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3L 4s: Difference between revisions

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| Pattern = LsLsLss
| Pattern = LsLsLss
}}
}}
{{MOS intro}}


{{MOS intro}}
== Name ==
==Name==
[[TAMNAMS]] suggests the temperament-agnostic name '''mosh''' for this scale, adopted from an older [[Graham Breed's MOS naming scheme|MOS naming scheme]] by Graham Breed. The name is a contraction of "mohajira-ish".
[[TAMNAMS]] suggests the temperament-agnostic name '''mosh''' for this scale, adopted from an older [[Graham Breed's MOS naming scheme|MOS naming scheme]] by Graham Breed. The name is a contraction of "mohajira-ish".
==Scale properties==
 
== Scale properties ==
{{TAMNAMS use}}
{{TAMNAMS use}}


===Intervals===
=== Intervals ===
{{MOS intervals}}
{{MOS intervals}}


=== Modes ===
=== Modes ===
{{MOS mode degrees}}
{{MOS mode degrees}}
====Proposed names====
 
==== Proposed names ====
One set of mode nicknames was coined by [[Andrew Heathwaite]]. The other set was coined by [[User:CellularAutomaton|CellularAutomaton]] and follows the diatonic modes' naming convention by using ancient Greek toponyms that sound similar to the Heathwaite names.
One set of mode nicknames was coined by [[Andrew Heathwaite]]. The other set was coined by [[User:CellularAutomaton|CellularAutomaton]] and follows the diatonic modes' naming convention by using ancient Greek toponyms that sound similar to the Heathwaite names.


{{MOS modes|Table Headers=Mode Names (Heathwaite); Mode Names (CA)|Table Entries=dril; Dalmatian; gil; Galatian; kleeth; Cilician; bish; Bithynian; fish; Pisidian; jwl; Illyrian; led; Lycian}}
{{MOS modes|Table Headers=Mode Names (Heathwaite); Mode Names (CA)|Table Entries=dril; Dalmatian; gil; Galatian; kleeth; Cilician; bish; Bithynian; fish; Pisidian; jwl; Illyrian; led; Lycian}}
== Theory ==
== Theory ==
=== Low harmonic entropy scales ===
=== Low harmonic entropy scales ===
There are two notable harmonic entropy minima:
There are two notable harmonic entropy minima:
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The sizes of the generator, large step and small step of mosh are as follows in various ultrasoft mosh tunings.  
The sizes of the generator, large step and small step of mosh are as follows in various ultrasoft mosh tunings.  
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
|-
|-
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| [[11/9]]
| [[11/9]]
|-
|-
| L (4g - octave)
| L ({{nowrap|4g − octave}})
| 4\24, 200.00
| 4\24, 200.00
| 5\31, 193.55
| 5\31, 193.55
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| [[9/8]], [[10/9]]
| [[9/8]], [[10/9]]
|-
|-
| s (octave - 3g)
| s ({{nowrap|octave − 3g}})
| 3\24, 150.00
| 3\24, 150.00
| 4\31, 154.84
| 4\31, 154.84
Line 83: Line 86:


=== 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 {{nowrap|5\17 {{=}} 352.94{{c}}}} and flatter than {{nowrap|8\27 {{=}} 355.56{{c}}}}.


