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
- Zocrian

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

Pitch Class Set | {0,2,6,7,8,10,11} |

Forte Number | 7-13 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1143 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 375 |

Deep Scale | no |

Interval Vector | 443532 |

Interval Spectrum | p^{3}m^{5}n^{3}s^{4}d^{4}t^{2} |

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

Spectra Variation | 2.857 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3525 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1905 | Katacrian | ||||

3rd mode: Scale 375 | Sodian | This is the prime mode | |||

4th mode: Scale 2235 | Bathian | ||||

5th mode: Scale 3165 | Mylian | ||||

6th mode: Scale 1815 | Godian | ||||

7th mode: Scale 2955 | Thorian |

The prime form of this scale is Scale 375

Scale 375 | Sodian |

The heptatonic modal family [3525, 1905, 375, 2235, 3165, 1815, 2955] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3525 is 1143

Scale 1143 | Styrian |

Only scales that are chiral will have an enantiomorph. Scale 3525 is chiral, and its enantiomorph is scale 1143

Scale 1143 | Styrian |

T_{0} | 3525 | T_{0}I | 1143 | |||||

T_{1} | 2955 | T_{1}I | 2286 | |||||

T_{2} | 1815 | T_{2}I | 477 | |||||

T_{3} | 3630 | T_{3}I | 954 | |||||

T_{4} | 3165 | T_{4}I | 1908 | |||||

T_{5} | 2235 | T_{5}I | 3816 | |||||

T_{6} | 375 | T_{6}I | 3537 | |||||

T_{7} | 750 | T_{7}I | 2979 | |||||

T_{8} | 1500 | T_{8}I | 1863 | |||||

T_{9} | 3000 | T_{9}I | 3726 | |||||

T_{10} | 1905 | T_{10}I | 3357 | |||||

T_{11} | 3810 | T_{11}I | 2619 |

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 3527 | Ronyllic | |||

Scale 3521 | ||||

Scale 3523 | ||||

Scale 3529 | Stalian | |||

Scale 3533 | Thadyllic | |||

Scale 3541 | Racryllic | |||

Scale 3557 | ||||

Scale 3461 | ||||

Scale 3493 | Rathian | |||

Scale 3397 | Sydimic | |||

Scale 3269 | Raga Malarani | |||

Scale 3781 | Gyphian | |||

Scale 4037 | Ionyllic | |||

Scale 2501 | Ralimic | |||

Scale 3013 | Thynian | |||

Scale 1477 | Raga Jaganmohanam |

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.