The Exciting Universe Of Music Theory

presents

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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).

- Carnatic Mela
- Mela Suryakanta
- Mela Suryakantam

- Hindustani
- Bhairubahar That

- Carnatic Raga
- Raga Supradhipam

- Unknown / Unsorted
- Sowrashtram
- Jaganmohini

- Western Modern
- Major-Melodic Phrygian

- Exoticisms
- Hungarian Romani Inverse

- Zeitler
- Zanian

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

Pitch Class Set | {0,1,4,5,7,9,11} |

Forte Number | 7-30 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2475 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 855 |

Deep Scale | no |

Interval Vector | 343542 |

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

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

Spectra Variation | 1.714 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.549 |

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 | 3 | 1.43 |

F | {5,9,0} | 2 | 3 | 1.71 | |

A | {9,1,4} | 3 | 3 | 1.43 | |

Minor Triads | em | {4,7,11} | 1 | 4 | 2.14 |

am | {9,0,4} | 3 | 2 | 1.29 | |

Augmented Triads | C♯+ | {1,5,9} | 2 | 4 | 1.86 |

Diminished Triads | c♯° | {1,4,7} | 2 | 3 | 1.57 |

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 | 4 |
---|---|

Radius | 2 |

Self-Centered | no |

Central Vertices | am |

Peripheral Vertices | C♯+, em |

Modes are the rotational transformation of this scale. Scale 2739 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3417 | Golian | ||||

3rd mode: Scale 939 | Mela Senavati | ||||

4th mode: Scale 2517 | Harmonic Lydian | ||||

5th mode: Scale 1653 | Minor Romani Inverse | ||||

6th mode: Scale 1437 | Sabach ascending | ||||

7th mode: Scale 1383 | Pynian |

The prime form of this scale is Scale 855

Scale 855 | Porian |

The heptatonic modal family [2739, 3417, 939, 2517, 1653, 1437, 1383] (Forte: 7-30) is the complement of the pentatonic modal family [339, 789, 1221, 1329, 2217] (Forte: 5-30)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2739 is 2475

Scale 2475 | Neapolitan Minor |

Only scales that are chiral will have an enantiomorph. Scale 2739 is chiral, and its enantiomorph is scale 2475

Scale 2475 | Neapolitan Minor |

T_{0} | 2739 | T_{0}I | 2475 | |||||

T_{1} | 1383 | T_{1}I | 855 | |||||

T_{2} | 2766 | T_{2}I | 1710 | |||||

T_{3} | 1437 | T_{3}I | 3420 | |||||

T_{4} | 2874 | T_{4}I | 2745 | |||||

T_{5} | 1653 | T_{5}I | 1395 | |||||

T_{6} | 3306 | T_{6}I | 2790 | |||||

T_{7} | 2517 | T_{7}I | 1485 | |||||

T_{8} | 939 | T_{8}I | 2970 | |||||

T_{9} | 1878 | T_{9}I | 1845 | |||||

T_{10} | 3756 | T_{10}I | 3690 | |||||

T_{11} | 3417 | T_{11}I | 3285 |

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 2737 | Raga Hari Nata | |||

Scale 2741 | Major | |||

Scale 2743 | Staptyllic | |||

Scale 2747 | Stythyllic | |||

Scale 2723 | Raga Jivantika | |||

Scale 2731 | Neapolitan Major | |||

Scale 2707 | Banimic | |||

Scale 2771 | Marva That | |||

Scale 2803 | Raga Bhatiyar | |||

Scale 2611 | Raga Vasanta | |||

Scale 2675 | Chromatic Lydian | |||

Scale 2867 | Socrian | |||

Scale 2995 | Raga Saurashtra | |||

Scale 2227 | Raga Gaula | |||

Scale 2483 | Double Harmonic | |||

Scale 3251 | Mela Hatakambari | |||

Scale 3763 | Modyllic | |||

Scale 691 | Raga Kalavati | |||

Scale 1715 | Harmonic Minor Inverse |

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.