43875

	~~Mapping:~~ {{~~mapping~~\| 1 0 0 25 62 82 \| 0 1 0 -14 -34 -43 \| 0 0 1 0 -2 -3 }}		{{Mapping\|legend=0\| 1 0 0 25 62 82 \| 0 1 0 -14 -34 -43 \| 0 0 1 0 -2 -3 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 1216/1215, 2080/2079, 3136/3135, 10648/10647		Comma list: 1216/1215, 2080/2079, 3136/3135, 10648/10647

	~~Mapping:~~ {{~~mapping~~\| 1 0 0 25 62 82 -6 \| 0 1 0 -14 -34 -43 5 \| 0 0 1 0 -2 -3 1 }}		{{Mapping\|legend=0\| 1 0 0 25 62 82 -6 \| 0 1 0 -14 -34 -43 5 \| 0 0 1 0 -2 -3 1 }}

	Optimal tunings:		Optimal tunings:

FloraC: Undo revision 237428 by Hotcrystal0 (talk)

2026-09-22T13:23:29Z

Undo revision 237428 by Hotcrystal0 (talk)

← Older revision		Revision as of 13:23, 22 September 2026
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	{{Main\| Septischismic }}		{{Main\| Septischismic }}

	The head of this family is septischismic (~~sometimes~~ ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.		The head of this family is septischismic (formerly ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.

	Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].		Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].

FloraC: /* Undecimal septischismic (cassaschismic) */ complete data

2026-09-22T13:21:44Z

Undecimal septischismic (cassaschismic): complete data

Show changes

FloraC: /* Undecimal septischismic (cassaschismic) */ sorting

2026-09-22T12:57:58Z

Undecimal septischismic (cassaschismic): sorting

@@ Line 33: / Line 33: @@
 Undecimal septischismic, a.k.a. cassaschismic, maps [[prime interval|prime]] [[11/1|11]] to +23 perfect fifths, so it is an [[expansion]] of the [[2.3.7.11 subgroup|2.3.7.11-subgroup]] version of [[gary]]. It is naturally a no-17 19-limit temperament, where the undevicesimal schisma of [[513/512]] is also added to the generic aberschisma step.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 67: / Line 69: @@
 Badness (Sintel): 0.815
-=== 2.3.5.7.11.13.19 subgroup ===
+==== 2.3.5.7.11.13.19 subgroup ====
 Subgroup: 2.3.5.7.11.13.19
@@ Line 84: / Line 86: @@
 Badness (Sintel): 0.486
-=== Septinoellismic ===
+===== Septiplanar =====
 Septischismic has two reasonable extensions to add 29 and 31 into the system, that like before, coalesce in newt. Septiplanar finds them in the chain of fifths, without need of third generators, thus they in the same plane to the rank-2 chain of fifths, mapped respectively to a major seventh – three commas (3sM7) and a perfect octave minus two commas (hP8). Because this extension is reached only through the septischismic chain of fifths, it is also available in [[gary]].
@@ Line 139: / Line 105: @@
 Badness (Sintel): 0.758
-===== 2.3.5.7.11.13.19.29.31 subgroup =====
+====== 2.3.5.7.11.13.19.29.31 subgroup ======
 Subgroup: 2.3.5.7.11.13.19.29.31
@@ Line 156: / Line 122: @@
 Badness (Sintel): 0.793
-=== Septifantasious ===
+===== Septifantasious =====
 Septifantasious tempers out [[1625/1624]] – the fantasia, and thus finds 29/16 as 3 aberschismas above 9/5 – that is to say, superminor seventh + 2 aberschismas (^^Sm7), and 31/16 one apotome higher as a hypermajor seventh + 2 aberschismas (^^HM7).
@@ Line 175: / Line 141: @@
 Badness (Sintel): 0.716
-===== 2.3.5.7.11.13.19.29.31 subgroup =====
+====== 2.3.5.7.11.13.19.29.31 subgroup ======
 Subgroup: 2.3.5.7.11.13.19.29.31
@@ Line 191: / Line 157: @@
 Badness (Sintel): 0.796
 == Androschismic ==

