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.

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
- Katygyllic

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

Pitch Class Set | {0,1,2,4,5,6,9,10} |

Forte Number | 8-19 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3533 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 887 |

Deep Scale | no |

Interval Vector | 545752 |

Interval Spectrum | p^{5}m^{7}n^{5}s^{4}d^{5}t^{2} |

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

Spectra Variation | 1.75 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1655 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 2875 | Ganyllic | ||||

3rd mode: Scale 3485 | Sabach | ||||

4th mode: Scale 1895 | Salyllic | ||||

5th mode: Scale 2995 | Raga Saurashtra | ||||

6th mode: Scale 3545 | Thyptyllic | ||||

7th mode: Scale 955 | Ionogyllic | ||||

8th mode: Scale 2525 | Aeolaryllic |

The prime form of this scale is Scale 887

Scale 887 | Sathyllic |

The octatonic modal family [1655, 2875, 3485, 1895, 2995, 3545, 955, 2525] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1655 is 3533

Scale 3533 | Thadyllic |

Only scales that are chiral will have an enantiomorph. Scale 1655 is chiral, and its enantiomorph is scale 3533

Scale 3533 | Thadyllic |

T_{0} | 1655 | T_{0}I | 3533 | |||||

T_{1} | 3310 | T_{1}I | 2971 | |||||

T_{2} | 2525 | T_{2}I | 1847 | |||||

T_{3} | 955 | T_{3}I | 3694 | |||||

T_{4} | 1910 | T_{4}I | 3293 | |||||

T_{5} | 3820 | T_{5}I | 2491 | |||||

T_{6} | 3545 | T_{6}I | 887 | |||||

T_{7} | 2995 | T_{7}I | 1774 | |||||

T_{8} | 1895 | T_{8}I | 3548 | |||||

T_{9} | 3790 | T_{9}I | 3001 | |||||

T_{10} | 3485 | T_{10}I | 1907 | |||||

T_{11} | 2875 | T_{11}I | 3814 |

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 1653 | Minor Romani Inverse | |||

Scale 1651 | Asian | |||

Scale 1659 | Maqam Shadd'araban | |||

Scale 1663 | Lydygic | |||

Scale 1639 | Aeolothian | |||

Scale 1647 | Polyllic | |||

Scale 1623 | Lothian | |||

Scale 1591 | Rodian | |||

Scale 1719 | Lyryllic | |||

Scale 1783 | Youlan Scale | |||

Scale 1911 | Messiaen Mode 3 | |||

Scale 1143 | Styrian | |||

Scale 1399 | Syryllic | |||

Scale 631 | Zygian | |||

Scale 2679 | Rathyllic | |||

Scale 3703 | Katalygic |

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