72nd-octave temperaments - Revision history

FloraC: - hafnium (addressed in landscape microtemps)

2026-04-24T13:47:12Z

- hafnium (addressed in landscape microtemps)

@@ Line 3: / Line 3: @@
 Temperaments discussed elsewhere include:
 * ''Omicronbeta'' → [[Compton family #Omicronbeta|Compton family]]
-* ''Omicronbeta'', → [[Compton family#Omicronbeta|Compton family]]
+* ''Hafnium'' → [[Landscape microtemperaments #Hafnium|Landscape microtemperaments]]
 == Jamala ==

ArrowHead294 at 03:55, 14 February 2025

2025-02-14T03:55:33Z

← Older revision		Revision as of 03:55, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|72}}		{{Infobox fractional-octave\|72}}
	[[72edo]] is a notable tuning system due to its 17-limit consistency, being a multiple of 12, and usage in various ecclesiastical forms of chanting.		[[72edo]] is a notable tuning system due to its 17-limit consistency, being a multiple of 12, and usage in various ecclesiastical forms of chanting.

Line 20:		Line 20:

	{{Optimal ET sequence\|legend=1\|1224, 1872def, 4320, 5544}}		{{Optimal ET sequence\|legend=1\|1224, 1872def, 4320, 5544}}
	===17-limit===
			=== 17-limit ===
	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

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	{{Optimal ET sequence\|legend=1\|1224, 1872def, 4320, 5544}}		{{Optimal ET sequence\|legend=1\|1224, 1872def, 4320, 5544}}

	===2.3.5.7.11.13.17.31 subgroup===		=== 2.3.5.7.11.13.17.31 subgroup ===
	Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.		Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.

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	Optimal tuning (CTE): ~3/2 = 701.948		Optimal tuning (CTE): ~3/2 = 701.948

	===2.3.5.7.11.13.17.31.37 subgroup===		=== 2.3.5.7.11.13.17.31.37 subgroup ===
	[[37/22]] is mapped to exact three-quarters of the octave.		[[37/22]] is mapped to exact three-quarters of the octave.

BudjarnLambeth: navbox

2024-12-05T07:40:11Z

navbox

← Older revision		Revision as of 07:40, 5 December 2024
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	{{Optimal ET sequence\|legend=1\|72, 1944, 2016, 3960}}		{{Optimal ET sequence\|legend=1\|72, 1944, 2016, 3960}}

			{{Navbox fractional-octave}}

Eliora: /* Jamala */

2023-12-08T16:37:36Z

Jamala

← Older revision		Revision as of 16:37, 8 December 2023
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	[[Optimal tuning]] ([[CTE]]): ~73205/53248 = 550.602		[[Optimal tuning]] ([[CTE]]): ~73205/53248 = 550.602

	~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~\|72~~, 1872f~~, 1944, 2016~~, 2088f, 2160fm~~, 3960}}		{{Optimal ET sequence\|legend=1\|72, 1944, 2016, 3960}}

Eliora: /* Jamala */

2023-07-10T22:29:05Z

Jamala

← Older revision		Revision as of 22:29, 10 July 2023
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	Jamala, described as the 1944 & 2016 temperament in the 2.5.11.13.19.41.47 subgroup was named by [[Eliora]] after a [[wikipedia:Jamala\|Ukrainian singer]] who won the [[wikipedia:2016 Eurovision Song Contest\|2016 Eurovision Song Contest]] with her song [[wikipedia:1944 (song)\|1944]].		Jamala, described as the 1944 & 2016 temperament in the 2.5.11.13.19.41.47 subgroup was named by [[Eliora]] after a [[wikipedia:Jamala\|Ukrainian singer]] who won the [[wikipedia:2016 Eurovision Song Contest\|2016 Eurovision Song Contest]] with her song [[wikipedia:1944 (song)\|1944]].

