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Scale 1323: "Ritsu"

Scale 1323: Ritsu, 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

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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
Ritsu
Carnatic Raga
Raga Suddha Todi
Zeitler
Eporimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,5,8,10}
Forte Number6-32
Rotational Symmetrynone
Reflection Axes0.5
Palindromicno
Chiralityno
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections1
Modes5
Prime?no
prime: 693
Deep Scaleyes
Interval Vector143250
Interval Spectrump5m2n3s4d
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {5,7}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.667
Maximally Evenno
Maximal Area Setno
Interior Area2.482
Myhill Propertyno
Balancedno
Ridge Tones[1]
ProprietyProper
Heliotonicno

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♯{1,5,8}221
G♯{8,0,3}131.5
Minor Triadsfm{5,8,0}221
a♯m{10,1,5}131.5
Parsimonious Voice Leading Between Common Triads of Scale 1323. Created by Ian Ring ©2019 C# C# fm fm C#->fm a#m a#m C#->a#m G# G# 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♯, fm
Peripheral VerticesG♯, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 1323 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2709
Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud
3rd mode:
Scale 1701
Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh
4th mode:
Scale 1449
Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
5th mode:
Scale 693
Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic HexachordThis is the prime mode
6th mode:
Scale 1197
Scale 1197: Minor Hexatonic, Ian Ring Music TheoryMinor Hexatonic

Prime

The prime form of this scale is Scale 693

Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord

Complement

The hexatonic modal family [1323, 2709, 1701, 1449, 693, 1197] (Forte: 6-32) is the complement of the hexatonic modal family [693, 1197, 1323, 1449, 1701, 2709] (Forte: 6-32)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1323 is 2709

Scale 2709Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud

Transformations:

T0 1323  T0I 2709
T1 2646  T1I 1323
T2 1197  T2I 2646
T3 2394  T3I 1197
T4 693  T4I 2394
T5 1386  T5I 693
T6 2772  T6I 1386
T7 1449  T7I 2772
T8 2898  T8I 1449
T9 1701  T9I 2898
T10 3402  T10I 1701
T11 2709  T11I 3402

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 1321Scale 1321: Blues Minor, Ian Ring Music TheoryBlues Minor
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 1327Scale 1327: Zalian, Ian Ring Music TheoryZalian
Scale 1315Scale 1315: Pyritonic, Ian Ring Music TheoryPyritonic
Scale 1319Scale 1319: Phronimic, Ian Ring Music TheoryPhronimic
Scale 1331Scale 1331: Raga Vasantabhairavi, Ian Ring Music TheoryRaga Vasantabhairavi
Scale 1339Scale 1339: Kycrian, Ian Ring Music TheoryKycrian
Scale 1291Scale 1291, Ian Ring Music Theory
Scale 1307Scale 1307: Katorimic, Ian Ring Music TheoryKatorimic
Scale 1355Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 1387Scale 1387: Locrian, Ian Ring Music TheoryLocrian
Scale 1451Scale 1451: Phrygian, Ian Ring Music TheoryPhrygian
Scale 1067Scale 1067, Ian Ring Music Theory
Scale 1195Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
Scale 1579Scale 1579: Sagimic, Ian Ring Music TheorySagimic
Scale 1835Scale 1835: Byptian, Ian Ring Music TheoryByptian
Scale 299Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga Chitthakarshini
Scale 811Scale 811: Radimic, Ian Ring Music TheoryRadimic
Scale 2347Scale 2347: Raga Viyogavarali, Ian Ring Music TheoryRaga Viyogavarali
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian

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.