Trisected: Difference between revisions

(3 intermediate revisions by one other user not shown)

Line 13:

| Odd limit 2 = 13-limit 21 | Mistuning 2 = 17.5 | Complexity 2 = 36

}}

'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]]. Since it tempers out 128/125, the [[~~2/1|~~octave]] is split into 3 ~[[5/4]]'s, each tuned to 400{{C}} if the octave is pure. Since it tempers out 1029/1024, the [[3/2|perfect fifth]] is split into three intervals of ~[[8/7]].Since it tempers out [[1029/1000]], the [[3/1|tritave]] is split into three intervals of [[10/7]]. This means that every [[Pythagorean tuning|Pythagorean]] interval is split into three equal parts.

'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]]. Since it tempers out 128/125, the [[octave]] is split into 3 ~[[5/4]]'s, each tuned to 400{{C}} if the octave is pure. Since it tempers out 1029/1024, the [[3/2|perfect fifth]] is split into three intervals of ~[[8/7]]. Since it tempers out 1029/1000, the [[3/1|tritave]] is split into three intervals of [[10/7]]. This means that every [[Pythagorean tuning|Pythagorean]] interval is split into three equal parts.

In the [[11-limit]], the [[4/3|perfect fourth]] is split into three ~[[11/10]]'s, thus tempering out [[4000/3993]]. Additionally, the 1/3-octave period represents [[14/11]], tempering out [[56/55]] and [[176/175]]. The [[13-limit]] extension equates the ~10/7 with [[13/9]], tempering out [[91/90]] and [[2197/2187]].

Line 234:

| [[7/6]]

| 633.282

|

| 7-odd-limit minimax

|-

| [[36edo|19\36]]

Line 244:

| [[9/7]]

| 633.583

|

| 9-odd-limit minimax

|-

|

Line 254:

| [[13/7]]

| 633.962

|

| 13- and 15-odd-limit minimax

|-

|

@@ Line 13: / Line 13: @@
 | Odd limit 2 = 13-limit 21 | Mistuning 2 = 17.5 | Complexity 2 = 36
 }}
-'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]]. Since it tempers out 128/125, the [[2/1|octave]] is split into 3 ~[[5/4]]'s, each tuned to 400{{C}} if the octave is pure. Since it tempers out 1029/1024, the [[3/2|perfect fifth]] is split into three intervals of ~[[8/7]].Since it tempers out [[1029/1000]], the [[3/1|tritave]] is split into three intervals of [[10/7]]. This means that every [[Pythagorean tuning|Pythagorean]] interval is split into three equal parts.
+'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]]. Since it tempers out 128/125, the [[octave]] is split into 3 ~[[5/4]]'s, each tuned to 400{{C}} if the octave is pure. Since it tempers out 1029/1024, the [[3/2|perfect fifth]] is split into three intervals of ~[[8/7]]. Since it tempers out 1029/1000, the [[3/1|tritave]] is split into three intervals of [[10/7]]. This means that every [[Pythagorean tuning|Pythagorean]] interval is split into three equal parts.
 In the [[11-limit]], the [[4/3|perfect fourth]] is split into three ~[[11/10]]'s, thus tempering out [[4000/3993]]. Additionally, the 1/3-octave period represents [[14/11]], tempering out [[56/55]] and [[176/175]]. The [[13-limit]] extension equates the ~10/7 with [[13/9]], tempering out [[91/90]] and [[2197/2187]].
@@ Line 234: / Line 234: @@
 | [[7/6]]
 | 633.282
-|
+| 7-odd-limit minimax
 |-
 | [[36edo|19\36]]
@@ Line 244: / Line 244: @@
 | [[9/7]]
 | 633.583
-|
+| 9-odd-limit minimax
 |-
 |
@@ Line 254: / Line 254: @@
 | [[13/7]]
 | 633.962
-|
+| 13- and 15-odd-limit minimax
 |-
 |