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Scale 3485: "Sabach"

Scale 3485: Sabach, 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

Modern Greek
Sabach
Sambah
Zeitler
Kyptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,7,8,10,11}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1847
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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 TriadsC{0,4,7}342.15
D♯{3,7,10}342.08
E{4,8,11}342
G{7,11,2}342.08
G♯{8,0,3}342.15
Minor Triadscm{0,3,7}331.92
em{4,7,11}431.77
gm{7,10,2}252.62
g♯m{8,11,3}431.77
Augmented TriadsC+{0,4,8}352.38
D♯+{3,7,11}531.54
Diminished Triads{4,7,10}242.31
g♯°{8,11,2}242.31
Parsimonious Voice Leading Between Common Triads of Scale 3485. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E C+->G# D# D# D#->D#+ D#->e° gm gm D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3485. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m e°->em em->E E->g#m gm->G g#° g#° G->g#° g#°->g#m g#m->G#

view full size

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.

Diameter5
Radius3
Self-Centeredno
Central Verticescm, D♯+, em, g♯m
Peripheral VerticesC+, gm

Modes

Modes are the rotational transformation of this scale. Scale 3485 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1895
Scale 1895: Salyllic, Ian Ring Music TheorySalyllic
3rd mode:
Scale 2995
Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
4th mode:
Scale 3545
Scale 3545: Thyptyllic, Ian Ring Music TheoryThyptyllic
5th mode:
Scale 955
Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
6th mode:
Scale 2525
Scale 2525: Aeolaryllic, Ian Ring Music TheoryAeolaryllic
7th mode:
Scale 1655
Scale 1655: Katygyllic, Ian Ring Music TheoryKatygyllic
8th mode:
Scale 2875
Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [3485, 1895, 2995, 3545, 955, 2525, 1655, 2875] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3485 is 1847

Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3485 is chiral, and its enantiomorph is scale 1847

Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic

Transformations:

T0 3485  T0I 1847
T1 2875  T1I 3694
T2 1655  T2I 3293
T3 3310  T3I 2491
T4 2525  T4I 887
T5 955  T5I 1774
T6 1910  T6I 3548
T7 3820  T7I 3001
T8 3545  T8I 1907
T9 2995  T9I 3814
T10 1895  T10I 3533
T11 3790  T11I 2971

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 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 3481Scale 3481: Katathian, Ian Ring Music TheoryKatathian
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
Scale 3469Scale 3469: Monian, Ian Ring Music TheoryMonian
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 3517Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 3357Scale 3357: Phrodian, Ian Ring Music TheoryPhrodian
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 2461Scale 2461: Sagian, Ian Ring Music TheorySagian
Scale 2973Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
Scale 1437Scale 1437: Sabach ascending, Ian Ring Music TheorySabach ascending

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.