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Scale 2637: "Raga Ranjani"
Bracelet Diagram
Tonnetz Diagram
Analysis
| Cardinality | 6 (hexatonic) |
|---|---|
| Pitch Class Set | {0,2,3,6,9,11} |
| Forte Number | 6-27 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 1611 |
| Hemitonia | 2 (dihemitonic) |
| Cohemitonia | 0 (ancohemitonic) |
| Imperfections | 4 |
| Modes | 5 |
| Prime? | no prime: 603 |
| Deep Scale | no |
| Interval Vector | 225222 |
| Interval Spectrum | p2m2n5s2d2t2 |
| Distribution Spectra | <1> = {1,2,3} <2> = {3,4,5,6} <3> = {4,5,6,7,8} <4> = {6,7,8,9} <5> = {9,10,11} |
| Spectra Variation | 2.333 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.366 |
| 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 |
|---|---|---|---|---|---|
| Major Triads | D | {2,6,9} | 3 | 3 | 1.43 |
| B | {11,3,6} | 3 | 3 | 1.43 | |
| Minor Triads | bm | {11,2,6} | 2 | 3 | 1.57 |
| Diminished Triads | c° | {0,3,6} | 2 | 3 | 1.57 |
| d♯° | {3,6,9} | 2 | 3 | 1.57 | |
| f♯° | {6,9,0} | 2 | 3 | 1.57 | |
| a° | {9,0,3} | 2 | 3 | 1.71 |
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 | 3 |
| Self-Centered | yes |
Modes
Modes are the rotational transformation of this scale. Scale 2637 can be rotated to make 5 other scales. The 1st mode is itself.
| 2nd mode: Scale 1683 |  | Raga Malayamarutam | |||
| 3rd mode: Scale 2889 |  | Thoptimic | |||
| 4th mode: Scale 873 |  | Bagimic | |||
| 5th mode: Scale 621 |  | Pyramid Hexatonic | |||
| 6th mode: Scale 1179 |  | Sonimic |
Prime
The prime form of this scale is Scale 603
| Scale 603 |  | Aeolygimic |
Complement
The hexatonic modal family [2637, 1683, 2889, 873, 621, 1179] (Forte: 6-27) is the complement of the hexatonic modal family [603, 729, 1611, 1737, 2349, 2853] (Forte: 6-27)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 2637 is 1611
| Scale 1611 |  | Dacrimic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 2637 is chiral, and its enantiomorph is scale 1611
| Scale 1611 | | Dacrimic |
Transformations:
| T0 | 2637 | T0I | 1611 | |||||
| T1 | 1179 | T1I | 3222 | |||||
| T2 | 2358 | T2I | 2349 | |||||
| T3 | 621 | T3I | 603 | |||||
| T4 | 1242 | T4I | 1206 | |||||
| T5 | 2484 | T5I | 2412 | |||||
| T6 | 873 | T6I | 729 | |||||
| T7 | 1746 | T7I | 1458 | |||||
| T8 | 3492 | T8I | 2916 | |||||
| T9 | 2889 | T9I | 1737 | |||||
| T10 | 1683 | T10I | 3474 | |||||
| T11 | 3366 | T11I | 2853 |
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 2639 |  | Dothian | ||
| Scale 2633 |  | Bartók Beta Chord | ||
| Scale 2635 |  | Gocrimic | ||
| Scale 2629 |  | Raga Shubravarni | ||
| Scale 2645 |  | Raga Mruganandana | ||
| Scale 2653 |  | Sygian | ||
| Scale 2669 |  | Jeths' Mode | ||
| Scale 2573 |  | |||
| Scale 2605 |  | Rylimic | ||
| Scale 2701 |  | Hawaiian | ||
| Scale 2765 |  | Lydian Diminished | ||
| Scale 2893 |  | Lylian | ||
| Scale 2125 |  | |||
| Scale 2381 |  | Takemitsu Linea Mode 1 | ||
| Scale 3149 |  | Phrycrimic | ||
| Scale 3661 |  | Mixodorian | ||
| Scale 589 |  | Ionalitonic | ||
| Scale 1613 |  | Thylimic |
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.