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Scale 575: "Ionydian"

Scale 575: Ionydian, 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
Ionydian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,4,5,9}
Forte Number7-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3977
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 319
Deep Scaleno
Interval Vector544431
Interval Spectrump3m4n4s4d5t
Distribution Spectra<1> = {1,3,4}
<2> = {2,4,5,7}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {5,7,8,10}
<6> = {8,9,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area2.183
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{5,9,0}221.33
A{9,1,4}221.33
Minor Triadsdm{2,5,9}142
am{9,0,4}331.33
Augmented TriadsC♯+{1,5,9}331.33
Diminished Triads{9,0,3}142
Parsimonious Voice Leading Between Common Triads of Scale 575. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F A A C#+->A am am F->am a°->am am->A

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
Radius2
Self-Centeredno
Central VerticesF, A
Peripheral Verticesdm, a°

Modes

Modes are the rotational transformation of this scale. Scale 575 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2335
Scale 2335: Epydian, Ian Ring Music TheoryEpydian
3rd mode:
Scale 3215
Scale 3215: Katydian, Ian Ring Music TheoryKatydian
4th mode:
Scale 3655
Scale 3655: Mathian, Ian Ring Music TheoryMathian
5th mode:
Scale 3875
Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
6th mode:
Scale 3985
Scale 3985: Thadian, Ian Ring Music TheoryThadian
7th mode:
Scale 505
Scale 505: Sanian, Ian Ring Music TheorySanian

Prime

The prime form of this scale is Scale 319

Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian

Complement

The heptatonic modal family [575, 2335, 3215, 3655, 3875, 3985, 505] (Forte: 7-3) is the complement of the pentatonic modal family [55, 1795, 2075, 2945, 3085] (Forte: 5-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 575 is 3977

Scale 3977Scale 3977: Kythian, Ian Ring Music TheoryKythian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 575 is chiral, and its enantiomorph is scale 3977

Scale 3977Scale 3977: Kythian, Ian Ring Music TheoryKythian

Transformations:

T0 575  T0I 3977
T1 1150  T1I 3859
T2 2300  T2I 3623
T3 505  T3I 3151
T4 1010  T4I 2207
T5 2020  T5I 319
T6 4040  T6I 638
T7 3985  T7I 1276
T8 3875  T8I 2552
T9 3655  T9I 1009
T10 3215  T10I 2018
T11 2335  T11I 4036

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 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 571Scale 571: Kynimic, Ian Ring Music TheoryKynimic
Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic
Scale 543Scale 543, Ian Ring Music Theory
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic
Scale 63Scale 63, Ian Ring Music Theory
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 1087Scale 1087, Ian Ring Music Theory
Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
Scale 2623Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic

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.