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
- Stythian

Cardinality | 7 (heptatonic) |
---|---|

Pitch Class Set | {0,4,5,7,8,9,11} |

Forte Number | 7-Z37 |

Rotational Symmetry | none |

Reflection Axes | 2 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 443 |

Deep Scale | no |

Interval Vector | 434541 |

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

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

Spectra Variation | 2.571 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [4] |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 2993 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 443 | Kothian | This is the prime mode | |||

3rd mode: Scale 2269 | Pygian | ||||

4th mode: Scale 1591 | Rodian | ||||

5th mode: Scale 2843 | Sorian | ||||

6th mode: Scale 3469 | Monian | ||||

7th mode: Scale 1891 | Thalian |

The prime form of this scale is Scale 443

Scale 443 | Kothian |

The heptatonic modal family [2993, 443, 2269, 1591, 2843, 3469, 1891] (Forte: 7-Z37) is the complement of the pentatonic modal family [313, 551, 913, 2323, 3209] (Forte: 5-Z37)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2993 is 443

Scale 443 | Kothian |

T_{0} | 2993 | T_{0}I | 443 | |||||

T_{1} | 1891 | T_{1}I | 886 | |||||

T_{2} | 3782 | T_{2}I | 1772 | |||||

T_{3} | 3469 | T_{3}I | 3544 | |||||

T_{4} | 2843 | T_{4}I | 2993 | |||||

T_{5} | 1591 | T_{5}I | 1891 | |||||

T_{6} | 3182 | T_{6}I | 3782 | |||||

T_{7} | 2269 | T_{7}I | 3469 | |||||

T_{8} | 443 | T_{8}I | 2843 | |||||

T_{9} | 886 | T_{9}I | 1591 | |||||

T_{10} | 1772 | T_{10}I | 3182 | |||||

T_{11} | 3544 | T_{11}I | 2269 |

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 2995 | Raga Saurashtra | |||

Scale 2997 | Major Bebop | |||

Scale 3001 | Lonyllic | |||

Scale 2977 | ||||

Scale 2985 | Epacrian | |||

Scale 2961 | Bygimic | |||

Scale 3025 | Epycrian | |||

Scale 3057 | Phroryllic | |||

Scale 2865 | Solimic | |||

Scale 2929 | Aeolathian | |||

Scale 2737 | Raga Hari Nata | |||

Scale 2481 | Raga Paraju | |||

Scale 3505 | Stygian | |||

Scale 4017 | Dolyllic | |||

Scale 945 | Raga Saravati | |||

Scale 1969 | Stylian |

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.