6L 1s: Difference between revisions
added info on what the 2.11.13 temp is and more details on didacus. |
ArrowHead294 (talk | contribs) m substitute deprecated template |
||
| (One intermediate revision by the same user not shown) | |||
| Line 5: | Line 5: | ||
== Scale properties == | == Scale properties == | ||
{{MOS | |||
=== Intervals === | |||
{{MOS intervals}} | |||
=== Generator chain === | |||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
==== Proposed names ==== | ==== Proposed names ==== | ||
| Line 13: | Line 21: | ||
There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family|tetracot]], in which the generator is identified with [[10/9]] and four generators make a [[3/2]]. These produce very soft tunings of archaeotonic, ranging from 4:3 in [[27edo]] to 7:6 in [[48edo]]. The second is known as [[didacus]], which is at a basic level the temperament in the [[2.5.7 subgroup]] defined by [[3136/3125]], where two generators make [[5/4]] and five make [[7/4]], and produces very hard tunings, ranging from 4:1 in [[25edo]] to 7:1 in [[43edo]]; it has various extensions that span portions of this range, including [[Hemimean clan#Roulette|roulette]] and [[Hemimean clan#Mediantone|mediantone]] to the no-twos 19-limit, and [[hemithirds]] (along with its 5-limit microtemperament restriction [[luna]]) and [[hemiwürschmidt]] to the full 7-limit. | There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family|tetracot]], in which the generator is identified with [[10/9]] and four generators make a [[3/2]]. These produce very soft tunings of archaeotonic, ranging from 4:3 in [[27edo]] to 7:6 in [[48edo]]. The second is known as [[didacus]], which is at a basic level the temperament in the [[2.5.7 subgroup]] defined by [[3136/3125]], where two generators make [[5/4]] and five make [[7/4]], and produces very hard tunings, ranging from 4:1 in [[25edo]] to 7:1 in [[43edo]]; it has various extensions that span portions of this range, including [[Hemimean clan#Roulette|roulette]] and [[Hemimean clan#Mediantone|mediantone]] to the no-twos 19-limit, and [[hemithirds]] (along with its 5-limit microtemperament restriction [[luna]]) and [[hemiwürschmidt]] to the full 7-limit. | ||
The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, i.e. [[No-threes subgroup temperaments#Bluebirds|Bluebirds]], where the generator is identified with [[143/128]]; for example L=7 s=4 (46 edo) is such a scale. | The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, i.e. [[No-threes subgroup temperaments#Bluebirds|Bluebirds]], where the generator is identified with [[143/128]]; for example {{nowrap|L {{=}} 7|s {{=}} 4}} (46 edo) is such a scale. | ||
== Scales == | == Scales == | ||
| Line 24: | Line 32: | ||
== Scale tree == | == Scale tree == | ||
{{ | {{MOS tuning spectrum | ||
5/4 | | 5/4 = [[Tetracot]] is in this region | ||
9/7 | | 9/7 = Tetracot/[[modus]]/[[wollemia]] | ||
13/8 | | 13/8 = Wilson Golden 2 (181.3227{{c}}) | ||
12/7 | | 12/7 = [[Bluebirds]] | ||
13/5 | | 13/5 = Golden [[glacial]] (188.0298{{c}}) | ||
3/1 | | 3/1 = [[Spell]] | ||
7/2 | | 7/2 = [[Isra]]/[[deutone]] | ||
4/1 | | 4/1 = Isra/[[leantone]] | ||
5/1 | | 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]] | ||
6/1 | | 6/1 = Didacus/[[roulette]] | ||
}} | }} | ||