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Scale 3415: "Ionaptyllic"

Scale 3415: Ionaptyllic, 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
Ionaptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,6,8,10,11}
Forte Number8-21
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 1375
Deep Scaleno
Interval Vector474643
Interval Spectrump4m6n4s7d4t3
Distribution Spectra<1> = {1,2}
<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> = {10,11}
Spectra Variation2
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tones[0]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 3415 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3755
Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
3rd mode:
Scale 3925
Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
4th mode:
Scale 2005
Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
5th mode:
Scale 1525
Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
6th mode:
Scale 1405
Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
7th mode:
Scale 1375
Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllicThis is the prime mode
8th mode:
Scale 2735
Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic

Prime

The prime form of this scale is Scale 1375

Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

Complement

The octatonic modal family [3415, 3755, 3925, 2005, 1525, 1405, 1375, 2735] (Forte: 8-21) is the complement of the tetratonic modal family [85, 1045, 1285, 1345] (Forte: 4-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3415 is itself, because it is a palindromic scale!

Scale 3415Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic

Transformations:

T0 3415  T0I 3415
T1 2735  T1I 2735
T2 1375  T2I 1375
T3 2750  T3I 2750
T4 1405  T4I 1405
T5 2810  T5I 2810
T6 1525  T6I 1525
T7 3050  T7I 3050
T8 2005  T8I 2005
T9 4010  T9I 4010
T10 3925  T10I 3925
T11 3755  T11I 3755

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 3413Scale 3413: Leading Whole-tone, Ian Ring Music TheoryLeading Whole-tone
Scale 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3399Scale 3399: Zonian, Ian Ring Music TheoryZonian
Scale 3407Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
Scale 3447Scale 3447: Mogyllian, Ian Ring Music TheoryMogyllian
Scale 3351Scale 3351: Karian, Ian Ring Music TheoryKarian
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3159Scale 3159: Stocrian, Ian Ring Music TheoryStocrian
Scale 3287Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse

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.