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4L 3s: Difference between revisions

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4L 3s can be thought of as a [[Warped diatonic|warped diatonic scale]], because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).
4L 3s can be thought of as a [[Warped diatonic|warped diatonic scale]], because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).
== Standing assumptions ==
== Standing assumptions ==
The [[TAMNAMS]] system is used in this article to name 4L 3s intervals and step size ratios and step ratio ranges.
The [[TAMNAMS]] system is used in this article to name 4L 3s intervals and step size ratios and step ratio ranges.
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== Names ==
== Names ==
The [[TAMNAMS]] MOS naming system (used in this article) uses the name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this pattern. The name is derived from 'sharp minor third', since the central range of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢, has minor third generators that are significantly sharp of 6/5.
The [[TAMNAMS]] MOS naming system (used in this article) uses the name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this pattern. The name is derived from 'sharp minor third', since the central range of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢, has minor third generators that are significantly sharp of 6/5.
== Intervals ==
== Intervals ==
Note: In TAMNAMS, a k-step interval class in smitonic may be called a "k-step", "k-mosstep", or "k-smistep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
Note: In TAMNAMS, a k-step interval class in smitonic may be called a "k-step", "k-mosstep", or "k-smistep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
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== Tuning ranges ==
== Tuning ranges ==
=== Simple tunings ===
=== Simple tunings ===
{| class="wikitable right-2 right-3 right-4 sortable "
{| class="wikitable right-2 right-3 right-4 sortable "
|-
|-
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== Scale tree ==
== Scale tree ==
The spectrum looks like this:
Generator ranges:
* Chroma-positive generator: 857.1429 cents (5\7) to 900 cents (3\4)
* Chroma-negative generator: 300 cents (1\4) to 342.8571 cents (2\7)


{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator
! colspan="6" rowspan="2" | Generator <br><small>(Chroma-positive)</small>
! colspan="2" | Cents
! colspan="2" | Cents
! rowspan="2" | L
! rowspan="2" | L
Line 1,021: Line 1,024:
! rowspan="2" | Comments
! rowspan="2" | Comments
|-
|-
!Chroma-positive
! <small>Chroma-positive</small>
!Chroma-negative
! <small>Chroma-negative</small>
|-
|-
| 5\7 || || || || || || 857.143 || 342.857 || 1 || 1 || 1.000 ||  
| 5\7 || || || || || || 857.143 || 342.857 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 28\39 || 861.538 || 338.462 || 6 || 5 || 1.200 || Amity/hitchcock↑
| || || || || || 28\39 || 861.538 || 338.462 || 6 || 5 || 1.200 || [[Amity]]/[[hitchcock]]↑
|-
|-
| || || || || 23\32 || || 862.500 || 337.500 || 5 || 4 || 1.250 || Sixix
| || || || || 23\32 || || 862.500 || 337.500 || 5 || 4 || 1.250 || [[Sixix]]
|-
|-
| || || || || || 41\57 || 863.158 || 336.842 || 9 || 7 || 1.286 ||  
| || || || || || 41\57 || 863.158 || 336.842 || 9 || 7 || 1.286 ||  
Line 1,038: Line 1,041:
| || || || || 31\43 || || 865.116 || 334.884 || 7 || 5 || 1.400 ||  
| || || || || 31\43 || || 865.116 || 334.884 || 7 || 5 || 1.400 ||  
|-
|-
| || || || || || 17\58 || 865.574 || 334.426 || 10 || 7 || 1.428 ||  
| || || || || || 17\58 || 865.574 || 334.426 || 10 || 7 || 1.429 ||  
|-
|-
| || || 13\18 || || || || 866.667 || 333.333 || 3 || 2 || 1.500 || L/s = 3/2
| || || 13\18 || || || || 866.667 || 333.333 || 3 || 2 || 1.500 ||  
|-
|-
| || || || || || 47\65 || 867.692 || 332.308 || 11 || 7 || 1.571 ||  
| || || || || || 47\65 || 867.692 || 332.308 || 11 || 7 || 1.571 ||  
Line 1,046: Line 1,049:
| || || || || 34\47 || || 868.085 || 331.915 || 8 || 5 || 1.600 ||  
| || || || || 34\47 || || 868.085 || 331.915 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 55\76 || 868.421 || 331.579 || 13 || 8 || 1.625 || Golden smitonic (?)
