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Scale 3813: "Aeologyllic"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Aeologyllic
Analysis
| Cardinality | 8 (octatonic) |
|---|---|
| Pitch Class Set | {0,2,5,6,7,9,10,11} |
| Forte Number | 8-14 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 1263 |
| Hemitonia | 5 (multihemitonic) |
| Cohemitonia | 3 (tricohemitonic) |
| Imperfections | 2 |
| Modes | 7 |
| Prime? | no prime: 759 |
| Deep Scale | no |
| Interval Vector | 555562 |
| Interval Spectrum | p6m5n5s5d5t2 |
| Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4,5} <3> = {3,4,5,6} <4> = {5,7} <5> = {6,7,8,9} <6> = {7,8,9,10} <7> = {9,10,11} |
| Spectra Variation | 2.25 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.616 |
| 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 | 1.7 |
| F | {5,9,0} | 2 | 5 | 2.5 | |
| G | {7,11,2} | 2 | 5 | 2.5 | |
| A♯ | {10,2,5} | 3 | 3 | 1.7 | |
| Minor Triads | dm | {2,5,9} | 3 | 4 | 1.9 |
| gm | {7,10,2} | 2 | 4 | 2.1 | |
| bm | {11,2,6} | 3 | 4 | 1.9 | |
| Augmented Triads | D+ | {2,6,10} | 4 | 3 | 1.5 |
| Diminished Triads | f♯° | {6,9,0} | 2 | 4 | 2.3 |
| b° | {11,2,5} | 2 | 4 | 2.1 |
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 | 3 |
| Self-Centered | no |
| Central Vertices | D, D+, A♯ |
| Peripheral Vertices | F, G |
Modes
Modes are the rotational transformation of this scale. Scale 3813 can be rotated to make 7 other scales. The 1st mode is itself.
| 2nd mode: Scale 1977 |  | Dagyllic | |||
| 3rd mode: Scale 759 |  | Katalyllic | This is the prime mode | ||
| 4th mode: Scale 2427 |  | Katoryllic | |||
| 5th mode: Scale 3261 |  | Dodyllic | |||
| 6th mode: Scale 1839 |  | Zogyllic | |||
| 7th mode: Scale 2967 |  | Madyllic | |||
| 8th mode: Scale 3531 |  | Neveseri |
Prime
The prime form of this scale is Scale 759
| Scale 759 | | Katalyllic |
Complement
The octatonic modal family [3813, 1977, 759, 2427, 3261, 1839, 2967, 3531] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 3813 is 1263
| Scale 1263 |  | Stynyllic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 3813 is chiral, and its enantiomorph is scale 1263
| Scale 1263 | | Stynyllic |
Transformations:
| T0 | 3813 | T0I | 1263 | |||||
| T1 | 3531 | T1I | 2526 | |||||
| T2 | 2967 | T2I | 957 | |||||
| T3 | 1839 | T3I | 1914 | |||||
| T4 | 3678 | T4I | 3828 | |||||
| T5 | 3261 | T5I | 3561 | |||||
| T6 | 2427 | T6I | 3027 | |||||
| T7 | 759 | T7I | 1959 | |||||
| T8 | 1518 | T8I | 3918 | |||||
| T9 | 3036 | T9I | 3741 | |||||
| T10 | 1977 | T10I | 3387 | |||||
| T11 | 3954 | T11I | 2679 |
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 3815 |  | Galygic | ||
| Scale 3809 |  | |||
| Scale 3811 |  | Epogyllic | ||
| Scale 3817 |  | Zoryllic | ||
| Scale 3821 |  | Epyrygic | ||
| Scale 3829 |  | Taishikicho | ||
| Scale 3781 |  | Gyphian | ||
| Scale 3797 |  | Rocryllic | ||
| Scale 3749 |  | Raga Sorati | ||
| Scale 3685 |  | Kodian | ||
| Scale 3941 |  | Stathyllic | ||
| Scale 4069 |  | Starygic | ||
| Scale 3301 |  | Chromatic Mixolydian Inverse | ||
| Scale 3557 |  | |||
| Scale 2789 |  | Zolian | ||
| Scale 1765 |  | Lonian |
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.