Eufalesio: add-17 extensions, WIP, things to thread back

2026-09-20T19:56:38Z

add-17 extensions, WIP, things to thread back

@@ Line 84: / Line 84: @@
 Badness (Sintel): 0.486
-==== Septiplanar ====
+=== Septinoellismic ===
-Septischismic has two reasonable extensions to add 29 and 31 into the system, both of which coalesce in the structurally very similar temperament [[newt]]. Septiplanar finds them in the chain of fifths, without need of third generators, thus they in the same plane to the rank-2 chain of fifths, mapped respectively to a major seventh – three commas (3sM7) and a perfect octave minus two commas (hP8). Because this extension is reached only through the septischismic chain of fifths, it is also available in [[gary]].
+Septischismic has two reasonable extensions to add 17, both of which coalesce in the structurally very similar temperament [[newt]]. Septinoellismic finds it a tad unintuitively as two aberschismas up and 4 commas down from a major second (^^4sM2) yet supported by 94edo, and septisperasmic finds it 4 aberschismas up from a minor second (4^m2), which can be deemed the more intuitive mapping, albeit it is not supported by any cassandra tuning except for 12edo which notably has a very well tuned 17/16.
 Subgroup: 2.3.5.7.11.13.19.29
@@ Line 120: / Line 156: @@
 Badness (Sintel): 0.793
-==== Septifantasious ====
+=== Septifantasious ===
 Septifantasious tempers out [[1625/1624]] – the fantasia, and thus finds 29/16 as 3 aberschismas above 9/5 – that is to say, superminor seventh + 2 aberschismas (^^Sm7), and 31/16 one apotome higher as a hypermajor seventh + 2 aberschismas (^^HM7).

Hotcrystal0: See my comment on the talk page. Undo revision 237425 by FloraC (talk)

2026-09-19T11:50:33Z

See my comment on the talk page. Undo revision 237425 by FloraC (talk)

← Older revision		Revision as of 11:50, 19 September 2026
Line 5:		Line 5:
	{{Main\| Septischismic }}		{{Main\| Septischismic }}

	The head of this family is septischismic (~~formerly~~ ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.		The head of this family is septischismic (sometimes ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.

	Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].		Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].

FloraC: Undo revision 237388 by Hotcrystal0 (talk)

2026-09-19T08:48:09Z

Undo revision 237388 by Hotcrystal0 (talk)

← Older revision		Revision as of 08:48, 19 September 2026
Line 5:		Line 5:
	{{Main\| Septischismic }}		{{Main\| Septischismic }}

	The head of this family is septischismic (~~sometimes~~ ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.		The head of this family is septischismic (formerly ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.

	Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].		Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].

FloraC: Fix formatting

2026-09-19T08:47:25Z

Fix formatting

Show changes

Hotcrystal0 at 20:52, 18 September 2026

2026-09-18T20:52:18Z

← Older revision		Revision as of 20:52, 18 September 2026
Line 5:		Line 5:
	{{Main\| Septischismic }}		{{Main\| Septischismic }}

	The head of this family is septischismic (~~formerly~~ ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.		The head of this family is septischismic (sometimes ''garischismic''), which is generated by a [[3/2\|perfect fifth]] and an independent generator for [[5/4]]. Two [[Pythagorean apotome]]s i.e. 14 fifths octave-reduced make a [[8/7\|septimal major second (8/7)]]. Equivalently stated, the [[7/4\|harmonic seventh (7/4)]] is found at the double-diminished octave (C–C𝄫), or the minor seventh minus a generic comma step which stands in for both the Pythagorean comma and the septimal comma.

	Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].		Septischismic can be easily notated with [[chain-of-fifths notation]] with two additional sets of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[schisma]] and the [[aberschisma]].