The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1757

Scale 1757, 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{0,2,3,4,6,7,9,10}
Forte Number8-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1901
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 TriadsC{0,4,7}342.15
D{2,6,9}342.23
D♯{3,7,10}441.85
Minor Triadscm{0,3,7}441.92
d♯m{3,6,10}441.92
gm{7,10,2}242.23
am{9,0,4}342.23
Augmented TriadsD+{2,6,10}342.15
Diminished Triads{0,3,6}242.15
d♯°{3,6,9}242.31
{4,7,10}242.23
f♯°{6,9,0}242.31
{9,0,3}242.31
Parsimonious Voice Leading Between Common Triads of Scale 1757. 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->e° am am C->am D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° D+->d#m gm gm D+->gm d#°->d#m d#m->D# D#->e° D#->gm f#°->am a°->am

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 1757 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1463
Scale 1463, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2779
Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich
4th mode:
Scale 3437
Scale 3437, Ian Ring Music Theory
5th mode:
Scale 1883
Scale 1883, Ian Ring Music Theory
6th mode:
Scale 2989
Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
7th mode:
Scale 1771
Scale 1771, Ian Ring Music Theory
8th mode:
Scale 2933
Scale 2933, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Complement

The octatonic modal family [1757, 1463, 2779, 3437, 1883, 2989, 1771, 2933] (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 1757 is 1901

Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1757 is chiral, and its enantiomorph is scale 1901

Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic

Transformations:

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

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 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II
Scale 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
Scale 1693Scale 1693: Dogian, Ian Ring Music TheoryDogian
Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian
Scale 1501Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic

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.