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Scale 1761

Scale 1761, 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

Cardinality6 (hexatonic)
Pitch Class Set{0,5,6,7,9,10}
Forte Number6-Z11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 237
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 183
Deep Scaleno
Interval Vector333231
Interval Spectrump3m2n3s3d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {4,5,7,8}
<4> = {5,6,9,10}
<5> = {7,10,11}
Spectra Variation3.667
Maximally Evenno
Maximal Area Setno
Interior Area1.866
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1761 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 183
Scale 183, Ian Ring Music TheoryThis is the prime mode
3rd mode:
Scale 2139
Scale 2139, Ian Ring Music Theory
4th mode:
Scale 3117
Scale 3117, Ian Ring Music Theory
5th mode:
Scale 1803
Scale 1803, Ian Ring Music Theory
6th mode:
Scale 2949
Scale 2949, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 183

Scale 183Scale 183, Ian Ring Music Theory

Complement

The hexatonic modal family [1761, 183, 2139, 3117, 1803, 2949] (Forte: 6-Z11) is the complement of the hexatonic modal family [303, 753, 1929, 2199, 3147, 3621] (Forte: 6-Z40)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1761 is 237

Scale 237Scale 237, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1761 is chiral, and its enantiomorph is scale 237

Scale 237Scale 237, Ian Ring Music Theory

Transformations:

T0 1761  T0I 237
T1 3522  T1I 474
T2 2949  T2I 948
T3 1803  T3I 1896
T4 3606  T4I 3792
T5 3117  T5I 3489
T6 2139  T6I 2883
T7 183  T7I 1671
T8 366  T8I 3342
T9 732  T9I 2589
T10 1464  T10I 1083
T11 2928  T11I 2166

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 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 1777Scale 1777: Saptian, Ian Ring Music TheorySaptian
Scale 1729Scale 1729, Ian Ring Music Theory
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1697Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali
Scale 1633Scale 1633, Ian Ring Music Theory
Scale 1889Scale 1889, Ian Ring Music Theory
Scale 2017Scale 2017, Ian Ring Music Theory
Scale 1249Scale 1249, Ian Ring Music Theory
Scale 1505Scale 1505, Ian Ring Music Theory
Scale 737Scale 737, Ian Ring Music Theory
Scale 2785Scale 2785, Ian Ring Music Theory
Scale 3809Scale 3809, Ian Ring Music Theory

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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.