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Scale 3735

Scale 3735, 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).

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,7,9,10,11}
Forte Number8-10
Rotational Symmetrynone
Reflection Axes5.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 765
Deep Scaleno
Interval Vector566452
Interval Spectrump5m4n6s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {7,9,10}
<7> = {9,10,11}
Spectra Variation2.75
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[11]
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}341.9
G{7,11,2}242.1
A{9,1,4}342.1
Minor Triadsem{4,7,11}341.9
gm{7,10,2}342.1
am{9,0,4}242.1
Diminished Triadsc♯°{1,4,7}242.1
{4,7,10}242.1
{7,10,1}242.1
a♯°{10,1,4}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3735. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em am am C->am A A c#°->A e°->em gm gm e°->gm Parsimonious Voice Leading Between Common Triads of Scale 3735. Created by Ian Ring ©2019 G em->G g°->gm a#° a#° g°->a#° gm->G am->A A->a#°

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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 3735 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3915
Scale 3915, Ian Ring Music Theory
3rd mode:
Scale 4005
Scale 4005, Ian Ring Music Theory
4th mode:
Scale 2025
Scale 2025, Ian Ring Music Theory
5th mode:
Scale 765
Scale 765, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 1215
Scale 1215, Ian Ring Music Theory
7th mode:
Scale 2655
Scale 2655, Ian Ring Music Theory
8th mode:
Scale 3375
Scale 3375, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 765

Scale 765Scale 765, Ian Ring Music Theory

Complement

The octatonic modal family [3735, 3915, 4005, 2025, 765, 1215, 2655, 3375] (Forte: 8-10) is the complement of the tetratonic modal family [45, 1035, 1665, 2565] (Forte: 4-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3735 is 3375

Scale 3375Scale 3375, Ian Ring Music Theory

Transformations:

T0 3735  T0I 3375
T1 3375  T1I 2655
T2 2655  T2I 1215
T3 1215  T3I 2430
T4 2430  T4I 765
T5 765  T5I 1530
T6 1530  T6I 3060
T7 3060  T7I 2025
T8 2025  T8I 4050
T9 4050  T9I 4005
T10 4005  T10I 3915
T11 3915  T11I 3735

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 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
Scale 3731Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
Scale 3739Scale 3739: Epanyllic, Ian Ring Music TheoryEpanyllic
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 3719Scale 3719, Ian Ring Music Theory
Scale 3727Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 3799Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
Scale 3607Scale 3607, Ian Ring Music Theory
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3863Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian

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.