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).

- Jazz and Blues
- Blues Minor

- Western Modern
- Phrygian Pentatonic

- Carnatic Raga
- Raga Malkauns
- Raga Malakosh
- Raga Hindola

- Chinese
- Jue
- Juédiào

- Unknown / Unsorted
- Man Gong
- Quan Ming
- Yi Ze
- Jiao

- Ethiopian
- Shegaye

- Zeitler
- Epathitonic

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

Pitch Class Set | {0,3,5,8,10} |

Forte Number | 5-35 |

Rotational Symmetry | none |

Reflection Axes | 4 |

Palindromic | no |

Chirality | no |

Hemitonia | 0 (anhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 1 |

Modes | 4 |

Prime? | no prime: 661 |

Deep Scale | no |

Interval Vector | 032140 |

Interval Spectrum | p^{4}mn^{2}s^{3} |

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

Spectra Variation | 0.8 |

Maximally Even | yes |

Myhill Property | yes |

Balanced | no |

Ridge Tones | [8] |

Propriety | Strictly Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1321 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode: Scale 677 | Scottish Pentatonic | ||||

3rd mode: Scale 1193 | Minor Pentatonic | ||||

4th mode: Scale 661 | Major Pentatonic | This is the prime mode | |||

5th mode: Scale 1189 | Suspended Pentatonic |

The prime form of this scale is Scale 661

Scale 661 | Major Pentatonic |

The pentatonic modal family [1321, 677, 1193, 661, 1189] (Forte: 5-35) is the complement of the heptatonic modal family [1387, 1451, 1453, 1709, 1717, 2741, 2773] (Forte: 7-35)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1321 is 661

Scale 661 | Major Pentatonic |

T_{0} | 1321 | T_{0}I | 661 | |||||

T_{1} | 2642 | T_{1}I | 1322 | |||||

T_{2} | 1189 | T_{2}I | 2644 | |||||

T_{3} | 2378 | T_{3}I | 1193 | |||||

T_{4} | 661 | T_{4}I | 2386 | |||||

T_{5} | 1322 | T_{5}I | 677 | |||||

T_{6} | 2644 | T_{6}I | 1354 | |||||

T_{7} | 1193 | T_{7}I | 2708 | |||||

T_{8} | 2386 | T_{8}I | 1321 | |||||

T_{9} | 677 | T_{9}I | 2642 | |||||

T_{10} | 1354 | T_{10}I | 1189 | |||||

T_{11} | 2708 | T_{11}I | 2378 |

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 1323 | Ritsu | |||

Scale 1325 | Phradimic | |||

Scale 1313 | ||||

Scale 1317 | Chaio | |||

Scale 1329 | Epygitonic | |||

Scale 1337 | Epogimic | |||

Scale 1289 | ||||

Scale 1305 | Dynitonic | |||

Scale 1353 | Raga Harikauns | |||

Scale 1385 | Phracrimic | |||

Scale 1449 | Raga Gopikavasantam | |||

Scale 1065 | ||||

Scale 1193 | Minor Pentatonic | |||

Scale 1577 | Raga Chandrakauns (Kafi) | |||

Scale 1833 | Ionacrimic | |||

Scale 297 | Mynic | |||

Scale 809 | Dogitonic | |||

Scale 2345 | Raga Chandrakauns | |||

Scale 3369 | Mixolimic |

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.