# Helmholtz-Ellis notation

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The **Helmholtz-Ellis JI pitch notation** (**HEJI**) is a musical notation system for just intonation intervals up to the 47-limit. It consists of a set of accidentals defined by formal commas for each prime harmonic.

Further accidentals were designed by richie for primes up to the 89-limit; see richie's HEJI extensions.

## Introductory materials

- The Helmholtz-Ellis JI Pitch Notation (HEJI) by Marc Sabat and Thomas Nicholson from Plainsound Music Edition – 2020 version with revised symbols for primes up to 47 entirely based on alterations of Pythagorean notes
- Extended Helmholtz-Ellis JI Pitch Notation by Marc Sabat and Wolfgang von Schweinitz from Plainsound Music Edition – deprecated
^{[1]}2004 version

## Quick reference

### Formal commas

Prime | Formal Comma |
---|---|

5 | 81/80 |

7 | 64/63 |

11 | 33/32 |

13 | 27/26 |

17 | 2187/2176 |

19 | 513/512 |

23 | 736/729 |

29 | 261/256 |

31 | 32/31 |

37 | 37/36 |

41 | 82/81 |

43 | 129/128 |

47 | 752/729 |

### Odd harmonics

## Helmholtz-Ellis glyphs

**Todo:** update

Update the 29-limit comma.

## External links

- HEWM Notation (Helmholtz-Ellis-Wolf-Monzo) – Tonalsoft enyclopedia of microtonal music theory
- Plainsound Harmonic Space Calculator

## See also

- Functional Just System (FJS) – a logical notation system for the entirety of just intonation
- Ben Johnston's notation