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Scale 3037: "Nine Tone Scale"
Bracelet Diagram
Tonnetz Diagram
Analysis
| Cardinality | 9 (nonatonic) |
|---|---|
| Pitch Class Set | {0,2,3,4,6,7,8,9,11} |
| Forte Number | 9-11 |
| Rotational Symmetry | none |
| Reflection Axes | none |
| Palindromic | no |
| Chirality | yes enantiomorph: 1915 |
| Hemitonia | 6 (multihemitonic) |
| Cohemitonia | 3 (tricohemitonic) |
| Imperfections | 2 |
| Modes | 8 |
| Prime? | no prime: 1775 |
| Deep Scale | no |
| Interval Vector | 667773 |
| Interval Spectrum | p7m7n7s6d6t3 |
| Distribution Spectra | <1> = {1,2} <2> = {2,3} <3> = {3,4,5} <4> = {5,6} <5> = {6,7} <6> = {7,8,9} <7> = {9,10} <8> = {10,11} |
| Spectra Variation | 1.111 |
| Maximally Even | no |
| Maximal Area Set | yes |
| Interior Area | 2.799 |
| Myhill Property | no |
| Balanced | no |
| Ridge Tones | none |
| Propriety | Proper |
| 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 | {0,4,7} | 3 | 4 | 2.44 |
| D | {2,6,9} | 3 | 4 | 2.67 | |
| E | {4,8,11} | 3 | 4 | 2.44 | |
| G | {7,11,2} | 3 | 4 | 2.39 | |
| G♯ | {8,0,3} | 4 | 4 | 2.22 | |
| B | {11,3,6} | 4 | 4 | 2.28 | |
| Minor Triads | cm | {0,3,7} | 4 | 4 | 2.17 |
| em | {4,7,11} | 3 | 4 | 2.39 | |
| g♯m | {8,11,3} | 4 | 4 | 2.17 | |
| am | {9,0,4} | 3 | 4 | 2.56 | |
| bm | {11,2,6} | 3 | 4 | 2.5 | |
| Augmented Triads | C+ | {0,4,8} | 4 | 4 | 2.33 |
| D♯+ | {3,7,11} | 5 | 4 | 2 | |
| Diminished Triads | c° | {0,3,6} | 2 | 4 | 2.56 |
| d♯° | {3,6,9} | 2 | 4 | 2.72 | |
| f♯° | {6,9,0} | 2 | 4 | 2.72 | |
| g♯° | {8,11,2} | 2 | 4 | 2.67 | |
| 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 3037 can be rotated to make 8 other scales. The 1st mode is itself.
| 2nd mode: Scale 1783 |  | Youlan Scale | |||
| 3rd mode: Scale 2939 |  | Goptygic | |||
| 4th mode: Scale 3517 |  | Epocrygic | |||
| 5th mode: Scale 1903 |  | Rocrygic | |||
| 6th mode: Scale 2999 |  | Chromatic and Permuted Diatonic Dorian Mixed | |||
| 7th mode: Scale 3547 |  | Sadygic | |||
| 8th mode: Scale 3821 |  | Epyrygic | |||
| 9th mode: Scale 1979 |  | Aeradygic |
Prime
The prime form of this scale is Scale 1775
| Scale 1775 |  | Lyrygic |
Complement
The nonatonic modal family [3037, 1783, 2939, 3517, 1903, 2999, 3547, 3821, 1979] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)
Inverse
The inverse of a scale is a reflection using the root as its axis. The inverse of 3037 is 1915
| Scale 1915 |  | Thydygic |
Enantiomorph
Only scales that are chiral will have an enantiomorph. Scale 3037 is chiral, and its enantiomorph is scale 1915
| Scale 1915 | | Thydygic |
Transformations:
| T0 | 3037 | T0I | 1915 | |||||
| T1 | 1979 | T1I | 3830 | |||||
| T2 | 3958 | T2I | 3565 | |||||
| T3 | 3821 | T3I | 3035 | |||||
| T4 | 3547 | T4I | 1975 | |||||
| T5 | 2999 | T5I | 3950 | |||||
| T6 | 1903 | T6I | 3805 | |||||
| T7 | 3806 | T7I | 3515 | |||||
| T8 | 3517 | T8I | 2935 | |||||
| T9 | 2939 | T9I | 1775 | |||||
| T10 | 1783 | T10I | 3550 | |||||
| T11 | 3566 | T11I | 3005 |
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 3039 |  | Godyllian | ||
| Scale 3033 |  | Doptyllic | ||
| Scale 3035 |  | Gocrygic | ||
| Scale 3029 |  | Ionocryllic | ||
| Scale 3021 |  | Stodyllic | ||
| Scale 3053 |  | Zycrygic | ||
| Scale 3069 |  | Maqam Shawq Afza | ||
| Scale 2973 |  | Panyllic | ||
| Scale 3005 |  | Gycrygic | ||
| Scale 2909 |  | Mocryllic | ||
| Scale 2781 |  | Gycryllic | ||
| Scale 2525 |  | Aeolaryllic | ||
| Scale 3549 |  | Messiaen Mode 3 Inverse | ||
| Scale 4061 |  | Staptyllian | ||
| Scale 989 |  | Phrolyllic | ||
| Scale 2013 |  | Mocrygic |
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.