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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:
Line 51: Line 53:


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"
|-
|-
Line 67: Line 70:
| [[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
Line 74: Line 77:
| [[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.
Line 102: Line 105:
| 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
Line 108: Line 111:
| 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
Line 123: Line 126:


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
Line 166: Line 170:
| 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
Line 173: Line 177:
| 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]]

Revision as of 15:15, 24 February 2025

↖ 2L 3s ↑ 3L 3s 4L 3s ↗
← 2L 4s 3L 4s 4L 4s →
↙ 2L 5s ↓ 3L 5s 4L 5s ↘ 
┌╥┬╥┬╥┬┬┐
│║│║│║│││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLss
ssLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\7 to 1\3 (342.9 ¢ to 400.0 ¢)
Dark 2\3 to 5\7 (800.0 ¢ to 857.1 ¢)
TAMNAMS information
Name mosh
Prefix mosh-
Abbrev. mosh
Related MOS scales
Parent 3L 1s
Sister 4L 3s
Daughters 7L 3s, 3L 7s
Neutralized 6L 1s
2-Flought 10L 4s, 3L 11s
Equal tunings
Equalized (L:s = 1:1) 2\7 (342.9 ¢)
Supersoft (L:s = 4:3) 7\24 (350.0 ¢)
Soft (L:s = 3:2) 5\17 (352.9 ¢)
Semisoft (L:s = 5:3) 8\27 (355.6 ¢)
Basic (L:s = 2:1) 3\10 (360.0 ¢)
Semihard (L:s = 5:2) 7\23 (365.2 ¢)
Hard (L:s = 3:1) 4\13 (369.2 ¢)
Superhard (L:s = 4:1) 5\16 (375.0 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 4s, named mosh in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 4 small steps, repeating every octave. Generators that produce this scale range from 342.9 ¢ to 400 ¢, or from 800 ¢ to 857.1 ¢.

Name

TAMNAMS suggests the temperament-agnostic name mosh for this scale, adopted from an older MOS naming scheme by Graham Breed. The name is a contraction of "mohajira-ish".

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 3L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-moshstep Perfect 0-moshstep P0moshs 0 0.0 ¢
1-moshstep Minor 1-moshstep m1moshs s 0.0 ¢ to 171.4 ¢
Major 1-moshstep M1moshs L 171.4 ¢ to 400.0 ¢
2-moshstep Diminished 2-moshstep d2moshs 2s 0.0 ¢ to 342.9 ¢
Perfect 2-moshstep P2moshs L + s 342.9 ¢ to 400.0 ¢
3-moshstep Minor 3-moshstep m3moshs L + 2s 400.0 ¢ to 514.3 ¢
Major 3-moshstep M3moshs 2L + s 514.3 ¢ to 800.0 ¢
4-moshstep Minor 4-moshstep m4moshs L + 3s 400.0 ¢ to 685.7 ¢
Major 4-moshstep M4moshs 2L + 2s 685.7 ¢ to 800.0 ¢
5-moshstep Perfect 5-moshstep P5moshs 2L + 3s 800.0 ¢ to 857.1 ¢
Augmented 5-moshstep A5moshs 3L + 2s 857.1 ¢ to 1200.0 ¢
6-moshstep Minor 6-moshstep m6moshs 2L + 4s 800.0 ¢ to 1028.6 ¢
Major 6-moshstep M6moshs 3L + 3s 1028.6 ¢ to 1200.0 ¢
7-moshstep Perfect 7-moshstep P7moshs 3L + 4s 1200.0 ¢

Modes

Scale degrees of the modes of 3L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (moshdegree)
0 1 2 3 4 5 6 7
6|0 1 LsLsLss Perf. Maj. Perf. Maj. Maj. Aug. Maj. Perf.
5|1 3 LsLssLs Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf.
4|2 5 LssLsLs Perf. Maj. Perf. Min. Maj. Perf. Maj. Perf.
3|3 7 sLsLsLs Perf. Min. Perf. Min. Maj. Perf. Maj. Perf.
2|4 2 sLsLssL Perf. Min. Perf. Min. Maj. Perf. Min. Perf.
1|5 4 sLssLsL Perf. Min. Perf. Min. Min. Perf. Min. Perf.
0|6 6 ssLsLsL Perf. Min. Dim. Min. Min. Perf. Min. Perf.

