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).

- Carnatic Raga
- Raga Suddha Simantini

- Zeitler
- Zothimic

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

Pitch Class Set | {0,1,3,5,7,8} |

Forte Number | 6-Z26 |

Rotational Symmetry | none |

Reflection Axes | 4 |

Palindromic | no |

Chirality | no |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 2 |

Modes | 5 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 232341 |

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

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

Spectra Variation | 2 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.232 |

Myhill Property | no |

Balanced | no |

Ridge Tones | [8] |

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♯ | {1,5,8} | 1 | 3 | 1.5 |

G♯ | {8,0,3} | 2 | 2 | 1 | |

Minor Triads | cm | {0,3,7} | 1 | 3 | 1.5 |

fm | {5,8,0} | 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 | 3 |
---|---|

Radius | 2 |

Self-Centered | no |

Central Vertices | fm, G♯ |

Peripheral Vertices | cm, C♯ |

Modes are the rotational transformation of this scale. Scale 427 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 2261 | Raga Caturangini | ||||

3rd mode: Scale 1589 | Raga Rageshri | ||||

4th mode: Scale 1421 | Raga Trimurti | ||||

5th mode: Scale 1379 | Kycrimic | ||||

6th mode: Scale 2737 | Raga Hari Nata |

This is the prime form of this scale.

The hexatonic modal family [427, 2261, 1589, 1421, 1379, 2737] (Forte: 6-Z26) is the complement of the hexatonic modal family [679, 917, 1253, 1337, 2387, 3241] (Forte: 6-Z48)

The inverse of a scale is a reflection using the root as its axis. The inverse of 427 is 2737

Scale 2737 | Raga Hari Nata |

T_{0} | 427 | T_{0}I | 2737 | |||||

T_{1} | 854 | T_{1}I | 1379 | |||||

T_{2} | 1708 | T_{2}I | 2758 | |||||

T_{3} | 3416 | T_{3}I | 1421 | |||||

T_{4} | 2737 | T_{4}I | 2842 | |||||

T_{5} | 1379 | T_{5}I | 1589 | |||||

T_{6} | 2758 | T_{6}I | 3178 | |||||

T_{7} | 1421 | T_{7}I | 2261 | |||||

T_{8} | 2842 | T_{8}I | 427 | |||||

T_{9} | 1589 | T_{9}I | 854 | |||||

T_{10} | 3178 | T_{10}I | 1708 | |||||

T_{11} | 2261 | T_{11}I | 3416 |

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 425 | Raga Kokil Pancham | |||

Scale 429 | Koptimic | |||

Scale 431 | Epyrian | |||

Scale 419 | Hon-kumoi-joshi | |||

Scale 423 | Sogimic | |||

Scale 435 | Raga Purna Pancama | |||

Scale 443 | Kothian | |||

Scale 395 | Phrygian Pentatonic | |||

Scale 411 | Lygimic | |||

Scale 459 | Zaptimic | |||

Scale 491 | Aeolyrian | |||

Scale 299 | Raga Chitthakarshini | |||

Scale 363 | Soptimic | |||

Scale 171 | ||||

Scale 683 | Stogimic | |||

Scale 939 | Mela Senavati | |||

Scale 1451 | Phrygian | |||

Scale 2475 | Neapolitan Minor |

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.