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Scale 2793: "Eporian"

Scale 2793: Eporian, 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

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
Eporian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,3,5,6,7,9,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-28

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 747

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

3 (trihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

1 (uncohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

4

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 747

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[3, 2, 1, 1, 2, 2, 1]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<3, 4, 4, 4, 3, 3>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p3m4n4s4d3t3

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<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 Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.549

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.967

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(6, 33, 96)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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}231.88
B{11,3,6}331.63
Minor Triadscm{0,3,7}331.63
Augmented TriadsD♯+{3,7,11}231.75
Diminished Triads{0,3,6}231.75
d♯°{3,6,9}231.75
f♯°{6,9,0}231.88
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2793. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° d#° d#° f#° f#° d#°->f#° d#°->B D#+->B F F F->f#° F->a°

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 2793 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 861
Scale 861: Rylian, Ian Ring Music TheoryRylian
3rd mode:
Scale 1239
Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
4th mode:
Scale 2667
Scale 2667: Byrian, Ian Ring Music TheoryByrian
5th mode:
Scale 3381
Scale 3381: Katanian, Ian Ring Music TheoryKatanian
6th mode:
Scale 1869
Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
7th mode:
Scale 1491
Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [2793, 861, 1239, 2667, 3381, 1869, 1491] (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 2793 is 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2793 is chiral, and its enantiomorph is scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 2793       T0I <11,0> 747
T1 <1,1> 1491      T1I <11,1> 1494
T2 <1,2> 2982      T2I <11,2> 2988
T3 <1,3> 1869      T3I <11,3> 1881
T4 <1,4> 3738      T4I <11,4> 3762
T5 <1,5> 3381      T5I <11,5> 3429
T6 <1,6> 2667      T6I <11,6> 2763
T7 <1,7> 1239      T7I <11,7> 1431
T8 <1,8> 2478      T8I <11,8> 2862
T9 <1,9> 861      T9I <11,9> 1629
T10 <1,10> 1722      T10I <11,10> 3258
T11 <1,11> 3444      T11I <11,11> 2421
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2763      T0MI <7,0> 2667
T1M <5,1> 1431      T1MI <7,1> 1239
T2M <5,2> 2862      T2MI <7,2> 2478
T3M <5,3> 1629      T3MI <7,3> 861
T4M <5,4> 3258      T4MI <7,4> 1722
T5M <5,5> 2421      T5MI <7,5> 3444
T6M <5,6> 747      T6MI <7,6> 2793
T7M <5,7> 1494      T7MI <7,7> 1491
T8M <5,8> 2988      T8MI <7,8> 2982
T9M <5,9> 1881      T9MI <7,9> 1869
T10M <5,10> 3762      T10MI <7,10> 3738
T11M <5,11> 3429      T11MI <7,11> 3381

The transformations that map this set to itself are: T0, T6MI

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 2795Scale 2795: Van der Horst Octatonic, Ian Ring Music TheoryVan der Horst Octatonic
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
Scale 2785Scale 2785, Ian Ring Music Theory
Scale 2789Scale 2789: Zolian, Ian Ring Music TheoryZolian
Scale 2801Scale 2801: Zogian, Ian Ring Music TheoryZogian
Scale 2809Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 2777Scale 2777: Aeolian Harmonic, Ian Ring Music TheoryAeolian Harmonic
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2665Scale 2665: Aeradimic, Ian Ring Music TheoryAeradimic
Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 2281Scale 2281: Rathimic, Ian Ring Music TheoryRathimic
Scale 2537Scale 2537: Laptian, Ian Ring Music TheoryLaptian
Scale 3305Scale 3305: Chromatic Hypophrygian, Ian Ring Music TheoryChromatic Hypophrygian
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 745Scale 745: Kolimic, Ian Ring Music TheoryKolimic
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. All other diagrams and visualizations are © Ian Ring. 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.