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 Gaula

- Zeitler
- Katadimic

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

Pitch Class Set | {0,1,4,5,7,11} |

Forte Number | 6-Z43 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2467 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 5 |

Prime? | no prime: 359 |

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> = {2,3,4,5,6} <3> = {5,6,7} <4> = {6,7,8,9,10} <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 | 1 | 0.67 |

Minor Triads | em | {4,7,11} | 1 | 2 | 1 |

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

Self-Centered | no |

Central Vertices | C |

Peripheral Vertices | c♯°, em |

Modes are the rotational transformation of this scale. Scale 2227 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 3161 | Kodimic | ||||

3rd mode: Scale 907 | Tholimic | ||||

4th mode: Scale 2501 | Ralimic | ||||

5th mode: Scale 1649 | Bolimic | ||||

6th mode: Scale 359 | Bothimic | This is the prime mode |

The prime form of this scale is Scale 359

Scale 359 | Bothimic |

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

The inverse of a scale is a reflection using the root as its axis. The inverse of 2227 is 2467

Scale 2467 | Raga Padi |

Only scales that are chiral will have an enantiomorph. Scale 2227 is chiral, and its enantiomorph is scale 2467

Scale 2467 | Raga Padi |

T_{0} | 2227 | T_{0}I | 2467 | |||||

T_{1} | 359 | T_{1}I | 839 | |||||

T_{2} | 718 | T_{2}I | 1678 | |||||

T_{3} | 1436 | T_{3}I | 3356 | |||||

T_{4} | 2872 | T_{4}I | 2617 | |||||

T_{5} | 1649 | T_{5}I | 1139 | |||||

T_{6} | 3298 | T_{6}I | 2278 | |||||

T_{7} | 2501 | T_{7}I | 461 | |||||

T_{8} | 907 | T_{8}I | 922 | |||||

T_{9} | 1814 | T_{9}I | 1844 | |||||

T_{10} | 3628 | T_{10}I | 3688 | |||||

T_{11} | 3161 | T_{11}I | 3281 |

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 2225 | Ionian Pentatonic | |||

Scale 2229 | Raga Nalinakanti | |||

Scale 2231 | Macrian | |||

Scale 2235 | Bathian | |||

Scale 2211 | Raga Gauri | |||

Scale 2219 | Phrydimic | |||

Scale 2195 | Zalitonic | |||

Scale 2259 | Raga Mandari | |||

Scale 2291 | Zydian | |||

Scale 2099 | Raga Megharanji | |||

Scale 2163 | ||||

Scale 2355 | Raga Lalita | |||

Scale 2483 | Double Harmonic | |||

Scale 2739 | Mela Suryakanta | |||

Scale 3251 | Mela Hatakambari | |||

Scale 179 | ||||

Scale 1203 | Pagimic |

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.