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Scale 2767: "Katydyllic"

Scale 2767: Katydyllic, 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

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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
Katydyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,6,7,9,11}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3691
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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
Major TriadsD{2,6,9}342
G{7,11,2}242.18
B{11,3,6}441.82
Minor Triadscm{0,3,7}342
f♯m{6,9,1}242.27
bm{11,2,6}341.91
Augmented TriadsD♯+{3,7,11}341.91
Diminished Triads{0,3,6}242.09
d♯°{3,6,9}242.09
f♯°{6,9,0}242.36
{9,0,3}242.27
Parsimonious Voice Leading Between Common Triads of Scale 2767. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° D D d#° d#° D->d#° f#m f#m D->f#m bm bm D->bm d#°->B Parsimonious Voice Leading Between Common Triads of Scale 2767. Created by Ian Ring ©2019 G D#+->G D#+->B f#° f#° f#°->f#m f#°->a° G->bm bm->B

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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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2767 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3431
Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
3rd mode:
Scale 3763
Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
4th mode:
Scale 3929
Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
5th mode:
Scale 1003
Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
6th mode:
Scale 2549
Scale 2549: Rydyllic, Ian Ring Music TheoryRydyllic
7th mode:
Scale 1661
Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
8th mode:
Scale 1439
Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [2767, 3431, 3763, 3929, 1003, 2549, 1661, 1439] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2767 is 3691

Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2767 is chiral, and its enantiomorph is scale 3691

Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic

Transformations:

T0 2767  T0I 3691
T1 1439  T1I 3287
T2 2878  T2I 2479
T3 1661  T3I 863
T4 3322  T4I 1726
T5 2549  T5I 3452
T6 1003  T6I 2809
T7 2006  T7I 1523
T8 4012  T8I 3046
T9 3929  T9I 1997
T10 3763  T10I 3994
T11 3431  T11I 3893

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 2765Scale 2765: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 2759Scale 2759: Mela Pavani, Ian Ring Music TheoryMela Pavani
Scale 2775Scale 2775: Godyllic, Ian Ring Music TheoryGodyllic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 2799Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 2255Scale 2255: Dylian, Ian Ring Music TheoryDylian
Scale 2511Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3791Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic

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.