The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3557

Scale 3557, 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{0,2,5,6,7,8,10,11}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1271
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 751
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3557 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1913
Scale 1913, Ian Ring Music Theory
3rd mode:
Scale 751
Scale 751, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2423
Scale 2423, Ian Ring Music Theory
5th mode:
Scale 3259
Scale 3259, Ian Ring Music Theory
6th mode:
Scale 3677
Scale 3677, Ian Ring Music Theory
7th mode:
Scale 1943
Scale 1943, Ian Ring Music Theory
8th mode:
Scale 3019
Scale 3019, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [3557, 1913, 751, 2423, 3259, 3677, 1943, 3019] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3557 is 1271

Scale 1271Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3557 is chiral, and its enantiomorph is scale 1271

Scale 1271Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic

Transformations:

T0 3557  T0I 1271
T1 3019  T1I 2542
T2 1943  T2I 989
T3 3886  T3I 1978
T4 3677  T4I 3956
T5 3259  T5I 3817
T6 2423  T6I 3539
T7 751  T7I 2983
T8 1502  T8I 1871
T9 3004  T9I 3742
T10 1913  T10I 3389
T11 3826  T11I 2683

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 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
Scale 3553Scale 3553, Ian Ring Music Theory
Scale 3555Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
Scale 3561Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
Scale 3565Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
Scale 3573Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
Scale 3525Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3301Scale 3301: Chromatic Mixolydian Inverse, Ian Ring Music TheoryChromatic Mixolydian Inverse
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 2533Scale 2533: Podian, Ian Ring Music TheoryPodian
Scale 3045Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
Scale 1509Scale 1509: Ragian, Ian Ring Music TheoryRagian

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.