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).

- Zeitler
- Ionyptitonic

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

Pitch Class Set | {0,4,5,6,9} |

Forte Number | 5-Z38 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 457 |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 4 |

Prime? | no prime: 295 |

Deep Scale | no |

Interval Vector | 212221 |

Interval Spectrum | p^{2}m^{2}n^{2}sd^{2}t |

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

Spectra Variation | 3.2 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 1.933 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

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 | F | {5,9,0} | 2 | 1 | 0.67 |

Minor Triads | am | {9,0,4} | 1 | 2 | 1 |

Diminished Triads | f♯° | {6,9,0} | 1 | 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 | 1 |

Self-Centered | no |

Central Vertices | F |

Peripheral Vertices | f♯°, am |

Modes are the rotational transformation of this scale. Scale 625 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode: Scale 295 | Gyritonic | This is the prime mode | |||

3rd mode: Scale 2195 | Zalitonic | ||||

4th mode: Scale 3145 | Stolitonic | ||||

5th mode: Scale 905 | Bylitonic |

The prime form of this scale is Scale 295

Scale 295 | Gyritonic |

The pentatonic modal family [625, 295, 2195, 3145, 905] (Forte: 5-Z38) is the complement of the heptatonic modal family [439, 1763, 1819, 2267, 2929, 2957, 3181] (Forte: 7-Z38)

The inverse of a scale is a reflection using the root as its axis. The inverse of 625 is 457

Scale 457 | Staptitonic |

Only scales that are chiral will have an enantiomorph. Scale 625 is chiral, and its enantiomorph is scale 457

Scale 457 | Staptitonic |

T_{0} | 625 | T_{0}I | 457 | |||||

T_{1} | 1250 | T_{1}I | 914 | |||||

T_{2} | 2500 | T_{2}I | 1828 | |||||

T_{3} | 905 | T_{3}I | 3656 | |||||

T_{4} | 1810 | T_{4}I | 3217 | |||||

T_{5} | 3620 | T_{5}I | 2339 | |||||

T_{6} | 3145 | T_{6}I | 583 | |||||

T_{7} | 2195 | T_{7}I | 1166 | |||||

T_{8} | 295 | T_{8}I | 2332 | |||||

T_{9} | 590 | T_{9}I | 569 | |||||

T_{10} | 1180 | T_{10}I | 1138 | |||||

T_{11} | 2360 | T_{11}I | 2276 |

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 627 | Mogimic | |||

Scale 629 | Aeronimic | |||

Scale 633 | Kydimic | |||

Scale 609 | ||||

Scale 617 | Katycritonic | |||

Scale 593 | Saric | |||

Scale 561 | Phratic | |||

Scale 689 | Raga Nagasvaravali | |||

Scale 753 | Aeronimic | |||

Scale 881 | Aerothimic | |||

Scale 113 | ||||

Scale 369 | Laditonic | |||

Scale 1137 | Stonitonic | |||

Scale 1649 | Bolimic | |||

Scale 2673 | Mythimic |

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.