Hibernal - Revision history

Ground at 23:35, 7 July 2026

2026-07-07T23:35:37Z

← Older revision		Revision as of 23:35, 7 July 2026
Line 86:		Line 86:
	Other useful edos may include 47, 71, 79, 83, 91, 106, and 111.		Other useful edos may include 47, 71, 79, 83, 91, 106, and 111.

	{{Cat\|~~Temperaments~~}}		{{Navbox regtemp}}
			{{Cat\|temperaments}}

Ground at 14:14, 7 July 2026

2026-07-07T14:14:27Z

← Older revision		Revision as of 14:14, 7 July 2026
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	For the tempering process, I will use [[erac]]s to show error accumulation. On a basic level, 25/21 * 19/15 is equated to >3/2, tempering out <190/189. This >3 is in the Archy range, so <<64/63 can be tempered out to add >7. At this point, tempering becomes less obvious. For 25/21 to be accurate, >>25 would be required to offset the very sharp Archy >>21. Assuming >>25 splits into (>5)^2, an accurate 19/15 would need an intolerably sharp >>19 to offset >>15. In my numerous attempts to turn Hibernal into a rank-3 2.3.5.7.19 temperament, I came to the conclusion that I have to make it straddle-5 to make any sense, with a roughly accurate 5 and an extra sharp >>5, equated to 19/15. It may look silly, 32edo actually works that way in my experience. This is my definitive 32edo temperament.		For the tempering process, I will use [[erac]]s to show error accumulation. On a basic level, 25/21 * 19/15 is equated to >3/2, tempering out <190/189. This >3 is in the Archy range, so <<64/63 can be tempered out to add >7. At this point, tempering becomes less obvious. For 25/21 to be accurate, >>25 would be required to offset the very sharp Archy >>21. Assuming >>25 splits into (>5)^2, an accurate 19/15 would need an intolerably sharp >>19 to offset >>15. In my numerous attempts to turn Hibernal into a rank-3 2.3.5.7.19 temperament, I came to the conclusion that I have to make it straddle-5 to make any sense, with a roughly accurate 5 and an extra sharp >>5, equated to 19/15. It may look silly, 32edo actually works that way in my experience. This is my definitive 32edo temperament.

	I use the Oceanfront mapping of 13/10, resulting in a straddled 13 as well. The following table equates it to 22/17. The exact distribution of eracs varies, but ~~is something like~~ 2.>3.5.>>5.>7.>19.(11.<<13.13.17).		I use the Oceanfront mapping of 13/10, resulting in a straddled 13 as well. The following table equates it to 22/17. The exact distribution of eracs varies, but 2.>3.5.>>5.>7.>19 always works out, and may be extended to include 11.13-.13+.17 which reflects the unpredictability of tuning 13.
	}}		}}
	{\| class="wikitable"		{\| class="wikitable"
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	\|}		\|}

	A simple rank-2 reduction uses Superpyth mappings for 25/21 and 19/15 in place of 6/5 and 5/4, seen in edos like 86, 59, 32, and 69. Other useful edos may include ~~44,~~ 47~~, 56, 64~~, 71~~, 76~~, 79, 83, 91~~, 100~~, 106~~, 108~~, and 111.		A simple rank-2 reduction uses Superpyth mappings for 25/21 and 19/15 in place of 6/5 and 5/4, seen in edos like 86, 59, 32, and 69.

			Another basic reduction is equating (25/21)^4 to 2/1, making a quadter-octave temperament. Edos include 32, 44, 56, 76, 100, and 108.

			Other useful edos may include 47, 71, 79, 83, 91, 106, and 111.

	{{Cat\|Temperaments}}		{{Cat\|Temperaments}}

Ground at 03:28, 7 July 2026

2026-07-07T03:28:42Z

← Older revision		Revision as of 03:28, 7 July 2026
Line 3:		Line 3:
	{{UserTag\|g_\|Ground\|7766ff\|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant than expected. I initially guessed it was 19/16 and 14/11, but I tried slight variations of the minor and major triads and realized that I was hearing the well of 19/15 instead.		{{UserTag\|g_\|Ground\|7766ff\|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant than expected. I initially guessed it was 19/16 and 14/11, but I tried slight variations of the minor and major triads and realized that I was hearing the well of 19/15 instead.

