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Scale 1113: "Locrian Pentatonic 2"
Bracelet Diagram
Tonnetz Diagram
Analysis
| Cardinality | 5 (pentatonic) |
|---|---|
| Pitch Class Set | {0,3,4,6,10} |
| Forte Number | 5-28 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 837 |
| Hemitonia | 1 (unhemitonic) |
| Cohemitonia | 0 (ancohemitonic) |
| Imperfections | 4 |
| Modes | 4 |
| Prime? | no prime: 333 |
| Deep Scale | no |
| Interval Vector | 122212 |
| Interval Spectrum | pm2n2s2dt2 |
| Distribution Spectra | <1> = {1,2,3,4} <2> = {3,4,5,6} <3> = {6,7,8,9} <4> = {8,9,10,11} |
| Spectra Variation | 2.4 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.049 |
| Myhill Property | no |
| Balanced | no |
| Ridge Tones | none |
| Propriety | Improper |
| Heliotonic | no |
Common Triads
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 |
|---|---|---|---|---|---|
| Minor Triads | d♯m | {3,6,10} | 1 | 1 | 0.5 |
| Diminished Triads | c° | {0,3,6} | 1 | 1 | 0.5 |
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 | 1 |
|---|---|
| Radius | 1 |
| Self-Centered | yes |
Modes
Modes are the rotational transformation of this scale. Scale 1113 can be rotated to make 4 other scales. The 1st mode is itself.
| 2nd mode: Scale 651 |  | Golitonic | |||
| 3rd mode: Scale 2373 |  | Dyptitonic | |||
| 4th mode: Scale 1617 |  | Phronitonic | |||
| 5th mode: Scale 357 |  | Banitonic |
Prime
The prime form of this scale is Scale 333
| Scale 333 |  | Bogitonic |
Complement
The pentatonic modal family [1113, 651, 2373, 1617, 357] (Forte: 5-28) is the complement of the heptatonic modal family [747, 1431, 1629, 1881, 2421, 2763, 3429] (Forte: 7-28)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 1113 is 837
| Scale 837 |  | Epaditonic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 1113 is chiral, and its enantiomorph is scale 837
| Scale 837 | | Epaditonic |
Transformations:
| T0 | 1113 | T0I | 837 | |||||
| T1 | 2226 | T1I | 1674 | |||||
| T2 | 357 | T2I | 3348 | |||||
| T3 | 714 | T3I | 2601 | |||||
| T4 | 1428 | T4I | 1107 | |||||
| T5 | 2856 | T5I | 2214 | |||||
| T6 | 1617 | T6I | 333 | |||||
| T7 | 3234 | T7I | 666 | |||||
| T8 | 2373 | T8I | 1332 | |||||
| T9 | 651 | T9I | 2664 | |||||
| T10 | 1302 | T10I | 1233 | |||||
| T11 | 2604 | T11I | 2466 |
Nearby Scales:
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 1115 |  | Superlocrian Hexamirror | ||
| Scale 1117 |  | Raptimic | ||
| Scale 1105 |  | Messiaen Truncated Mode 6 Inverse | ||
| Scale 1109 |  | Kataditonic | ||
| Scale 1097 |  | Aeraphic | ||
| Scale 1129 |  | Raga Jayakauns | ||
| Scale 1145 |  | Zygimic | ||
| Scale 1049 |  | |||
| Scale 1081 |  | |||
| Scale 1177 |  | Garitonic | ||
| Scale 1241 |  | Pygimic | ||
| Scale 1369 |  | Boptimic | ||
| Scale 1625 |  | Lythimic | ||
| Scale 89 |  | |||
| Scale 601 |  | Bycritonic | ||
| Scale 2137 |  | |||
| Scale 3161 |  | Kodimic |
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. Special thanks to Richard Repp for helping with technical accuracy.