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Scale 695: "Sarian"

Scale 695: Sarian, 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
Sarian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,5,7,9}
Forte Number7-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3497
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes6
Prime?yes
Deep Scaleno
Interval Vector344451
Interval Spectrump5m4n4s4d3t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.286
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}241.86
F{5,9,0}231.57
A{9,1,4}321.29
Minor Triadsdm{2,5,9}142.14
am{9,0,4}331.43
Augmented TriadsC♯+{1,5,9}331.43
Diminished Triadsc♯°{1,4,7}231.71
Parsimonious Voice Leading Between Common Triads of Scale 695. Created by Ian Ring ©2019 C C c#° c#° C->c#° am am C->am A A c#°->A C#+ C#+ dm dm C#+->dm F F C#+->F C#+->A F->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 VerticesA
Peripheral VerticesC, dm

Modes

Modes are the rotational transformation of this scale. Scale 695 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2395		Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
3rd mode:
Scale 3245		Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
4th mode:
Scale 1835		Scale 1835: Byptian, Ian Ring Music TheoryByptian
5th mode:
Scale 2965		Scale 2965: Darian, Ian Ring Music TheoryDarian
6th mode:
Scale 1765		Scale 1765: Lonian, Ian Ring Music TheoryLonian
7th mode:
Scale 1465		Scale 1465: Mela Ragavardhani, Ian Ring Music TheoryMela Ragavardhani

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [695, 2395, 3245, 1835, 2965, 1765, 1465] (Forte: 7-27) is the complement of the pentatonic modal family [299, 689, 1417, 1573, 2197] (Forte: 5-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 695 is 3497

Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 695 is chiral, and its enantiomorph is scale 3497

Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian

Transformations:

T0 695  T0I 3497
T1 1390  T1I 2899
T2 2780  T2I 1703
T3 1465  T3I 3406
T4 2930  T4I 2717
T5 1765  T5I 1339
T6 3530  T6I 2678
T7 2965  T7I 1261
T8 1835  T8I 2522
T9 3670  T9I 949
T10 3245  T10I 1898
T11 2395  T11I 3796

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 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 691Scale 691: Raga Kalavati, Ian Ring Music TheoryRaga Kalavati
Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 679Scale 679: Lanimic, Ian Ring Music TheoryLanimic
Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian
Scale 663Scale 663: Phrynimic, Ian Ring Music TheoryPhrynimic
Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian
Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
Scale 631Scale 631: Zygian, Ian Ring Music TheoryZygian
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic
Scale 183Scale 183, Ian Ring Music Theory
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
Scale 1719Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic
Scale 2743Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic

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.