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{{Interwiki
|en=3L 4s
|es=
|de=
|ja=3L 4s
}}
{{Infobox MOS
{{Infobox MOS
| Name = mosh
| Name = mosh
Line 18: Line 24:
=== Intervals ===
=== Intervals ===
{{MOS intervals}}
{{MOS intervals}}
=== Generator chain ===
{{MOS genchain}}


=== 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.
The first 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 Heathwaite's names. The third shows which modes are a mixture of which diatonic modes, as discussed in [[#Theory]].
{{MOS modes|Table Headers=Mode names<br>(Heathwaite); Mode names<br>(CA)|Table Entries=Dril; Dalmatian; Gil; Galatian; Kleeth; Cilician; Bish; Bithynian; Fish; Pisidian; Jwl; Illyrian; Led; Lycian}}
{{MOS modes
| Table Headers=
Mode names<br>(Heathwaite) $
Mode names<br>(CA) $
Mixed diatonic<br>modes $
| Table Entries=
Dril $
Dalmatian $
Dorian + Lydian $
Gil $
Galatian $
Aeolian + Lydian $
Kleeth $
Cilician $
Aeolian + Ionian $
Bish $
Bithynian $
Phrygian + Ionian $
Fish $
Pisidian $
Phrygian + Mixolydian $
Jwl $
Illyrian $
Locrian + Mixolydian $
Led $
Lycian $
Locrian + Dorian $
}}


== Theory ==
== Theory ==
Mosh can be thought of as a midpoint between two diatonic scales which are two cyclic orders away from each other. For example, sLsLsLs is the midpoint between the Ionian (major, LLsLLLs) and Phrygian (sLLLsLL) modes. You can prove this by simple addition:
<pre>
  2 2 1 2 2 2 1 (LLsLLLs)
+ 1 2 2 2 1 2 2 (sLLLsLL)
= 3 4 3 4 3 4 3 (sLsLsLs)
</pre>
The rest of the equivalencies are listed in [[#Proposed names]].
=== Low harmonic entropy scales ===
=== Low harmonic entropy scales ===
There are two notable harmonic entropy minima:
There are two notable harmonic entropy minima:


* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral 3rd (around 350{{c}}) and two of them make a 3/2 (702{{c}}).
* [[Neutral third scales]], such as dicot, hemififth, and mohajira, in which the generator is a neutral third (around 350{{c}}) and two of them make a 3/2 (702{{c}}).
* [[Magic]], in which the generator is 5/4 (386{{c}}) and 5 of them make a 3/1 (1902{{c}}).
* [[Magic]], in which the generator is a flattened 5/4 (around 380{{c}}) and five of them make a 3/1 (around 1902{{c}}), though the step ratios in this range are very hard to the point of being lopsided.


== Tuning ranges ==
== Tuning ranges ==
Line 68: Line 113:
| [[11/9]]
| [[11/9]]
|-
|-
| L ({{nowrap| 4g - octave }})
| L ({{nowrap| 4g − octave }})
| 4\24, 200.00
| 4\24, 200.00
| 5\31, 193.55
| 5\31, 193.55
Line 75: Line 120:
| [[9/8]], [[10/9]]
| [[9/8]], [[10/9]]
|-
|-
| s ({{nowrap| octave - 3g }})
| s ({{nowrap| octave − 3g }})
| 3\24, 150.00
| 3\24, 150.00
| 4\31, 154.84
| 4\31, 154.84
Line 103: Line 148:
| 16/13, 11/9
| 16/13, 11/9
|-
|-
| L ({{nowrap| 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 ({{nowrap| 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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| 7\23, 365.22
| 7\23, 365.22
|-
|-
| L ({{nowrap| 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 ({{nowrap| octave - 3g }})
| s ({{nowrap| octave − 3g }})
| 1\10, 120.00
| 1\10, 120.00
| 1\13, 92.31
| 1\13, 92.31
Line 167: Line 212:
| 5/4
| 5/4
|-
|-
| L ({{nowrap| 4g - octave }})
| L ({{nowrap| 4g − octave }})
| 4\16, 300.00
| 4\16, 300.00
| 5\19, 315.79
| 5\19, 315.79
Line 174: Line 219:
| 6/5
| 6/5
|-
|-
| s ({{nowrap| 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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| 25/24
| 25/24
|}
|}
== Scales ==
* [[Mohaha7]] – 38\131 tuning
* [[Neutral7]] – 111\380 tuning
* [[Namo7]] – 128\437 tuning
* [[Rastgross1]] – POTE tuning of [[namo]]
* [[Hemif7]] – 17\58 tuning
* [[Suhajira7]] – POTE tuning of [[suhajira]]
* [[Sephiroth7]] – 9\29 tuning
* [[Magic7]] – 46\145 tuning


== Scale tree ==
== Scale tree ==
Generator ranges:  
Generator ranges:  
* Chroma-positive generator: 342.8571 cents (2\7) to 400.0000 cents (1\3)
* Chroma-positive generator: 342.8571{{c}} (2\7) to 400.0000{{c}} (1\3)
* Chroma-negative generator: 800.0000 cents (2\3) to 857.1429 cents (5\7)
* Chroma-negative generator: 800.0000{{c}} (2\3) to 857.1429{{c}} (5\7)
{{Scale tree|Comments=
{{MOS tuning spectrum
6/5: [[Mohaha]] / ptolemy↑;  
| 6/5 = [[Mohaha]] / ptolemy&nbsp;↑
5/4: Mohaha / migration / [[mohajira]];
| 5/4 = Mohaha / migration / [[mohajira]]  
11/8: Mohaha / mohamaq;
| 11/8 = Mohaha / [[mohamaq ]]
7/5: Mohaha / [[neutrominant]];
| 7/5 = Mohaha / [[neutrominant]]  
10/7: [[Hemif]] / [[hemififths]];
| 10/7 = [[Hemif]] / [[hemififths]]  
11/7: [[Suhajira]];
| 11/7 = [[Suhajira]]  
13/8: Golden suhajira (354.8232¢);
| 13/8 = Golden suhajira (354.8232{{c}})  
5/3: Suhajira / [[ringo]];
| 5/3 = Suhajira / [[ringo]]  
12/7: [[Beatles]];
| 12/7 = [[Beatles]]  
13/5: Unnamed golden tuning (366.2564¢);
| 13/5 = Unnamed golden tuning (366.2564{{c}})  
7/2: [[Sephiroth]];
| 7/2 = [[Sephiroth]]  
9/2: [[Muggles]];
| 9/2 = [[Muggles]]  
5/1: [[Magic]];
| 5/1 = [[Magic]]  
6/1: [[Würschmidt]]↓
| 6/1 = [[Würschmidt]]&nbsp;↓
}}
}}


[[Category:Mosh]]
[[Category:Mosh]]
[[Category:7-tone scales]]
[[Category:7-tone scales]]
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