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Scale 2505: "Mydimic"

Scale 2505: Mydimic, 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
Mydimic

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

{0,3,6,7,8,11}

Forte Number

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

6-Z44

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: 627

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.

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.

5

Prime Form

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

no
prime: 615

Deep Scale

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

no

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, 1, 3, 4, 3, 1]

Interval Spectrum

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

p3m4n3sd3t

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

Spectra Variation

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

2.333

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.

2.25

Polygon Perimeter

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

5.796

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

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 TriadsG♯{8,0,3}231.5
B{11,3,6}231.5
Minor Triadscm{0,3,7}321.17
g♯m{8,11,3}231.5
Augmented TriadsD♯+{3,7,11}321.17
Diminished Triads{0,3,6}231.5
Parsimonious Voice Leading Between Common Triads of Scale 2505. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# g#m g#m D#+->g#m D#+->B g#m->G#

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
Radius2
Self-Centeredno
Central Verticescm, D♯+
Peripheral Verticesc°, g♯m, G♯, B

Modes

Modes are the rotational transformation of this scale. Scale 2505 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 825
Scale 825: Thyptimic, Ian Ring Music TheoryThyptimic
3rd mode:
Scale 615
Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimicThis is the prime mode
4th mode:
Scale 2355
Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita
5th mode:
Scale 3225
Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
6th mode:
Scale 915
Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada

Prime

The prime form of this scale is Scale 615

Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic

Complement

The hexatonic modal family [2505, 825, 615, 2355, 3225, 915] (Forte: 6-Z44) is the complement of the hexatonic modal family [411, 867, 1587, 2253, 2481, 2841] (Forte: 6-Z19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2505 is 627

Scale 627Scale 627: Mogimic, Ian Ring Music TheoryMogimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2505 is chiral, and its enantiomorph is scale 627

Scale 627Scale 627: Mogimic, Ian Ring Music TheoryMogimic

Transformations:

T0 2505  T0I 627
T1 915  T1I 1254
T2 1830  T2I 2508
T3 3660  T3I 921
T4 3225  T4I 1842
T5 2355  T5I 3684
T6 615  T6I 3273
T7 1230  T7I 2451
T8 2460  T8I 807
T9 825  T9I 1614
T10 1650  T10I 3228
T11 3300  T11I 2361

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 2507Scale 2507: Todi That, Ian Ring Music TheoryTodi That
Scale 2509Scale 2509: Double Harmonic Minor, Ian Ring Music TheoryDouble Harmonic Minor
Scale 2497Scale 2497, Ian Ring Music Theory
Scale 2501Scale 2501: Ralimic, Ian Ring Music TheoryRalimic
Scale 2513Scale 2513: Aerycrimic, Ian Ring Music TheoryAerycrimic
Scale 2521Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
Scale 2537Scale 2537: Laptian, Ian Ring Music TheoryLaptian
Scale 2441Scale 2441: Kyritonic, Ian Ring Music TheoryKyritonic
Scale 2473Scale 2473: Raga Takka, Ian Ring Music TheoryRaga Takka
Scale 2377Scale 2377: Bartók Gamma Chord, Ian Ring Music TheoryBartók Gamma Chord
Scale 2249Scale 2249: Raga Multani, Ian Ring Music TheoryRaga Multani
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 3017Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
Scale 3529Scale 3529: Stalian, Ian Ring Music TheoryStalian
Scale 457Scale 457: Staptitonic, Ian Ring Music TheoryStaptitonic
Scale 1481Scale 1481: Zagimic, Ian Ring Music TheoryZagimic

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.