DiArMaqAr

There is a bunch of data about maqamat here: https://github.com/Music-Intelligence-Lab/DiArMaqAr

I have already spent too much time on maqamat for my textbook and should surely focus on other things, or at least focus on finishing what I've already written before starting in on a new source. But I probably won't.

...

Here are pitch names for different ajnas from DiArMaqAr/data/ajnas.json. I've turned it into a flat list instead of a json thing.

[awj, kurdān, muḥayyar, buzurk]: jins awj

[chahārgāh, nawā, ḥusaynī, ʿajam]: jins chahārgāh

[dūgāh, būselīk/ʿushshāq, chahārgāh, nawā]: jins būselīk (al-Ḥilū)

[dūgāh, kurdī, chahārgāh, nawā]: jins kurd

[dūgāh, kurdī, chahārgāh, ḥijāz]: jins ṣabā zamzam

[dūgāh, kurdī, chahārgāh, ḥiṣār, ḥusaynī]: jins athar kurd

[dūgāh, kurdī, ḥijāz, nawā]: jins ḥijāz

[dūgāh, nīm būselīk, chahārgāh, nawā]: jins būselīk (al-Shawwā)

[dūgāh, nīm būselīk, chahārgāh, ḥiṣār]: jins ḥiṣār

[dūgāh, segāh, chahārgāh, nawā]: jins bayyāt

[dūgāh, segāh, chahārgāh, ḥijāz]: jins ṣabā

[kawasht, rāst, kurdī, būselīk/ʿushshāq]: jins awj ʾārāʾ (al-Ḥilū)

[rāst, dūgāh, kurdī, chahārgāh]: jins nahāwand

[rāst, dūgāh, kurdī, ḥijāz, nawā]: jins nikrīz

[rāst, dūgāh, kurdī, ḥijāz]: jins nawā athar

[rāst, dūgāh, segāh, chahārgāh]: jins rāst

[rāst, zīrgūleh, būselīk/ʿushshāq, chahārgāh]: jins ḥijāz kār

[rāst, zīrgūleh, kurdī, chahārgāh]: jins ḥijāz kār kurd

[segāh, chahārgāh, nawā, ḥiṣār]: jins huzām

[segāh, chahārgāh, nawā, ḥusaynī]: jins segāh

[yegāh, qarār ḥiṣār, kawasht, rāst]: jins shad ʿarabān

[yegāh, qarār ḥiṣār, ʿajam ʿushayrān, zīrgūleh]: jins qāf

[yegāh, ʿushayrān, ʿirāq, rāst]: jins yegāh

[ʿajam ʿushayrān, rāst, dūgāh, kurdī]: jins ʿajam ʿushayrān

[ʿajam ʿushayrān, rāst, dūgāh, segāh]: jins mahrān

[ʿajam ʿushayrān, zīrgūleh, dūgāh, kurdī]: jins ʿajam sulṭānī

[ʿirāq, rāst, būselīk/ʿushshāq, chahārgāh]: jins ṭuraf

[ʿirāq, rāst, dūgāh, būselīk/ʿushshāq]: jins faraḥnāk

[ʿirāq, rāst, dūgāh, būselīk/ʿushshāq]: jins māyeh

[ʿirāq, rāst, dūgāh, kurdī]: jins rāḥat al-arwāḥ

[ʿirāq, rāst, dūgāh, segāh]: jins ʿirāq

[ʿirāq, rāst, dūgāh, tīk būselīk]: jins bulbula

[ʿirāq, rāst, kurdī, segāh]: jins awj ʾārāʾ (al-Shawwā)