	For the tempering process, I will use [[erac]]s to show error accumulation. On a basic level, 25/21 * 19/15 is equated to >3/2, tempering out <190/189. This >3 is in the Archy range, so <<64/63 can be tempered out to add >7. At this point, tempering becomes less obvious. For 25/21 to be accurate, >>25 would be required to offset the very sharp Archy >>21. Assuming >>25 splits into (>5)^2, an accurate 19/15 would need an intolerably sharp >>19 to offset >>15. In my numerous attempts to turn Hibernal into a rank-3 2.3.5.7.19 temperament, I came to the conclusion that I have to make it straddle-5 to make any sense, with a roughly accurate 5 and an extra sharp >>5, equated to 19/15. It may look silly, 32edo actually works that way in my experience. This is my definitive 32edo temperament. I use the Oceanfront mapping of 13/10, resulting in a straddled 13 as well.}}		For the tempering process, I will use [[erac]]s to show error accumulation. On a basic level, 25/21 * 19/15 is equated to >3/2, tempering out <190/189. This >3 is in the Archy range, so <<64/63 can be tempered out to add >7. At this point, tempering becomes less obvious. For 25/21 to be accurate, >>25 would be required to offset the very sharp Archy >>21. Assuming >>25 splits into (>5)^2, an accurate 19/15 would need an intolerably sharp >>19 to offset >>15. In my numerous attempts to turn Hibernal into a rank-3 2.3.5.7.19 temperament, I came to the conclusion that I have to make it straddle-5 to make any sense, with a roughly accurate 5 and an extra sharp >>5, equated to 19/15. It may look silly, 32edo actually works that way in my experience. This is my definitive 32edo temperament.

			I use the Oceanfront mapping of 13/10, resulting in a straddled 13 as well. The following table equates it to 22/17. The exact distribution of eracs varies, but is something like 2.>3.5.>>5.>7.>19.(11.<<13.13.17).
			}}
	{\| class="wikitable"		{\| class="wikitable"
	\|+19-limit Hibernal Stradle-5-13, JI tuning in cents (generators 95/63 and 19/15), primes highlighted		\|+19-limit Hibernal Stradle-5-13, JI tuning in cents (generators 95/63 and 19/15), primes highlighted

Inthar at 03:03, 7 July 2026

2026-07-07T03:03:01Z

← Older revision		Revision as of 03:03, 7 July 2026
Line 3:		Line 3:
	{{UserTag\|g_\|Ground\|7766ff\|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant than expected. I initially guessed it was 19/16 and 14/11, but I tried slight variations of the minor and major triads and realized that I was hearing the well of 19/15 instead.		{{UserTag\|g_\|Ground\|7766ff\|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant than expected. I initially guessed it was 19/16 and 14/11, but I tried slight variations of the minor and major triads and realized that I was hearing the well of 19/15 instead.

	For the tempering process, I will use ~~eracs~~ to show error accumulation. On a basic level, 25/21 * 19/15 is equated to >3/2, tempering out <190/189. This >3 is in the Archy range, so <<64/63 can be tempered out to add >7. At this point, tempering becomes less obvious. For 25/21 to be accurate, >>25 would be required to offset the very sharp Archy >>21. Assuming >>25 splits into (>5)^2, an accurate 19/15 would need an intolerably sharp >>19 to offset >>15. In my numerous attempts to turn Hibernal into a rank-3 2.3.5.7.19 temperament, I came to the conclusion that I have to make it straddle-5 to make any sense, with a roughly accurate 5 and an extra sharp >>5, equated to 19/15. It may look silly, 32edo actually works that way in my experience. This is my definitive 32edo temperament. I use the Oceanfront mapping of 13/10, resulting in a straddled 13 as well.}}		For the tempering process, I will use [[erac]]s to show error accumulation. On a basic level, 25/21 * 19/15 is equated to >3/2, tempering out <190/189. This >3 is in the Archy range, so <<64/63 can be tempered out to add >7. At this point, tempering becomes less obvious. For 25/21 to be accurate, >>25 would be required to offset the very sharp Archy >>21. Assuming >>25 splits into (>5)^2, an accurate 19/15 would need an intolerably sharp >>19 to offset >>15. In my numerous attempts to turn Hibernal into a rank-3 2.3.5.7.19 temperament, I came to the conclusion that I have to make it straddle-5 to make any sense, with a roughly accurate 5 and an extra sharp >>5, equated to 19/15. It may look silly, 32edo actually works that way in my experience. This is my definitive 32edo temperament. I use the Oceanfront mapping of 13/10, resulting in a straddled 13 as well.}}
	{\| class="wikitable"		{\| class="wikitable"
	\|+19-limit Hibernal Stradle-5-13, JI tuning in cents (generators 95/63 and 19/15), primes highlighted		\|+19-limit Hibernal Stradle-5-13, JI tuning in cents (generators 95/63 and 19/15), primes highlighted

Inthar at 03:02, 7 July 2026

2026-07-07T03:02:16Z

← Older revision		Revision as of 03:02, 7 July 2026
Line 78:		Line 78:

	A simple rank-2 reduction uses Superpyth mappings for 25/21 and 19/15 in place of 6/5 and 5/4, seen in edos like 86, 59, 32, and 69. Other useful edos may include 44, 47, 56, 64, 71, 76, 79, 83, 91, 100, 106, 108, and 111.		A simple rank-2 reduction uses Superpyth mappings for 25/21 and 19/15 in place of 6/5 and 5/4, seen in edos like 86, 59, 32, and 69. Other useful edos may include 44, 47, 56, 64, 71, 76, 79, 83, 91, 100, 106, 108, and 111.

