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
- Stycrimic

Cardinality | 6 (hexatonic) |
---|---|

Pitch Class Set | {0,2,3,5,6,10} |

Forte Number | 6-Z24 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1733 |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 3 |

Modes | 5 |

Prime? | no prime: 347 |

Deep Scale | no |

Interval Vector | 233331 |

Interval Spectrum | p^{3}m^{3}n^{3}s^{3}d^{2}t |

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

Spectra Variation | 2.667 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1133 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 1307 | Katorimic | ||||

3rd mode: Scale 2701 | Hawaiian | ||||

4th mode: Scale 1699 | Raga Rasavali | ||||

5th mode: Scale 2897 | Rycrimic | ||||

6th mode: Scale 437 | Ronimic |

The prime form of this scale is Scale 347

Scale 347 | Barimic |

The hexatonic modal family [1133, 1307, 2701, 1699, 2897, 437] (Forte: 6-Z24) is the complement of the hexatonic modal family [599, 697, 1481, 1829, 2347, 3221] (Forte: 6-Z46)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1133 is 1733

Scale 1733 | Raga Sarasvati |

Only scales that are chiral will have an enantiomorph. Scale 1133 is chiral, and its enantiomorph is scale 1733

Scale 1733 | Raga Sarasvati |

T_{0} | 1133 | T_{0}I | 1733 | |||||

T_{1} | 2266 | T_{1}I | 3466 | |||||

T_{2} | 437 | T_{2}I | 2837 | |||||

T_{3} | 874 | T_{3}I | 1579 | |||||

T_{4} | 1748 | T_{4}I | 3158 | |||||

T_{5} | 3496 | T_{5}I | 2221 | |||||

T_{6} | 2897 | T_{6}I | 347 | |||||

T_{7} | 1699 | T_{7}I | 694 | |||||

T_{8} | 3398 | T_{8}I | 1388 | |||||

T_{9} | 2701 | T_{9}I | 2776 | |||||

T_{10} | 1307 | T_{10}I | 1457 | |||||

T_{11} | 2614 | T_{11}I | 2914 |

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 1135 | Katolian | |||

Scale 1129 | Raga Jayakauns | |||

Scale 1131 | Honchoshi Plagal Form | |||

Scale 1125 | Ionaritonic | |||

Scale 1141 | Rynimic | |||

Scale 1149 | Bydian | |||

Scale 1101 | Stothitonic | |||

Scale 1117 | Raptimic | |||

Scale 1069 | ||||

Scale 1197 | Minor Hexatonic | |||

Scale 1261 | Modified Blues | |||

Scale 1389 | Minor Locrian | |||

Scale 1645 | Dorian Flat 5 | |||

Scale 109 | ||||

Scale 621 | Pyramid Hexatonic | |||

Scale 2157 | ||||

Scale 3181 | Rolian |

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.