The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2901: "Lydian Augmented"

Scale 2901: Lydian Augmented, 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

Western Modern
Lydian Augmented
Western Altered
Lydian Sharp 5
Zeitler
Larian
Dozenal
Hinian

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

{0,2,4,6,8,9,11}

Forte Number

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

7-34

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.

[4]

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.

no

Hemitonia

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

2 (dihemitonic)

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.

6

Prime Form

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

no
prime: 1371

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.

[2, 2, 2, 2, 1, 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.

<2, 5, 4, 4, 4, 2>

Interval Spectrum

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

p4m4n4s5d2t2

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

Spectra Variation

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

1.143

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.

yes

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.

2.665

Polygon Perimeter

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

6.035

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.

[8]

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".

Proper

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.

(0, 10, 72)

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 TriadsD{2,6,9}231.71
E{4,8,11}231.71
Minor Triadsam{9,0,4}231.71
bm{11,2,6}231.71
Augmented TriadsC+{0,4,8}231.71
Diminished Triadsf♯°{6,9,0}231.71
g♯°{8,11,2}231.71
Parsimonious Voice Leading Between Common Triads of Scale 2901. Created by Ian Ring ©2019 C+ C+ E E C+->E am am C+->am D D f#° f#° D->f#° bm bm D->bm g#° g#° E->g#° f#°->am g#°->bm

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 2901 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1749
Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
3rd mode:
Scale 1461
Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
4th mode:
Scale 1389
Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
5th mode:
Scale 1371
Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrianThis is the prime mode
6th mode:
Scale 2733
Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
7th mode:
Scale 1707
Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2

Prime

The prime form of this scale is Scale 1371

Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian

Complement

The heptatonic modal family [2901, 1749, 1461, 1389, 1371, 2733, 1707] (Forte: 7-34) is the complement of the pentatonic modal family [597, 681, 1173, 1317, 1353] (Forte: 5-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2901 is 1371

Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian

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> 2901       T0I <11,0> 1371
T1 <1,1> 1707      T1I <11,1> 2742
T2 <1,2> 3414      T2I <11,2> 1389
T3 <1,3> 2733      T3I <11,3> 2778
T4 <1,4> 1371      T4I <11,4> 1461
T5 <1,5> 2742      T5I <11,5> 2922
T6 <1,6> 1389      T6I <11,6> 1749
T7 <1,7> 2778      T7I <11,7> 3498
T8 <1,8> 1461      T8I <11,8> 2901
T9 <1,9> 2922      T9I <11,9> 1707
T10 <1,10> 1749      T10I <11,10> 3414
T11 <1,11> 3498      T11I <11,11> 2733
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2001      T0MI <7,0> 381
T1M <5,1> 4002      T1MI <7,1> 762
T2M <5,2> 3909      T2MI <7,2> 1524
T3M <5,3> 3723      T3MI <7,3> 3048
T4M <5,4> 3351      T4MI <7,4> 2001
T5M <5,5> 2607      T5MI <7,5> 4002
T6M <5,6> 1119      T6MI <7,6> 3909
T7M <5,7> 2238      T7MI <7,7> 3723
T8M <5,8> 381      T8MI <7,8> 3351
T9M <5,9> 762      T9MI <7,9> 2607
T10M <5,10> 1524      T10MI <7,10> 1119
T11M <5,11> 3048      T11MI <7,11> 2238

The transformations that map this set to itself are: T0, T8I

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 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2897Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2905Scale 2905: Aeolian Flat 1, Ian Ring Music TheoryAeolian Flat 1
Scale 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 2933Scale 2933: Sizian, Ian Ring Music TheorySizian
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 2869Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 2645Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana
Scale 2773Scale 2773: Lydian, Ian Ring Music TheoryLydian
Scale 2389Scale 2389: Eskimo Hexatonic 2, Ian Ring Music TheoryEskimo Hexatonic 2
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 853Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian

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.