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).

- Western Chromatic
- Chromatic Hypolydian

- Hindustani
- Purvi That
- Purvi Theta

- Carnatic Mela
- Mela Kamavardhani

- Carnatic Raga
- Raga Shri

- Unknown / Unsorted
- Pantuvarali
- Basant
- Kasiramakriya
- Suddharamakriya
- Puriya Dhanashri
- Dhipaka
- Pireotikos

- Zeitler
- Stylian

Cardinality | 7 (heptatonic) |
---|---|

Pitch Class Set | {0,1,4,6,7,8,11} |

Forte Number | 7-20 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2419 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 2 |

Modes | 6 |

Prime? | no prime: 743 |

Deep Scale | no |

Interval Vector | 433452 |

Interval Spectrum | p^{5}m^{4}n^{3}s^{3}d^{4}t^{2} |

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

Spectra Variation | 2 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.433 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

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 | C | {0,4,7} | 3 | 2 | 1.17 |

E | {4,8,11} | 2 | 3 | 1.5 | |

Minor Triads | c♯m | {1,4,8} | 2 | 3 | 1.5 |

em | {4,7,11} | 2 | 3 | 1.5 | |

Augmented Triads | C+ | {0,4,8} | 3 | 2 | 1.17 |

Diminished Triads | c♯° | {1,4,7} | 2 | 3 | 1.5 |

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, C+ |

Peripheral Vertices | c♯°, c♯m, em, E |

Modes are the rotational transformation of this scale. Scale 2515 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3305 | Chromatic Hypophrygian | ||||

3rd mode: Scale 925 | Chromatic Hypodorian | ||||

4th mode: Scale 1255 | Chromatic Mixolydian | ||||

5th mode: Scale 2675 | Chromatic Lydian | ||||

6th mode: Scale 3385 | Chromatic Phrygian | ||||

7th mode: Scale 935 | Chromatic Dorian |

The prime form of this scale is Scale 743

Scale 743 | Chromatic Hypophrygian Inverse |

The heptatonic modal family [2515, 3305, 925, 1255, 2675, 3385, 935] (Forte: 7-20) is the complement of the pentatonic modal family [355, 395, 1585, 2225, 2245] (Forte: 5-20)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2515 is 2419

Scale 2419 | Raga Lalita |

Only scales that are chiral will have an enantiomorph. Scale 2515 is chiral, and its enantiomorph is scale 2419

Scale 2419 | Raga Lalita |

T_{0} | 2515 | T_{0}I | 2419 | |||||

T_{1} | 935 | T_{1}I | 743 | |||||

T_{2} | 1870 | T_{2}I | 1486 | |||||

T_{3} | 3740 | T_{3}I | 2972 | |||||

T_{4} | 3385 | T_{4}I | 1849 | |||||

T_{5} | 2675 | T_{5}I | 3698 | |||||

T_{6} | 1255 | T_{6}I | 3301 | |||||

T_{7} | 2510 | T_{7}I | 2507 | |||||

T_{8} | 925 | T_{8}I | 919 | |||||

T_{9} | 1850 | T_{9}I | 1838 | |||||

T_{10} | 3700 | T_{10}I | 3676 | |||||

T_{11} | 3305 | T_{11}I | 3257 |

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 2513 | Aerycrimic | |||

Scale 2517 | Harmonic Lydian | |||

Scale 2519 | Dathyllic | |||

Scale 2523 | Mirage Scale | |||

Scale 2499 | ||||

Scale 2507 | Todi That | |||

Scale 2531 | Danian | |||

Scale 2547 | Raga Ramkali | |||

Scale 2451 | Raga Bauli | |||

Scale 2483 | Double Harmonic | |||

Scale 2387 | Paptimic | |||

Scale 2259 | Raga Mandari | |||

Scale 2771 | Marva That | |||

Scale 3027 | Rythyllic | |||

Scale 3539 | Aeoryllic | |||

Scale 467 | Raga Dhavalangam | |||

Scale 1491 | Mela Namanarayani |

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.