The large step is a sharper major second in these tunings than in ultrasoft tunings. These tunings could be considered "parapyth mosh" or "archy mosh", in analogy to ultrasoft mosh being meantone mosh.
The large step is a sharper major second in these tunings than in ultrasoft tunings. These tunings could be considered "parapyth mosh" or "archy mosh", in analogy to ultrasoft mosh being meantone mosh.
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| 16/13, 11/9
| 16/13, 11/9
|-
|-
| L (4g - octave)
| L ({{nowrap|4g − octave}})
| 3\17, 211.76
| 3\17, 211.76
| 5\27, 222.22
| 5\27, 222.22
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| 9/8, 8/7
| 9/8, 8/7
|-
|-
| s (octave - 3g)
| s ({{nowrap|octave − 3g}})
| 2\17, 141.18
| 2\17, 141.18
| 3\27, 133.33
| 3\27, 133.33
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This range is associated with [[sephiroth]] temperament.
This range is associated with [[sephiroth]] temperament.
{| class="wikitable right-2 right-3 right-4 right-5"
{| class="wikitable right-2 right-3 right-4 right-5"
|-
|-
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| 7\23, 365.22
| 7\23, 365.22
|-
|-
| L (4g - octave)
| L ({{nowrap|4g − octave}})
| 2\10, 240.00
| 2\10, 240.00
| 3\13, 276.92
| 3\13, 276.92
| 5\23, 260.87
| 5\23, 260.87
|-
|-
| s (octave - 3g)
| s ({{nowrap|octave − 3g}})
| 1\10, 120.00
| 1\10, 120.00
| 1\13, 92.31
| 1\13, 92.31
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| 5/4
| 5/4
|-
|-
| L (4g - octave)
| L ({{nowrap|4g − octave}})
| 4\16, 300.00
| 4\16, 300.00
| 5\19, 315.79
| 5\19, 315.79
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| 6/5
| 6/5
|-
|-
| s (octave - 3g)
| s ({{nowrap|octave − 3g}})
| 1\16, 75.00
| 1\16, 75.00
| 1\19, 63.16
| 1\19, 63.16
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== Scale tree ==
== Scale tree ==
Generator ranges:  
Generator ranges:  
* Chroma-positive generator: 342.8571 cents (2\7) to 400 cents (1\3)
* Chroma-positive generator: 342.8571{{c}} (2\7) to 400{{c}} (1\3)
* Chroma-negative generator: 800 cents (2\3) to 857.1429 cents (5\7)
* Chroma-negative generator: 800{{c}} (2\3) to 857.1429{{c}} (5\7)
 
{{Scale tree}}
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 2\7 || || || || || || 342.857 || 1 || 1 || 1.000 ||
|-
| || || || || || 11\38 || 347.368 || 6 || 5 || 1.200 || [[Mohaha]] / ptolemy↑
|-
| || || || || 9\31 || || 348.387 || 5 || 4 || 1.250 || Mohaha / migration / [[mohajira]]
|-
| || || || || || 16\55 || 349.091 || 9 || 7 || 1.286 ||
|-
| || || || 7\24 || || || 350.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 19\65 || 350.769 || 11 || 8 || 1.375 || Mohaha / mohamaq
|-
| || || || || 12\41 || || 351.220 || 7 || 5 || 1.400 || Mohaha / [[neutrominant]]
|-
| || || || || || 17\58 || 351.724 || 10 || 7 || 1.429 || [[Hemif]] / [[Hemififths]]
|-
| || || 5\17 || || || || 352.941 || 3 || 2 || 1.500 ||
|-
| || || || || || 18\61 || 354.098 || 11 || 7 || 1.571 || [[Suhajira]]
|-
| || || || || 13\44 || || 354.545 || 8 || 5 || 1.600 ||
|-
| || || || || || 21\71 || 354.930 || 13 || 8 || 1.625 || Golden suhajira (354.8232¢)
|-
| || || || 8\27 || || || 355.556 || 5 || 3 || 1.667 || Suhajira / [[ringo]]
|-
| || || || || || 19\64 || 356.250 || 12 || 7 || 1.714 || [[Beatles]]
|-
| || || || || 11\37 || || 356.757 || 7 || 4 || 1.750 ||
|-
| || || || || || 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)
|-
| || || || || || 13\43 || 362.791 || 9 || 4 || 2.250 ||
|-
| || || || || 10\33 || || 363.636 || 7 || 3 || 2.333 ||
|-
| || || || || || 17\56 || 364.286 || 12 || 5 || 2.400 ||
|-
| || || || 7\23 || || || 365.217 || 5 || 2 || 2.500 ||
|-
| || || || || || 18\59 || 366.102 || 13 || 5 || 2.600 || Unnamed golden tuning (366.2564¢)
|-
| || || || || 11\36 || || 366.667 || 8 || 3 || 2.667 ||
|-
| || || || || || 15\49 || 367.347 || 11 || 4 || 2.750 ||
|-
| || || 4\13 || || || || 369.231 || 3 || 1 || 3.000 ||
|-
| || || || || || 13\42 || 371.429 || 10 || 3 || 3.333 ||
|-
| || || || || 9\29 || || 372.414 || 7 || 2 || 3.500 || [[Sephiroth]]
|-
| || || || || || 14\45 || 373.333 || 11 || 3 || 3.667 ||
|-
| || || || 5\16 || || || 375.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 11\35 || 377.143 || 9 || 2 || 4.500 || [[Muggles]]
|-
| || || || || 6\19 || || 378.947 || 5 || 1 || 5.000 || [[Magic]]
|-
| || || || || || 7\22 || 381.818 || 6 || 1 || 6.000 || [[Wuerschmidt]]↓
|-
| 1\3 || || || || || || 400.000 || 1 || 0 || → inf ||
|}


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