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Scale 3997: "Dogygic"

Scale 3997: Dogygic, 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
Dogygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,4,7,8,9,10,11}
Forte Number9-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1855
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 959
Deep Scaleno
Interval Vector766773
Interval Spectrump7m7n6s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3997 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2023
Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
3rd mode:
Scale 3059
Scale 3059: Madygic, Ian Ring Music TheoryMadygic
4th mode:
Scale 3577
Scale 3577: Loptygic, Ian Ring Music TheoryLoptygic
5th mode:
Scale 959
Scale 959: Katylygic, Ian Ring Music TheoryKatylygicThis is the prime mode
6th mode:
Scale 2527
Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
7th mode:
Scale 3311
Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
8th mode:
Scale 3703
Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
9th mode:
Scale 3899
Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic

Prime

The prime form of this scale is Scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Complement

The nonatonic modal family [3997, 2023, 3059, 3577, 959, 2527, 3311, 3703, 3899] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3997 is 1855

Scale 1855Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3997 is chiral, and its enantiomorph is scale 1855

Scale 1855Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic

Transformations:

T0 3997  T0I 1855
T1 3899  T1I 3710
T2 3703  T2I 3325
T3 3311  T3I 2555
T4 2527  T4I 1015
T5 959  T5I 2030
T6 1918  T6I 4060
T7 3836  T7I 4025
T8 3577  T8I 3955
T9 3059  T9I 3815
T10 2023  T10I 3535
T11 4046  T11I 2975

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 3999Scale 3999: Dydyllian, Ian Ring Music TheoryDydyllian
Scale 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
Scale 3995Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
Scale 3989Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
Scale 3981Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 4029Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 3869Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
Scale 3933Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
Scale 3485Scale 3485: Sabach, Ian Ring Music TheorySabach
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 1949Scale 1949: Mathyllic, Ian Ring Music TheoryMathyllic

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.