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Scale 2857: "Stythimic"

Scale 2857: Stythimic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Stythimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,5,8,9,11}
Forte Number6-Z49
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 667
Deep Scaleno
Interval Vector224322
Interval Spectrump2m3n4s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,6,8}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[8]
ProprietyImproper
Heliotonicno

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 TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsF{5,9,0}231.5
G♯{8,0,3}321.17
Minor Triadsfm{5,8,0}321.17
g♯m{8,11,3}231.5
Diminished Triads{5,8,11}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 2857. Created by Ian Ring ©2019 fm fm f°->fm g#m g#m f°->g#m F F fm->F G# G# fm->G# F->a° g#m->G# G#->a°

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesfm, G♯
Peripheral Verticesf°, F, g♯m, a°

Modes

Modes are the rotational transformation of this scale. Scale 2857 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 869
Scale 869: Kothimic, Ian Ring Music TheoryKothimic
3rd mode:
Scale 1241
Scale 1241: Pygimic, Ian Ring Music TheoryPygimic
4th mode:
Scale 667
Scale 667: Rodimic, Ian Ring Music TheoryRodimicThis is the prime mode
5th mode:
Scale 2381
Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
6th mode:
Scale 1619
Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan

Prime

The prime form of this scale is Scale 667

Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic

Complement

The hexatonic modal family [2857, 869, 1241, 667, 2381, 1619] (Forte: 6-Z49) is the complement of the hexatonic modal family [619, 857, 1427, 1613, 2357, 2761] (Forte: 6-Z28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2857 is 667

Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic

Transformations:

T0 2857  T0I 667
T1 1619  T1I 1334
T2 3238  T2I 2668
T3 2381  T3I 1241
T4 667  T4I 2482
T5 1334  T5I 869
T6 2668  T6I 1738
T7 1241  T7I 3476
T8 2482  T8I 2857
T9 869  T9I 1619
T10 1738  T10I 3238
T11 3476  T11I 2381

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 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2849Scale 2849, Ian Ring Music Theory
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic
Scale 2873Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2
Scale 2825Scale 2825, Ian Ring Music Theory
Scale 2841Scale 2841: Sothimic, Ian Ring Music TheorySothimic
Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic
Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian
Scale 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 2601Scale 2601: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2345Scale 2345: Raga Chandrakauns, Ian Ring Music TheoryRaga Chandrakauns
Scale 3369Scale 3369: Mixolimic, Ian Ring Music TheoryMixolimic
Scale 3881Scale 3881: Morian, Ian Ring Music TheoryMorian
Scale 809Scale 809: Dogitonic, Ian Ring Music TheoryDogitonic
Scale 1833Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic

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.