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Scale 1123: "Iwato"

Scale 1123: Iwato, 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
Iwato
Zeitler
Lanitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,1,5,6,10}
Forte Number5-20
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2245
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes4
Prime?no
prime: 355
Deep Scaleno
Interval Vector211231
Interval Spectrump3m2nsd2t
Distribution Spectra<1> = {1,2,4}
<2> = {3,5,6}
<3> = {6,7,9}
<4> = {8,10,11}
Spectra Variation2.4
Maximally Evenno
Maximal Area Setno
Interior Area1.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
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 TriadsF♯{6,10,1}110.5
Minor Triadsa♯m{10,1,5}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1123. Created by Ian Ring ©2019 F# F# a#m a#m F#->a#m

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1123 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 2609
Scale 2609: Raga Bhinna Shadja, Ian Ring Music TheoryRaga Bhinna Shadja
3rd mode:
Scale 419
Scale 419: Hon-kumoi-joshi, Ian Ring Music TheoryHon-kumoi-joshi
4th mode:
Scale 2257
Scale 2257: Lydian Pentatonic, Ian Ring Music TheoryLydian Pentatonic
5th mode:
Scale 397
Scale 397: Aeolian Pentatonic, Ian Ring Music TheoryAeolian Pentatonic

Prime

The prime form of this scale is Scale 355

Scale 355Scale 355: Aeoloritonic, Ian Ring Music TheoryAeoloritonic

Complement

The pentatonic modal family [1123, 2609, 419, 2257, 397] (Forte: 5-20) is the complement of the heptatonic modal family [743, 919, 1849, 2419, 2507, 3257, 3301] (Forte: 7-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1123 is 2245

Scale 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1123 is chiral, and its enantiomorph is scale 2245

Scale 2245Scale 2245: Raga Vaijayanti, Ian Ring Music TheoryRaga Vaijayanti

Transformations:

T0 1123  T0I 2245
T1 2246  T1I 395
T2 397  T2I 790
T3 794  T3I 1580
T4 1588  T4I 3160
T5 3176  T5I 2225
T6 2257  T6I 355
T7 419  T7I 710
T8 838  T8I 1420
T9 1676  T9I 2840
T10 3352  T10I 1585
T11 2609  T11I 3170

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 1121Scale 1121, Ian Ring Music Theory
Scale 1125Scale 1125: Ionaritonic, Ian Ring Music TheoryIonaritonic
Scale 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1139Scale 1139: Aerygimic, Ian Ring Music TheoryAerygimic
Scale 1091Scale 1091, Ian Ring Music Theory
Scale 1107Scale 1107: Mogitonic, Ian Ring Music TheoryMogitonic
Scale 1059Scale 1059, Ian Ring Music Theory
Scale 1187Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi
Scale 1251Scale 1251: Sylimic, Ian Ring Music TheorySylimic
Scale 1379Scale 1379: Kycrimic, Ian Ring Music TheoryKycrimic
Scale 1635Scale 1635: Sygimic, Ian Ring Music TheorySygimic
Scale 99Scale 99, Ian Ring Music Theory
Scale 611Scale 611: Anchihoye, Ian Ring Music TheoryAnchihoye
Scale 2147Scale 2147, Ian Ring Music Theory
Scale 3171Scale 3171: Zythimic, Ian Ring Music TheoryZythimic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.