# 4L 2s

↖3L 1s | ↑4L 1s | 5L 1s↗ |

←3L 2s | 4L 2s | 5L 2s→ |

↙3L 3s | ↓4L 3s | 5L 3s↘ |

**Equal tunings****4L 2s**, also called **citric**, is a moment of symmetry scale consisting of 4 large steps and 2 small steps, with a period of 2 large steps and 1 small step that repeats twice every octave, or every 600¢. This scale is made using a generator ranging from 200¢ to 300¢, or from 300¢ to 400¢.

This MOS resembles 5L 2s, but with one large step removed.

There are three scales with this MOS pattern that are significant minima of harmonic entropy. The first is antikythera, or no-3's srutal/pajara, which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.

The second is decimal, in which two generators make a 4/3, and the third is Doublewide, in which the generator is 7/6 so the period minus the generator is 6/5.

In addition to the true MOS with pattern LLsLLs, all these scales also come in a near-MOS version, LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The true MOS is always proper, but the near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).

## Modes

UDP | Step pattern |
---|---|

4|0 | LLsLLs |

2|2 | LsLLsL |

0|4 | sLLsLL |

## Scale tree

Generator | Cents | Comments | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1\6 | 200 | |||||||||||

6\34 | 211.76 | |||||||||||

5\28 | 214.29 | Antikythera is around here | ||||||||||

4\22 | 218.18 | |||||||||||

3\16 | 225 | |||||||||||

227.56 | ||||||||||||

8\42 | 228.57 | |||||||||||

600/(1+phi) | Golden lemba | |||||||||||

13\68 | 229.41 | |||||||||||

5\26 | 230.77 | |||||||||||

232.8 | ||||||||||||

7\36 | 233.33 | Lemba is around here | ||||||||||

2\10 | 240 | Boundary of propriety for near-MOS
Optimum rank range (L/s=2/1) for MOS | ||||||||||

5\24 | 250 | Decimal is around here | ||||||||||

251.89 | ||||||||||||

8\38 | 252.63 | |||||||||||

253.39 | L/s = e | |||||||||||

3\14 | 257.14 | L/s = 3 | ||||||||||

258.81 | L/s = pi | |||||||||||

4\18 | 266.67 | L/s = 4 | ||||||||||

5\22 | 272.73 | |||||||||||

6\26 | 276.92 | Doublewide is around here | ||||||||||

7\30 | 280 | |||||||||||

8\34 | 282.35 | |||||||||||

9\38 | 284.21 | |||||||||||

10\42 | 285.71 | |||||||||||

11\46 | 286.96 | |||||||||||

1\4 | 300 |