# Carlos Alpha

**Carlos Alpha** is a non-octave equal temperament with step size about 77.965 ¢ in the standard tuning^{[1]}. It was invented by Wendy Carlos.

In this temperament, the interval of 9 steps approximates 3/2, that of 5 steps approximates 5/4, and that of 4 steps approximates 6/5.

## Theory

Carlos optimized the tuning on 3/2, 5/4 and 6/5, such that the tuning divides the octave in [math]\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}[/math] ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the equal division of the just perfect fifth into nine parts of 77.995 cents each (9ed3/2), corresponding to 15.3856edo.

Carlos Alpha is very closely related to valentine temperament. For a list of 11-limit dyadic chords of Carlos Alpha, see Chords of valentine.

It has a very good representation of the 7:8:10:11:12 chord from the harmonic series.

Sequence of EDOs with lower and lower relative error: 15, 31, 46, 77, 354

## Intervals

Degrees | Cents ~ Cents octave-reduced | Approximate JI interval (11-limit) |
---|---|---|

0 | 0 | 1/1 (exact) |

1 | 78 | 25/24, 22/21, 21/20 |

2 | 156 | 12/11, 35/32, 11/10 |

3 | 234 | 8/7, 55/48 |

4 | 312 | 6/5 |

5 | 390 | 5/4 |

6 | 468 | 72/55, 21/16 |

7 | 546 | 15/11, 48/35, 11/8 |

8 | 624 | 10/7, 63/44, 36/25 |

9 | 702 | 3/2 (exact) |

10 | 780 | 25/16, 11/7, 63/40 |

11 | 858 | 18/11, 105/64, 33/20 |

12 | 936 | 12/7, 55/32 |

13 | 1014 | 9/5 |

14 | 1092 | 15/8 |

15 | 1170 | 108/55, 63/32 |

16 | 1248 ~ 48 | 45/22, 72/35, 33/16 |

17 | 1326 ~ 126 | 15/7, 189/88, 54/25 |

18 | 1404 ~ 204 | 9/4 (exact) |

19 | 1482 ~ 282 | |

20 | 1560 ~ 360 | |

21 | 1638 ~ 438 | |

22 | 1716 ~ 516 | |

23 | 1794 ~ 594 | |

24 | 1872 ~ 672 | |

25 | 1950 ~ 750 | |

26 | 2028 ~ 828 | |

27 | 2106 ~ 906 | |

28 | 2184 ~ 984 | |

29 | 2262 ~ 1062 | |

30 | 2340 ~ 1140 | |

31 | 2418 ~ 18 | |

32 | 2496 ~ 96 | |

33 | 2574 ~ 174 | |

34 | 2652 ~ 252 | |

35 | 2730 ~ 330 | |

36 | 2808 ~ 408 |

## Music

*See also: Category:Carlos Alpha tracks*

*Bourdigal*by Jean-Pierre Poulin*Alpha study 7 - melody study*by Joel Grant Taylor^{[dead link]}*Alphablues*by Carlo Serafini*Alphapanther*by Carlo Serafini (blog entry)*Alphadesert*by Carlo Serafini (blog entry)*AlphaDulcimer*by Carlo Serafini (blog entry)*AlphaTherem Waltz*by Carlo Serafini (blog entry)*Cubana Al Cubana Pha*by Carlo Serafini (blog entry)*DisMLosphere - video*by Carlo Serafini (blog entry)*Alpha El Din*by Carlo Serafini (blog entry)*Alpha Choir*by Carlo Serafini (blog entry)*Alpha Seems To Be The Hardest World*by Carlo Serafini (blog entry)*Bossa Sbilenca*by Carlo Serafini (blog entry)*Galactic Overload*by Carlo Serafini (blog entry)*Alpha Rain (video)*by Carlo Serafini (blog entry)*Alpha Delinquent*by Carlo Serafini (blog entry)*Alpha Abstract 1*by Carlo Serafini (blog entry)*Miles of Space*by Carlo Serafini (blog entry)*MacAtar (video)*by Carlo Serafini (blog entry)*Fuzzy Logic*by Carlo Serafini (blog entry)*Alpha Asana (video)*by Carlo Serafini (blog entry)*Alpha Penguin Tanz (video)*by Carlo Serafini (blog entry)*White Woman Speaks Up For #blacklivesmatter (video)*by Carlo Serafini (blog entry)*Jayni's song*by Carlo Serafini (blog entry)- 01.03.12 W.C.a. by Omega9

## See also

## References

- ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43