Proposed names

One set of mode nicknames was coined by Andrew Heathwaite. The other set was coined by CellularAutomaton and follows the diatonic modes' naming convention by using ancient Greek toponyms that sound similar to the Heathwaite names.


Modes of 3L 4s
UDP Cyclic
order		 Step
pattern
6|0 1 LsLsLss
5|1 3 LsLssLs
4|2 5 LssLsLs
3|3 7 sLsLsLs
2|4 2 sLsLssL
1|5 4 sLssLsL
0|6 6 ssLsLsL

Theory

Low harmonic entropy scales

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¢) and two of them make a 3/2 (702¢).
  • Magic, in which the generator is 5/4 (386¢) and 5 of them make a 3/1 (1902¢).

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).

In dicoid, the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

In sephiroid, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.

Ultrasoft

Ultrasoft mosh tunings have step ratios that are less than 4:3, which implies a generator flatter than 7\24 = 350¢.

Ultrasoft mosh can be considered "meantone mosh". This is because the large step is a "meantone" in these tunings, somewhere between near-10/9 (as in 38edo) and near-9/8 (as in 24edo).

Ultrasoft mosh EDOs include 24edo, 31edo, 38edo, and 55edo.

  • 24edo can be used to make large and small steps more distinct (the step ratio is 4/3), or for its nearly pure 3/2.
  • 38edo can be used to tune the diminished and perfect mosthirds near 6/5 and 11/9, respectively.

These identifications are associated with mohajira temperament.

The sizes of the generator, large step and small step of mosh are as follows in various ultrasoft mosh tunings.

24edo (supersoft) 31edo 38edo 55edo JI intervals represented
generator (g) 7\24, 350.00 9\31, 348.39 11\38, 347.37 16\55, 349.09 11/9
L (4g − octave) 4\24, 200.00 5\31, 193.55 6\38, 189.47 9\55, 196.36 9/8, 10/9
s (octave − 3g) 3\24, 150.00 4\31, 154.84 5\38, 157.89 7\55, 152.72 11/10, 12/11

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 ¢.

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.

These identifications are associated with beatles and suhajira temperaments.

17edo (soft) 27edo (semisoft) 44edo JI intervals represented
generator (g) 5\17, 352.94 8\27, 355.56 13\44, 354.55 16/13, 11/9
L (4g − octave) 3\17, 211.76 5\27, 222.22 8\44, 218.18 9/8, 8/7
s (octave − 3g) 2\17, 141.18 3\27, 133.33 5\44, 137.37 12/11, 13/12, 14/13

Hypohard

Hypohard tunings of mosh have a step ratio between 2 and 3, implying a generator sharper than 3\10 = 360¢ and flatter than 4\13 = 369.23¢.

The large step ranges from a semifourth to a subminor third in these tunings. The small step is now clearly a semitone, ranging from 1\10 (120¢) to 1\13 (92.31¢).

The symmetric mode sLsLsLs becomes a distorted double harmonic major in these tunings.

This range is associated with sephiroth temperament.

10edo (basic) 13edo (hard) 23edo (semihard)
generator (g) 3\10, 360.00 4\13, 369.23 7\23, 365.22
L (4g − octave) 2\10, 240.00 3\13, 276.92 5\23, 260.87
s (octave − 3g) 1\10, 120.00 1\13, 92.31 2\23, 104.35

Ultrahard

Ultra tunings of mosh have a step ratio greater than 4/1, implying a generator sharper than 5\16 = 375¢. The generator is thus near a 5/4 major third, five of which add up to an approximate 3/1. The 7-note MOS only has two perfect fifths, so extending the chain to bigger MOSes, such as the 3L 7s 10-note MOS, is suggested for getting 5-limit harmony.

This range is associated with magic temperament.

16edo (superhard) 19edo 22edo 41edo JI intervals represented
generator (g) 5\16, 375.00 6\19, 378.95 7\22, 381.82 13\41, 380.49 5/4
L (4g − octave) 4\16, 300.00 5\19, 315.79 6\22, 327.27 11\41, 321.95 6/5
s (octave − 3g) 1\16, 75.00 1\19, 63.16 1\22, 54.54 2\41, 58.54 25/24

Scale tree

Generator ranges:

  • Chroma-positive generator: 342.8571 ¢ (2\7) to 400 ¢ (1\3)
  • Chroma-negative generator: 800 ¢ (2\3) to 857.1429 ¢ (5\7)

Template:Scale tree

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