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
- Pyrian

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

Pitch Class Set | {0,2,5,7,8,9,10} |

Forte Number | 7-23 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1213 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 2 |

Modes | 6 |

Prime? | no prime: 701 |

Deep Scale | no |

Interval Vector | 354351 |

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

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

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 1957 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1513 | Stathian | ||||

3rd mode: Scale 701 | Mixonyphian | This is the prime mode | |||

4th mode: Scale 1199 | Magian | ||||

5th mode: Scale 2647 | Dadian | ||||

6th mode: Scale 3371 | Aeolylian | ||||

7th mode: Scale 3733 | Gycrian |

The prime form of this scale is Scale 701

Scale 701 | Mixonyphian |

The heptatonic modal family [1957, 1513, 701, 1199, 2647, 3371, 3733] (Forte: 7-23) is the complement of the pentatonic modal family [173, 1067, 1441, 1669, 2581] (Forte: 5-23)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1957 is 1213

Scale 1213 | Gyrian |

Only scales that are chiral will have an enantiomorph. Scale 1957 is chiral, and its enantiomorph is scale 1213

Scale 1213 | Gyrian |

T_{0} | 1957 | T_{0}I | 1213 | |||||

T_{1} | 3914 | T_{1}I | 2426 | |||||

T_{2} | 3733 | T_{2}I | 757 | |||||

T_{3} | 3371 | T_{3}I | 1514 | |||||

T_{4} | 2647 | T_{4}I | 3028 | |||||

T_{5} | 1199 | T_{5}I | 1961 | |||||

T_{6} | 2398 | T_{6}I | 3922 | |||||

T_{7} | 701 | T_{7}I | 3749 | |||||

T_{8} | 1402 | T_{8}I | 3403 | |||||

T_{9} | 2804 | T_{9}I | 2711 | |||||

T_{10} | 1513 | T_{10}I | 1327 | |||||

T_{11} | 3026 | T_{11}I | 2654 |

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 1959 | Katolyllic | |||

Scale 1953 | ||||

Scale 1955 | Sonian | |||

Scale 1961 | Soptian | |||

Scale 1965 | Raga Mukhari | |||

Scale 1973 | Zyryllic | |||

Scale 1925 | ||||

Scale 1941 | Aeranian | |||

Scale 1989 | Dydian | |||

Scale 2021 | Katycryllic | |||

Scale 1829 | Pathimic | |||

Scale 1893 | Ionylian | |||

Scale 1701 | Dominant Seventh | |||

Scale 1445 | Raga Navamanohari | |||

Scale 933 | Dadimic | |||

Scale 2981 | Ionolian | |||

Scale 4005 |

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.