			{{Cat\|Temperaments}}

Ground at 02:56, 7 July 2026

2026-07-07T02:56:26Z

← Older revision		Revision as of 02:56, 7 July 2026
Line 77:		Line 77:
	\|}		\|}

	~~Useful~~ edos ~~for this temperament~~ may include 32, 76, 86, and 111.		A simple rank-2 reduction uses Superpyth mappings for 25/21 and 19/15 in place of 6/5 and 5/4, seen in edos like 86, 59, 32, and 69. Other useful edos may include 44, 47, 56, 64, 71, 76, 79, 83, 91, 100, 106, 108, and 111.

Ground: Created page with "'''Hibernal''' is a set of temperaments based on stacking a 25/21 minor third and 19/15 major third. 25 and 15 are both divisible by 5, resulting in 63:75:95, which is also delta-rational +3+5. The name is the adjective form of "winter" after the 32edo song that uses it extensively, Winter's Mortal Hope. {{UserTag|g_|Ground|7766ff|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant t..."

2026-07-07T02:37:52Z

Created page with "'''Hibernal''' is a set of temperaments based on stacking a 25/21 minor third and 19/15 major third. 25 and 15 are both divisible by 5, resulting in 63:75:95, which is also delta-rational +3+5. The name is the adjective form of "winter" after the 32edo song that uses it extensively, Winter's Mortal Hope. {{UserTag|g_|Ground|7766ff|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant t..."

New page

'''Hibernal''' is a set of temperaments based on stacking a 25/21 minor third and 19/15 major third. 25 and 15 are both divisible by 5, resulting in 63:75:95, which is also delta-rational +3+5. The name is the adjective form of "winter" after the 32edo song that uses it extensively, Winter's Mortal Hope.

{{UserTag|g_|Ground|7766ff|I used Hibernal in 32edo for a while because I loved the melodic properties of its blackdye, without knowing why it sounded more concordant than expected. I initially guessed it was 19/16 and 14/11, but I tried slight variations of the minor and major triads and realized that I was hearing the well of 19/15 instead.

For the tempering process, I will use eracs to show error accumulation. On a basic level, 25/21 * 19/15 is equated to >3/2, tempering out <190/189. This >3 is in the Archy range, so <<64/63 can be tempered out to add >7. At this point, tempering becomes less obvious. For 25/21 to be accurate, >>25 would be required to offset the very sharp Archy >>21. Assuming >>25 splits into (>5)^2, an accurate 19/15 would need an intolerably sharp >>19 to offset >>15. In my numerous attempts to turn Hibernal into a rank-3 2.3.5.7.19 temperament, I came to the conclusion that I have to make it straddle-5 to make any sense, with a roughly accurate 5 and an extra sharp >>5, equated to 19/15. It may look silly, 32edo actually works that way in my experience. This is my definitive 32edo temperament. I use the Oceanfront mapping of 13/10, resulting in a straddled 13 as well.}}
{| class="wikitable"
|+19-limit Hibernal Stradle-5-13, JI tuning in cents (generators 95/63 and 19/15), primes highlighted
|
| -2
| -1
|0
|1
|2
|-
| -4
|1137
|346
|756
|1165
|374
|-
| -3
|648
|1057
|267
|676
|1085
|-
| -2
|159
|569
| class="thl" |'''978'''
|187
|596
|-
| -1
|870
|80
|489
|898
| class="thl" |'''107'''
|-
|0
| class="thl" |'''382'''
|791
| class="thl" |'''0'''
| class="thl" |''409''
|818
|-
|1
|1093
| class="thl" |'''302'''
| class="thl" |'''711'''
|1120
|330
|-
|2
|604
|1013
|222
|631
|1041
|-
|3
|115
|524
|933
|143
| class="thl" |'''552'''
|-
|4
| class="thl" |'''826'''
|35
|444
| class="thl" |''854''
|63
|}

Useful edos for this temperament may include 32, 76, 86, and 111.