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Scale 2761: "Dagimic"

Scale 2761: Dagimic, 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
Dagimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,6,7,9,11}
Forte Number6-Z28
Rotational Symmetrynone
Reflection Axes3
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 619
Deep Scaleno
Interval Vector224322
Interval Spectrump2m3n4s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,6}
<3> = {5,6,7}
<4> = {6,8,9}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[6]
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 TriadsB{11,3,6}331.43
Minor Triadscm{0,3,7}331.43
Augmented TriadsD♯+{3,7,11}231.57
Diminished Triads{0,3,6}231.57
d♯°{3,6,9}231.57
f♯°{6,9,0}231.71
{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 2761. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° d#° d#° f#° f#° d#°->f#° d#°->B D#+->B f#°->a°

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2761 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 857
Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
3rd mode:
Scale 619
Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian HexatonicThis is the prime mode
4th mode:
Scale 2357
Scale 2357: Raga Sarasanana, Ian Ring Music TheoryRaga Sarasanana
5th mode:
Scale 1613
Scale 1613: Thylimic, Ian Ring Music TheoryThylimic
6th mode:
Scale 1427
Scale 1427: Lolimic, Ian Ring Music TheoryLolimic

Prime

The prime form of this scale is Scale 619

Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic

Complement

The hexatonic modal family [2761, 857, 619, 2357, 1613, 1427] (Forte: 6-Z28) is the complement of the hexatonic modal family [667, 869, 1241, 1619, 2381, 2857] (Forte: 6-Z49)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2761 is 619

Scale 619Scale 619: Double-Phrygian Hexatonic, Ian Ring Music TheoryDouble-Phrygian Hexatonic

Transformations:

T0 2761  T0I 619
T1 1427  T1I 1238
T2 2854  T2I 2476
T3 1613  T3I 857
T4 3226  T4I 1714
T5 2357  T5I 3428
T6 619  T6I 2761
T7 1238  T7I 1427
T8 2476  T8I 2854
T9 857  T9I 1613
T10 1714  T10I 3226
T11 3428  T11I 2357

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 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 2765Scale 2765: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 2753Scale 2753, Ian Ring Music Theory
Scale 2757Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi
Scale 2769Scale 2769: Dyrimic, Ian Ring Music TheoryDyrimic
Scale 2777Scale 2777: Aeolian Harmonic, Ian Ring Music TheoryAeolian Harmonic
Scale 2793Scale 2793: Eporian, Ian Ring Music TheoryEporian
Scale 2697Scale 2697: Katagitonic, Ian Ring Music TheoryKatagitonic
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2633Scale 2633: Bartók Beta Chord, Ian Ring Music TheoryBartók Beta Chord
Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic
Scale 3017Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
Scale 2249Scale 2249: Raga Multani, Ian Ring Music TheoryRaga Multani
Scale 2505Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
Scale 3273Scale 3273: Raga Jivantini, Ian Ring Music TheoryRaga Jivantini
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 713Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns

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.