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Scale 1125: "Ionaritonic"

Scale 1125: Ionaritonic, 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

Zeitler
Ionaritonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,5,6,10}
Forte Number5-30
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1221
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes4
Prime?no
prime: 339
Deep Scaleno
Interval Vector121321
Interval Spectrump2m3ns2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {4,5,6}
<3> = {6,7,8}
<4> = {8,9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.049
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsA♯{10,2,5}110.5
Augmented TriadsD+{2,6,10}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1125. Created by Ian Ring ©2019 D+ D+ A# A# D+->A#

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 1125 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1305
Scale 1305: Dynitonic, Ian Ring Music TheoryDynitonic
3rd mode:
Scale 675
Scale 675: Altered Pentatonic, Ian Ring Music TheoryAltered Pentatonic
4th mode:
Scale 2385
Scale 2385: Aeolanitonic, Ian Ring Music TheoryAeolanitonic
5th mode:
Scale 405
Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari

Prime

The prime form of this scale is Scale 339

Scale 339Scale 339: Zaptitonic, Ian Ring Music TheoryZaptitonic

Complement

The pentatonic modal family [1125, 1305, 675, 2385, 405] (Forte: 5-30) is the complement of the heptatonic modal family [855, 1395, 1485, 1845, 2475, 2745, 3285] (Forte: 7-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1125 is 1221

Scale 1221Scale 1221: Epyritonic, Ian Ring Music TheoryEpyritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1125 is chiral, and its enantiomorph is scale 1221

Scale 1221Scale 1221: Epyritonic, Ian Ring Music TheoryEpyritonic

Transformations:

T0 1125  T0I 1221
T1 2250  T1I 2442
T2 405  T2I 789
T3 810  T3I 1578
T4 1620  T4I 3156
T5 3240  T5I 2217
T6 2385  T6I 339
T7 675  T7I 678
T8 1350  T8I 1356
T9 2700  T9I 2712
T10 1305  T10I 1329
T11 2610  T11I 2658

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 1127Scale 1127: Eparimic, Ian Ring Music TheoryEparimic
Scale 1121Scale 1121, Ian Ring Music Theory
Scale 1123Scale 1123: Iwato, Ian Ring Music TheoryIwato
Scale 1129Scale 1129: Raga Jayakauns, Ian Ring Music TheoryRaga Jayakauns
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1141Scale 1141: Rynimic, Ian Ring Music TheoryRynimic
Scale 1093Scale 1093: Lydic, Ian Ring Music TheoryLydic
Scale 1109Scale 1109: Kataditonic, Ian Ring Music TheoryKataditonic
Scale 1061Scale 1061, Ian Ring Music Theory
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1253Scale 1253: Zolimic, Ian Ring Music TheoryZolimic
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1637Scale 1637: Syptimic, Ian Ring Music TheorySyptimic
Scale 101Scale 101, Ian Ring Music Theory
Scale 613Scale 613: Phralitonic, Ian Ring Music TheoryPhralitonic
Scale 2149Scale 2149, Ian Ring Music Theory
Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic

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.