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
- Phracrimic

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

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

Forte Number | 6-33 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 725 |

Hemitonia | 1 (unhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 2 |

Modes | 5 |

Prime? | no prime: 685 |

Deep Scale | no |

Interval Vector | 143241 |

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

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

Spectra Variation | 1.667 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.482 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | 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 |
---|---|---|---|---|---|

Major Triads | G♯ | {8,0,3} | 2 | 2 | 1 |

Minor Triads | d♯m | {3,6,10} | 1 | 3 | 1.5 |

fm | {5,8,0} | 1 | 3 | 1.5 | |

Diminished Triads | c° | {0,3,6} | 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 | 3 |
---|---|

Radius | 2 |

Self-Centered | no |

Central Vertices | c°, G♯ |

Peripheral Vertices | d♯m, fm |

Modes are the rotational transformation of this scale. Scale 1385 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 685 | Raga Suddha Bangala | This is the prime mode | |||

3rd mode: Scale 1195 | Raga Gandharavam | ||||

4th mode: Scale 2645 | Raga Mruganandana | ||||

5th mode: Scale 1685 | Zeracrimic | ||||

6th mode: Scale 1445 | Raga Navamanohari |

The prime form of this scale is Scale 685

Scale 685 | Raga Suddha Bangala |

The hexatonic modal family [1385, 685, 1195, 2645, 1685, 1445] (Forte: 6-33) is the complement of the hexatonic modal family [685, 1195, 1385, 1445, 1685, 2645] (Forte: 6-33)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1385 is 725

Scale 725 | Raga Yamuna Kalyani |

Only scales that are chiral will have an enantiomorph. Scale 1385 is chiral, and its enantiomorph is scale 725

Scale 725 | Raga Yamuna Kalyani |

T_{0} | 1385 | T_{0}I | 725 | |||||

T_{1} | 2770 | T_{1}I | 1450 | |||||

T_{2} | 1445 | T_{2}I | 2900 | |||||

T_{3} | 2890 | T_{3}I | 1705 | |||||

T_{4} | 1685 | T_{4}I | 3410 | |||||

T_{5} | 3370 | T_{5}I | 2725 | |||||

T_{6} | 2645 | T_{6}I | 1355 | |||||

T_{7} | 1195 | T_{7}I | 2710 | |||||

T_{8} | 2390 | T_{8}I | 1325 | |||||

T_{9} | 685 | T_{9}I | 2650 | |||||

T_{10} | 1370 | T_{10}I | 1205 | |||||

T_{11} | 2740 | T_{11}I | 2410 |

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 1387 | Locrian | |||

Scale 1389 | Minor Locrian | |||

Scale 1377 | ||||

Scale 1381 | Padimic | |||

Scale 1393 | Mycrimic | |||

Scale 1401 | Pagian | |||

Scale 1353 | Raga Harikauns | |||

Scale 1369 | Boptimic | |||

Scale 1321 | Blues Minor | |||

Scale 1449 | Raga Gopikavasantam | |||

Scale 1513 | Stathian | |||

Scale 1129 | Raga Jayakauns | |||

Scale 1257 | Blues Scale | |||

Scale 1641 | Bocrimic | |||

Scale 1897 | Ionopian | |||

Scale 361 | Bocritonic | |||

Scale 873 | Bagimic | |||

Scale 2409 | Zacrimic | |||

Scale 3433 | Thonian |

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.