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Scale 1423: "Doptian"

Scale 1423: Doptian, 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
Doptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,7,8,10}
Forte Number7-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3637
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes6
Prime?no
prime: 431
Deep Scaleno
Interval Vector443352
Interval Spectrump5m3n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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 TriadsD♯{3,7,10}221.2
G♯{8,0,3}142
Minor Triadscm{0,3,7}231.4
gm{7,10,2}231.4
Diminished Triads{7,10,1}142
Parsimonious Voice Leading Between Common Triads of Scale 1423. Created by Ian Ring ©2019 cm cm D# D# cm->D# G# G# cm->G# gm gm D#->gm g°->gm

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 VerticesD♯
Peripheral Verticesg°, G♯

Modes

Modes are the rotational transformation of this scale. Scale 1423 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2759
Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
3rd mode:
Scale 3427
Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
4th mode:
Scale 3761
Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri
5th mode:
Scale 491
Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
6th mode:
Scale 2293
Scale 2293: Gorian, Ian Ring Music TheoryGorian
7th mode:
Scale 1597
Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian

Prime

The prime form of this scale is Scale 431

Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian

Complement

The heptatonic modal family [1423, 2759, 3427, 3761, 491, 2293, 1597] (Forte: 7-14) is the complement of the pentatonic modal family [167, 901, 1249, 2131, 3113] (Forte: 5-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1423 is 3637

Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1423 is chiral, and its enantiomorph is scale 3637

Scale 3637Scale 3637: Raga Rageshri, Ian Ring Music TheoryRaga Rageshri

Transformations:

T0 1423  T0I 3637
T1 2846  T1I 3179
T2 1597  T2I 2263
T3 3194  T3I 431
T4 2293  T4I 862
T5 491  T5I 1724
T6 982  T6I 3448
T7 1964  T7I 2801
T8 3928  T8I 1507
T9 3761  T9I 3014
T10 3427  T10I 1933
T11 2759  T11I 3866

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 1421Scale 1421: Raga Trimurti, Ian Ring Music TheoryRaga Trimurti
Scale 1419Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
Scale 1415Scale 1415, Ian Ring Music Theory
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
Scale 1455Scale 1455: Phrygiolian, Ian Ring Music TheoryPhrygiolian
Scale 1487Scale 1487: Mothyllic, Ian Ring Music TheoryMothyllic
Scale 1295Scale 1295, Ian Ring Music Theory
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 1167Scale 1167: Aerodimic, Ian Ring Music TheoryAerodimic
Scale 1679Scale 1679: Kydian, Ian Ring Music TheoryKydian
Scale 1935Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
Scale 399Scale 399: Zynimic, Ian Ring Music TheoryZynimic
Scale 911Scale 911: Radian, Ian Ring Music TheoryRadian
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 3471Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic

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.