	Subgroup: 2.5.11.13.19.41.47		[[Subgroup]]: 2.5.11.13.19.41.47

	Comma basis: 47012251/47000000, 2502280/2501369, 410041489/410000000, 2680291328/2679296875, 52448351813/52428800000		[[Comma basis]]: 47012251/47000000, 2502280/2501369, 410041489/410000000, 2680291328/2679296875, 52448351813/52428800000

	Sval {{mapping\|legend=1\|72 2 183 -130 438 617 466\|0 5 2 12 -4 -7 -2}}		[[Sval]] {{mapping\|legend=1\|72 2 183 -130 438 617 466\|0 5 2 12 -4 -7 -2}}

	: sval mapping generators: ~517/512 = 1\72, ~73205/53248 = 550.602		: sval mapping generators: ~517/512 = 1\72, ~73205/53248 = 550.602

	Optimal tuning (CTE): ~73205/53248 = 550.602		[[Optimal tuning]] ([[CTE]]): ~73205/53248 = 550.602

			[[Support]]ing [[ET]]s: {{EDOs\|72, 1872f, 1944, 2016, 2088f, 2160fm, 3960}}

Eliora: I should have documented this temperament a year ago when I composed the song Hemoclysm Totem in it. + moving hafnium here.

2023-07-08T23:52:56Z

I should have documented this temperament a year ago when I composed the song Hemoclysm Totem in it. + moving hafnium here.

New page

{{Fractional-octave navigation|72}}
[[72edo]] is a notable tuning system due to its 17-limit consistency, being a multiple of 12, and usage in various ecclesiastical forms of chanting.

Temperaments discussed elsewhere include:

* ''Omicronbeta'', → [[Compton family#Omicronbeta|Compton family]]

== Hafnium ==
Hafnium is a period-72 temperament created by temperament-merging 4320edo and 5544edo, equal temperaments notable for their high divisibility. Named after the 72nd element.

Subgroup: 2.3.5.7.11.13

Comma list: 9801/9800, 250047/250000, 184549376/184528125, 463373664/463203125

Mapping: [{{val|72 72 462 876 1302 1193}}, {{val|0 1 -7 -16 -25 -22}}]

: mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948

{{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}
===17-limit===
Subgroup: 2.3.5.7.11.13.17

Comma list: 9801/9800, 12376/12375, 21879/21875, 194481/194480, 1713660/1713481, 97144749/97140736

Mapping: [{{val|72 72 462 876 1302 1193 547}}, {{val|0 1 -7 -16 -25 -22 -6}}]

: mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948

{{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}

===2.3.5.7.11.13.17.31 subgroup===
Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.

Subgroup: 2.3.5.7.11.13.17.31

Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625

Sval mapping: [{{val|72 72 462 876 1302 1193 547 356}}, {{val|0 1 -7 -16 -25 -22 -6 6}}]

: mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948

===2.3.5.7.11.13.17.31.37 subgroup===
[[37/22]] is mapped to exact three-quarters of the octave.

Subgroup: 2.3.5.7.11.13.17.31

Comma list: 10881/10880, 12376/12375, 16576/16575, 93093/93092, 954304/954261, 2737889/2737800, 126607131/126605120

Sval mapping: [{{val|72 72 462 876 1302 1193 547 356 378}}, {{val|0 1 -7 -16 -25 -22 -6 6 -25}}]

: mapping generators: ~105/104 = 1\72, ~3/2 = 701.948

Optimal tuning (CTE): ~3/2 = 701.948

== Jamala ==
Jamala, described as the 1944 & 2016 temperament in the 2.5.11.13.19.41.47 subgroup was named by [[Eliora]] after a [[wikipedia:Jamala|Ukrainian singer]] who won the [[wikipedia:2016 Eurovision Song Contest|2016 Eurovision Song Contest]] with her song [[wikipedia:1944 (song)|1944]].

Subgroup: 2.5.11.13.19.41.47

Comma basis: 47012251/47000000, 2502280/2501369, 410041489/410000000, 2680291328/2679296875, 52448351813/52428800000

Sval {{mapping|legend=1|72 2 183 -130 438 617 466|0 5 2 12 -4 -7 -2}}

: sval mapping generators: ~517/512 = 1\72, ~73205/53248 = 550.602

Optimal tuning (CTE): ~73205/53248 = 550.602