The Exciting Universe Of Music Theory

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The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks *imperfect* tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

- Zeitler
- Phrygimic

Cardinality | 6 (hexatonic) |
---|---|

Pitch Class Set | {0,2,6,8,9,10} |

Forte Number | 6-21 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1117 |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 5 |

Modes | 5 |

Prime? | no prime: 349 |

Deep Scale | no |

Interval Vector | 242412 |

Interval Spectrum | pm^{4}n^{2}s^{4}d^{2}t^{2} |

Distribution Spectra | <1> = {1,2,4} <2> = {2,3,4,6} <3> = {4,5,7,8} <4> = {6,8,9,10} <5> = {8,10,11} |

Spectra Variation | 3 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.232 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1861 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 1489 | Raga Jyoti | ||||

3rd mode: Scale 349 | Borimic | This is the prime mode | |||

4th mode: Scale 1111 | Sycrimic | ||||

5th mode: Scale 2603 | Gadimic | ||||

6th mode: Scale 3349 | Aeolocrimic |

The prime form of this scale is Scale 349

Scale 349 | Borimic |

The hexatonic modal family [1861, 1489, 349, 1111, 2603, 3349] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1861 is 1117

Scale 1117 | Raptimic |

Only scales that are chiral will have an enantiomorph. Scale 1861 is chiral, and its enantiomorph is scale 1117

Scale 1117 | Raptimic |

T_{0} | 1861 | T_{0}I | 1117 | |||||

T_{1} | 3722 | T_{1}I | 2234 | |||||

T_{2} | 3349 | T_{2}I | 373 | |||||

T_{3} | 2603 | T_{3}I | 746 | |||||

T_{4} | 1111 | T_{4}I | 1492 | |||||

T_{5} | 2222 | T_{5}I | 2984 | |||||

T_{6} | 349 | T_{6}I | 1873 | |||||

T_{7} | 698 | T_{7}I | 3746 | |||||

T_{8} | 1396 | T_{8}I | 3397 | |||||

T_{9} | 2792 | T_{9}I | 2699 | |||||

T_{10} | 1489 | T_{10}I | 1303 | |||||

T_{11} | 2978 | T_{11}I | 2606 |

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 1863 | Pycrian | |||

Scale 1857 | ||||

Scale 1859 | ||||

Scale 1865 | Thagimic | |||

Scale 1869 | Katyrian | |||

Scale 1877 | Aeroptian | |||

Scale 1893 | Ionylian | |||

Scale 1797 | ||||

Scale 1829 | Pathimic | |||

Scale 1925 | ||||

Scale 1989 | Dydian | |||

Scale 1605 | Zanitonic | |||

Scale 1733 | Raga Sarasvati | |||

Scale 1349 | Tholitonic | |||

Scale 837 | Epaditonic | |||

Scale 2885 | Byrimic | |||

Scale 3909 | Rydian |

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.