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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
- Aerothyllic

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

Pitch Class Set | {0,2,3,4,6,8,10,11} |

Forte Number | 8-24 |

Rotational Symmetry | none |

Reflection Axes | 1 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 4 |

Modes | 7 |

Prime? | no prime: 1399 |

Deep Scale | no |

Interval Vector | 464743 |

Interval Spectrum | p^{4}m^{7}n^{4}s^{6}d^{4}t^{3} |

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

Spectra Variation | 1.5 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [2] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3421 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 1879 | Mixoryllic | ||||

3rd mode: Scale 2987 | Neapolitan Major and Minor Mixed | ||||

4th mode: Scale 3541 | Racryllic | ||||

5th mode: Scale 1909 | Epicryllic | ||||

6th mode: Scale 1501 | Stygyllic | ||||

7th mode: Scale 1399 | Syryllic | This is the prime mode | |||

8th mode: Scale 2747 | Stythyllic |

The prime form of this scale is Scale 1399

Scale 1399 | Syryllic |

The octatonic modal family [3421, 1879, 2987, 3541, 1909, 1501, 1399, 2747] (Forte: 8-24) is the complement of the tetratonic modal family [277, 337, 1093, 1297] (Forte: 4-24)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3421 is 1879

Scale 1879 | Mixoryllic |

T_{0} | 3421 | T_{0}I | 1879 | |||||

T_{1} | 2747 | T_{1}I | 3758 | |||||

T_{2} | 1399 | T_{2}I | 3421 | |||||

T_{3} | 2798 | T_{3}I | 2747 | |||||

T_{4} | 1501 | T_{4}I | 1399 | |||||

T_{5} | 3002 | T_{5}I | 2798 | |||||

T_{6} | 1909 | T_{6}I | 1501 | |||||

T_{7} | 3818 | T_{7}I | 3002 | |||||

T_{8} | 3541 | T_{8}I | 1909 | |||||

T_{9} | 2987 | T_{9}I | 3818 | |||||

T_{10} | 1879 | T_{10}I | 3541 | |||||

T_{11} | 3758 | T_{11}I | 2987 |

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 3423 | Lothygic | |||

Scale 3417 | Golian | |||

Scale 3419 | Magen Abot 1 | |||

Scale 3413 | Leading Whole-tone | |||

Scale 3405 | Stynian | |||

Scale 3437 | ||||

Scale 3453 | Katarygic | |||

Scale 3357 | Phrodian | |||

Scale 3389 | Socryllic | |||

Scale 3485 | Sabach | |||

Scale 3549 | Messiaen Mode 3 Inverse | |||

Scale 3165 | Mylian | |||

Scale 3293 | Saryllic | |||

Scale 3677 | ||||

Scale 3933 | Ionidygic | |||

Scale 2397 | Stagian | |||

Scale 2909 | Mocryllic | |||

Scale 1373 | Storian |

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