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 Navamanohari

- Zeitler
- Byptimic

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

Pitch Class Set | {0,2,5,7,8,10} |

Forte Number | 6-33 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1205 |

Hemitonia | 1 (unhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 2 |

Modes | 5 |

Prime? | no prime: 685 |

Deep Scale | no |

Interval Vector | 143241 |

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

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

Spectra Variation | 1.667 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.482 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Proper |

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 | A♯ | {10,2,5} | 2 | 2 | 1 |

Minor Triads | fm | {5,8,0} | 1 | 3 | 1.5 |

gm | {7,10,2} | 1 | 3 | 1.5 | |

Diminished Triads | d° | {2,5,8} | 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 | d°, A♯ |

Peripheral Vertices | fm, gm |

Modes are the rotational transformation of this scale. Scale 1445 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 1385 | Phracrimic | ||||

3rd mode: Scale 685 | Raga Suddha Bangala | This is the prime mode | |||

4th mode: Scale 1195 | Raga Gandharavam | ||||

5th mode: Scale 2645 | Raga Mruganandana | ||||

6th mode: Scale 1685 | Zeracrimic |

The prime form of this scale is Scale 685

Scale 685 | Raga Suddha Bangala |

The hexatonic modal family [1445, 1385, 685, 1195, 2645, 1685] (Forte: 6-33) is the complement of the hexatonic modal family [685, 1195, 1385, 1445, 1685, 2645] (Forte: 6-33)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1445 is 1205

Scale 1205 | Raga Siva Kambhoji |

Only scales that are chiral will have an enantiomorph. Scale 1445 is chiral, and its enantiomorph is scale 1205

Scale 1205 | Raga Siva Kambhoji |

T_{0} | 1445 | T_{0}I | 1205 | |||||

T_{1} | 2890 | T_{1}I | 2410 | |||||

T_{2} | 1685 | T_{2}I | 725 | |||||

T_{3} | 3370 | T_{3}I | 1450 | |||||

T_{4} | 2645 | T_{4}I | 2900 | |||||

T_{5} | 1195 | T_{5}I | 1705 | |||||

T_{6} | 2390 | T_{6}I | 3410 | |||||

T_{7} | 685 | T_{7}I | 2725 | |||||

T_{8} | 1370 | T_{8}I | 1355 | |||||

T_{9} | 2740 | T_{9}I | 2710 | |||||

T_{10} | 1385 | T_{10}I | 1325 | |||||

T_{11} | 2770 | T_{11}I | 2650 |

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 1447 | Mela Ratnangi | |||

Scale 1441 | ||||

Scale 1443 | Raga Phenadyuti | |||

Scale 1449 | Raga Gopikavasantam | |||

Scale 1453 | Aeolian | |||

Scale 1461 | Major-Minor | |||

Scale 1413 | ||||

Scale 1429 | Bythimic | |||

Scale 1477 | Raga Jaganmohanam | |||

Scale 1509 | Ragian | |||

Scale 1317 | Chaio | |||

Scale 1381 | Padimic | |||

Scale 1189 | Suspended Pentatonic | |||

Scale 1701 | Dominant Seventh | |||

Scale 1957 | Pyrian | |||

Scale 421 | Han-kumoi | |||

Scale 933 | Dadimic | |||

Scale 2469 | Raga Bhinna Pancama | |||

Scale 3493 | Rathian |

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.