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3L 4s: Difference between revisions

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| Equalized = 2
| Equalized = 2
| Paucitonic = 1
| Paucitonic = 1
| Pattern = sLsLsLs
| Pattern = LsLsLss
}}
}}


'''3L 4s''' is the [[MOS scale]] built from a generator that falls between 1\3 (one degree of [[3edo]] – 400 cents) and 2\7 (two degrees of [[7edo]] – 343 cents).
'''3L 4s''' is the [[MOS scale]] built from a generator that falls between 1\3 (one degree of [[3edo]] – 400 cents) and 2\7 (two degrees of [[7edo]] – 343 cents).
== Standing assumptions ==
== Standing assumptions ==
The [[TAMNAMS]] system is used in this article to name 3L 4s intervals and step size ratios and step ratio ranges.
The [[TAMNAMS]] system is used in this article to name 3L 4s intervals and step size ratios and step ratio ranges.
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== Names ==
== Names ==
[[TAMNAMS]] (used by this article) uses the name '''mosh''' for this pattern. This is taken from an older [[MOS naming]] scheme by Graham Breed.
[[TAMNAMS]] (used by this article) uses the name '''mosh''' for this pattern. This is taken from an older [[MOS naming]] scheme by Graham Breed.
== Intervals ==
== Intervals ==
Note: In TAMNAMS, a k-step interval class in mosh may be called a "k-step", "k-mosstep", or "k-moshstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
Note: In TAMNAMS, a k-step interval class in mosh may be called a "k-step", "k-mosstep", or "k-moshstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.


== Low-harmonic-entropy scales ==
== Low-harmonic-entropy scales ==
The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and magic, where the generator is a 5/4 but five of them make a 3/1.
The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and magic, where the generator is a 5/4 but five of them make a 3/1.


== Tuning ranges ==
== Tuning ranges ==
3\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make MOS [[7L 3s]] (dicoid); the other scales make MOS [[3L 7s]] (sephiroid).
3\10 represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and scales generated by submajor and major thirds at the top, with 10edo standing in between. The neutral third scales, after three more generators, make MOS [[7L 3s]] (dicoid); the other scales make MOS [[3L 7s]] (sephiroid).


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=== Quasisoft ===
=== Quasisoft ===
Quasisoft tunings of mosh have a step ratio between 3/2 and 5/3, implying a generator sharper than 5\17 = 352.94¢ and flatter than 8\27 = 355.56¢.
Quasisoft tunings of mosh have a step ratio between 3/2 and 5/3, implying a generator sharper than 5\17 = 352.94¢ and flatter than 8\27 = 355.56¢.


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== Modes ==
== Modes ==
The various modes of 3L 4s (with [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are:
The various modes of 3L 4s (with [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are:


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== Scale tree ==
== Scale tree ==
The spectrum looks like this:
Generator ranges:  
* Chroma-positive generator: 342.8571 cents (2\7) to 400 cents (1\3)
* Chroma-negative generator: 800 cents (2\3) to 857.1429 cents (5\7)


