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).

- Western Modern
- Major Locrian

- Exoticisms
- Arabian (b)

- Zeitler
- Gothian

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

Pitch Class Set | {0,2,4,5,6,8,10} |

Forte Number | 7-33 |

Rotational Symmetry | none |

Reflection Axes | 5 |

Palindromic | no |

Chirality | no |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 5 |

Modes | 6 |

Prime? | no prime: 1367 |

Deep Scale | no |

Interval Vector | 262623 |

Interval Spectrum | p^{2}m^{6}n^{2}s^{6}d^{2}t^{3} |

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

Spectra Variation | 1.429 |

Maximally Even | no |

Maximal Area Set | yes |

Interior Area | 2.665 |

Myhill Property | no |

Balanced | no |

Ridge Tones | [10] |

Propriety | Proper |

Heliotonic | yes |

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 | A♯ | {10,2,5} | 2 | 3 | 1.4 |

Minor Triads | fm | {5,8,0} | 2 | 3 | 1.4 |

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

D+ | {2,6,10} | 1 | 4 | 2 | |

Diminished Triads | d° | {2,5,8} | 2 | 2 | 1.2 |

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 | 4 |
---|---|

Radius | 2 |

Self-Centered | no |

Central Vertices | d° |

Peripheral Vertices | C+, D+ |

Modes are the rotational transformation of this scale. Scale 1397 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1373 | Storian | ||||

3rd mode: Scale 1367 | Leading Whole-Tone Inverse | This is the prime mode | |||

4th mode: Scale 2731 | Neapolitan Major | ||||

5th mode: Scale 3413 | Leading Whole-tone | ||||

6th mode: Scale 1877 | Aeroptian | ||||

7th mode: Scale 1493 | Lydian Minor |

The prime form of this scale is Scale 1367

Scale 1367 | Leading Whole-Tone Inverse |

The heptatonic modal family [1397, 1373, 1367, 2731, 3413, 1877, 1493] (Forte: 7-33) is the complement of the pentatonic modal family [341, 1109, 1301, 1349, 1361] (Forte: 5-33)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1397 is 1493

Scale 1493 | Lydian Minor |

T_{0} | 1397 | T_{0}I | 1493 | |||||

T_{1} | 2794 | T_{1}I | 2986 | |||||

T_{2} | 1493 | T_{2}I | 1877 | |||||

T_{3} | 2986 | T_{3}I | 3754 | |||||

T_{4} | 1877 | T_{4}I | 3413 | |||||

T_{5} | 3754 | T_{5}I | 2731 | |||||

T_{6} | 3413 | T_{6}I | 1367 | |||||

T_{7} | 2731 | T_{7}I | 2734 | |||||

T_{8} | 1367 | T_{8}I | 1373 | |||||

T_{9} | 2734 | T_{9}I | 2746 | |||||

T_{10} | 1373 | T_{10}I | 1397 | |||||

T_{11} | 2746 | T_{11}I | 2794 |

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 1399 | Syryllic | |||

Scale 1393 | Mycrimic | |||

Scale 1395 | Asian (a) | |||

Scale 1401 | Pagian | |||

Scale 1405 | Goryllic | |||

Scale 1381 | Padimic | |||

Scale 1389 | Minor Locrian | |||

Scale 1365 | Whole Tone | |||

Scale 1333 | Lyptimic | |||

Scale 1461 | Major-Minor | |||

Scale 1525 | Sodyllic | |||

Scale 1141 | Rynimic | |||

Scale 1269 | Katythian | |||

Scale 1653 | Minor Romani Inverse | |||

Scale 1909 | Epicryllic | |||

Scale 373 | Epagimic | |||

Scale 885 | Sathian | |||

Scale 2421 | Malian | |||

Scale 3445 | Messiaen Mode 6 Inverse |

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.