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Scale 2397: "Stagian"

Scale 2397: Stagian, 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
Stagian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,6,8,11}
Forte Number7-26
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1875
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 699
Deep Scaleno
Interval Vector344532
Interval Spectrump3m5n4s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.286
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 TriadsE{4,8,11}231.75
G♯{8,0,3}331.5
B{11,3,6}331.5
Minor Triadsg♯m{8,11,3}421.25
bm{11,2,6}242
Augmented TriadsC+{0,4,8}242
Diminished Triads{0,3,6}231.75
g♯°{8,11,2}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2397. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E C+->G# g#m g#m E->g#m g#° g#° g#°->g#m bm bm g#°->bm g#m->G# g#m->B bm->B

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 Verticesg♯m
Peripheral VerticesC+, bm

Modes

Modes are the rotational transformation of this scale. Scale 2397 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1623
Scale 1623: Lothian, Ian Ring Music TheoryLothian
3rd mode:
Scale 2859
Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
4th mode:
Scale 3477
Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
5th mode:
Scale 1893
Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
6th mode:
Scale 1497
Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
7th mode:
Scale 699
Scale 699: Aerothian, Ian Ring Music TheoryAerothianThis is the prime mode

Prime

The prime form of this scale is Scale 699

Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian

Complement

The heptatonic modal family [2397, 1623, 2859, 3477, 1893, 1497, 699] (Forte: 7-26) is the complement of the pentatonic modal family [309, 849, 1101, 1299, 2697] (Forte: 5-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2397 is 1875

Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2397 is chiral, and its enantiomorph is scale 1875

Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale

Transformations:

T0 2397  T0I 1875
T1 699  T1I 3750
T2 1398  T2I 3405
T3 2796  T3I 2715
T4 1497  T4I 1335
T5 2994  T5I 2670
T6 1893  T6I 1245
T7 3786  T7I 2490
T8 3477  T8I 885
T9 2859  T9I 1770
T10 1623  T10I 3540
T11 3246  T11I 2985

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 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 2393Scale 2393: Zathimic, Ian Ring Music TheoryZathimic
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 2389Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
Scale 2381Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2
Scale 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 2333Scale 2333: Stynimic, Ian Ring Music TheoryStynimic
Scale 2365Scale 2365: Sythian, Ian Ring Music TheorySythian
Scale 2461Scale 2461: Sagian, Ian Ring Music TheorySagian
Scale 2525Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
Scale 2141Scale 2141, Ian Ring Music Theory
Scale 2269Scale 2269: Pygian, Ian Ring Music TheoryPygian
Scale 2653Scale 2653: Sygian, Ian Ring Music TheorySygian
Scale 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic
Scale 1373Scale 1373: Storian, Ian Ring Music TheoryStorian

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.