[ʿirāq, zīrgūleh, dūgāh, būselīk/ʿushshāq]: jins mustaʿār

[ʿirāq, zīrgūleh, dūgāh, kurdī]: jins ashwāq al-kharīf

[ʿirāq, zīrgūleh, dūgāh, segāh]: jins mazīj al-ṭīb

[ʿushayrān, ʿajam ʿushayrān, rāst, zīrgūleh]: jins bint ʿabqar

[ʿushayrān, ʿajam ʿushayrān, zīrgūleh, dūgāh]: jins sūzdal

Next shall we look at some maqamat? The source has data for one hundred and eleven of them, and some of them are new to me. That's exciting. Here are the names at least:

    [al-lāmī, athar kurd, awj būselīk, awj ʾārāʾ, awj, banjegāh 2, banjegāh zāʾid, banjegāh, bayyāt būselīk, bayyāt ʿarabān, bayyāt, bayyātī ʿushayrān, besendīdah, beste ḥiṣār, bestenegār, bābā ṭāhir, būselīk, chahārgāh, dhawq ṭarab, dilkesh ḥūrān, dilkeshīdah, dilkishā, dilnishīn, dūgāh, faraḥfazzā, faraḥnāk, gulʿazār, humāyūn, huzām, iṣfahān būselīk, iṣfahān, jānfazā, khuzām jadīd, kurd, kurdān, kūchek, majlis afrūz, mustaʿār, muḥayyar kurdī, muḥayyar, māhūr būselīk, māhūr, māyeh, nahāwand kabīr, nahāwand, nairūz, nawrūz sulṭānī, nawā athar, nawā būselīk, nawā kurdī, nawā, negār, nikrīz, nishābūrek, niyāz, nuhuft, nāz, nīshābūr, qarjahār, qārjighār, rawnaq namā, rāst, rāḥat al-arwāḥ, rāḥatfazzā, segāh, shahnāz būselīk, shahnāz kurdī, shahnāz, shahr nāz, shat ʿarabān, shawq afzā, shawq dil, shawq āwr, shawq ṭarab, sulṭānī yegāh, sunbula nahāwand, sāzkār, sūzdalārah, sūzdāl, sūznāk, wajh ʿarḍibār, yegāh, zingulah, zāwīl, ʿajam būselīk, ʿajam kurdī, ʿajam ʿushayrān, ʿajam/ʿajam muraṣṣaʿ, ʿanbar afshān, ʿarḍibār, ʿirāq, ʿushayrān, ʿushshāq miṣrī, ʿushshāq, ḥijāz būselīk, ḥijāz kār kurd, ḥijāz kār, ḥijāz ʿushayrān, ḥijāz, ḥiṣār kurdī, ḥiṣār, ḥusaynī būselīk, ḥusaynī ʿushayrān, ḥusaynī, ṣabā būselīk, ṣabā kurdī, ṣabā zamzam, ṣabā, ṣafā, ṭarz jadīd, ṭarznwīn]

The file on maqamat is huge. I'm definitely not going to share it all. Here are note names, ascending and descending, for the maqamat. That's a good start, I think.

* maqām rāst:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj]

Descending: [ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām ḥijāz:

Ascending: [dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, awj, kurdān, muḥayyar, jawāb nīm būselīk, māhūrān]

Descending: [māhūrān, jawāb nīm būselīk, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, ḥijāz, kurdī, dūgāh]

* maqām kurd:

Ascending: [dūgāh, kurdī, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh]

* maqām ḥijāz kār kurd:

Ascending: [rāst, zīrgūleh, kurdī, chahārgāh, nawā, ḥiṣār, ʿajam]

Descending: [ʿajam, ḥiṣār, nawā, chahārgāh, kurdī, zīrgūleh, rāst]

* maqām nikrīz:

Ascending: [rāst, dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, ʿajam]

Descending: [ʿajam, ḥusaynī, nawā, ḥijāz, kurdī, dūgāh, rāst]

* maqām nawā athar:

Ascending: [rāst, dūgāh, kurdī, ḥijāz, nawā, ḥiṣār, nīm māhūr]

Descending: [nīm māhūr, ḥiṣār, nawā, ḥijāz, kurdī, dūgāh, rāst]

