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
- Phraptyllic

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

Pitch Class Set | {0,1,3,4,5,6,7,11} |

Forte Number | 8-5 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3043 |

Hemitonia | 6 (multihemitonic) |

Cohemitonia | 4 (multicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 479 |

Deep Scale | no |

Interval Vector | 654553 |

Interval Spectrum | p^{5}m^{5}n^{4}s^{5}d^{6}t^{3} |

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

Spectra Variation | 2.75 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.366 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 2299 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3197 | Gylyllic | ||||

3rd mode: Scale 1823 | Phralyllic | ||||

4th mode: Scale 2959 | Dygyllic | ||||

5th mode: Scale 3527 | Ronyllic | ||||

6th mode: Scale 3811 | Epogyllic | ||||

7th mode: Scale 3953 | Thagyllic | ||||

8th mode: Scale 503 | Thoptyllic |

The prime form of this scale is Scale 479

Scale 479 | Kocryllic |

The octatonic modal family [2299, 3197, 1823, 2959, 3527, 3811, 3953, 503] (Forte: 8-5) is the complement of the tetratonic modal family [71, 449, 2083, 3089] (Forte: 4-5)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2299 is 3043

Scale 3043 | Ionayllic |

Only scales that are chiral will have an enantiomorph. Scale 2299 is chiral, and its enantiomorph is scale 3043

Scale 3043 | Ionayllic |

T_{0} | 2299 | T_{0}I | 3043 | |||||

T_{1} | 503 | T_{1}I | 1991 | |||||

T_{2} | 1006 | T_{2}I | 3982 | |||||

T_{3} | 2012 | T_{3}I | 3869 | |||||

T_{4} | 4024 | T_{4}I | 3643 | |||||

T_{5} | 3953 | T_{5}I | 3191 | |||||

T_{6} | 3811 | T_{6}I | 2287 | |||||

T_{7} | 3527 | T_{7}I | 479 | |||||

T_{8} | 2959 | T_{8}I | 958 | |||||

T_{9} | 1823 | T_{9}I | 1916 | |||||

T_{10} | 3646 | T_{10}I | 3832 | |||||

T_{11} | 3197 | T_{11}I | 3569 |

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 2297 | Thylian | |||

Scale 2301 | Bydyllic | |||

Scale 2303 | Stanygic | |||

Scale 2291 | Zydian | |||

Scale 2295 | Kogyllic | |||

Scale 2283 | Aeolyptian | |||

Scale 2267 | Padian | |||

Scale 2235 | Bathian | |||

Scale 2171 | ||||

Scale 2427 | Katoryllic | |||

Scale 2555 | Bythygic | |||

Scale 2811 | Barygic | |||

Scale 3323 | Lacrygic | |||

Scale 251 | ||||

Scale 1275 | Stagyllic |

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.