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Scale 1755: "Octatonic"

Scale 1755: Octatonic, 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

Unknown / Unsorted
Octatonic
Half-Whole Step Scale
Dominant
Messiaen
Messiaen Mode 2
Second Mode Of Limited Transposition
Western Modern
Dominant Diminished
Jazz and Blues
Diminished Blues
Auxiliary Diminished Blues
Zeitler
Ladyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,6,7,9,10}
Forte Number8-28
Rotational Symmetry3, 6, 9 semitones
Reflection Axes0.5, 2, 3.5, 5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes1
Prime?yes
Deep Scaleno
Interval Vector448444
Interval Spectrump4m4n8s4d4t4
Distribution Spectra<1> = {1,2}
<2> = {3}
<3> = {4,5}
<4> = {6}
<5> = {7,8}
<6> = {9}
<7> = {10,11}
Spectra Variation0.5
Maximally Evenyes
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedyes
Ridge Tones[1,4,7,10]
ProprietyStrictly Proper
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 TriadsC{0,4,7}442.13
D♯{3,7,10}442.13
F♯{6,10,1}442.13
A{9,1,4}442.13
Minor Triadscm{0,3,7}442.13
d♯m{3,6,10}442.13
f♯m{6,9,1}442.13
am{9,0,4}442.13
Diminished Triads{0,3,6}242.38
c♯°{1,4,7}242.38
d♯°{3,6,9}242.38
{4,7,10}242.38
f♯°{6,9,0}242.38
{7,10,1}242.38
{9,0,3}242.38
a♯°{10,1,4}242.38
Parsimonious Voice Leading Between Common Triads of Scale 1755. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# cm->a° c#° c#° C->c#° C->e° am am C->am A A c#°->A d#° d#° d#°->d#m f#m f#m d#°->f#m d#m->D# F# F# d#m->F# D#->e° D#->g° f#° f#° f#°->f#m f#°->am f#m->F# f#m->A F#->g° a#° a#° F#->a#° a°->am am->A A->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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1755 can be rotated to make 1 other scales. The 1st mode is itself.

2nd mode:
Scale 2925
Scale 2925: Diminished, Ian Ring Music TheoryDiminished

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [1755, 2925] (Forte: 8-28) is the complement of the tetratonic modal family [585] (Forte: 4-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1755 is 2925

Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished

Transformations:

T0 1755  T0I 2925
T1 3510  T1I 1755
T2 2925  T2I 3510
T3 1755  T3I 2925
T4 3510  T4I 1755
T5 2925  T5I 3510
T6 1755  T6I 2925
T7 3510  T7I 1755
T8 2925  T8I 3510
T9 1755  T9I 2925
T10 3510  T10I 1755
T11 2925  T11I 3510

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 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1757Scale 1757, Ian Ring Music Theory
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
Scale 1739Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
Scale 1771Scale 1771, Ian Ring Music Theory
Scale 1787Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian
Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
Scale 1627Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
Scale 1883Scale 1883, Ian Ring Music Theory
Scale 2011Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
Scale 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
Scale 3803Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic

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.