{| class="wikitable center-all"
{| class="wikitable center-all"
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| 2\7 || || || || || || 342.857 || 1 || 1 || 1.000 ||  
| 2\7 || || || || || || 342.857 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 11\38 || 347.368 || 6 || 5 || 1.200 || Mohaha/ptolemy↑
| || || || || || 11\38 || 347.368 || 6 || 5 || 1.200 || [[Mohaha]] / ptolemy↑
|-
|-
| || || || || 9\31 || || 348.387 || 5 || 4 || 1.250 || Mohaha/migration/mohajira
| || || || || 9\31 || || 348.387 || 5 || 4 || 1.250 || Mohaha / migration / [[mohajira]]
|-
|-
| || || || || || 16\55 || 349.091 || 9 || 7 || 1.286 ||  
| || || || || || 16\55 || 349.091 || 9 || 7 || 1.286 ||  
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| || || || 7\24 || || || 350.000 || 4 || 3 || 1.333 ||  
| || || || 7\24 || || || 350.000 || 4 || 3 || 1.333 ||  
|-
|-
| || || || || || 19\65 || 350.769 || 11 || 8 || 1.375 || Mohaha/mohamaq
| || || || || || 19\65 || 350.769 || 11 || 8 || 1.375 || Mohaha / mohamaq
|-
|-
| || || || || 12\41 || || 351.220 || 7 || 5 || 1.400 || Mohaha/neutrominant
| || || || || 12\41 || || 351.220 || 7 || 5 || 1.400 || Mohaha / [[neutrominant]]
|-
|-
| || || || || || 17\58 || 351.724 || 10 || 7 || 1.428 || Hemif
| || || || || || 17\58 || 351.724 || 10 || 7 || 1.428 || [[Hemif]] / [[Hemififths]]
|-
|-
| || || 5\17 || || || || 352.941 || 3 || 2 || 1.500 || L/s = 3/2
| || || 5\17 || || || || 352.941 || 3 || 2 || 1.500 ||  
|-
|-
| || || || || || 18\61 || 354.098 || 11 || 7 || 1.571 || Suhajira
| || || || || || 18\61 || 354.098 || 11 || 7 || 1.571 || [[Suhajira]]
|-
|-
| || || || || 13\44 || || 354.545 || 8 || 5 || 1.600 ||  
| || || || || 13\44 || || 354.545 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 21\71 || 354.783 || 13 || 8 || 1.625 || Golden suhajira
| || || || || || 21\71 || 354.783 || 13 || 8 || 1.625 || Golden suhajira (354.8232¢)
|-
|-
| || || || 8\27 || || || 355.556 || 5 || 3 || 1.667 || Suhajira/ringo
| || || || 8\27 || || || 355.556 || 5 || 3 || 1.667 || Suhajira / [[ringo]]
|-
|-
| || || || || || 19\64 || 356.250 || 12 || 7 || 1.714 || Beatles
| || || || || || 19\64 || 356.250 || 12 || 7 || 1.714 || [[Beatles]]
|-
|-
| || || || || 11\37 || || 356.757 || 7 || 4 || 1.750 ||
| || || || || 11\37 || || 356.757 || 7 || 4 || 1.750 ||
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| || || || || || 14\47 || 357.447 || 9 || 5 || 1.800 ||
| || || || || || 14\47 || 357.447 || 9 || 5 || 1.800 ||
|-
|-
| || 3\10 || || || || || 360.000 || 2 || 1 || 2.000 || Basic mosh<br>(Generators smaller than this are proper)
| || 3\10 || || || || || 360.000 || 2 || 1 || 2.000 || Basic mosh <br>(Generators smaller than this are proper)
|-
|-
| || || || || || 13\43 || 362.264 || 9 || 4 || 2.250 ||
| || || || || || 13\43 || 362.264 || 9 || 4 || 2.250 ||
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| || || || 7\23 || || || 365.217 || 5 || 2 || 2.500 ||  
| || || || 7\23 || || || 365.217 || 5 || 2 || 2.500 ||  
|-
|-
| || || || || || 18\59 || 366.102 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || || 18\59 || 366.102 || 13 || 5 || 2.600 || Unnamed golden tuning (366.2564¢)
|-
|-
| || || || || 11\36 || || 366.667 || 8 || 3 || 2.667 ||
| || || || || 11\36 || || 366.667 || 8 || 3 || 2.667 ||
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| || || || || || 15\49 || 367.347 || 11 || 4 || 2.750 ||
| || || || || || 15\49 || 367.347 || 11 || 4 || 2.750 ||
|-
|-
| || || 4\13 || || || || 369.231 || 3 || 1 || 3.000 || L/s = 3/1
| || || 4\13 || || || || 369.231 || 3 || 1 || 3.000 ||  
|-
|-
| || || || || || 13\42 || 371.429 || 10 || 3 || 3.333 ||
| || || || || || 13\42 || 371.429 || 10 || 3 || 3.333 ||
|-
|-
| || || || || 9\29 || || 372.414 || 7 || 2 || 3.500 || Sephiroth
| || || || || 9\29 || || 372.414 || 7 || 2 || 3.500 || [[Sephiroth]]
|-
|-
| || || || || || 14\45 || 373.333 || 11 || 3 || 3.667 ||
| || || || || || 14\45 || 373.333 || 11 || 3 || 3.667 ||
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| || || || 5\16 || || || 375.000 || 4 || 1 || 4.000 ||
| || || || 5\16 || || || 375.000 || 4 || 1 || 4.000 ||
|-
|-
| || || || || || 11\35 || 377.143 || 9 || 2 || 4.500 || Muggles
| || || || || || 11\35 || 377.143 || 9 || 2 || 4.500 || [[Muggles]]
|-
|-
| || || || || 6\19 || || 378.947 || 5 || 1 || 5.000 || Magic
| || || || || 6\19 || || 378.947 || 5 || 1 || 5.000 || [[Magic]]
|-
|-
| || || || || || 7\22 || 381.818 || 6 || 1 || 6.000 ||
| || || || || || 7\22 || 381.818 || 6 || 1 || 6.000 || [[Wuerschmidt]]↓
|-
|-
| 1\3 || || || || || || 400.000 || 1 || 0 || → inf ||
| 1\3 || || || || || || 400.000 || 1 || 0 || → inf ||
|}
|}


[[Category:Mosh]]
[[Category:Scales]]
[[Category:Scales]]
[[Category:7-tone scales]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
Retrieved from "https://en.xen.wiki/w/3L_4s"