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
- Gythyllic

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

Pitch Class Set | {0,3,4,5,6,7,9,11} |

Forte Number | 8-Z15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1003 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 863 |

Deep Scale | no |

Interval Vector | 555553 |

Interval Spectrum | p^{5}m^{5}n^{5}s^{5}d^{5}t^{3} |

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

Spectra Variation | 2.25 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.616 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 2809 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 863 | Pyryllic | This is the prime mode | |||

3rd mode: Scale 2479 | Harmonic and Neapolitan Minor Mixed | ||||

4th mode: Scale 3287 | Phrathyllic | ||||

5th mode: Scale 3691 | Badyllic | ||||

6th mode: Scale 3893 | Phrocryllic | ||||

7th mode: Scale 1997 | Raga Cintamani | ||||

8th mode: Scale 1523 | Zothyllic |

The prime form of this scale is Scale 863

Scale 863 | Pyryllic |

The octatonic modal family [2809, 863, 2479, 3287, 3691, 3893, 1997, 1523] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2809 is 1003

Scale 1003 | Ionyryllic |

Only scales that are chiral will have an enantiomorph. Scale 2809 is chiral, and its enantiomorph is scale 1003

Scale 1003 | Ionyryllic |

T_{0} | 2809 | T_{0}I | 1003 | |||||

T_{1} | 1523 | T_{1}I | 2006 | |||||

T_{2} | 3046 | T_{2}I | 4012 | |||||

T_{3} | 1997 | T_{3}I | 3929 | |||||

T_{4} | 3994 | T_{4}I | 3763 | |||||

T_{5} | 3893 | T_{5}I | 3431 | |||||

T_{6} | 3691 | T_{6}I | 2767 | |||||

T_{7} | 3287 | T_{7}I | 1439 | |||||

T_{8} | 2479 | T_{8}I | 2878 | |||||

T_{9} | 863 | T_{9}I | 1661 | |||||

T_{10} | 1726 | T_{10}I | 3322 | |||||

T_{11} | 3452 | T_{11}I | 2549 |

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 2811 | Barygic | |||

Scale 2813 | Zolygic | |||

Scale 2801 | Zogian | |||

Scale 2805 | Ishikotsucho | |||

Scale 2793 | Eporian | |||

Scale 2777 | Aeolian Harmonic | |||

Scale 2745 | Mela Sulini | |||

Scale 2681 | Aerycrian | |||

Scale 2937 | Phragyllic | |||

Scale 3065 | Zothygic | |||

Scale 2297 | Thylian | |||

Scale 2553 | Aeolaptyllic | |||

Scale 3321 | Epagyllic | |||

Scale 3833 | Dycrygic | |||

Scale 761 | Ponian | |||

Scale 1785 | Tharyllic |

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.