The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1693: "Dogian"

Scale 1693: Dogian, 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
Dogian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,7,9,10}
Forte Number7-29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1837
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes6
Prime?no
prime: 727
Deep Scaleno
Interval Vector344352
Interval Spectrump5m3n4s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}331.43
D♯{3,7,10}331.43
Minor Triadscm{0,3,7}321.29
gm{7,10,2}142.14
am{9,0,4}241.86
Diminished Triads{4,7,10}231.57
{9,0,3}231.71
Parsimonious Voice Leading Between Common Triads of Scale 1693. Created by Ian Ring ©2019 cm cm C C cm->C D# D# cm->D# cm->a° C->e° am am C->am D#->e° gm gm D#->gm 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
Radius2
Self-Centeredno
Central Verticescm
Peripheral Verticesgm, am

Modes

Modes are the rotational transformation of this scale. Scale 1693 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1447
Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
3rd mode:
Scale 2771
Scale 2771: Marva That, Ian Ring Music TheoryMarva That
4th mode:
Scale 3433
Scale 3433: Thonian, Ian Ring Music TheoryThonian
5th mode:
Scale 941
Scale 941: Mela Jhankaradhvani, Ian Ring Music TheoryMela Jhankaradhvani
6th mode:
Scale 1259
Scale 1259: Stadian, Ian Ring Music TheoryStadian
7th mode:
Scale 2677
Scale 2677: Thodian, Ian Ring Music TheoryThodian

Prime

The prime form of this scale is Scale 727

Scale 727Scale 727: Phradian, Ian Ring Music TheoryPhradian

Complement

The heptatonic modal family [1693, 1447, 2771, 3433, 941, 1259, 2677] (Forte: 7-29) is the complement of the pentatonic modal family [331, 709, 1201, 1577, 2213] (Forte: 5-29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1693 is 1837

Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1693 is chiral, and its enantiomorph is scale 1837

Scale 1837Scale 1837: Dalian, Ian Ring Music TheoryDalian

Transformations:

T0 1693  T0I 1837
T1 3386  T1I 3674
T2 2677  T2I 3253
T3 1259  T3I 2411
T4 2518  T4I 727
T5 941  T5I 1454
T6 1882  T6I 2908
T7 3764  T7I 1721
T8 3433  T8I 3442
T9 2771  T9I 2789
T10 1447  T10I 1483
T11 2894  T11I 2966

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 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
Scale 1689Scale 1689: Lorimic, Ian Ring Music TheoryLorimic
Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 1677Scale 1677: Raga Manavi, Ian Ring Music TheoryRaga Manavi
Scale 1709Scale 1709: Dorian, Ian Ring Music TheoryDorian
Scale 1725Scale 1725: Minor Bebop, Ian Ring Music TheoryMinor Bebop
Scale 1757Scale 1757, Ian Ring Music Theory
Scale 1565Scale 1565, Ian Ring Music Theory
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
Scale 1949Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic
Scale 1181Scale 1181: Katagimic, Ian Ring Music TheoryKatagimic
Scale 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending
Scale 669Scale 669: Gycrimic, Ian Ring Music TheoryGycrimic
Scale 2717Scale 2717: Epygian, Ian Ring Music TheoryEpygian
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic

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.