* maqām bayyāt:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām zingulah:

Ascending: [rāst, zīrgūleh, būselīk/ʿushshāq, chahārgāh, nawā, ḥusaynī, nīm ʿajam]

Descending: [nīm ʿajam, ḥusaynī, nawā, chahārgāh, būselīk/ʿushshāq, zīrgūleh, rāst]

* maqām al-lāmī:

Ascending: [dūgāh, kurdī, chahārgāh, nawā, ḥiṣār, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥiṣār, nawā, chahārgāh, kurdī, dūgāh]

* maqām nahāwand:

Ascending: [rāst, dūgāh, kurdī, chahārgāh, nawā, ḥiṣār, nīm māhūr]

Descending: [ʿajam, ḥiṣār, nawā, chahārgāh, kurdī, dūgāh, rāst]

* maqām nahāwand kabīr:

Ascending: [rāst, dūgāh, kurdī, chahārgāh, nawā, ḥiṣār, māhūr]

Descending: [māhūr, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh, rāst]

* maqām athar kurd:

Ascending: [rāst, zīrgūleh, kurdī, ḥijāz, nawā, ḥiṣār, māhūr]

Descending: [ʿajam, ḥiṣār, nawā, ḥijāz, kurdī, zīrgūleh, rāst]

* maqām qārjighār:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥiṣār, māhūr, kurdān]

Descending: [kurdān, māhūr, ḥiṣār, nawā, chahārgāh, segāh, dūgāh]

* maqām ṣabā:

Ascending: [dūgāh, segāh, chahārgāh, ḥijāz, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, ḥijāz, chahārgāh, segāh, dūgāh]

* maqām ṣabā zamzam:

Ascending: [dūgāh, kurdī, chahārgāh, ḥijāz, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, ḥijāz, chahārgāh, kurdī, dūgāh]

* maqām ʿajam ʿushayrān:

Ascending: [ʿajam ʿushayrān, rāst, dūgāh, kurdī, chahārgāh, nawā, ḥusaynī]

Descending: [ḥusaynī, nawā, chahārgāh, kurdī, dūgāh, rāst, ʿajam ʿushayrān]

* maqām nairūz:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, tīk ḥiṣār, ʿajam]

Descending: [ʿajam, tīk ḥiṣār, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām segāh:

Ascending: [segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān, muḥayyar]

Descending: [muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh]

* maqām huzām:

Ascending: [segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr, kurdān, muḥayyar]

Descending: [muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh]

* maqām rāḥat al-arwāḥ:

Ascending: [ʿirāq, rāst, dūgāh, kurdī, ḥijāz, nawā, ḥusaynī]

Descending: [ḥusaynī, nawā, ḥijāz, kurdī, dūgāh, rāst, ʿirāq]

* maqām sūzdalārah:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam]

Descending: [ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh, rāst]

* maqām ḥijāz kār:

Ascending: [rāst, zīrgūleh, nīm būselīk, chahārgāh, nawā, ḥiṣār, nīm māhūr]

Descending: [nīm māhūr, ḥiṣār, nawā, chahārgāh, nīm būselīk, zīrgūleh, rāst]

* maqām mustaʿār:

Ascending: [segāh, ḥijāz, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar]

Descending: [muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, ḥijāz, segāh]

* maqām ʿirāq:

Ascending: [ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī]

Descending: [ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst, ʿirāq]

* maqām sūznāk:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr, kurdān, muḥayyar, sunbuleh/zawāl]

Descending: [buzurk, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām yegāh:

Ascending: [yegāh, ʿushayrān, ʿirāq, rāst, dūgāh, nīm būselīk, nīm ḥijāz]

Descending: [chahārgāh, segāh, dūgāh, rāst, ʿirāq, ʿushayrān, yegāh]

* maqām faraḥfazzā:

