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Scale 1347: "Igoian"

Scale 1347: Igoian, 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

Dozenal
Igoian

Analysis

Cardinality

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

5 (pentatonic)

Pitch Class Set

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

{0,1,6,8,10}

Forte Number

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

5-24

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: 2133

Hemitonia

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

1 (unhemitonic)

Cohemitonia

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

0 (ancohemitonic)

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.

3

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.

4

Prime Form

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

no
prime: 171

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 Structure

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

[1, 5, 2, 2, 2]

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.

<1, 3, 1, 2, 2, 1>

Interval Spectrum

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

p2m2ns3dt

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> = {1,2,5}
<2> = {3,4,6,7}
<3> = {5,6,8,9}
<4> = {7,10,11}

Spectra Variation

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

3.2

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.

1.799

Polygon Perimeter

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

5.449

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.

(9, 3, 32)

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♯{6,10,1}000

The following pitch classes are not present in any of the common triads: {0,8}

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 1347 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2721
Scale 2721: Raga Puruhutika, Ian Ring Music TheoryRaga Puruhutika
3rd mode:
Scale 213
Scale 213: Bitian, Ian Ring Music TheoryBitian
4th mode:
Scale 1077
Scale 1077: Govian, Ian Ring Music TheoryGovian
5th mode:
Scale 1293
Scale 1293: Huxian, Ian Ring Music TheoryHuxian

Prime

The prime form of this scale is Scale 171

Scale 171Scale 171: Pruian, Ian Ring Music TheoryPruian

Complement

The pentatonic modal family [1347, 2721, 213, 1077, 1293] (Forte: 5-24) is the complement of the heptatonic modal family [687, 1401, 1509, 1941, 2391, 3243, 3669] (Forte: 7-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1347 is 2133

Scale 2133Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1347 is chiral, and its enantiomorph is scale 2133

Scale 2133Scale 2133: Raga Kumurdaki, Ian Ring Music TheoryRaga Kumurdaki

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> 1347       T0I <11,0> 2133
T1 <1,1> 2694      T1I <11,1> 171
T2 <1,2> 1293      T2I <11,2> 342
T3 <1,3> 2586      T3I <11,3> 684
T4 <1,4> 1077      T4I <11,4> 1368
T5 <1,5> 2154      T5I <11,5> 2736
T6 <1,6> 213      T6I <11,6> 1377
T7 <1,7> 426      T7I <11,7> 2754
T8 <1,8> 852      T8I <11,8> 1413
T9 <1,9> 1704      T9I <11,9> 2826
T10 <1,10> 3408      T10I <11,10> 1557
T11 <1,11> 2721      T11I <11,11> 3114
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 117      T0MI <7,0> 1473
T1M <5,1> 234      T1MI <7,1> 2946
T2M <5,2> 468      T2MI <7,2> 1797
T3M <5,3> 936      T3MI <7,3> 3594
T4M <5,4> 1872      T4MI <7,4> 3093
T5M <5,5> 3744      T5MI <7,5> 2091
T6M <5,6> 3393      T6MI <7,6> 87
T7M <5,7> 2691      T7MI <7,7> 174
T8M <5,8> 1287      T8MI <7,8> 348
T9M <5,9> 2574      T9MI <7,9> 696
T10M <5,10> 1053      T10MI <7,10> 1392
T11M <5,11> 2106      T11MI <7,11> 2784

The transformations that map this set to itself are: T0

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 1345Scale 1345: Iskian, Ian Ring Music TheoryIskian
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
Scale 1355Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 1363Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
Scale 1379Scale 1379: Kycrimic, Ian Ring Music TheoryKycrimic
Scale 1283Scale 1283: Hurian, Ian Ring Music TheoryHurian
Scale 1315Scale 1315: Pyritonic, Ian Ring Music TheoryPyritonic
Scale 1411Scale 1411: Iroian, Ian Ring Music TheoryIroian
Scale 1475Scale 1475: Uffian, Ian Ring Music TheoryUffian
Scale 1091Scale 1091: Pedian, Ian Ring Music TheoryPedian
Scale 1219Scale 1219: Hidian, Ian Ring Music TheoryHidian
Scale 1603Scale 1603: Juxian, Ian Ring Music TheoryJuxian
Scale 1859Scale 1859: Lixian, Ian Ring Music TheoryLixian
Scale 323Scale 323: Cajian, Ian Ring Music TheoryCajian
Scale 835Scale 835: Fecian, Ian Ring Music TheoryFecian
Scale 2371Scale 2371: Omoian, Ian Ring Music TheoryOmoian
Scale 3395Scale 3395: Vepian, Ian Ring Music TheoryVepian

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, and George Howlett for assistance with the Carnatic ragas.