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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
- Thygian

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

Pitch Class Set | {0,2,3,7,8,9,11} |

Forte Number | 7-Z38 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1595 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 439 |

Deep Scale | no |

Interval Vector | 434442 |

Interval Spectrum | p^{4}m^{4}n^{4}s^{3}d^{4}t^{2} |

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

Spectra Variation | 2.571 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 2957 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1763 | Katalian | ||||

3rd mode: Scale 2929 | Aeolathian | ||||

4th mode: Scale 439 | Bythian | This is the prime mode | |||

5th mode: Scale 2267 | Padian | ||||

6th mode: Scale 3181 | Rolian | ||||

7th mode: Scale 1819 | Pydian |

The prime form of this scale is Scale 439

Scale 439 | Bythian |

The heptatonic modal family [2957, 1763, 2929, 439, 2267, 3181, 1819] (Forte: 7-Z38) is the complement of the pentatonic modal family [295, 625, 905, 2195, 3145] (Forte: 5-Z38)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2957 is 1595

Scale 1595 | Dacrian |

Only scales that are chiral will have an enantiomorph. Scale 2957 is chiral, and its enantiomorph is scale 1595

Scale 1595 | Dacrian |

T_{0} | 2957 | T_{0}I | 1595 | |||||

T_{1} | 1819 | T_{1}I | 3190 | |||||

T_{2} | 3638 | T_{2}I | 2285 | |||||

T_{3} | 3181 | T_{3}I | 475 | |||||

T_{4} | 2267 | T_{4}I | 950 | |||||

T_{5} | 439 | T_{5}I | 1900 | |||||

T_{6} | 878 | T_{6}I | 3800 | |||||

T_{7} | 1756 | T_{7}I | 3505 | |||||

T_{8} | 3512 | T_{8}I | 2915 | |||||

T_{9} | 2929 | T_{9}I | 1735 | |||||

T_{10} | 1763 | T_{10}I | 3470 | |||||

T_{11} | 3526 | T_{11}I | 2845 |

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 2959 | Dygyllic | |||

Scale 2953 | Ionylimic | |||

Scale 2955 | Thorian | |||

Scale 2949 | ||||

Scale 2965 | Darian | |||

Scale 2973 | Panyllic | |||

Scale 2989 | Bebop Minor | |||

Scale 3021 | Stodyllic | |||

Scale 2829 | ||||

Scale 2893 | Lylian | |||

Scale 2701 | Hawaiian | |||

Scale 2445 | Zadimic | |||

Scale 3469 | Monian | |||

Scale 3981 | Phrycryllic | |||

Scale 909 | Katarimic | |||

Scale 1933 | Mocrian |

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.