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
- Pylygic

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

Pitch Class Set | {0,1,2,3,4,6,7,9,10} |

Forte Number | 9-10 |

Rotational Symmetry | none |

Reflection Axes | 2 |

Palindromic | no |

Chirality | no |

Hemitonia | 6 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 3 |

Modes | 8 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 668664 |

Interval Spectrum | p^{6}m^{6}n^{8}s^{6}d^{6}t^{4} |

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

Spectra Variation | 1.333 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [4] |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1759 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 2927 | Rodygic | ||||

3rd mode: Scale 3511 | Epolygic | ||||

4th mode: Scale 3803 | Epidygic | ||||

5th mode: Scale 3949 | Koptygic | ||||

6th mode: Scale 2011 | Raphygic | ||||

7th mode: Scale 3053 | Zycrygic | ||||

8th mode: Scale 1787 | Mycrygic | ||||

9th mode: Scale 2941 | Laptygic |

This is the prime form of this scale.

The nonatonic modal family [1759, 2927, 3511, 3803, 3949, 2011, 3053, 1787, 2941] (Forte: 9-10) is the complement of the tritonic modal family [73, 521, 577] (Forte: 3-10)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1759 is 3949

Scale 3949 | Koptygic |

T_{0} | 1759 | T_{0}I | 3949 | |||||

T_{1} | 3518 | T_{1}I | 3803 | |||||

T_{2} | 2941 | T_{2}I | 3511 | |||||

T_{3} | 1787 | T_{3}I | 2927 | |||||

T_{4} | 3574 | T_{4}I | 1759 | |||||

T_{5} | 3053 | T_{5}I | 3518 | |||||

T_{6} | 2011 | T_{6}I | 2941 | |||||

T_{7} | 4022 | T_{7}I | 1787 | |||||

T_{8} | 3949 | T_{8}I | 3574 | |||||

T_{9} | 3803 | T_{9}I | 3053 | |||||

T_{10} | 3511 | T_{10}I | 2011 | |||||

T_{11} | 2927 | T_{11}I | 4022 |

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 1757 | ||||

Scale 1755 | Octatonic | |||

Scale 1751 | Aeolyryllic | |||

Scale 1743 | Epigyllic | |||

Scale 1775 | Lyrygic | |||

Scale 1791 | Aerygyllian | |||

Scale 1695 | Phrodyllic | |||

Scale 1727 | Sydygic | |||

Scale 1631 | Rynyllic | |||

Scale 1887 | Aerocrygic | |||

Scale 2015 | Messiaen Mode 7 | |||

Scale 1247 | Aeodyllic | |||

Scale 1503 | Epiryllian | |||

Scale 735 | Sylyllic | |||

Scale 2783 | Gothygic | |||

Scale 3807 | Bagyllian |

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.