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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.

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
- Dacryllic

Cardinality | 8 (octatonic) |
---|---|

Pitch Class Set | {0,1,2,3,4,5,7,11} |

Forte Number | 8-2 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 4003 |

Hemitonia | 6 (multihemitonic) |

Cohemitonia | 5 (multicohemitonic) |

Imperfections | 4 |

Modes | 7 |

Prime? | no prime: 383 |

Deep Scale | no |

Interval Vector | 665542 |

Interval Spectrum | p^{4}m^{5}n^{5}s^{6}d^{6}t^{2} |

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

Spectra Variation | 3.25 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 2239 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3167 | Thynyllic | ||||

3rd mode: Scale 3631 | Gydyllic | ||||

4th mode: Scale 3863 | Eparyllic | ||||

5th mode: Scale 3979 | Dynyllic | ||||

6th mode: Scale 4037 | Ionyllic | ||||

7th mode: Scale 2033 | Stolyllic | ||||

8th mode: Scale 383 | Logyllic | This is the prime mode |

The prime form of this scale is Scale 383

Scale 383 | Logyllic |

The octatonic modal family [2239, 3167, 3631, 3863, 3979, 4037, 2033, 383] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2239 is 4003

Scale 4003 | Sadyllic |

Only scales that are chiral will have an enantiomorph. Scale 2239 is chiral, and its enantiomorph is scale 4003

Scale 4003 | Sadyllic |

T_{0} | 2239 | T_{0}I | 4003 | |||||

T_{1} | 383 | T_{1}I | 3911 | |||||

T_{2} | 766 | T_{2}I | 3727 | |||||

T_{3} | 1532 | T_{3}I | 3359 | |||||

T_{4} | 3064 | T_{4}I | 2623 | |||||

T_{5} | 2033 | T_{5}I | 1151 | |||||

T_{6} | 4066 | T_{6}I | 2302 | |||||

T_{7} | 4037 | T_{7}I | 509 | |||||

T_{8} | 3979 | T_{8}I | 1018 | |||||

T_{9} | 3863 | T_{9}I | 2036 | |||||

T_{10} | 3631 | T_{10}I | 4072 | |||||

T_{11} | 3167 | T_{11}I | 4049 |

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 2237 | Epothian | |||

Scale 2235 | Bathian | |||

Scale 2231 | Macrian | |||

Scale 2223 | Konian | |||

Scale 2207 | Mygian | |||

Scale 2271 | Poptyllic | |||

Scale 2303 | Stanygic | |||

Scale 2111 | ||||

Scale 2175 | ||||

Scale 2367 | Laryllic | |||

Scale 2495 | Aeolocrygic | |||

Scale 2751 | Sylygic | |||

Scale 3263 | Pyrygic | |||

Scale 191 | ||||

Scale 1215 |

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. Bibliography