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Scale 1513: "Stathian"

Scale 1513: Stathian, 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

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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
Stathian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,5,6,7,8,10}
Forte Number7-23
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 757
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 701
Deep Scaleno
Interval Vector354351
Interval Spectrump5m3n4s5d3t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsD♯{3,7,10}231.5
G♯{8,0,3}231.5
Minor Triadscm{0,3,7}321.17
d♯m{3,6,10}241.83
fm{5,8,0}142.17
Diminished Triads{0,3,6}231.5
Parsimonious Voice Leading Between Common Triads of Scale 1513. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# G# G# cm->G# d#m->D# fm fm fm->G#

view full size

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.

Diameter4
Radius2
Self-Centeredno
Central Verticescm
Peripheral Verticesd♯m, fm

Modes

Modes are the rotational transformation of this scale. Scale 1513 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 701
Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphianThis is the prime mode
3rd mode:
Scale 1199
Scale 1199: Magian, Ian Ring Music TheoryMagian
4th mode:
Scale 2647
Scale 2647: Dadian, Ian Ring Music TheoryDadian
5th mode:
Scale 3371
Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
6th mode:
Scale 3733
Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
7th mode:
Scale 1957
Scale 1957: Pyrian, Ian Ring Music TheoryPyrian

Prime

The prime form of this scale is Scale 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Complement

The heptatonic modal family [1513, 701, 1199, 2647, 3371, 3733, 1957] (Forte: 7-23) is the complement of the pentatonic modal family [173, 1067, 1441, 1669, 2581] (Forte: 5-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1513 is 757

Scale 757Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1513 is chiral, and its enantiomorph is scale 757

Scale 757Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian

Transformations:

T0 1513  T0I 757
T1 3026  T1I 1514
T2 1957  T2I 3028
T3 3914  T3I 1961
T4 3733  T4I 3922
T5 3371  T5I 3749
T6 2647  T6I 3403
T7 1199  T7I 2711
T8 2398  T8I 1327
T9 701  T9I 2654
T10 1402  T10I 1213
T11 2804  T11I 2426

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 1515Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed
Scale 1517Scale 1517: Sagyllic, Ian Ring Music TheorySagyllic
Scale 1505Scale 1505, Ian Ring Music Theory
Scale 1509Scale 1509: Ragian, Ian Ring Music TheoryRagian
Scale 1521Scale 1521: Stanian, Ian Ring Music TheoryStanian
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
Scale 1481Scale 1481: Zagimic, Ian Ring Music TheoryZagimic
Scale 1497Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1385Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 2025Scale 2025, Ian Ring Music Theory
Scale 489Scale 489: Phrathimic, Ian Ring Music TheoryPhrathimic
Scale 1001Scale 1001: Badian, Ian Ring Music TheoryBadian
Scale 2537Scale 2537: Laptian, Ian Ring Music TheoryLaptian
Scale 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic

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.