No-fives subgroup temperaments: Difference between revisions
meantone != septimal meantone |
sorted the temperaments by prime horizon |
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[[Tp tuning #T2 tuning|RMS error]]: 0.5073 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.5073 cents | ||
== Hemif == | == Hemif == | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | ||
== Purpleheart == | |||
[[Subgroup]]: 2.3.7 | |||
[[Comma list]]: 2187/2048 | |||
{{Mapping|legend=1| 7 11 0 | 0 0 1 }} | |||
: mapping generators: ~9/8, ~7 | |||
[[Optimal tuning]] ([[CTE]]): ~9/8 = 1\7, ~7/4 = 968.826 (~64/63 = 59.746) | |||
{{Optimal ET sequence|legend=1| 7, 14, 35, 49bd }} | |||
[[Badness]]: 0.0875 | |||
== Heartland (rank 3) == | |||
{{Main| Heartland }} | |||
Heartland, with a generator of ~21/19, is named for its tempering of the heartlandisma, [[3971/3969]]. Aside from the heartlandisma, the heartland temperament tempers out 243/242 (rastma) and 1083/1078 (bihendrixma), and slices the fifth in four (the number of chambers of the heart). | |||
Subgroup: 2.3.7.11.19 | |||
[[Comma list]]: 243/242, 1083/1078 | |||
[[Gencom]]: [2 21/19 7; 243/242 1083/1078] | |||
[[Mapping|Sval mapping]]: [{{val|1 1 0 2 1}}, {{val|0 4 0 10 3}}, {{val| 0 0 1 0 1 }}] | |||
[[Tp tuning|POL2 generator]]: ~21/19 = 175.2713, ~7 = 3369.3784 | |||
{{Optimal ET sequence|legend=1| 7, 14, 27e, 34dh, 41, 89, 130 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.3066 cents | |||
== Io aka undecimal == | |||
Io is a very low-complexity temperament which tempers out the undecimal quartertone [[33/32]], and with a generator representing both [[3/2]] and [[16/11]]. It may be considered an [[exotemperament]] by some definitions and not one by others. It has an extremely wide generator range, but the most accurate tunings are generally inside the range of [[flattone]] temperament. | |||
The name Io was coined by [[User:CompactStar|CompactStar]] in 2024 based on the [[color notation|color name]] ilo, prior to which it could only be termed as "undecimal temperament" with 33/32 being known as the undecimal comma. | |||
[[Subgroup]]: 2.3.11 | |||
[[Comma list]]: 33/32 | |||
{{Mapping|legend=2| 1 1 4 | 0 1 -1 }} | |||
: mapping generators: ~2/1, ~3/2 | |||
[[Optimal tuning]] ([[CTE]]): ~2/1 = 1\1, ~3/2 = 692.713 | |||
{{Optimal ET sequence|legend=1| 2, 5, 7, 12e }} | |||
[[Badness]]: 0.185 | |||
== Paralimmal == | == Paralimmal == | ||
| Line 960: | Line 984: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents | ||
== Aerophore == | == Aerophore == | ||
| Line 1,070: | Line 1,075: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.2247 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2247 cents | ||
== Gigapyth == | |||
[[Subgroup]]: 2.3.85 | |||
[[Comma list]]: 2.3.85 {{val|-40 1 6 }} | |||
{{mapping|legend=2| 1 4 6 | 0 -6 1 }} | |||
: mapping generators: ~2, ~85/64 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~85/64 = 483.034 | |||
[[Support]]ing [[ET]]s: 5, 47, 52, 57, 62, 67, 72, 77*, 82*, 87*, 92*, 139*, 149*, 159* | |||
<nowiki>*</nowiki>Wart for 85 | |||
=== 2.3.7.85 subgroup === | |||
[[Subgroup]]: 2.3.7.85 | |||
[[Comma list]]: 1029/1024, 7225/7203 | |||
{{mapping|legend=2| 1 4 2 6 | 0 -6 2 1}} | |||
: mapping generators: ~2, ~85/64 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~85/64 = 483.031 | |||
[[Support]]ing [[ET]]s: 5, 47, 52, 57, 62, 67, 72, 77*, 82*, 87*, 92*, 139*, 149*, 159* | |||
<nowiki>*</nowiki>Wart for 85 | |||
== Dog == | == Dog == | ||
| Line 1,104: | Line 1,140: | ||
[[Badness]]: 0.000374 | [[Badness]]: 0.000374 | ||
== Lipsett == | |||
Lipsett temperament is a pleasantly melodic little temperament with a highly useable 5-tone and 9-tone mos. It is audibly similar to [[semaphore]] temperament, so it could be thought of as semaphore but for the 23rd harmonic instead of the 7th. It is named for Arthur Lipsett, the director off the Canadian short film ’21-87’. Leia’s prison cell in Star Wars is numbered ‘2187’, as a nod to the influence the film had on George Lucas. | |||
[[Subgroup]]: 2.3.23 | |||
[[Comma list]]: [[2187/2116]] | |||
{{Mapping|legend=2| 1 0 -1 | 0 2 7}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~46/27 = 948.526 | |||
{{Optimal ET sequence|legend=1| 5, 14, 19, 43, 62i, 81i }} | |||
[[Badness]] (Smith): 8.998 × 10<sup>-3</sup> | |||
== Porpoise == | == Porpoise == | ||
| Line 1,229: | Line 1,280: | ||
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }} | {{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }} | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Subgroup temperaments]] | [[Category:Subgroup temperaments]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||