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Scale 1655: "Katygyllic"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Katygyllic
Analysis
| Cardinality | 8 (octatonic) |
|---|---|
| Pitch Class Set | {0,1,2,4,5,6,9,10} |
| Forte Number | 8-19 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 3533 |
| Hemitonia | 5 (multihemitonic) |
| Cohemitonia | 2 (dicohemitonic) |
| Imperfections | 3 |
| Modes | 7 |
| Prime? | no prime: 887 |
| Deep Scale | no |
| Interval Vector | 545752 |
| Interval Spectrum | p5m7n5s4d5t2 |
| Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4} <3> = {4,5,6} <4> = {5,6,7} <5> = {6,7,8} <6> = {8,9,10} <7> = {9,10,11} |
| Spectra Variation | 1.75 |
| 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 | 4 | 2.15 |
| F | {5,9,0} | 3 | 4 | 2.08 | |
| F♯ | {6,10,1} | 3 | 4 | 2 | |
| A | {9,1,4} | 3 | 4 | 2.08 | |
| A♯ | {10,2,5} | 3 | 4 | 2.15 | |
| Minor Triads | dm | {2,5,9} | 3 | 3 | 1.92 |
| f♯m | {6,9,1} | 4 | 3 | 1.77 | |
| am | {9,0,4} | 2 | 5 | 2.62 | |
| a♯m | {10,1,5} | 4 | 3 | 1.77 | |
| Augmented Triads | C♯+ | {1,5,9} | 5 | 3 | 1.54 |
| D+ | {2,6,10} | 3 | 5 | 2.38 | |
| Diminished Triads | f♯° | {6,9,0} | 2 | 4 | 2.31 |
| a♯° | {10,1,4} | 2 | 4 | 2.31 |
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 | C♯+, dm, f♯m, a♯m |
| Peripheral Vertices | D+, am |
Modes
Modes are the rotational transformation of this scale. Scale 1655 can be rotated to make 7 other scales. The 1st mode is itself.
| 2nd mode: Scale 2875 |  | Ganyllic | |||
| 3rd mode: Scale 3485 |  | Sabach | |||
| 4th mode: Scale 1895 |  | Salyllic | |||
| 5th mode: Scale 2995 |  | Raga Saurashtra | |||
| 6th mode: Scale 3545 |  | Thyptyllic | |||
| 7th mode: Scale 955 |  | Ionogyllic | |||
| 8th mode: Scale 2525 |  | Aeolaryllic |
Prime
The prime form of this scale is Scale 887
| Scale 887 |  | Sathyllic |
Complement
The octatonic modal family [1655, 2875, 3485, 1895, 2995, 3545, 955, 2525] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 1655 is 3533
| Scale 3533 |  | Thadyllic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 1655 is chiral, and its enantiomorph is scale 3533
| Scale 3533 | | Thadyllic |
Transformations:
| T0 | 1655 | T0I | 3533 | |||||
| T1 | 3310 | T1I | 2971 | |||||
| T2 | 2525 | T2I | 1847 | |||||
| T3 | 955 | T3I | 3694 | |||||
| T4 | 1910 | T4I | 3293 | |||||
| T5 | 3820 | T5I | 2491 | |||||
| T6 | 3545 | T6I | 887 | |||||
| T7 | 2995 | T7I | 1774 | |||||
| T8 | 1895 | T8I | 3548 | |||||
| T9 | 3790 | T9I | 3001 | |||||
| T10 | 3485 | T10I | 1907 | |||||
| T11 | 2875 | T11I | 3814 |
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 1653 |  | Minor Romani Inverse | ||
| Scale 1651 |  | Asian | ||
| Scale 1659 |  | Maqam Shadd'araban | ||
| Scale 1663 |  | Lydygic | ||
| Scale 1639 |  | Aeolothian | ||
| Scale 1647 |  | Polyllic | ||
| Scale 1623 |  | Lothian | ||
| Scale 1591 |  | Rodian | ||
| Scale 1719 |  | Lyryllic | ||
| Scale 1783 |  | Youlan Scale | ||
| Scale 1911 |  | Messiaen Mode 3 | ||
| Scale 1143 |  | Styrian | ||
| Scale 1399 |  | Syryllic | ||
| Scale 631 |  | Zygian | ||
| Scale 2679 |  | Rathyllic | ||
| Scale 3703 |  | Katalygic |
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.