4L 3s: Difference between revisions

Inthar (talk | contribs)
Tuning ranges: being careful about saying that a certain set of JI interpretations "is" a certain temperament (given that many different abstract temperaments use the same name)
Inthar (talk | contribs)
Updated for consistency with 5L 3s
Line 57: Line 57:
| 1
| 1
| L
| L
| perfect smithird
| perfect mosthird
| 1L + 1s
| 1L + 1s
| -1
| -1
| O
| O
| perfect smisixth
| perfect mossixth
| 3L + 2s
| 3L + 2s
|-
|-
Line 158: Line 158:


Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]].
Parasoft smitonic EDOs include [[18edo]], [[25edo]], and [[43edo]].
* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect smisixth) and falling fifths (666.7c, a major mosfifth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* 18edo can be used to make large and small steps more distinct (the step ratio is 3/2, thus 18edo smitonic is distorted [[19edo]] diatonic), or for its nearly pure 9/8. It also makes rising fifths (733.3c, a perfect mossixth) and falling fifths (666.7c, a major mosfifth) almost equally off from a just fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* [[25edo]] can be used to make the augmented mosthird a good [[5/4]] (384¢).
* [[25edo]] can be used to make the augmented mosthird a good [[5/4]] (384¢).


Line 217: Line 217:
| -7
| -7
|-
|-
| dim. smi2nd
| dim. mos2nd
| 1\18, 66.7
| 1\18, 66.7
| 2\25, 96.0
| 2\25, 96.0
Line 249: Line 249:
| -10
| -10
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. smi3rd
| dim. mos3rd
| 4\18, 266.7
| 4\18, 266.7
| 6\25, 288.0
| 6\25, 288.0
Line 281: Line 281:
| -13
| -13
|-
|-
| dim. smi4th
| dim. mos4th
| 6\18, 400.0
| 6\18, 400.0
| 9\25, 432.0
| 9\25, 432.0
Line 313: Line 313:
| -9
| -9
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. smi5th
| dim. mos5th
| 9\18, 600.0
| 9\18, 600.0
| 13\25, 624.0
| 13\25, 624.0
Line 345: Line 345:
| -12
| -12
|-
|-
| doubly dim. smi6th
| doubly dim. mos6th
| 11\18, 733.3
| 11\18, 733.3
| 16\25, 768.0
| 16\25, 768.0
Line 353: Line 353:
| +13
| +13
|-
|-
| dim. smi6th
| dim. mos6th
| 12\18, 800.0
| 12\18, 800.0
| 17\25, 816.0
| 17\25, 816.0
Line 377: Line 377:
| -8
| -8
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| dim. smi7th
| dim. mos7th
| 14\18, 933.3
| 14\18, 933.3
| 20\25, 960.0
| 20\25, 960.0
Line 409: Line 409:
| -11
| -11
|-
|-
| dim. smioctave
| dim. mosoctave
| 17\18, 1133.3
| 17\18, 1133.3
| 24\25, 1152.0  
| 24\25, 1152.0  
Line 509: Line 509:
| -5
| -5
|-
|-
| dim. smi6th
| dim. mos6th
| 19\29, 786.2
| 19\29, 786.2
| O@
| O@
Line 649: Line 649:
| -5
| -5
|-
|-
| dim. smi6th
| dim. mos6th
| 7\11, 763.6
| 7\11, 763.6
| 9\15, 720.0
| 9\15, 720.0
Line 801: Line 801:
| -5
| -5
|-
|-
| dim. smi6th
| dim. mos6th
| 11\19, 694.7
| 11\19, 694.7
| 20\34, 705.9
| 20\34, 705.9