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 | 4 (tetratonic) |
---|---|

Pitch Class Set | {0,3,6,9} |

Forte Number | 4-28 |

Rotational Symmetry | 3, 6, 9 semitones |

Reflection Axes | 0, 1.5, 3, 4.5 |

Palindromic | yes |

Chirality | no |

Hemitonia | 0 (anhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 4 |

Modes | 0 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 004002 |

Interval Spectrum | n^{4}t^{2} |

Distribution Spectra | <1> = {3} <2> = {6} <3> = {9} |

Spectra Variation | 0 |

Maximally Even | yes |

Maximal Area Set | yes |

Interior Area | 2 |

Myhill Property | no |

Balanced | yes |

Ridge Tones | [0,3,6,9] |

Propriety | Strictly Proper |

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 |
---|---|---|---|---|---|

Diminished Triads | c° | {0,3,6} | 2 | 2 | 1 |

d♯° | {3,6,9} | 2 | 2 | 1 | |

f♯° | {6,9,0} | 2 | 2 | 1 | |

a° | {9,0,3} | 2 | 2 | 1 |

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 | 2 |
---|---|

Radius | 2 |

Self-Centered | yes |

Modes are the rotational transformation of this scale. This scale has no modes, becaue any rotation of this scale will produce another copy of itself.

This is the prime form of this scale.

The tetratonic modal family [585] (Forte: 4-28) is the complement of the octatonic modal family [1755, 2925] (Forte: 8-28)

The inverse of a scale is a reflection using the root as its axis. The inverse of 585 is itself, because it is a palindromic scale!

Scale 585 | Diminished Seventh |

T_{0} | 585 | T_{0}I | 585 | |||||

T_{1} | 1170 | T_{1}I | 1170 | |||||

T_{2} | 2340 | T_{2}I | 2340 | |||||

T_{3} | 585 | T_{3}I | 585 | |||||

T_{4} | 1170 | T_{4}I | 1170 | |||||

T_{5} | 2340 | T_{5}I | 2340 | |||||

T_{6} | 585 | T_{6}I | 585 | |||||

T_{7} | 1170 | T_{7}I | 1170 | |||||

T_{8} | 2340 | T_{8}I | 2340 | |||||

T_{9} | 585 | T_{9}I | 585 | |||||

T_{10} | 1170 | T_{10}I | 1170 | |||||

T_{11} | 2340 | T_{11}I | 2340 |

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 587 | Pathitonic | |||

Scale 589 | Ionalitonic | |||

Scale 577 | ||||

Scale 581 | Eporic | |||

Scale 593 | Saric | |||

Scale 601 | Bycritonic | |||

Scale 617 | Katycritonic | |||

Scale 521 | ||||

Scale 553 | Rothic | |||

Scale 649 | Byptic | |||

Scale 713 | Thoptitonic | |||

Scale 841 | Phrothitonic | |||

Scale 73 | ||||

Scale 329 | Mynic | |||

Scale 1097 | Aeraphic | |||

Scale 1609 | Thyritonic | |||

Scale 2633 | Bartók Beta Chord |

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.