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
- Rolyllic

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

Pitch Class Set | {0,1,2,3,4,7,8,10} |

Forte Number | 8-Z15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3893 |

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 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1439 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 2767 | Katydyllic | ||||

3rd mode: Scale 3431 | Zyptyllic | ||||

4th mode: Scale 3763 | Modyllic | ||||

5th mode: Scale 3929 | Aeolothyllic | ||||

6th mode: Scale 1003 | Ionyryllic | ||||

7th mode: Scale 2549 | Rydyllic | ||||

8th mode: Scale 1661 | Gonyllic |

The prime form of this scale is Scale 863

Scale 863 | Pyryllic |

The octatonic modal family [1439, 2767, 3431, 3763, 3929, 1003, 2549, 1661] (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 1439 is 3893

Scale 3893 | Phrocryllic |

Only scales that are chiral will have an enantiomorph. Scale 1439 is chiral, and its enantiomorph is scale 3893

Scale 3893 | Phrocryllic |

T_{0} | 1439 | T_{0}I | 3893 | |||||

T_{1} | 2878 | T_{1}I | 3691 | |||||

T_{2} | 1661 | T_{2}I | 3287 | |||||

T_{3} | 3322 | T_{3}I | 2479 | |||||

T_{4} | 2549 | T_{4}I | 863 | |||||

T_{5} | 1003 | T_{5}I | 1726 | |||||

T_{6} | 2006 | T_{6}I | 3452 | |||||

T_{7} | 4012 | T_{7}I | 2809 | |||||

T_{8} | 3929 | T_{8}I | 1523 | |||||

T_{9} | 3763 | T_{9}I | 3046 | |||||

T_{10} | 3431 | T_{10}I | 1997 | |||||

T_{11} | 2767 | T_{11}I | 3994 |

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 1437 | Sabach ascending | |||

Scale 1435 | Makam Huzzam | |||

Scale 1431 | Phragian | |||

Scale 1423 | Doptian | |||

Scale 1455 | Phrygiolian | |||

Scale 1471 | Radygic | |||

Scale 1503 | Epiryllian | |||

Scale 1311 | Bynian | |||

Scale 1375 | Bothyllic | |||

Scale 1183 | Sadian | |||

Scale 1695 | Phrodyllic | |||

Scale 1951 | Marygic | |||

Scale 415 | Aeoladian | |||

Scale 927 | Gaptyllic | |||

Scale 2463 | Ionathyllic | |||

Scale 3487 | Byptygic |

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.