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4L 3s: Difference between revisions

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tamnams consistency correction
Line 60: Line 60:
| 2
| 2
| N
| N
| small smififth (aka minor fifth)
| minor smififth (aka minor fifth)
| -2
| -2
| M
| M
| large smifourth (aka major fourth)
| major smifourth (aka major fourth)
|-
|-
| 3
| 3
| P
| P
| small smiseventh
| minor smiseventh
| -3
| -3
| K
| K
| large smisecond
| major smisecond
|-
|-
| 4
| 4
| K@
| K@
| small smisecond
| minor smisecond
| -4
| -4
| Q&
| Q&
| large smiseventh
| major smiseventh
|-
|-
| 5
| 5
| M@
| M@
| small smifourth (aka minor fourth)
| minor smifourth (aka minor fourth)
| -5
| -5
| N&
| N&
| large smififth (aka major fifth)
| major smififth (aka major fifth)
|-
|-
| 6
| 6
Line 134: Line 134:


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 large smififth) 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 smisixth) and falling fifths (666.7c, a major smififth) 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 smithird a good [[5/4]] (384¢).
* [[25edo]] can be used to make the augmented smithird a good [[5/4]] (384¢).


Line 201: Line 201:
| +11
| +11
|-
|-
| small smi2nd
| minor smi2nd
| 2\18, 133.3
| 2\18, 133.3
| 3\25, 144.0
| 3\25, 144.0
Line 209: Line 209:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 3\18, 200.0
| 3\18, 200.0
| 4\25, 192.0
| 4\25, 192.0
Line 265: Line 265:
| +12
| +12
|-
|-
| small smi4th
| minor smi4th
| 7\18, 466.7
| 7\18, 466.7
| 10\25, 480.0
| 10\25, 480.0
Line 273: Line 273:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 8\18, 533.3  
| 8\18, 533.3  
| 11\25, 528.0
| 11\25, 528.0
Line 297: Line 297:
| +9
| +9
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 10\18, 666.7
| 10\18, 666.7
| 14\25, 672.0
| 14\25, 672.0
Line 305: Line 305:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 11\18, 733.3
| 11\18, 733.3
| 15\25, 720.0
| 15\25, 720.0
Line 361: Line 361:
| +10
| +10
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 15\18, 1000.0
| 15\18, 1000.0
| 21\25, 1008.0
| 21\25, 1008.0
Line 369: Line 369:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 16\18, 1066.7
| 16\18, 1066.7
| 22\25, 1056.0
| 22\25, 1056.0
Line 437: Line 437:
| 0
| 0
|-
|-
| small smi2nd
| minor smi2nd
| 3\29, 124.1
| 3\29, 124.1
| K@
| K@
Line 443: Line 443:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 5\29, 206.9
| 5\29, 206.9
| K
| K
Line 461: Line 461:
| -6
| -6
|-
|-
| small smi4th
| minor smi4th
| 11\29, 455.2
| 11\29, 455.2
| M@
| M@
Line 467: Line 467:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 13\29, 537.9
| 13\29, 537.9
| M
| M
Line 473: Line 473:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 16\29, 662.1
| 16\29, 662.1
| N
| N
Line 479: Line 479:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 18\26, 744.8
| 18\26, 744.8
| N&
| N&
Line 497: Line 497:
| -1
| -1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 24\29, 993.1
| 24\29, 993.1
| P
| P
Line 503: Line 503:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 26\28, 1075.9
| 26\28, 1075.9
| P&
| P&
Line 511: Line 511:


=== Hypohard ===
=== Hypohard ===
[[Hypohard]] tunings have [[step ratio]]s between 2 and 3, implying a generator sharper than 4\15 = 320¢ and flatter than 3\11 = 327.27¢. The large step tends to approximate [[8/7]], and the large smifourth (2 large steps + 1 small step) tends to approximate [[11/8]]; [[26edo]] is stellar in both of these approximations. This set of JI approximations is called [[orgone]] temperament.
[[Hypohard]] tunings have [[step ratio]]s between 2 and 3, implying a generator sharper than 4\15 = 320¢ and flatter than 3\11 = 327.27¢. The large step tends to approximate [[8/7]], and the major smifourth (2 large steps + 1 small step) tends to approximate [[11/8]]; [[26edo]] is stellar in both of these approximations. This set of JI approximations is called [[orgone]] temperament.


Hypohard smitonic edos include [[11edo]], [[15edo]], [[26edo]], and [[37edo]].
Hypohard smitonic edos include [[11edo]], [[15edo]], [[26edo]], and [[37edo]].
Line 561: Line 561:
| 0
| 0
|-
|-
| small smi2nd
| minor smi2nd
| 1\11, 109.1
| 1\11, 109.1
| 1\15, 80.0
| 1\15, 80.0
Line 569: Line 569:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 2\11, 218.2
| 2\11, 218.2
| 3\15, 240.0
| 3\15, 240.0
Line 593: Line 593:
| -6
| -6
|-
|-
| small smi4th
| minor smi4th
| 4\11, 436.4
| 4\11, 436.4
| 5\15, 400.0
| 5\15, 400.0
Line 601: Line 601:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 5\11, 545.5
| 5\11, 545.5
| 7\15, 560.0
| 7\15, 560.0
Line 609: Line 609:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 6\11, 656.6
| 6\11, 656.6
| 8\15, 640.0
| 8\15, 640.0
Line 617: Line 617:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 7\11, 763.6
| 7\11, 763.6
| 10\15, 800.0
| 10\15, 800.0
Line 641: Line 641:
| -1
| -1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 9\11, 981.8
| 9\11, 981.8
| 12\15, 960.0
| 12\15, 960.0
Line 649: Line 649:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 10\11, 1090.9
| 10\11, 1090.9
| 14\15, 1120.0
| 14\15, 1120.0
Line 711: Line 711:
| 0
| 0
|-
|-
| small smi2nd
| minor smi2nd
| 1\19, 63.2
| 1\19, 63.2
| 2\34, 70.6
| 2\34, 70.6
Line 719: Line 719:
| +4
| +4
|-
|-
| large smi2nd
| major smi2nd
| 4\19, 252.6
| 4\19, 252.6
| 7\34, 247.1
| 7\34, 247.1
Line 743: Line 743:
| -6
| -6
|-
|-
| small smi4th
| minor smi4th
| 6\19, 378.9
| 6\19, 378.9
| 11\34, 388.2
| 11\34, 388.2
Line 751: Line 751:
| +5
| +5
|-
|-
| large smi4th
| major smi4th
| 9\19, 568.4
| 9\19, 568.4
| 16\34, 564.7
| 16\34, 564.7
Line 759: Line 759:
| -2
| -2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi5th
| minor smi5th
| 10\19, 631.6
| 10\19, 631.6
| 18\34, 635.3
| 18\34, 635.3
Line 767: Line 767:
| +2
| +2
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi5th
| major smi5th
| 16\19, 821.1
| 16\19, 821.1
| 23\34, 811.8
| 23\34, 811.8
Line 791: Line 791:
| -1
| -1
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| small smi7th
| minor smi7th
| 15\19, 947.4
| 15\19, 947.4
| 27\34, 952.9
| 27\34, 952.9
Line 799: Line 799:
| +3
| +3
|-bgcolor="#eaeaff"
|-bgcolor="#eaeaff"
| large smi7th
| major smi7th
| 18\19, 1136.8
| 18\19, 1136.8
| 32\34, 1129.4
| 32\34, 1129.4
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