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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
- Stydyllic

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

Pitch Class Set | {0,2,4,5,6,7,8,9} |

Forte Number | 8-11 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1529 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 4 (multicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 703 |

Deep Scale | no |

Interval Vector | 565552 |

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

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

Spectra Variation | 2.75 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1013 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 1277 | Zadyllic | ||||

3rd mode: Scale 1343 | Zalyllic | ||||

4th mode: Scale 2719 | Zocryllic | ||||

5th mode: Scale 3407 | Katocryllic | ||||

6th mode: Scale 3751 | Aerathyllic | ||||

7th mode: Scale 3923 | Stoptyllic | ||||

8th mode: Scale 4009 | Phranyllic |

The prime form of this scale is Scale 703

Scale 703 | Aerocryllic |

The octatonic modal family [1013, 1277, 1343, 2719, 3407, 3751, 3923, 4009] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1013 is 1529

Scale 1529 | Kataryllic |

Only scales that are chiral will have an enantiomorph. Scale 1013 is chiral, and its enantiomorph is scale 1529

Scale 1529 | Kataryllic |

T_{0} | 1013 | T_{0}I | 1529 | |||||

T_{1} | 2026 | T_{1}I | 3058 | |||||

T_{2} | 4052 | T_{2}I | 2021 | |||||

T_{3} | 4009 | T_{3}I | 4042 | |||||

T_{4} | 3923 | T_{4}I | 3989 | |||||

T_{5} | 3751 | T_{5}I | 3883 | |||||

T_{6} | 3407 | T_{6}I | 3671 | |||||

T_{7} | 2719 | T_{7}I | 3247 | |||||

T_{8} | 1343 | T_{8}I | 2399 | |||||

T_{9} | 2686 | T_{9}I | 703 | |||||

T_{10} | 1277 | T_{10}I | 1406 | |||||

T_{11} | 2554 | T_{11}I | 2812 |

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 1015 | Ionodygic | |||

Scale 1009 | Katyptian | |||

Scale 1011 | Kycryllic | |||

Scale 1017 | Dythyllic | |||

Scale 1021 | Ladygic | |||

Scale 997 | Rycrian | |||

Scale 1005 | Radyllic | |||

Scale 981 | Mela Kantamani | |||

Scale 949 | Mela Mararanjani | |||

Scale 885 | Sathian | |||

Scale 757 | Ionyptian | |||

Scale 501 | Katylian | |||

Scale 1525 | Sodyllic | |||

Scale 2037 | Sythygic | |||

Scale 3061 | Apinygic |

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