Ascending: [yegāh, ʿushayrān, ʿajam ʿushayrān, rāst, dūgāh, kurdī, chahārgāh]

Descending: [ḥijāz, kurdī, dūgāh, rāst, ʿajam ʿushayrān, ʿushayrān, yegāh]

* maqām shat ʿarabān:

Ascending: [yegāh, qarār ḥiṣār, nīm kawasht, rāst, dūgāh, kurdī, ḥijāz]

Descending: [chahārgāh, kurdī, dūgāh, rāst, nīm kawasht, qarār ḥiṣār, yegāh]

* maqām sulṭānī yegāh:

Ascending: [yegāh, ʿushayrān, ʿajam ʿushayrān, rāst, dūgāh, kurdī, ḥijāz]

Descending: [ḥijāz, kurdī, dūgāh, rāst, ʿajam ʿushayrān, ʿushayrān, yegāh]

* maqām majlis afrūz:

Ascending: [yegāh, ʿushayrān, ʿirāq, rāst, dūgāh, segāh, chahārgāh]

Descending: [chahārgāh, segāh, dūgāh, rāst, ʿirāq, ʿushayrān, yegāh]

* maqām dilkeshīdah:

Ascending: [yegāh, ʿushayrān, ʿajam ʿushayrān, rāst, dūgāh, segāh, ḥijāz]

Descending: [chahārgāh, segāh, dūgāh, rāst, ʿajam ʿushayrān, ʿushayrān, yegāh]

* maqām ʿushayrān:

Ascending: [ʿushayrān, ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā]

Descending: [nawā, chahārgāh, nīm būselīk, dūgāh, rāst, ʿirāq, ʿushayrān]

* maqām bayyātī ʿushayrān:

Ascending: [ʿushayrān, ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar]

Descending: [muḥayyar, kurdān, awj, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh, rāst, ʿirāq, ʿushayrān]

* maqām ḥusaynī ʿushayrān:

Ascending: [ʿushayrān, ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā]

Descending: [nawā, ḥijāz, kurdī, dūgāh, rāst, ʿirāq, ʿushayrān]

* maqām sūzdāl:

Ascending: [ʿushayrān, ʿajam ʿushayrān, zīrgūleh, dūgāh, nīm būselīk, chahārgāh, ḥiṣār, ḥusaynī, ʿajam, shahnāz, muḥayyar]

Descending: [muḥayyar, shahnāz, ʿajam, ḥusaynī, ḥiṣār, chahārgāh, nīm būselīk, dūgāh, zīrgūleh, ʿajam ʿushayrān, ʿushayrān]

* maqām shawq ṭarab:

Ascending: [ʿushayrān, ʿajam ʿushayrān, rāst, dūgāh, segāh, chahārgāh, ḥijāz, ḥusaynī, ʿajam, kurdān, shahnāz, jawāb nīm būselīk, māhūrān]

Descending: [māhūrān, buzurk, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh, rāst, ʿajam ʿushayrān, ʿushayrān]

* maqām nuhuft:

Ascending: [ʿushayrān, ʿirāq, rāst, dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, awj, kurdān, muḥayyar, buzurk, māhūrān]

Descending: [māhūrān, buzurk, muḥayyar, kurdān, awj, ḥusaynī, nawā, ḥijāz, kurdī, dūgāh, rāst, ʿirāq, ʿushayrān]

* maqām shawq afzā:

Ascending: [ʿajam ʿushayrān, rāst, dūgāh, segāh, chahārgāh, ḥijāz, ḥusaynī, ʿajam, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, jawāb nīm būselīk, shahnāz, kurdān, ʿajam, ḥusaynī, ḥijāz, chahārgāh, kurdī, dūgāh, rāst, ʿajam ʿushayrān]

* maqām shawq āwr:

Ascending: [ʿajam ʿushayrān, rāst, dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, ʿajam, ḥiṣār, nawā, chahārgāh, kurdī, dūgāh, rāst, ʿajam ʿushayrān]

