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Scale 1635: "Sygimic"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Sygimic
Analysis
| Cardinality | 6 (hexatonic) |
|---|---|
| Pitch Class Set | {0,1,5,6,9,10} |
| Forte Number | 6-Z19 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 2253 |
| Hemitonia | 3 (trihemitonic) |
| Cohemitonia | 0 (ancohemitonic) |
| Imperfections | 3 |
| Modes | 5 |
| Prime? | no prime: 411 |
| Deep Scale | no |
| Interval Vector | 313431 |
| Interval Spectrum | p3m4n3sd3t |
| Distribution Spectra | <1> = {1,2,3,4} <2> = {3,4,5} <3> = {4,5,6,7,8} <4> = {7,8,9} <5> = {8,9,10,11} |
| Spectra Variation | 2.333 |
| Maximally Even | no |
| Maximal Area Set | no |
| Interior Area | 2.116 |
| 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 | F | {5,9,0} | 2 | 3 | 1.5 |
| F♯ | {6,10,1} | 2 | 3 | 1.5 | |
| Minor Triads | f♯m | {6,9,1} | 3 | 2 | 1.17 |
| a♯m | {10,1,5} | 2 | 3 | 1.5 | |
| Augmented Triads | C♯+ | {1,5,9} | 3 | 2 | 1.17 |
| Diminished Triads | f♯° | {6,9,0} | 2 | 3 | 1.5 |
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 | 3 |
|---|---|
| Radius | 2 |
| Self-Centered | no |
| Central Vertices | C♯+, f♯m |
| Peripheral Vertices | F, f♯°, F♯, a♯m |
Modes
Modes are the rotational transformation of this scale. Scale 1635 can be rotated to make 5 other scales. The 1st mode is itself.
| 2nd mode: Scale 2865 |  | Solimic | |||
| 3rd mode: Scale 435 |  | Raga Purna Pancama | |||
| 4th mode: Scale 2265 |  | Raga Rasamanjari | |||
| 5th mode: Scale 795 |  | Aeologimic | |||
| 6th mode: Scale 2445 |  | Zadimic |
Prime
The prime form of this scale is Scale 411
| Scale 411 |  | Lygimic |
Complement
The hexatonic modal family [1635, 2865, 435, 2265, 795, 2445] (Forte: 6-Z19) is the complement of the hexatonic modal family [615, 825, 915, 2355, 2505, 3225] (Forte: 6-Z44)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 1635 is 2253
| Scale 2253 |  | Raga Amarasenapriya |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 1635 is chiral, and its enantiomorph is scale 2253
| Scale 2253 | | Raga Amarasenapriya |
Transformations:
| T0 | 1635 | T0I | 2253 | |||||
| T1 | 3270 | T1I | 411 | |||||
| T2 | 2445 | T2I | 822 | |||||
| T3 | 795 | T3I | 1644 | |||||
| T4 | 1590 | T4I | 3288 | |||||
| T5 | 3180 | T5I | 2481 | |||||
| T6 | 2265 | T6I | 867 | |||||
| T7 | 435 | T7I | 1734 | |||||
| T8 | 870 | T8I | 3468 | |||||
| T9 | 1740 | T9I | 2841 | |||||
| T10 | 3480 | T10I | 1587 | |||||
| T11 | 2865 | T11I | 3174 |
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 1633 |  | |||
| Scale 1637 |  | Syptimic | ||
| Scale 1639 |  | Aeolothian | ||
| Scale 1643 |  | Locrian Natural 6 | ||
| Scale 1651 |  | Asian | ||
| Scale 1603 |  | |||
| Scale 1619 |  | Prometheus Neapolitan | ||
| Scale 1571 |  | Lagitonic | ||
| Scale 1699 |  | Raga Rasavali | ||
| Scale 1763 |  | Katalian | ||
| Scale 1891 |  | Thalian | ||
| Scale 1123 |  | Iwato | ||
| Scale 1379 |  | Kycrimic | ||
| Scale 611 |  | Anchihoye | ||
| Scale 2659 |  | Katynimic | ||
| Scale 3683 |  | Dycrian |
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.