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Scale 757: "Ionyptian"

Scale 757: Ionyptian, 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
Ionyptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,4,5,6,7,9}
Forte Number7-23
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1513
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 701
Deep Scaleno
Interval Vector354351
Interval Spectrump5m3n4s5d3t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}142.17
D{2,6,9}241.83
F{5,9,0}321.17
Minor Triadsdm{2,5,9}231.5
am{9,0,4}231.5
Diminished Triadsf♯°{6,9,0}231.5
Parsimonious Voice Leading Between Common Triads of Scale 757. Created by Ian Ring ©2019 C C am am C->am dm dm D D dm->D F F dm->F f#° f#° D->f#° F->f#° F->am

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
Peripheral VerticesC, D

Modes

Modes are the rotational transformation of this scale. Scale 757 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1213
Scale 1213: Gyrian, Ian Ring Music TheoryGyrian
3rd mode:
Scale 1327
Scale 1327: Zalian, Ian Ring Music TheoryZalian
4th mode:
Scale 2711
Scale 2711: Stolian, Ian Ring Music TheoryStolian
5th mode:
Scale 3403
Scale 3403: Bylian, Ian Ring Music TheoryBylian
6th mode:
Scale 3749
Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
7th mode:
Scale 1961
Scale 1961: Soptian, Ian Ring Music TheorySoptian

Prime

The prime form of this scale is Scale 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Complement

The heptatonic modal family [757, 1213, 1327, 2711, 3403, 3749, 1961] (Forte: 7-23) is the complement of the pentatonic modal family [173, 1067, 1441, 1669, 2581] (Forte: 5-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 757 is 1513

Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 757 is chiral, and its enantiomorph is scale 1513

Scale 1513Scale 1513: Stathian, Ian Ring Music TheoryStathian

Transformations:

T0 757  T0I 1513
T1 1514  T1I 3026
T2 3028  T2I 1957
T3 1961  T3I 3914
T4 3922  T4I 3733
T5 3749  T5I 3371
T6 3403  T6I 2647
T7 2711  T7I 1199
T8 1327  T8I 2398
T9 2654  T9I 701
T10 1213  T10I 1402
T11 2426  T11I 2804

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 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 753Scale 753: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian
Scale 761Scale 761: Ponian, Ian Ring Music TheoryPonian
Scale 765Scale 765, Ian Ring Music Theory
Scale 741Scale 741: Gathimic, Ian Ring Music TheoryGathimic
Scale 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 725Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 629Scale 629: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 1013Scale 1013: Stydyllic, Ian Ring Music TheoryStydyllic
Scale 245Scale 245: Raga Dipak, Ian Ring Music TheoryRaga Dipak
Scale 501Scale 501: Katylian, Ian Ring Music TheoryKatylian
Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian
Scale 1781Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
Scale 2805Scale 2805: Ishikotsucho, Ian Ring Music TheoryIshikotsucho

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. Special thanks to Richard Repp for helping with technical accuracy.