* maqām awj:

Ascending: [ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī]

Descending: [ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst, ʿirāq]

* maqām faraḥnāk:

Ascending: [ʿirāq, rāst, dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī]

Descending: [ḥusaynī, nawā, nīm ḥijāz, nīm būselīk, dūgāh, rāst, ʿirāq]

* maqām bestenegār:

Ascending: [ʿirāq, rāst, dūgāh, segāh, chahārgāh, ḥijāz, ḥusaynī, ʿajam, kurdān, muḥayyar]

Descending: [shahnāz, kurdān, ʿajam, ḥusaynī, ḥijāz, chahārgāh, segāh, dūgāh, rāst, ʿirāq]

* maqām awj ʾārāʾ:

Ascending: [ʿirāq, rāst, kurdī, segāh, ḥijāz, nawā, ʿajam, awj, shahnāz, muḥayyar]

Descending: [muḥayyar, shahnāz, awj, ʿajam, nawā, ḥijāz, segāh, kurdī, rāst, ʿirāq]

* maqām rawnaq namā:

Ascending: [ʿirāq, rāst, kurdī, segāh, ḥijāz, nawā, ḥusaynī, ʿajam, kurdān, sunbuleh/zawāl, buzurk]

Descending: [buzurk, sunbuleh/zawāl, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, kurdī, rāst, ʿirāq]

* maqām būselīk:

Ascending: [dūgāh, nīm būselīk, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām chahārgāh:

Ascending: [chahārgāh, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar, buzurk]

Descending: [buzurk, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh]

* maqām dilkishā:

Ascending: [rāst, zīrgūleh, segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr]

Descending: [nīm māhūr, ḥiṣār, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām dilkesh ḥūrān:

Ascending: [ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān, shahnāz]

Descending: [shahnāz, kurdān, awj, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst, ʿirāq]

* maqām māhūr:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, nīm māhūr]

Descending: [ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām sāzkār:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj]

Descending: [ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, kurdī, rāst]

* maqām rāḥatfazzā:

Ascending: [ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, chahārgāh, kurdī, dūgāh, rāst, ʿirāq]

* maqām zāwīl:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr]

Descending: [ʿajam, ḥusaynī, nawā, ḥijāz, kurdī, dūgāh, rāst]

* maqām sunbula nahāwand:

Ascending: [rāst, dūgāh, kurdī, chahārgāh, ṣabā, ḥusaynī, ʿajam, kurdān, shahnāz, jawāb nīm būselīk, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, chahārgāh, kurdī, dūgāh, rāst]

* maqām besendīdah:

Ascending: [rāst, dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, ʿajam]

Descending: [awj, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām ṭarznwīn:

Ascending: [rāst, zīrgūleh, kurdī, chahārgāh, ṣabā, ḥusaynī, ʿajam, kurdān, shahnāz, jawāb nīm būselīk, māhūrān, saham/ramal tūtī]

Descending: [saham/ramal tūtī, māhūrān, sunbuleh/zawāl, shahnāz, kurdān, ʿajam, ḥusaynī, ṣabā, chahārgāh, kurdī, zīrgūleh, rāst]

* maqām ʿushshāq:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām ʿushshāq miṣrī:

Ascending: [dūgāh, nīm būselīk, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām muḥayyar:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, awj, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām ḥusaynī:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām qarjahār:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām shahnāz:

Ascending: [dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, ʿajam, shahnāz, muḥayyar, jawāb nīm būselīk, māhūrān]

Descending: [jawāb ḥijāz, sunbuleh/zawāl, muḥayyar, shahnāz, ʿajam, ḥusaynī, nawā, ḥijāz, kurdī, dūgāh]

* maqām humāyūn:

Ascending: [dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, ḥijāz, kurdī, dūgāh]

* maqām bayyāt ʿarabān:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, buzurk, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām nishābūrek:

