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Scale 1239: "Epaptian"

Scale 1239: Epaptian, 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
Epaptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,6,7,10}
Forte Number7-28
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3429
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes6
Prime?no
prime: 747
Deep Scaleno
Interval Vector344433
Interval Spectrump3m4n4s4d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
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 TriadsC{0,4,7}231.88
F♯{6,10,1}331.63
Minor Triadsgm{7,10,2}331.63
Augmented TriadsD+{2,6,10}231.75
Diminished Triadsc♯°{1,4,7}231.88
{4,7,10}231.75
{7,10,1}231.75
a♯°{10,1,4}231.75
Parsimonious Voice Leading Between Common Triads of Scale 1239. Created by Ian Ring ©2019 C C c#° c#° C->c#° C->e° a#° a#° c#°->a#° D+ D+ F# F# D+->F# gm gm D+->gm e°->gm F#->g° F#->a#° g°->gm

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1239 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2667
Scale 2667: Byrian, Ian Ring Music TheoryByrian
3rd mode:
Scale 3381
Scale 3381: Katanian, Ian Ring Music TheoryKatanian
4th mode:
Scale 1869
Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
5th mode:
Scale 1491
Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani
6th mode:
Scale 2793
Scale 2793: Eporian, Ian Ring Music TheoryEporian
7th mode:
Scale 861
Scale 861: Rylian, Ian Ring Music TheoryRylian

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [1239, 2667, 3381, 1869, 1491, 2793, 861] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1239 is 3429

Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1239 is chiral, and its enantiomorph is scale 3429

Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian

Transformations:

T0 1239  T0I 3429
T1 2478  T1I 2763
T2 861  T2I 1431
T3 1722  T3I 2862
T4 3444  T4I 1629
T5 2793  T5I 3258
T6 1491  T6I 2421
T7 2982  T7I 747
T8 1869  T8I 1494
T9 3738  T9I 2988
T10 3381  T10I 1881
T11 2667  T11I 3762

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 1237Scale 1237: Salimic, Ian Ring Music TheorySalimic
Scale 1235Scale 1235: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 1223Scale 1223: Phryptimic, Ian Ring Music TheoryPhryptimic
Scale 1231Scale 1231: Logian, Ian Ring Music TheoryLogian
Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian
Scale 1271Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic
Scale 1175Scale 1175: Epycrimic, Ian Ring Music TheoryEpycrimic
Scale 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic
Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
Scale 215Scale 215, Ian Ring Music Theory
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 2263Scale 2263: Lycrian, Ian Ring Music TheoryLycrian
Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic

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.