The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1385: "Phracrimic"

Scale 1385: Phracrimic, 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
Phracrimic
Dozenal
Itrian

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

{0,3,5,6,8,10}

Forte Number

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

6-33

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: 725

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.

2

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: 685

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.

[3, 2, 1, 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, 4, 3, 2, 4, 1>

Interval Spectrum

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

p4m2n3s4dt

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

Spectra Variation

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

1.667

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.

2.482

Polygon Perimeter

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

5.932

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".

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, 12, 54)

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}221
Minor Triadsd♯m{3,6,10}131.5
fm{5,8,0}131.5
Diminished Triads{0,3,6}221
Parsimonious Voice Leading Between Common Triads of Scale 1385. Created by Ian Ring ©2019 d#m d#m c°->d#m G# G# c°->G# fm fm fm->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 Verticesc°, G♯
Peripheral Verticesd♯m, fm

Triad Polychords

Also known as Bi-Triadic Hexatonics (a term coined by mDecks), and related to Generic Modality Compression (a method for guitar by Mick Goodrick and Tim Miller), these are two common triads that when combined use all the tones in this scale.

There is 1 way that this hexatonic scale can be split into two common triads.


Minor: {3, 6, 10}
Minor: {5, 8, 0}

Modes

Modes are the rotational transformation of this scale. Scale 1385 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 685
Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha BangalaThis is the prime mode
3rd mode:
Scale 1195
Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
4th mode:
Scale 2645
Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana
5th mode:
Scale 1685
Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
6th mode:
Scale 1445
Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari

Prime

The prime form of this scale is Scale 685

Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala

Complement

The hexatonic modal family [1385, 685, 1195, 2645, 1685, 1445] (Forte: 6-33) is the complement of the hexatonic modal family [685, 1195, 1385, 1445, 1685, 2645] (Forte: 6-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1385 is 725

Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1385 is chiral, and its enantiomorph is scale 725

Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani

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> 1385       T0I <11,0> 725
T1 <1,1> 2770      T1I <11,1> 1450
T2 <1,2> 1445      T2I <11,2> 2900
T3 <1,3> 2890      T3I <11,3> 1705
T4 <1,4> 1685      T4I <11,4> 3410
T5 <1,5> 3370      T5I <11,5> 2725
T6 <1,6> 2645      T6I <11,6> 1355
T7 <1,7> 1195      T7I <11,7> 2710
T8 <1,8> 2390      T8I <11,8> 1325
T9 <1,9> 685      T9I <11,9> 2650
T10 <1,10> 1370      T10I <11,10> 1205
T11 <1,11> 2740      T11I <11,11> 2410
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 95      T0MI <7,0> 3905
T1M <5,1> 190      T1MI <7,1> 3715
T2M <5,2> 380      T2MI <7,2> 3335
T3M <5,3> 760      T3MI <7,3> 2575
T4M <5,4> 1520      T4MI <7,4> 1055
T5M <5,5> 3040      T5MI <7,5> 2110
T6M <5,6> 1985      T6MI <7,6> 125
T7M <5,7> 3970      T7MI <7,7> 250
T8M <5,8> 3845      T8MI <7,8> 500
T9M <5,9> 3595      T9MI <7,9> 1000
T10M <5,10> 3095      T10MI <7,10> 2000
T11M <5,11> 2095      T11MI <7,11> 4000

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 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
Scale 1377Scale 1377: Insian, Ian Ring Music TheoryInsian
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1393Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 1321Scale 1321: Blues Minor, Ian Ring Music TheoryBlues Minor
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian
Scale 1129Scale 1129: Raga Jayakauns, Ian Ring Music TheoryRaga Jayakauns
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1641Scale 1641: Bocrimic, Ian Ring Music TheoryBocrimic
Scale 1897Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
Scale 361Scale 361: Bocritonic, Ian Ring Music TheoryBocritonic
Scale 873Scale 873: Bagimic, Ian Ring Music TheoryBagimic
Scale 2409Scale 2409: Zacrimic, Ian Ring Music TheoryZacrimic
Scale 3433Scale 3433: Thonian, Ian Ring Music TheoryThonian

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.