| || || || || || 55\76 || 868.421 || 331.579 || 13 || 8 || 1.625 || Golden smitonic (868.3282¢)
|-
|-
| || || || 21\29 || || || 868.966 || 331.034 || 5 || 3 || 1.667 ||  
| || || || 21\29 || || || 868.966 || 331.034 || 5 || 3 || 1.667 ||  
Line 1,056: Line 1,059:
| || || || || || 37\51 || 870.588 || 329.422 || 9 || 5 || 1.800 ||
| || || || || || 37\51 || 870.588 || 329.422 || 9 || 5 || 1.800 ||
|-
|-
| || 8\11 || || || || || 872.727 || 327.273 || 2 || 1 || 2.000 || Basic smitonic<br>(Generators smaller than this are proper)
| || 8\11 || || || || || 872.727 || 327.273 || 2 || 1 || 2.000 || Basic smitonic <br>(Generators smaller than this are proper)
|-
|-
| || || || || || 35\48 || 875.000 || 325.000 || 9 || 4 || 2.250 ||
| || || || || || 35\48 || 875.000 || 325.000 || 9 || 4 || 2.250 ||
Line 1,062: Line 1,065:
| || || || || 27\37 || || 875.676 || 324.324 || 7 || 3 || 2.333 ||  
| || || || || 27\37 || || 875.676 || 324.324 || 7 || 3 || 2.333 ||  
|-
|-
| || || || || || 46\63 || 876.190 || 323.810 || 12 || 5 || 2.400 ||
| || || || || || 46\63 || 876.190 || 323.810 || 12 || 5 || 2.400 || [[Hyperkleismic]]
|-
|-
| || || || 19\26 || || || 876.923 || 323.077 || 5 || 2 || 2.500 || Orgone is in this region
| || || || 19\26 || || || 876.923 || 323.077 || 5 || 2 || 2.500 || [[Orgone]] is in this region
|-
|-
| || || || || || 49\67 || 877.612 || 322.388 || 13 || 5 || 2.600 || Golden superkleismic
| || || || || || 49\67 || 877.612 || 322.388 || 13 || 5 || 2.600 || Golden superkleismic (877.7318¢)
|-
|-
| || || || || 30\41 || || 878.049 || 321.951 || 8 || 3 || 2.667 || Superkleismic
| || || || || 30\41 || || 878.049 || 321.951 || 8 || 3 || 2.667 || [[Superkleismic]]
|-
|-
| || || || || || 41\56 || 878.571 || 321.429 || 11 || 4 || 2.750 ||
| || || || || || 41\56 || 878.571 || 321.429 || 11 || 4 || 2.750 ||
|-
|-
| || || 11\15 || || || || 880.000 || 320.000 || 3 || 1 || 3.000 || L/s = 3/1
| || || 11\15 || || || || 880.000 || 320.000 || 3 || 1 || 3.000 ||  
|-
|-
| || || || || || 36\49 || 881.633 || 318.367 || 10 || 3 || 3.333 ||
| || || || || || 36\49 || 881.633 || 318.367 || 10 || 3 || 3.333 ||
Line 1,078: Line 1,081:
| || || || || 25\34 || || 882.353 || 317.647 || 7 || 2 || 3.500 ||  
| || || || || 25\34 || || 882.353 || 317.647 || 7 || 2 || 3.500 ||  
|-
|-
| || || || || || 39\53 || 883.019 || 316.981 || 11 || 3 || 3.667 || Hanson/keemun is in this region
| || || || || || 39\53 || 883.019 || 316.981 || 11 || 3 || 3.667 || [[Hanson]]/[[keemun]] is in this region
|-
|-
| || || || 14\19 || || || 884.211 || 315.789 || 4 || 1 || 4.000 ||
| || || || 14\19 || || || 884.211 || 315.789 || 4 || 1 || 4.000 ||
Line 1,086: Line 1,089:
| || || || || 17\23 || || 886.957 || 313.043 || 5 || 1 || 5.000 ||  
| || || || || 17\23 || || 886.957 || 313.043 || 5 || 1 || 5.000 ||  
|-
|-
| || || || || || 20\27 || 888.889 || 311.111 || 6 || 1 || 6.000 || Oolong, myna↓
| || || || || || 20\27 || 888.889 || 311.111 || 6 || 1 || 6.000 || [[Oolong]], [[myna]]↓
|-
|-
| 3\4 || || || || || || 900.000 || 300.000 || 1 || 0 || → inf ||
| 3\4 || || || || || || 900.000 || 300.000 || 1 || 0 || → inf ||
Line 1,094: Line 1,097:
[[Category:Smitonic|*]]<!--Main article-->
[[Category:Smitonic|*]]<!--Main article-->
[[Category:Scales]]
[[Category:Scales]]
[[Category:7-tone scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
Retrieved from "https://en.xen.wiki/w/4L_3s"