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Scale 3829: "Taishikicho"

Scale 3829: Taishikicho, 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

Japanese
Taishikicho
Ryo
Carnatic Raga
Raga Chayanat
Western Mixed
Lydian/Mixolydian Mixed
Zeitler
Aerycrygic

Analysis

Cardinality

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

9 (nonatonic)

Pitch Class Set

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

{0,2,4,5,6,7,9,10,11}

Forte Number

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

9-9

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.

[2]

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.

6 (multihemitonic)

Cohemitonia

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

4 (multicohemitonic)

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.

1

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.

8

Prime Form

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

no
prime: 1519

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

<6, 7, 6, 6, 8, 3>

Interval Spectrum

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

p8m6n6s7d6t3

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

Spectra Variation

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

1.333

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.

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.

2.799

Polygon Perimeter

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

6.106

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.

[4]

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 TriadsC{0,4,7}242.57
D{2,6,9}342.21
F{5,9,0}342.43
G{7,11,2}342.29
A♯{10,2,5}342.21
Minor Triadsdm{2,5,9}342.29
em{4,7,11}342.43
gm{7,10,2}342.21
am{9,0,4}242.57
bm{11,2,6}342.21
Augmented TriadsD+{2,6,10}442
Diminished Triads{4,7,10}242.57
f♯°{6,9,0}242.57
{11,2,5}242.57
Parsimonious Voice Leading Between Common Triads of Scale 3829. Created by Ian Ring ©2019 C C em em C->em am am C->am dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm D+->A# bm bm D+->bm e°->em e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3829. Created by Ian Ring ©2019 G em->G F->f#° F->am gm->G G->bm A#->b° b°->bm

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3829 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1981
Scale 1981: Houseini, Ian Ring Music TheoryHouseini
3rd mode:
Scale 1519
Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian MixedThis is the prime mode
4th mode:
Scale 2807
Scale 2807: Zylygic, Ian Ring Music TheoryZylygic
5th mode:
Scale 3451
Scale 3451: Garygic, Ian Ring Music TheoryGarygic
6th mode:
Scale 3773
Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
7th mode:
Scale 1967
Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
8th mode:
Scale 3031
Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
9th mode:
Scale 3563
Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic

Prime

The prime form of this scale is Scale 1519

Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed

Complement

The nonatonic modal family [3829, 1981, 1519, 2807, 3451, 3773, 1967, 3031, 3563] (Forte: 9-9) is the complement of the tritonic modal family [133, 161, 1057] (Forte: 3-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3829 is 1519

Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed

Transformations:

T0 3829  T0I 1519
T1 3563  T1I 3038
T2 3031  T2I 1981
T3 1967  T3I 3962
T4 3934  T4I 3829
T5 3773  T5I 3563
T6 3451  T6I 3031
T7 2807  T7I 1967
T8 1519  T8I 3934
T9 3038  T9I 3773
T10 1981  T10I 3451
T11 3962  T11I 2807

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 3831Scale 3831: Ionyllian, Ian Ring Music TheoryIonyllian
Scale 3825Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic
Scale 3827Scale 3827: Bodygic, Ian Ring Music TheoryBodygic
Scale 3833Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 4085Scale 4085: Rechberger's Decamode, Ian Ring Music TheoryRechberger's Decamode
Scale 3317Scale 3317: Katynyllic, Ian Ring Music TheoryKatynyllic
Scale 3573Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
Scale 2805Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho
Scale 1781Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic

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.