6L 1s: Difference between revisions

 

 

 

=== Modes ===

 

==== Proposed names ====

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 {{nowrap|L {{=}} 7|s {{=}} 4}} (46 edo) is such a scale.

{{MOS tuning spectrum

| 5/4 = [[Tetracot]] is in this region

| 9/7 = Tetracot/[[modus]]/[[wollemia]]

| 13/8 = Wilson Golden 2 (181.3227{{c}})

| 12/7 = [[Bluebirds]]

| 13/5 = Golden [[glacial]] (188.0298{{c}})

| 3/1 = [[Spell]]

| 7/2 = [[Isra]]/[[deutone]]

| 4/1 = Isra/[[leantone]]

| 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]]

| 6/1 = Didacus/[[roulette]]