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).

- Zeitler
- Epyritonic

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

Pitch Class Set | {0,2,6,7,10} |

Forte Number | 5-30 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1125 |

Hemitonia | 1 (unhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 3 |

Modes | 4 |

Prime? | no prime: 339 |

Deep Scale | no |

Interval Vector | 121321 |

Interval Spectrum | p^{2}m^{3}ns^{2}dt |

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

Spectra Variation | 2 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.049 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1221 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode: Scale 1329 | Epygitonic | ||||

3rd mode: Scale 339 | Zaptitonic | This is the prime mode | |||

4th mode: Scale 2217 | Kagitonic | ||||

5th mode: Scale 789 | Zogitonic |

The prime form of this scale is Scale 339

Scale 339 | Zaptitonic |

The pentatonic modal family [1221, 1329, 339, 2217, 789] (Forte: 5-30) is the complement of the heptatonic modal family [855, 1395, 1485, 1845, 2475, 2745, 3285] (Forte: 7-30)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1221 is 1125

Scale 1125 | Ionaritonic |

Only scales that are chiral will have an enantiomorph. Scale 1221 is chiral, and its enantiomorph is scale 1125

Scale 1125 | Ionaritonic |

T_{0} | 1221 | T_{0}I | 1125 | |||||

T_{1} | 2442 | T_{1}I | 2250 | |||||

T_{2} | 789 | T_{2}I | 405 | |||||

T_{3} | 1578 | T_{3}I | 810 | |||||

T_{4} | 3156 | T_{4}I | 1620 | |||||

T_{5} | 2217 | T_{5}I | 3240 | |||||

T_{6} | 339 | T_{6}I | 2385 | |||||

T_{7} | 678 | T_{7}I | 675 | |||||

T_{8} | 1356 | T_{8}I | 1350 | |||||

T_{9} | 2712 | T_{9}I | 2700 | |||||

T_{10} | 1329 | T_{10}I | 1305 | |||||

T_{11} | 2658 | T_{11}I | 2610 |

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 1223 | Phryptimic | |||

Scale 1217 | ||||

Scale 1219 | ||||

Scale 1225 | Raga Samudhra Priya | |||

Scale 1229 | Raga Simharava | |||

Scale 1237 | Salimic | |||

Scale 1253 | Zolimic | |||

Scale 1157 | ||||

Scale 1189 | Suspended Pentatonic | |||

Scale 1093 | Lydic | |||

Scale 1349 | Tholitonic | |||

Scale 1477 | Raga Jaganmohanam | |||

Scale 1733 | Raga Sarasvati | |||

Scale 197 | ||||

Scale 709 | Raga Shri Kalyan | |||

Scale 2245 | Raga Vaijayanti | |||

Scale 3269 | Raga Malarani |

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.