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Scale 1197: "Minor Hexatonic"

Scale 1197: Minor Hexatonic, 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

Western Modern
Minor Hexatonic
Carnatic Raga
Raga Manirangu
Nayaki
Pushpalithika
Puspalatika
Suha Sughrai
Hindustani
Palasi
Unknown / Unsorted
Yo
Exoticisms
Eskimo Hexatonic 1
Zeitler
Rocrimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,5,7,10}
Forte Number6-32
Rotational Symmetrynone
Reflection Axes2.5
Palindromicno
Chiralityno
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections1
Modes5
Prime?no
prime: 693
Deep Scaleyes
Interval Vector143250
Interval Spectrump5m2n3s4d
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {5,7}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.667
Maximally Evenno
Maximal Area Setno
Interior Area2.482
Myhill Propertyno
Balancedno
Ridge Tones[5]
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 TriadsD♯{3,7,10}221
A♯{10,2,5}131.5
Minor Triadscm{0,3,7}131.5
gm{7,10,2}221
Parsimonious Voice Leading Between Common Triads of Scale 1197. Created by Ian Ring ©2019 cm cm D# D# cm->D# gm gm D#->gm A# A# gm->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.

Diameter3
Radius2
Self-Centeredno
Central VerticesD♯, gm
Peripheral Verticescm, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1197 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1323
Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
3rd mode:
Scale 2709
Scale 2709: Raga Kumud, Ian Ring Music TheoryRaga Kumud
4th mode:
Scale 1701
Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh
5th mode:
Scale 1449
Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
6th mode:
Scale 693
Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic HexachordThis is the prime mode

Prime

The prime form of this scale is Scale 693

Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord

Complement

The hexatonic modal family [1197, 1323, 2709, 1701, 1449, 693] (Forte: 6-32) is the complement of the hexatonic modal family [693, 1197, 1323, 1449, 1701, 2709] (Forte: 6-32)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1197 is 1701

Scale 1701Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh

Transformations:

T0 1197  T0I 1701
T1 2394  T1I 3402
T2 693  T2I 2709
T3 1386  T3I 1323
T4 2772  T4I 2646
T5 1449  T5I 1197
T6 2898  T6I 2394
T7 1701  T7I 693
T8 3402  T8I 1386
T9 2709  T9I 2772
T10 1323  T10I 1449
T11 2646  T11I 2898

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 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 1193Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic
Scale 1195Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji
Scale 1213Scale 1213: Gyrian, Ian Ring Music TheoryGyrian
Scale 1165Scale 1165: Gycritonic, Ian Ring Music TheoryGycritonic
Scale 1181Scale 1181: Katagimic, Ian Ring Music TheoryKatagimic
Scale 1229Scale 1229: Raga Simharava, Ian Ring Music TheoryRaga Simharava
Scale 1261Scale 1261: Modified Blues, Ian Ring Music TheoryModified Blues
Scale 1069Scale 1069, Ian Ring Music Theory
Scale 1133Scale 1133: Stycrimic, Ian Ring Music TheoryStycrimic
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 1453Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
Scale 1709Scale 1709: Dorian, Ian Ring Music TheoryDorian
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala
Scale 2221Scale 2221: Raga Sindhura Kafi, Ian Ring Music TheoryRaga Sindhura Kafi
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya

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.