Subgroup temperaments: Difference between revisions
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= Fractional subgroup temperaments = | = Fractional subgroup temperaments = | ||
== 2.5/ | == 2.5/3.… subgroups == | ||
=== Magicaltet === | === Magicaltet === | ||
{{See also| Chromatic pairs #Magicaltet }} | {{See also| Chromatic pairs #Magicaltet }} | ||
| Line 1,095: | Line 1,095: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents | ||
== 2.….7/ | == 2.….7/3.… subgroups == | ||
=== Guanyintet === | === Guanyintet === | ||
{{See also | Chromatic pairs #Guanyintet }} | {{See also | Chromatic pairs #Guanyintet }} | ||
| Line 1,213: | Line 1,213: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.064 cents | ||
== 2.….9/ | == 2.….9/7.… subgroups == | ||
=== Marveltri === | === Marveltri === | ||
{{See also| Chromatic pairs #Marveltri }} | {{See also| Chromatic pairs #Marveltri }} | ||
| Line 1,255: | Line 1,255: | ||
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents | [[Tp tuning #T2 tuning|RMS error]]: 1.074 cents | ||
== 2.….7/ | == 2.….7/5.… subgroups == | ||
=== Hydrothermal === | === Hydrothermal === | ||
A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of. | A tuning whose distinctively sharp (but still consonant) fifth, and flat (but still consonant) octave, lend it a mysterious, heavy atmosphere. The 6-tone (hexatonic) MOS is melodically interesting and flavorful. The 18-tone MOS is a useful 'chromatic' scale for taking subsets of. | ||
| Line 1,393: | Line 1,392: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.7521 cents | ||
== 2.….11/ | == 2.….11/5.… subgroups == | ||
=== Petrtri === | === Petrtri === | ||
{{See also| Chromatic pairs #Petrtri }} | {{See also| Chromatic pairs #Petrtri }} | ||
| Line 1,452: | Line 1,450: | ||
=== Trisect === | === Trisect === | ||
Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]]. | Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup restriction of [[Augmented family #Trisected|trisected]]. | ||
| Line 1,470: | Line 1,467: | ||
==== 2.3.7.11/5.13 subgroup ==== | ==== 2.3.7.11/5.13 subgroup ==== | ||
[[Subgroup]]: 2.3.7.11/5.13 | [[Subgroup]]: 2.3.7.11/5.13 | ||
| Line 1,484: | Line 1,480: | ||
==== 2.3.7.11/5.13.17 subgroup ==== | ==== 2.3.7.11/5.13.17 subgroup ==== | ||
[[Subgroup]]: 2.3.7.11/5.13.17 | [[Subgroup]]: 2.3.7.11/5.13.17 | ||
| Line 1,498: | Line 1,493: | ||
===== Trisector ===== | ===== Trisector ===== | ||
[[Subgroup]]: 2.3.7.11/5.13.17.19 | [[Subgroup]]: 2.3.7.11/5.13.17.19 | ||
| Line 1,512: | Line 1,506: | ||
===== 2.3.7.11/5.13.17.19.23 subgroup ===== | ===== 2.3.7.11/5.13.17.19.23 subgroup ===== | ||
[[Subgroup]]: 2.3.7.11/5.13.17.19.23 | [[Subgroup]]: 2.3.7.11/5.13.17.19.23 | ||
| Line 1,526: | Line 1,519: | ||
===== 2.3.7.11/5.13.17.19.23.29 subgroup ===== | ===== 2.3.7.11/5.13.17.19.23.29 subgroup ===== | ||
[[Subgroup]]: 2.3.7.11/5.13.17.19.23.29 | [[Subgroup]]: 2.3.7.11/5.13.17.19.23.29 | ||
| Line 1,539: | Line 1,531: | ||
[[Tp tuning #T2 tuning|RMS error]]: ??? | [[Tp tuning #T2 tuning|RMS error]]: ??? | ||
== 2.….11/ | == 2.….11/7.… subgroups == | ||
=== Pepperoni === | === Pepperoni === | ||
{{Main| Parapyth }} | {{Main| Parapyth }} | ||
| Line 1,563: | Line 1,555: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents | ||
== 2.….13/ | == 2.….13/5.… subgroups == | ||
=== Barbados === | === Barbados === | ||
The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. | The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales. | ||
| Line 1,633: | Line 1,625: | ||
Scales: [[Oceanfront scales]] | Scales: [[Oceanfront scales]] | ||
== 2.….49/ | == 2.….49/5.… subgroups == | ||
=== Direct breedsmic === | === Direct breedsmic === | ||
Related temperament: [[hemithirds]], [[newt]] | Related temperament: [[hemithirds]], [[newt]] | ||
| Line 1,649: | Line 1,641: | ||
[[Tp tuning #T2 tuning|RMS error]]: ? | [[Tp tuning #T2 tuning|RMS error]]: ? | ||
== 3/2.5/ | == 3/2.5/2.… subgroups == | ||
{{Main|Half-prime subgroup}} | {{Main|Half-prime subgroup}} | ||
| Line 1,738: | Line 1,730: | ||
[[Optimal ET sequence]]: [[8edf]], [[11edf]] | [[Optimal ET sequence]]: [[8edf]], [[11edf]] | ||
== 3/2.5/ | == 3/2.5/4.… subgroups == | ||
=== Poseidon === | === Poseidon === | ||
'''This temperament will be subjected to renaming due to a conflict.''' | '''This temperament will be subjected to renaming due to a conflict.''' | ||
| Line 1,784: | Line 1,776: | ||
== 5/2-equave subgroups == | == 5/2-equave subgroups == | ||
=== Hyperion === | === Hyperion === | ||
[[Subgroup]]: 5/2.7.11 | [[Subgroup]]: 5/2.7.11 | ||
| Line 1,804: | Line 1,795: | ||
* [[Substitute harmonic]] temperaments | * [[Substitute harmonic]] temperaments | ||
<!-- main article --> | [[Category:Subgroup temperaments| ]] <!-- main article --> | ||
[[Category:Temperament collections]] | |||
[[Category:Temperament collections]] | {{Todo| review | cleanup }} | ||