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Scale 3895: "Eparygic"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Eparygic
Analysis
| Cardinality | 9 (nonatonic) |
|---|---|
| Pitch Class Set | {0,1,2,4,5,8,9,10,11} |
| Forte Number | 9-3 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 3487 |
| Hemitonia | 7 (multihemitonic) |
| Cohemitonia | 5 (multicohemitonic) |
| Imperfections | 3 |
| Modes | 8 |
| Prime? | no prime: 895 |
| Deep Scale | no |
| Interval Vector | 767763 |
| Interval Spectrum | p6m7n7s6d7t3 |
| Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4} <3> = {3,4,5,6} <4> = {4,5,6,7} <5> = {5,6,7,8} <6> = {6,7,8,9} <7> = {8,9,10} <8> = {9,10,11} |
| Spectra Variation | 2.222 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.683 |
| 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 | C♯ | {1,5,8} | 4 | 4 | 2.12 |
| E | {4,8,11} | 3 | 4 | 2.53 | |
| F | {5,9,0} | 3 | 4 | 2.24 | |
| A | {9,1,4} | 4 | 4 | 2.24 | |
| A♯ | {10,2,5} | 3 | 4 | 2.53 | |
| Minor Triads | c♯m | {1,4,8} | 3 | 4 | 2.24 |
| dm | {2,5,9} | 3 | 4 | 2.35 | |
| fm | {5,8,0} | 4 | 4 | 2.24 | |
| am | {9,0,4} | 3 | 4 | 2.35 | |
| a♯m | {10,1,5} | 3 | 4 | 2.35 | |
| Augmented Triads | C+ | {0,4,8} | 4 | 4 | 2.24 |
| C♯+ | {1,5,9} | 5 | 4 | 2 | |
| Diminished Triads | d° | {2,5,8} | 2 | 4 | 2.59 |
| f° | {5,8,11} | 2 | 5 | 2.71 | |
| g♯° | {8,11,2} | 2 | 4 | 2.76 | |
| a♯° | {10,1,4} | 2 | 5 | 2.71 | |
| b° | {11,2,5} | 2 | 4 | 2.76 |
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 | 5 |
|---|---|
| Radius | 4 |
| Self-Centered | no |
| Central Vertices | C+, c♯m, C♯, C♯+, d°, dm, E, fm, F, g♯°, am, A, a♯m, A♯, b° |
| Peripheral Vertices | f°, a♯° |
Modes
Modes are the rotational transformation of this scale. Scale 3895 can be rotated to make 8 other scales. The 1st mode is itself.
| 2nd mode: Scale 3995 |  | Ionygic | |||
| 3rd mode: Scale 4045 |  | Gyptygic | |||
| 4th mode: Scale 2035 |  | Aerythygic | |||
| 5th mode: Scale 3065 |  | Zothygic | |||
| 6th mode: Scale 895 |  | Aeolathygic | This is the prime mode | ||
| 7th mode: Scale 2495 |  | Aeolocrygic | |||
| 8th mode: Scale 3295 |  | Phroptygic | |||
| 9th mode: Scale 3695 |  | Kodygic |
Prime
The prime form of this scale is Scale 895
| Scale 895 | | Aeolathygic |
Complement
The nonatonic modal family [3895, 3995, 4045, 2035, 3065, 895, 2495, 3295, 3695] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 3895 is 3487
| Scale 3487 |  | Byptygic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 3895 is chiral, and its enantiomorph is scale 3487
| Scale 3487 | | Byptygic |
Transformations:
| T0 | 3895 | T0I | 3487 | |||||
| T1 | 3695 | T1I | 2879 | |||||
| T2 | 3295 | T2I | 1663 | |||||
| T3 | 2495 | T3I | 3326 | |||||
| T4 | 895 | T4I | 2557 | |||||
| T5 | 1790 | T5I | 1019 | |||||
| T6 | 3580 | T6I | 2038 | |||||
| T7 | 3065 | T7I | 4076 | |||||
| T8 | 2035 | T8I | 4057 | |||||
| T9 | 4070 | T9I | 4019 | |||||
| T10 | 4045 | T10I | 3943 | |||||
| T11 | 3995 | T11I | 3791 |
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 3893 |  | Phrocryllic | ||
| Scale 3891 |  | Ryryllic | ||
| Scale 3899 |  | Katorygic | ||
| Scale 3903 |  | Aeogyllian | ||
| Scale 3879 |  | Pathyllic | ||
| Scale 3887 |  | Phrathygic | ||
| Scale 3863 |  | Eparyllic | ||
| Scale 3927 |  | Monygic | ||
| Scale 3959 |  | Katagyllian | ||
| Scale 4023 |  | Styptyllian | ||
| Scale 3639 |  | Paptyllic | ||
| Scale 3767 |  | Chromatic Bebop | ||
| Scale 3383 |  | Zoptyllic | ||
| Scale 2871 |  | Stanyllic | ||
| Scale 1847 |  | Thacryllic |
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.