The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3397: "Sydimic"

Scale 3397: Sydimic, 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).

Common Names

Zeitler
Sydimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,6,8,10,11}
Forte Number6-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1111
Hemitonia2 (dihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections5
Modes5
Prime?no
prime: 349
Deep Scaleno
Interval Vector242412
Interval Spectrumpm4n2s4d2t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,6}
<3> = {4,5,7,8}
<4> = {6,8,9,10}
<5> = {8,10,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.232
Myhill Propertyno
Balancedno
Ridge Tonesnone
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
Minor Triadsbm{11,2,6}210.67
Augmented TriadsD+{2,6,10}121
Diminished Triadsg♯°{8,11,2}121
Parsimonious Voice Leading Between Common Triads of Scale 3397. Created by Ian Ring ©2019 D+ D+ bm bm D+->bm g#° g#° g#°->bm

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.

Diameter2
Radius1
Self-Centeredno
Central Verticesbm
Peripheral VerticesD+, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 3397 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1873
Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
3rd mode:
Scale 373
Scale 373: Epagimic, Ian Ring Music TheoryEpagimic
4th mode:
Scale 1117
Scale 1117: Raptimic, Ian Ring Music TheoryRaptimic
5th mode:
Scale 1303
Scale 1303: Epolimic, Ian Ring Music TheoryEpolimic
6th mode:
Scale 2699
Scale 2699: Sythimic, Ian Ring Music TheorySythimic

Prime

The prime form of this scale is Scale 349

Scale 349Scale 349: Borimic, Ian Ring Music TheoryBorimic

Complement

The hexatonic modal family [3397, 1873, 373, 1117, 1303, 2699] (Forte: 6-21) is the complement of the hexatonic modal family [349, 1111, 1489, 1861, 2603, 3349] (Forte: 6-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3397 is 1111

Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3397 is chiral, and its enantiomorph is scale 1111

Scale 1111Scale 1111: Sycrimic, Ian Ring Music TheorySycrimic

Transformations:

T0 3397  T0I 1111
T1 2699  T1I 2222
T2 1303  T2I 349
T3 2606  T3I 698
T4 1117  T4I 1396
T5 2234  T5I 2792
T6 373  T6I 1489
T7 746  T7I 2978
T8 1492  T8I 1861
T9 2984  T9I 3722
T10 1873  T10I 3349
T11 3746  T11I 2603

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 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 3393Scale 3393, Ian Ring Music Theory
Scale 3395Scale 3395, Ian Ring Music Theory
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian
Scale 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3333Scale 3333, Ian Ring Music Theory
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3461Scale 3461, Ian Ring Music Theory
Scale 3525Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
Scale 3141Scale 3141: Kanitonic, Ian Ring Music TheoryKanitonic
Scale 3269Scale 3269: Raga Malarani, Ian Ring Music TheoryRaga Malarani
Scale 3653Scale 3653: Sathimic, Ian Ring Music TheorySathimic
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian
Scale 2373Scale 2373: Dyptitonic, Ian Ring Music TheoryDyptitonic
Scale 2885Scale 2885: Byrimic, Ian Ring Music TheoryByrimic
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic

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.