The Exciting Universe Of Music Theory

presents

more than you ever wanted to know about...

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
- Zylimic

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

Pitch Class Set | {0,1,2,4,7,8} |

Forte Number | 6-Z17 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3377 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 5 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 322332 |

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

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

Spectra Variation | 2.667 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.116 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

** Pitches are shown with C as the root*

Triad Type | Triad^{*} | Pitch Classes | Degree | Eccentricity | Closeness Centrality |
---|---|---|---|---|---|

Major Triads | C | {0,4,7} | 2 | 2 | 1 |

Minor Triads | c♯m | {1,4,8} | 2 | 2 | 1 |

Augmented Triads | C+ | {0,4,8} | 2 | 2 | 1 |

Diminished Triads | c♯° | {1,4,7} | 2 | 2 | 1 |

Above is a graph showing opportunities for parsimonious voice leading between triads^{*}. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter | 2 |
---|---|

Radius | 2 |

Self-Centered | yes |

Modes are the rotational transformation of this scale. Scale 407 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 2251 | Zodimic | ||||

3rd mode: Scale 3173 | Zarimic | ||||

4th mode: Scale 1817 | Phrythimic | ||||

5th mode: Scale 739 | Rorimic | ||||

6th mode: Scale 2417 | Kanimic |

This is the prime form of this scale.

The hexatonic modal family [407, 2251, 3173, 1817, 739, 2417] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)

The inverse of a scale is a reflection using the root as its axis. The inverse of 407 is 3377

Scale 3377 | Phralimic |

Only scales that are chiral will have an enantiomorph. Scale 407 is chiral, and its enantiomorph is scale 3377

Scale 3377 | Phralimic |

T_{0} | 407 | T_{0}I | 3377 | |||||

T_{1} | 814 | T_{1}I | 2659 | |||||

T_{2} | 1628 | T_{2}I | 1223 | |||||

T_{3} | 3256 | T_{3}I | 2446 | |||||

T_{4} | 2417 | T_{4}I | 797 | |||||

T_{5} | 739 | T_{5}I | 1594 | |||||

T_{6} | 1478 | T_{6}I | 3188 | |||||

T_{7} | 2956 | T_{7}I | 2281 | |||||

T_{8} | 1817 | T_{8}I | 467 | |||||

T_{9} | 3634 | T_{9}I | 934 | |||||

T_{10} | 3173 | T_{10}I | 1868 | |||||

T_{11} | 2251 | T_{11}I | 3736 |

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 405 | Raga Bhupeshwari | |||

Scale 403 | Raga Reva | |||

Scale 411 | Lygimic | |||

Scale 415 | Aeoladian | |||

Scale 391 | ||||

Scale 399 | Zynimic | |||

Scale 423 | Sogimic | |||

Scale 439 | Bythian | |||

Scale 471 | Dodian | |||

Scale 279 | Poditonic | |||

Scale 343 | Ionorimic | |||

Scale 151 | ||||

Scale 663 | Phrynimic | |||

Scale 919 | Chromatic Phrygian Inverse | |||

Scale 1431 | Phragian | |||

Scale 2455 | Bothian |

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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.