Hedgehog - Revision history

Inthar at 23:58, 8 July 2026

2026-07-08T23:58:39Z

← Older revision		Revision as of 23:58, 8 July 2026
Line 1:		Line 1:
	Conventionally, '''Hedgehog''' (2.3.5.7[22 & 36c]) tempers out Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the [[Sensamagic]] comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways.		Conventionally, '''Hedgehog''' (2.3.5.7[22 & 36c]) tempers out the Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the [[Sensamagic]] comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways.

	{{UserTag\|g_\|Ground\|7766ff\|The 2.3.7 temperament is extremely useful in virtually any even edo with a decent 3, 7, and 9/7 due to its low complexity. Equating the difference between 9/7 and half an octave to 9/7 / (7/6) <nowiki>=</nowiki> 54/49 is an obvious thing to do because (9/7)^2 / (7/6) <nowiki>=</nowiki> 486/343 is 603¢. It is also obvious to equate 16/13 plus half an octave to 7/4. With this in mind, I propose two temperaments on either side of 22edo:		{{UserTag\|g_\|Ground\|7766ff\|The 2.3.7 temperament is extremely useful in virtually any even edo with a decent 3, 7, and 9/7 due to its low complexity. Equating the difference between 9/7 and half an octave to 9/7 / (7/6) <nowiki>=</nowiki> 54/49 is an obvious thing to do because (9/7)^2 / (7/6) <nowiki>=</nowiki> 486/343 is 603¢. It is also obvious to equate 16/13 plus half an octave to 7/4. With this in mind, I propose two temperaments on either side of 22edo:

Inthar at 23:58, 8 July 2026

2026-07-08T23:58:05Z

← Older revision		Revision as of 23:58, 8 July 2026
Line 1:		Line 1:
	Conventionally, '''Hedgehog''' tempers out Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the [[Sensamagic]] comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways.		Conventionally, '''Hedgehog''' (2.3.5.7[22 & 36c]) tempers out Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the [[Sensamagic]] comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways.

	{{UserTag\|g_\|Ground\|7766ff\|The 2.3.7 temperament is extremely useful in virtually any even edo with a decent 3, 7, and 9/7 due to its low complexity. Equating the difference between 9/7 and half an octave to 9/7 / (7/6) <nowiki>=</nowiki> 54/49 is an obvious thing to do because (9/7)^2 / (7/6) <nowiki>=</nowiki> 486/343 is 603¢. It is also obvious to equate 16/13 plus half an octave to 7/4. With this in mind, I propose two temperaments on either side of 22edo:		{{UserTag\|g_\|Ground\|7766ff\|The 2.3.7 temperament is extremely useful in virtually any even edo with a decent 3, 7, and 9/7 due to its low complexity. Equating the difference between 9/7 and half an octave to 9/7 / (7/6) <nowiki>=</nowiki> 54/49 is an obvious thing to do because (9/7)^2 / (7/6) <nowiki>=</nowiki> 486/343 is 603¢. It is also obvious to equate 16/13 plus half an octave to 7/4. With this in mind, I propose two temperaments on either side of 22edo:

Ground: Created page with "Conventionally, '''Hedgehog''' tempers out Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the Sensamagic comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways. {{UserTag|g_|Ground|7766ff|The 2.3.7 temperament is extremely useful in virtually any even ed..."

2026-07-08T00:47:22Z

Created page with "Conventionally, '''Hedgehog''' tempers out Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the Sensamagic comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways. {{UserTag|g_|Ground|7766ff|The 2.3.7 temperament is extremely useful in virtually any even ed..."

New page

Conventionally, '''Hedgehog''' tempers out Jubilisma 50/49, splitting the octave in half into a tritone representing both 7/5 and 10/7, and the [[Sensamagic]] comma 245/243, equating a stack of two 9/7s with 5/3. If the subgroup is reduced to just 2.3.7, it tempers out the Stearnsma 118098/117649, resulting in a much more accurate temperament that can be extended in other ways.

{{UserTag|g_|Ground|7766ff|The 2.3.7 temperament is extremely useful in virtually any even edo with a decent 3, 7, and 9/7 due to its low complexity. Equating the difference between 9/7 and half an octave to 9/7 / (7/6) <nowiki>=</nowiki> 54/49 is an obvious thing to do because (9/7)^2 / (7/6) <nowiki>=</nowiki> 486/343 is 603¢. It is also obvious to equate 16/13 plus half an octave to 7/4. With this in mind, I propose two temperaments on either side of 22edo:
* The meantone version, 23-limit 36&50
* The straddle version (half-octave Porcupine), 23-limit 22&74bgh with alternate flat versions of 3, 17, and 19 at 11 generators away.
}}

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{{Cat|temperaments}}