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Scale 1273: "Ronian"

Scale 1273: Ronian, 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
Ronian

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

{0,3,4,5,6,7,10}

Forte Number

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

7-Z12

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.

[5]

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.

4 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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: 671

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.

[4, 4, 4, 3, 4, 2]

Interval Spectrum

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

p4m3n4s4d4t2

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

Spectra Variation

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

2.857

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.

2.433

Polygon Perimeter

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

5.899

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.

[10]

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

Harmonic Chords

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 TriadsC{0,4,7}231.5
D♯{3,7,10}321.17
Minor Triadscm{0,3,7}321.17
d♯m{3,6,10}231.5
Diminished Triads{0,3,6}231.5
{4,7,10}231.5

The following pitch classes are not present in any of the common triads: {5}

Parsimonious Voice Leading Between Common Triads of Scale 1273. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# C->e° d#m->D# D#->e°

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°, C, d♯m, e°

Modes

Modes are the rotational transformation of this scale. Scale 1273 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 671
Scale 671: Stycrian, Ian Ring Music TheoryStycrianThis is the prime mode
3rd mode:
Scale 2383
Scale 2383: Katorian, Ian Ring Music TheoryKatorian
4th mode:
Scale 3239
Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
5th mode:
Scale 3667
Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
6th mode:
Scale 3881
Scale 3881: Morian, Ian Ring Music TheoryMorian
7th mode:
Scale 997
Scale 997: Rycrian, Ian Ring Music TheoryRycrian

Prime

The prime form of this scale is Scale 671

Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian

Complement

The heptatonic modal family [1273, 671, 2383, 3239, 3667, 3881, 997] (Forte: 7-Z12) is the complement of the pentatonic modal family [107, 1411, 1549, 2101, 2753] (Forte: 5-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1273 is 997

Scale 997Scale 997: Rycrian, Ian Ring Music TheoryRycrian

Transformations:

T0 1273  T0I 997
T1 2546  T1I 1994
T2 997  T2I 3988
T3 1994  T3I 3881
T4 3988  T4I 3667
T5 3881  T5I 3239
T6 3667  T6I 2383
T7 3239  T7I 671
T8 2383  T8I 1342
T9 671  T9I 2684
T10 1342  T10I 1273
T11 2684  T11I 2546

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 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic
Scale 1277Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic
Scale 1265Scale 1265: Pynimic, Ian Ring Music TheoryPynimic
Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1241Scale 1241: Pygimic, Ian Ring Music TheoryPygimic
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1145Scale 1145: Zygimic, Ian Ring Music TheoryZygimic
Scale 1401Scale 1401: Pagian, Ian Ring Music TheoryPagian
Scale 1529Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
Scale 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
Scale 249Scale 249, Ian Ring Music Theory
Scale 761Scale 761: Ponian, Ian Ring Music TheoryPonian
Scale 2297Scale 2297: Thylian, Ian Ring Music TheoryThylian
Scale 3321Scale 3321: Epagyllic, Ian Ring Music TheoryEpagyllic

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.