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).

Cardinality | 5 (pentatonic) |
---|---|

Pitch Class Set | {0,2,6,7,11} |

Forte Number | 5-20 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1123 |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 2 |

Modes | 4 |

Prime? | no prime: 355 |

Deep Scale | no |

Interval Vector | 211231 |

Interval Spectrum | p^{3}m^{2}nsd^{2}t |

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

Spectra Variation | 2.4 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 1.799 |

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 | G | {7,11,2} | 1 | 1 | 0.5 |

Minor Triads | bm | {11,2,6} | 1 | 1 | 0.5 |

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 | 1 |
---|---|

Radius | 1 |

Self-Centered | yes |

Modes are the rotational transformation of this scale. Scale 2245 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode: Scale 1585 | Raga Khamaji Durga | ||||

3rd mode: Scale 355 | Aeoloritonic | This is the prime mode | |||

4th mode: Scale 2225 | Ionian Pentatonic | ||||

5th mode: Scale 395 | Phrygian Pentatonic |

The prime form of this scale is Scale 355

Scale 355 | Aeoloritonic |

The pentatonic modal family [2245, 1585, 355, 2225, 395] (Forte: 5-20) is the complement of the heptatonic modal family [743, 919, 1849, 2419, 2507, 3257, 3301] (Forte: 7-20)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2245 is 1123

Scale 1123 | Iwato |

Only scales that are chiral will have an enantiomorph. Scale 2245 is chiral, and its enantiomorph is scale 1123

Scale 1123 | Iwato |

T_{0} | 2245 | T_{0}I | 1123 | |||||

T_{1} | 395 | T_{1}I | 2246 | |||||

T_{2} | 790 | T_{2}I | 397 | |||||

T_{3} | 1580 | T_{3}I | 794 | |||||

T_{4} | 3160 | T_{4}I | 1588 | |||||

T_{5} | 2225 | T_{5}I | 3176 | |||||

T_{6} | 355 | T_{6}I | 2257 | |||||

T_{7} | 710 | T_{7}I | 419 | |||||

T_{8} | 1420 | T_{8}I | 838 | |||||

T_{9} | 2840 | T_{9}I | 1676 | |||||

T_{10} | 1585 | T_{10}I | 3352 | |||||

T_{11} | 3170 | T_{11}I | 2609 |

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 2247 | Raga Vijayasri | |||

Scale 2241 | ||||

Scale 2243 | ||||

Scale 2249 | Raga Multani | |||

Scale 2253 | Raga Amarasenapriya | |||

Scale 2261 | Raga Caturangini | |||

Scale 2277 | Kagimic | |||

Scale 2181 | ||||

Scale 2213 | Raga Desh | |||

Scale 2117 | Raga Sumukam | |||

Scale 2373 | Dyptitonic | |||

Scale 2501 | Ralimic | |||

Scale 2757 | Raga Nishadi | |||

Scale 3269 | Raga Malarani | |||

Scale 197 | ||||

Scale 1221 | Epyritonic |

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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.