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Scale 1917: "Sacrygic"
Bracelet Diagram
Tonnetz Diagram
Common Names
- Zeitler
- Sacrygic
Analysis
| Cardinality | 9 (nonatonic) |
|---|---|
| Pitch Class Set | {0,2,3,4,5,6,8,9,10} |
| Forte Number | 9-8 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 2013 |
| Hemitonia | 6 (multihemitonic) |
| Cohemitonia | 4 (multicohemitonic) |
| Imperfections | 3 |
| Modes | 8 |
| Prime? | no prime: 1503 |
| Deep Scale | no |
| Interval Vector | 676764 |
| Interval Spectrum | p6m7n6s7d6t4 |
| Distribution Spectra | <1> = {1,2} <2> = {2,3,4} <3> = {3,4,5} <4> = {4,5,6} <5> = {6,7,8} <6> = {7,8,9} <7> = {8,9,10} <8> = {10,11} |
| Spectra Variation | 1.556 |
| Maximally Even | no |
| Maximal Area Set | yes |
| Interior Area | 2.799 |
| 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} | 4 | 4 | 2.2 |
| F | {5,9,0} | 4 | 4 | 2.07 | |
| G♯ | {8,0,3} | 3 | 4 | 2.47 | |
| A♯ | {10,2,5} | 2 | 4 | 2.47 | |
| Minor Triads | dm | {2,5,9} | 4 | 4 | 2.07 |
| d♯m | {3,6,10} | 3 | 4 | 2.47 | |
| fm | {5,8,0} | 3 | 4 | 2.33 | |
| am | {9,0,4} | 3 | 4 | 2.33 | |
| Augmented Triads | C+ | {0,4,8} | 3 | 4 | 2.4 |
| D+ | {2,6,10} | 3 | 4 | 2.4 | |
| Diminished Triads | c° | {0,3,6} | 2 | 4 | 2.53 |
| d° | {2,5,8} | 2 | 4 | 2.47 | |
| d♯° | {3,6,9} | 2 | 4 | 2.53 | |
| f♯° | {6,9,0} | 2 | 4 | 2.33 | |
| a° | {9,0,3} | 2 | 4 | 2.67 |
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 | 4 |
|---|---|
| Radius | 4 |
| Self-Centered | yes |
Modes
Modes are the rotational transformation of this scale. Scale 1917 can be rotated to make 8 other scales. The 1st mode is itself.
| 2nd mode: Scale 1503 |  | Padygic | This is the prime mode | ||
| 3rd mode: Scale 2799 |  | Epilygic | |||
| 4th mode: Scale 3447 |  | Kynygic | |||
| 5th mode: Scale 3771 |  | Stophygic | |||
| 6th mode: Scale 3933 |  | Ionidygic | |||
| 7th mode: Scale 2007 |  | Stonygic | |||
| 8th mode: Scale 3051 |  | Stalygic | |||
| 9th mode: Scale 3573 |  | Kaptygic |
Prime
The prime form of this scale is Scale 1503
| Scale 1503 | | Padygic |
Complement
The nonatonic modal family [1917, 1503, 2799, 3447, 3771, 3933, 2007, 3051, 3573] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 1917 is 2013
| Scale 2013 |  | Mocrygic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 1917 is chiral, and its enantiomorph is scale 2013
| Scale 2013 | | Mocrygic |
Transformations:
| T0 | 1917 | T0I | 2013 | |||||
| T1 | 3834 | T1I | 4026 | |||||
| T2 | 3573 | T2I | 3957 | |||||
| T3 | 3051 | T3I | 3819 | |||||
| T4 | 2007 | T4I | 3543 | |||||
| T5 | 4014 | T5I | 2991 | |||||
| T6 | 3933 | T6I | 1887 | |||||
| T7 | 3771 | T7I | 3774 | |||||
| T8 | 3447 | T8I | 3453 | |||||
| T9 | 2799 | T9I | 2811 | |||||
| T10 | 1503 | T10I | 1527 | |||||
| T11 | 3006 | T11I | 3054 |
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 1919 |  | Rocryllian | ||
| Scale 1913 |  | |||
| Scale 1915 |  | Thydygic | ||
| Scale 1909 |  | Epicryllic | ||
| Scale 1901 |  | Ionidyllic | ||
| Scale 1885 |  | Saptyllic | ||
| Scale 1853 |  | Maryllic | ||
| Scale 1981 |  | Houseini | ||
| Scale 2045 |  | Katogyllian | ||
| Scale 1661 |  | Gonyllic | ||
| Scale 1789 |  | Blues Enneatonic II | ||
| Scale 1405 |  | Goryllic | ||
| Scale 893 |  | Dadyllic | ||
| Scale 2941 |  | Laptygic | ||
| Scale 3965 |  | Messiaen Mode 7 Inverse |
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.