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Scale 2655

Scale 2655, 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{0,1,2,3,4,6,9,11}
Forte Number8-10
Rotational Symmetrynone
Reflection Axes1.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 765
Deep Scaleno
Interval Vector566452
Interval Spectrump5m4n6s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {9,10,11}
Spectra Variation2.75
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[3]
ProprietyImproper
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{2,6,9}341.9
A{9,1,4}242.1
B{11,3,6}342.1
Minor Triadsf♯m{6,9,1}341.9
am{9,0,4}342.1
bm{11,2,6}242.1
Diminished Triads{0,3,6}242.1
d♯°{3,6,9}242.1
f♯°{6,9,0}242.1
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 2655. Created by Ian Ring ©2019 c°->a° B B c°->B D D d#° d#° D->d#° f#m f#m D->f#m bm bm D->bm d#°->B f#° f#° f#°->f#m am am f#°->am A A f#m->A a°->am am->A bm->B

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 2655 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3375
Scale 3375, Ian Ring Music Theory
3rd mode:
Scale 3735
Scale 3735, Ian Ring Music Theory
4th mode:
Scale 3915
Scale 3915, Ian Ring Music Theory
5th mode:
Scale 4005
Scale 4005, Ian Ring Music Theory
6th mode:
Scale 2025
Scale 2025, Ian Ring Music Theory
7th mode:
Scale 765
Scale 765, Ian Ring Music TheoryThis is the prime mode
8th mode:
Scale 1215
Scale 1215, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 765

Scale 765Scale 765, Ian Ring Music Theory

Complement

The octatonic modal family [2655, 3375, 3735, 3915, 4005, 2025, 765, 1215] (Forte: 8-10) is the complement of the tetratonic modal family [45, 1035, 1665, 2565] (Forte: 4-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2655 is 3915

Scale 3915Scale 3915, Ian Ring Music Theory

Transformations:

T0 2655  T0I 3915
T1 1215  T1I 3735
T2 2430  T2I 3375
T3 765  T3I 2655
T4 1530  T4I 1215
T5 3060  T5I 2430
T6 2025  T6I 765
T7 4050  T7I 1530
T8 4005  T8I 3060
T9 3915  T9I 2025
T10 3735  T10I 4050
T11 3375  T11I 4005

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 2653Scale 2653: Sygian, Ian Ring Music TheorySygian
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 2647Scale 2647: Dadian, Ian Ring Music TheoryDadian
Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian
Scale 2671Scale 2671: Aerolyllic, Ian Ring Music TheoryAerolyllic
Scale 2687Scale 2687: Thacrygic, Ian Ring Music TheoryThacrygic
Scale 2591Scale 2591, Ian Ring Music Theory
Scale 2623Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
Scale 2719Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 2911Scale 2911: Katygic, Ian Ring Music TheoryKatygic
Scale 2143Scale 2143, Ian Ring Music Theory
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 3167Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic

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.