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Scale 2853: "Baptimic"

Scale 2853: Baptimic, 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
Baptimic

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

{0,2,5,8,9,11}

Forte Number

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

6-27

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: 1179

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.

4

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: 603

Deep Scale

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

no

Interval Formula

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

[2, 3, 3, 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, 2, 5, 2, 2, 2>

Interval Spectrum

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

p2m2n5s2d2t2

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

Spectra Variation

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

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.

2.366

Polygon Perimeter

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

5.864

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 TriadsF{5,9,0}231.57
Minor Triadsdm{2,5,9}331.43
fm{5,8,0}331.43
Diminished Triads{2,5,8}231.57
{5,8,11}231.57
g♯°{8,11,2}231.71
{11,2,5}231.57
Parsimonious Voice Leading Between Common Triads of Scale 2853. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm F F dm->F dm->b° f°->fm g#° g#° f°->g#° fm->F g#°->b°

view full size

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 2853 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1737
Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
3rd mode:
Scale 729
Scale 729: Stygimic, Ian Ring Music TheoryStygimic
4th mode:
Scale 603
Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimicThis is the prime mode
5th mode:
Scale 2349
Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
6th mode:
Scale 1611
Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic

Prime

The prime form of this scale is Scale 603

Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic

Complement

The hexatonic modal family [2853, 1737, 729, 603, 2349, 1611] (Forte: 6-27) is the complement of the hexatonic modal family [603, 729, 1611, 1737, 2349, 2853] (Forte: 6-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2853 is 1179

Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2853 is chiral, and its enantiomorph is scale 1179

Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic

Transformations:

T0 2853  T0I 1179
T1 1611  T1I 2358
T2 3222  T2I 621
T3 2349  T3I 1242
T4 603  T4I 2484
T5 1206  T5I 873
T6 2412  T6I 1746
T7 729  T7I 3492
T8 1458  T8I 2889
T9 2916  T9I 1683
T10 1737  T10I 3366
T11 3474  T11I 2637

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 2855Scale 2855: Epocrain, Ian Ring Music TheoryEpocrain
Scale 2849Scale 2849, Ian Ring Music Theory
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 2857Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
Scale 2861Scale 2861: Katothian, Ian Ring Music TheoryKatothian
Scale 2869Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 2821Scale 2821, Ian Ring Music Theory
Scale 2837Scale 2837: Aelothimic, Ian Ring Music TheoryAelothimic
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 2597Scale 2597: Raga Rasranjani, Ian Ring Music TheoryRaga Rasranjani
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 2341Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 805Scale 805: Rothitonic, Ian Ring Music TheoryRothitonic
Scale 1829Scale 1829: Pathimic, Ian Ring Music TheoryPathimic

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. 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.