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Scale 855: "Porian"

Scale 855: Porian, 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
Porian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,6,8,9}
Forte Number7-30
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3417
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector343542
Interval Spectrump4m5n3s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {8,9,10}
<6> = {9,10,11}
Spectra Variation1.714
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 TriadsD{2,6,9}142.14
A{9,1,4}321.29
Minor Triadsc♯m{1,4,8}231.71
f♯m{6,9,1}331.43
am{9,0,4}331.43
Augmented TriadsC+{0,4,8}241.86
Diminished Triadsf♯°{6,9,0}231.57
Parsimonious Voice Leading Between Common Triads of Scale 855. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m am am C+->am A A c#m->A D D f#m f#m D->f#m f#° f#° f#°->f#m f#°->am f#m->A 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 VerticesA
Peripheral VerticesC+, D

Modes

Modes are the rotational transformation of this scale. Scale 855 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2475
Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
3rd mode:
Scale 3285
Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
4th mode:
Scale 1845
Scale 1845: Lagian, Ian Ring Music TheoryLagian
5th mode:
Scale 1485
Scale 1485: Minor Romani, Ian Ring Music TheoryMinor Romani
6th mode:
Scale 1395
Scale 1395: Locrian Dominant, Ian Ring Music TheoryLocrian Dominant
7th mode:
Scale 2745
Scale 2745: Mela Sulini, Ian Ring Music TheoryMela Sulini

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [855, 2475, 3285, 1845, 1485, 1395, 2745] (Forte: 7-30) is the complement of the pentatonic modal family [339, 789, 1221, 1329, 2217] (Forte: 5-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 855 is 3417

Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 855 is chiral, and its enantiomorph is scale 3417

Scale 3417Scale 3417: Golian, Ian Ring Music TheoryGolian

Transformations:

T0 855  T0I 3417
T1 1710  T1I 2739
T2 3420  T2I 1383
T3 2745  T3I 2766
T4 1395  T4I 1437
T5 2790  T5I 2874
T6 1485  T6I 1653
T7 2970  T7I 3306
T8 1845  T8I 2517
T9 3690  T9I 939
T10 3285  T10I 1878
T11 2475  T11I 3756

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 853Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
Scale 851Scale 851: Raga Hejjajji, Ian Ring Music TheoryRaga Hejjajji
Scale 859Scale 859: Ultralocrian, Ian Ring Music TheoryUltralocrian
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 839Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic
Scale 847Scale 847: Ganian, Ian Ring Music TheoryGanian
Scale 871Scale 871: Locrian Double-flat 3 Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 3 Double-flat 7
Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic
Scale 791Scale 791: Aeoloptimic, Ian Ring Music TheoryAeoloptimic
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 983Scale 983: Thocryllic, Ian Ring Music TheoryThocryllic
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic
Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic

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.