The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1771

Scale 1771, 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).

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,6,7,9,10}
Forte Number8-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2797
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes7
Prime?no
prime: 1463
Deep Scaleno
Interval Vector456553
Interval Spectrump5m5n6s5d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.25
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tonesnone
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}342.15
F{5,9,0}342.23
F♯{6,10,1}441.85
Minor Triadscm{0,3,7}342.23
d♯m{3,6,10}441.92
f♯m{6,9,1}441.92
a♯m{10,1,5}242.23
Augmented TriadsC♯+{1,5,9}342.15
Diminished Triads{0,3,6}242.31
d♯°{3,6,9}242.15
f♯°{6,9,0}242.31
{7,10,1}242.23
{9,0,3}242.31
Parsimonious Voice Leading Between Common Triads of Scale 1771. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# cm->a° C#+ C#+ F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m d#° d#° d#°->d#m d#°->f#m d#m->D# F# F# d#m->F# D#->g° f#° f#° F->f#° F->a° f#°->f#m f#m->F# F#->g° F#->a#m

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 1771 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2933
Scale 2933, Ian Ring Music Theory
3rd mode:
Scale 1757
Scale 1757, Ian Ring Music Theory
4th mode:
Scale 1463
Scale 1463, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2779
Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
6th mode:
Scale 3437
Scale 3437, Ian Ring Music Theory
7th mode:
Scale 1883
Scale 1883, Ian Ring Music Theory
8th mode:
Scale 2989
Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor

Prime

The prime form of this scale is Scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Complement

The octatonic modal family [1771, 2933, 1757, 1463, 2779, 3437, 1883, 2989] (Forte: 8-27) is the complement of the tetratonic modal family [293, 593, 649, 1097] (Forte: 4-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1771 is 2797

Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1771 is chiral, and its enantiomorph is scale 2797

Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic

Transformations:

T0 1771  T0I 2797
T1 3542  T1I 1499
T2 2989  T2I 2998
T3 1883  T3I 1901
T4 3766  T4I 3802
T5 3437  T5I 3509
T6 2779  T6I 2923
T7 1463  T7I 1751
T8 2926  T8I 3502
T9 1757  T9I 2909
T10 3514  T10I 1723
T11 2933  T11I 3446

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 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic
Scale 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian
Scale 1767Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic
Scale 1779Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
Scale 1787Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
Scale 1739Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 1899Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic
Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic
Scale 1259Scale 1259: Stadian, Ian Ring Music TheoryStadian
Scale 1515Scale 1515: Phrygian/Locrian Mixed, Ian Ring Music TheoryPhrygian/Locrian Mixed
Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 2795Scale 2795: Van der Horst Octatonic, Ian Ring Music TheoryVan der Horst Octatonic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic

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.