11859211/11859210: Difference between revisions

{{Infobox Interval

| Name = tredekisma

| Color name = quadno-athoquadlu-azogu 4th, <br>19o^43o1u^4zg4, <br>Quadno-athoquadlu-azogu comma

| Sound =  

| Comma = yes

}}

'''11859211/11859210''', the '''tredekisma''', is the smallest [[superparticular ratio]] in the [[19-limit]] and [[23-limit]].

It can be seen as the difference between a stack of four [[38/33]]'s and a stack consisting of [[10/7]] and [[16/13]]: (38/33)⁴/((10/7)⋅(16/13)).

A possible S-expression of it is (S76⋅S441)/(S77⋅S324).

Only being 0.00014 cents, it is an insanely, unfathomably narrow comma; hundreds of times narrower than well known atomic commas like the [[chalmersia]] and [[Kirnberger's atom]]. As such, tempering out or fudging this alone either way is aurally identical to JI to human ears. It is tempered out in notable edos like {{EDOs| 24, 84, 94, 118, 152, 176, 364, 388, 624, 742, 3125, 8269, 8539, }} … among others. It is also tempered out in any union between these edos, such as [[vishnu]] and [[gariwizmic]].

| [⟨ || 1 || 0 || 0 || 0 || 0 || 1 || 0 || ],

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],

| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || 0 || ],

| ⟨ || 0 || 0 || 0 || 1 || 0 || 3 || -1 || ],

| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 1 || ],

| ⟨ || 0 || 0 || 0 || 0 || 0 || -4 || 1 || ]]

* mapping generators: ~2, ~3, ~5, ~7, ~11, ~133/33

[[Optimal tuning]]s: TBA

{{Optimal ET sequence||legend=1|TBA }}

| [⟨ || 1 || 0 || 0 || 0 || 0 || 1 || 0 || 0 |],

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 1 || ],

| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || 0 || 0 || ],

| ⟨ || 0 || 0 || 0 || 1 || 0 || 3 || 0 || -1 || ],

| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 1 || ],

| ⟨ || 0 || 0 || 0 || 0 || 0 || -4 || 0 || 1 || ],

| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]

* mapping generators: ~2, ~3, ~5, ~7, ~11, ~17, ~133/33

[[Optimal tuning]]s: TBA

{{Optimal ET sequence|legend=1|TBA}}