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Scale 1329: "Epygitonic"

Scale 1329: Epygitonic, 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
Epygitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,4,5,8,10}
Forte Number5-30
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 405
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes4
Prime?no
prime: 339
Deep Scaleno
Interval Vector121321
Interval Spectrump2m3ns2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {4,5,6}
<3> = {6,7,8}
<4> = {8,9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.049
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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
Minor Triadsfm{5,8,0}110.5
Augmented TriadsC+{0,4,8}110.5
Parsimonious Voice Leading Between Common Triads of Scale 1329. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm

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.

Diameter1
Radius1
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1329 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 339
Scale 339: Zaptitonic, Ian Ring Music TheoryZaptitonicThis is the prime mode
3rd mode:
Scale 2217
Scale 2217: Kagitonic, Ian Ring Music TheoryKagitonic
4th mode:
Scale 789
Scale 789: Zogitonic, Ian Ring Music TheoryZogitonic
5th mode:
Scale 1221
Scale 1221: Epyritonic, Ian Ring Music TheoryEpyritonic

Prime

The prime form of this scale is Scale 339

Scale 339Scale 339: Zaptitonic, Ian Ring Music TheoryZaptitonic

Complement

The pentatonic modal family [1329, 339, 2217, 789, 1221] (Forte: 5-30) is the complement of the heptatonic modal family [855, 1395, 1485, 1845, 2475, 2745, 3285] (Forte: 7-30)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1329 is 405

Scale 405Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1329 is chiral, and its enantiomorph is scale 405

Scale 405Scale 405: Raga Bhupeshwari, Ian Ring Music TheoryRaga Bhupeshwari

Transformations:

T0 1329  T0I 405
T1 2658  T1I 810
T2 1221  T2I 1620
T3 2442  T3I 3240
T4 789  T4I 2385
T5 1578  T5I 675
T6 3156  T6I 1350
T7 2217  T7I 2700
T8 339  T8I 1305
T9 678  T9I 2610
T10 1356  T10I 1125
T11 2712  T11I 2250

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 1331Scale 1331: Raga Vasantabhairavi, Ian Ring Music TheoryRaga Vasantabhairavi
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
Scale 1313Scale 1313, Ian Ring Music Theory
Scale 1321Scale 1321: Blues Minor, Ian Ring Music TheoryBlues Minor
Scale 1297Scale 1297: Aeolic, Ian Ring Music TheoryAeolic
Scale 1361Scale 1361: Bolitonic, Ian Ring Music TheoryBolitonic
Scale 1393Scale 1393: Mycrimic, Ian Ring Music TheoryMycrimic
Scale 1457Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
Scale 1073Scale 1073, Ian Ring Music Theory
Scale 1201Scale 1201: Mixolydian Pentatonic, Ian Ring Music TheoryMixolydian Pentatonic
Scale 1585Scale 1585: Raga Khamaji Durga, Ian Ring Music TheoryRaga Khamaji Durga
Scale 1841Scale 1841: Thogimic, Ian Ring Music TheoryThogimic
Scale 305Scale 305: Gonic, Ian Ring Music TheoryGonic
Scale 817Scale 817: Zothitonic, Ian Ring Music TheoryZothitonic
Scale 2353Scale 2353: Raga Girija, Ian Ring Music TheoryRaga Girija
Scale 3377Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic

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.