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).

- Zeitler
- Loptygic

Cardinality | 9 (nonatonic) |
---|---|

Pitch Class Set | {0,3,4,5,6,7,8,10,11} |

Forte Number | 9-4 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1015 |

Hemitonia | 7 (multihemitonic) |

Cohemitonia | 5 (multicohemitonic) |

Imperfections | 2 |

Modes | 8 |

Prime? | no prime: 959 |

Deep Scale | no |

Interval Vector | 766773 |

Interval Spectrum | p^{7}m^{7}n^{6}s^{6}d^{7}t^{3} |

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

Spectra Variation | 2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3577 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 959 | Katylygic | This is the prime mode | |||

3rd mode: Scale 2527 | Phradygic | ||||

4th mode: Scale 3311 | Mixodygic | ||||

5th mode: Scale 3703 | Katalygic | ||||

6th mode: Scale 3899 | Katorygic | ||||

7th mode: Scale 3997 | Dogygic | ||||

8th mode: Scale 2023 | Zodygic | ||||

9th mode: Scale 3059 | Madygic |

The prime form of this scale is Scale 959

Scale 959 | Katylygic |

The nonatonic modal family [3577, 959, 2527, 3311, 3703, 3899, 3997, 2023, 3059] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3577 is 1015

Scale 1015 | Ionodygic |

Only scales that are chiral will have an enantiomorph. Scale 3577 is chiral, and its enantiomorph is scale 1015

Scale 1015 | Ionodygic |

T_{0} | 3577 | T_{0}I | 1015 | |||||

T_{1} | 3059 | T_{1}I | 2030 | |||||

T_{2} | 2023 | T_{2}I | 4060 | |||||

T_{3} | 4046 | T_{3}I | 4025 | |||||

T_{4} | 3997 | T_{4}I | 3955 | |||||

T_{5} | 3899 | T_{5}I | 3815 | |||||

T_{6} | 3703 | T_{6}I | 3535 | |||||

T_{7} | 3311 | T_{7}I | 2975 | |||||

T_{8} | 2527 | T_{8}I | 1855 | |||||

T_{9} | 959 | T_{9}I | 3710 | |||||

T_{10} | 1918 | T_{10}I | 3325 | |||||

T_{11} | 3836 | T_{11}I | 2555 |

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 3579 | Zyphyllian | |||

Scale 3581 | Epocryllian | |||

Scale 3569 | Aeoladyllic | |||

Scale 3573 | Kaptygic | |||

Scale 3561 | Pothyllic | |||

Scale 3545 | Thyptyllic | |||

Scale 3513 | Dydyllic | |||

Scale 3449 | Bacryllic | |||

Scale 3321 | Epagyllic | |||

Scale 3833 | Dycrygic | |||

Scale 4089 | Katoryllian | |||

Scale 2553 | Aeolaptyllic | |||

Scale 3065 | Zothygic | |||

Scale 1529 | Kataryllic |

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.