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Scale 3145: "Stolitonic"

Scale 3145: Stolitonic, 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
Stolitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,6,10,11}
Forte Number5-Z38
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 583
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes4
Prime?no
prime: 295
Deep Scaleno
Interval Vector212221
Interval Spectrump2m2n2sd2t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,6,7}
<3> = {5,6,7,8,10}
<4> = {8,9,11}
Spectra Variation3.2
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsB{11,3,6}210.67
Minor Triadsd♯m{3,6,10}121
Diminished Triads{0,3,6}121
Parsimonious Voice Leading Between Common Triads of Scale 3145. Created by Ian Ring ©2019 B B c°->B d#m d#m d#m->B

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.

Diameter2
Radius1
Self-Centeredno
Central VerticesB
Peripheral Verticesc°, d♯m

Modes

Modes are the rotational transformation of this scale. Scale 3145 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 905
Scale 905: Bylitonic, Ian Ring Music TheoryBylitonic
3rd mode:
Scale 625
Scale 625: Ionyptitonic, Ian Ring Music TheoryIonyptitonic
4th mode:
Scale 295
Scale 295: Gyritonic, Ian Ring Music TheoryGyritonicThis is the prime mode
5th mode:
Scale 2195
Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic

Prime

The prime form of this scale is Scale 295

Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic

Complement

The pentatonic modal family [3145, 905, 625, 295, 2195] (Forte: 5-Z38) is the complement of the heptatonic modal family [439, 1763, 1819, 2267, 2929, 2957, 3181] (Forte: 7-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3145 is 583

Scale 583Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3145 is chiral, and its enantiomorph is scale 583

Scale 583Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic

Transformations:

T0 3145  T0I 583
T1 2195  T1I 1166
T2 295  T2I 2332
T3 590  T3I 569
T4 1180  T4I 1138
T5 2360  T5I 2276
T6 625  T6I 457
T7 1250  T7I 914
T8 2500  T8I 1828
T9 905  T9I 3656
T10 1810  T10I 3217
T11 3620  T11I 2339

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 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3149Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
Scale 3137Scale 3137, Ian Ring Music Theory
Scale 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 3153Scale 3153: Zathitonic, Ian Ring Music TheoryZathitonic
Scale 3161Scale 3161: Kodimic, Ian Ring Music TheoryKodimic
Scale 3177Scale 3177: Rothimic, Ian Ring Music TheoryRothimic
Scale 3081Scale 3081, Ian Ring Music Theory
Scale 3113Scale 3113, Ian Ring Music Theory
Scale 3209Scale 3209: Aeraphitonic, Ian Ring Music TheoryAeraphitonic
Scale 3273Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 2121Scale 2121, Ian Ring Music Theory
Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord
Scale 1097Scale 1097: Aeraphic, Ian Ring Music TheoryAeraphic

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.