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Scale 1375: "Bothyllic"

Scale 1375: Bothyllic, 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
Bothyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,6,8,10}
Forte Number8-21
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?yes
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[4]
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1375 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2735
Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
3rd mode:
Scale 3415
Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
4th mode:
Scale 3755
Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
5th mode:
Scale 3925
Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
6th mode:
Scale 2005
Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
7th mode:
Scale 1525
Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
8th mode:
Scale 1405
Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [1375, 2735, 3415, 3755, 3925, 2005, 1525, 1405] (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 1375 is 3925

Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic

Transformations:

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

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 1373Scale 1373: Storian, Ian Ring Music TheoryStorian
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian
Scale 1367Scale 1367: Leading Whole-Tone Inverse, Ian Ring Music TheoryLeading Whole-Tone Inverse
Scale 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic
Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic
Scale 1311Scale 1311: Bynian, Ian Ring Music TheoryBynian
Scale 1343Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
Scale 1503Scale 1503: Epiryllian, Ian Ring Music TheoryEpiryllian
Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic

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.