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.

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
- Epytimic

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

Pitch Class Set | {0,1,2,6,9,10} |

Forte Number | 6-15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3149 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 4 |

Modes | 5 |

Prime? | no prime: 311 |

Deep Scale | no |

Interval Vector | 323421 |

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

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

Spectra Variation | 3.333 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1607 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 2851 | Katoptimic | ||||

3rd mode: Scale 3473 | Lathimic | ||||

4th mode: Scale 473 | Aeralimic | ||||

5th mode: Scale 571 | Kynimic | ||||

6th mode: Scale 2333 | Stynimic |

The prime form of this scale is Scale 311

Scale 311 | Stagimic |

The hexatonic modal family [1607, 2851, 3473, 473, 571, 2333] (Forte: 6-15) is the complement of the hexatonic modal family [311, 881, 1811, 2203, 2953, 3149] (Forte: 6-15)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1607 is 3149

Scale 3149 | Phrycrimic |

Only scales that are chiral will have an enantiomorph. Scale 1607 is chiral, and its enantiomorph is scale 3149

Scale 3149 | Phrycrimic |

T_{0} | 1607 | T_{0}I | 3149 | |||||

T_{1} | 3214 | T_{1}I | 2203 | |||||

T_{2} | 2333 | T_{2}I | 311 | |||||

T_{3} | 571 | T_{3}I | 622 | |||||

T_{4} | 1142 | T_{4}I | 1244 | |||||

T_{5} | 2284 | T_{5}I | 2488 | |||||

T_{6} | 473 | T_{6}I | 881 | |||||

T_{7} | 946 | T_{7}I | 1762 | |||||

T_{8} | 1892 | T_{8}I | 3524 | |||||

T_{9} | 3784 | T_{9}I | 2953 | |||||

T_{10} | 3473 | T_{10}I | 1811 | |||||

T_{11} | 2851 | T_{11}I | 3622 |

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 1605 | Zanitonic | |||

Scale 1603 | ||||

Scale 1611 | Dacrimic | |||

Scale 1615 | Sydian | |||

Scale 1623 | Lothian | |||

Scale 1639 | Aeolothian | |||

Scale 1543 | ||||

Scale 1575 | Zycrimic | |||

Scale 1671 | ||||

Scale 1735 | Mela Navanitam | |||

Scale 1863 | Pycrian | |||

Scale 1095 | Phrythitonic | |||

Scale 1351 | Aeraptimic | |||

Scale 583 | Aeritonic | |||

Scale 2631 | Macrimic | |||

Scale 3655 | Mathian |

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. Bibliography