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).

- Western Altered
- Dorian Flat 5
- Locrian Natural Sharp 2 Sharp 6

- Jazz and Blues
- Blues Heptatonic

- Turkish
- Makam Karcigar

- Arabic
- Maqam Nahawand Murassah

- Unknown / Unsorted
- Kiourdi ascending
- Kartzihiar

- Zeitler
- Katagian

Cardinality | 7 (heptatonic) |
---|---|

Pitch Class Set | {0,2,3,5,6,9,10} |

Forte Number | 7-32 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1741 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 859 |

Deep Scale | no |

Interval Vector | 335442 |

Interval Spectrum | p^{4}m^{4}n^{5}s^{3}d^{3}t^{2} |

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

Spectra Variation | 1.429 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.549 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Proper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 1645 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1435 | Makam Huzzam | ||||

3rd mode: Scale 2765 | Lydian Diminished | ||||

4th mode: Scale 1715 | Harmonic Minor Inverse | ||||

5th mode: Scale 2905 | Aeolian Flat 1 | ||||

6th mode: Scale 875 | Locrian Double-flat 7 | ||||

7th mode: Scale 2485 | Harmonic Major |

The prime form of this scale is Scale 859

Scale 859 | Ultralocrian |

The heptatonic modal family [1645, 1435, 2765, 1715, 2905, 875, 2485] (Forte: 7-32) is the complement of the pentatonic modal family [595, 665, 805, 1225, 2345] (Forte: 5-32)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1645 is 1741

Scale 1741 | Lydian Diminished |

Only scales that are chiral will have an enantiomorph. Scale 1645 is chiral, and its enantiomorph is scale 1741

Scale 1741 | Lydian Diminished |

T_{0} | 1645 | T_{0}I | 1741 | |||||

T_{1} | 3290 | T_{1}I | 3482 | |||||

T_{2} | 2485 | T_{2}I | 2869 | |||||

T_{3} | 875 | T_{3}I | 1643 | |||||

T_{4} | 1750 | T_{4}I | 3286 | |||||

T_{5} | 3500 | T_{5}I | 2477 | |||||

T_{6} | 2905 | T_{6}I | 859 | |||||

T_{7} | 1715 | T_{7}I | 1718 | |||||

T_{8} | 3430 | T_{8}I | 3436 | |||||

T_{9} | 2765 | T_{9}I | 2777 | |||||

T_{10} | 1435 | T_{10}I | 1459 | |||||

T_{11} | 2870 | T_{11}I | 2918 |

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 1647 | Polyllic | |||

Scale 1641 | Bocrimic | |||

Scale 1643 | Locrian Natural 6 | |||

Scale 1637 | Syptimic | |||

Scale 1653 | Minor Romani Inverse | |||

Scale 1661 | Gonyllic | |||

Scale 1613 | Thylimic | |||

Scale 1629 | Synian | |||

Scale 1581 | Raga Bagesri | |||

Scale 1709 | Dorian | |||

Scale 1773 | Blues Scale II | |||

Scale 1901 | Ionidyllic | |||

Scale 1133 | Stycrimic | |||

Scale 1389 | Minor Locrian | |||

Scale 621 | Pyramid Hexatonic | |||

Scale 2669 | Jeths' Mode | |||

Scale 3693 | Stadyllic |

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.