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

Pitch Class Set | {0,1,3,7,9,10} |

Forte Number | 6-Z23 |

Rotational Symmetry | none |

Reflection Axes | 5 |

Palindromic | no |

Chirality | no |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 4 |

Modes | 5 |

Prime? | no prime: 365 |

Deep Scale | no |

Interval Vector | 234222 |

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

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

Spectra Variation | 2.667 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.232 |

Myhill Property | no |

Balanced | no |

Ridge Tones | [10] |

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 | D♯ | {3,7,10} | 2 | 2 | 1 |

Minor Triads | cm | {0,3,7} | 2 | 2 | 1 |

Diminished Triads | g° | {7,10,1} | 1 | 3 | 1.5 |

a° | {9,0,3} | 1 | 3 | 1.5 |

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 | 3 |
---|---|

Radius | 2 |

Self-Centered | no |

Central Vertices | cm, D♯ |

Peripheral Vertices | g°, a° |

Modes are the rotational transformation of this scale. Scale 1675 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 2885 | Byrimic | ||||

3rd mode: Scale 1745 | Raga Vutari | ||||

4th mode: Scale 365 | Marimic | This is the prime mode | |||

5th mode: Scale 1115 | Superlocrian Hexamirror | ||||

6th mode: Scale 2605 | Rylimic |

The prime form of this scale is Scale 365

Scale 365 | Marimic |

The hexatonic modal family [1675, 2885, 1745, 365, 1115, 2605] (Forte: 6-Z23) is the complement of the hexatonic modal family [605, 745, 1175, 1865, 2635, 3365] (Forte: 6-Z45)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1675 is 2605

Scale 2605 | Rylimic |

T_{0} | 1675 | T_{0}I | 2605 | |||||

T_{1} | 3350 | T_{1}I | 1115 | |||||

T_{2} | 2605 | T_{2}I | 2230 | |||||

T_{3} | 1115 | T_{3}I | 365 | |||||

T_{4} | 2230 | T_{4}I | 730 | |||||

T_{5} | 365 | T_{5}I | 1460 | |||||

T_{6} | 730 | T_{6}I | 2920 | |||||

T_{7} | 1460 | T_{7}I | 1745 | |||||

T_{8} | 2920 | T_{8}I | 3490 | |||||

T_{9} | 1745 | T_{9}I | 2885 | |||||

T_{10} | 3490 | T_{10}I | 1675 | |||||

T_{11} | 2885 | T_{11}I | 3350 |

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 1673 | Thocritonic | |||

Scale 1677 | Raga Manavi | |||

Scale 1679 | Kydian | |||

Scale 1667 | ||||

Scale 1671 | ||||

Scale 1683 | Raga Malayamarutam | |||

Scale 1691 | Kathian | |||

Scale 1707 | Dorian Flat 2 | |||

Scale 1739 | Mela Sadvidhamargini | |||

Scale 1547 | ||||

Scale 1611 | Dacrimic | |||

Scale 1803 | ||||

Scale 1931 | Stogian | |||

Scale 1163 | Raga Rukmangi | |||

Scale 1419 | Raga Kashyapi | |||

Scale 651 | Golitonic | |||

Scale 2699 | Sythimic | |||

Scale 3723 | Myptian |

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. Special thanks to Richard Repp for helping with technical accuracy.