Ascending: [dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, awj, ḥusaynī, nawā, nīm ḥijāz, nīm būselīk, dūgāh]

* maqām ḥiṣār:

Ascending: [dūgāh, nīm būselīk, chahārgāh, ḥiṣār, ḥusaynī, ʿajam, shahnāz]

Descending: [shahnāz, ʿajam, ḥusaynī, ḥiṣār, chahārgāh, nīm būselīk, dūgāh]

* maqām dūgāh:

Ascending: [dūgāh, segāh, chahārgāh, ṣabā, ḥusaynī, ʿajam, kurdān, shahnāz, jawāb nīm būselīk, māhūrān]

Descending: [māhūrān, buzurk, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, ḥijāz, kurdī, dūgāh]

* maqām ʿarḍibār:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar, buzurk, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, chahārgāh, segāh, dūgāh]

* maqām ʿajam/ʿajam muraṣṣaʿ:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, chahārgāh, segāh, dūgāh]

* maqām nīshābūr:

Ascending: [segāh, ḥijāz, nawā, ḥusaynī, awj, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, ḥijāz, segāh]

* maqām māyeh:

Ascending: [segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān, muḥayyar]

Descending: [muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh]

* maqām wajh ʿarḍibār:

Ascending: [segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān, muḥayyar, sunbuleh/zawāl, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, chahārgāh, segāh]

* maqām shawq dil:

Ascending: [yegāh, ʿushayrān, nīm kawasht, rāst, dūgāh, segāh, chahārgāh]

Descending: [chahārgāh, segāh, dūgāh, rāst, nīm kawasht, qarār ḥiṣār, yegāh]

* maqām bābā ṭāhir:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām gulʿazār:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar, buzurk, māhūrān]

Descending: [māhūrān, sunbuleh/zawāl, muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, chahārgāh, segāh, dūgāh]

* maqām iṣfahān:

Ascending: [dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, awj, ḥusaynī, nawā, nīm ḥijāz, nīm būselīk, dūgāh]

* maqām nawā:

Ascending: [dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, nīm ḥijāz, nīm būselīk, dūgāh]

* maqām niyāz:

Ascending: [dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, awj, ḥusaynī, nawā, nīm ḥijāz, nīm būselīk, dūgāh]

* maqām dilnishīn:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj]

Descending: [ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām kūchek:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, ḥijāz, chahārgāh, segāh, dūgāh]

* maqām kurdān:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh]

* maqām khuzām jadīd:

Ascending: [ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr, kurdān, muḥayyar]

Descending: [muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst, ʿirāq]

* maqām dhawq ṭarab:

Ascending: [dūgāh, kurdī, chahārgāh, nawā, ḥiṣār, nīm māhūr, kurdān, muḥayyar, sunbuleh/zawāl]

Descending: [sunbuleh/zawāl, muḥayyar, kurdān, nīm māhūr, ḥiṣār, nawā, ḥijāz, kurdī, dūgāh]

* maqām ḥijāz ʿushayrān:

Ascending: [ʿushayrān, ʿajam ʿushayrān, rāst, dūgāh, kurdī, ḥijāz, nawā]

Descending: [nawā, ḥijāz, kurdī, dūgāh, rāst, ʿajam ʿushayrān, ʿushayrān]

* maqām jānfazā:

Ascending: [ʿushayrān, ʿirāq, rāst, dūgāh, segāh, chahārgāh, ḥijāz]

Descending: [ḥijāz, chahārgāh, segāh, dūgāh, rāst, ʿirāq, ʿushayrān]

* maqām banjegāh zāʾid:

Ascending: [rāst, dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, awj]

Descending: [awj, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh, rāst]

* maqām negār:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥiṣār, nīm māhūr]

Descending: [nīm māhūr, ḥiṣār, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām ṭarz jadīd:

Ascending: [ʿajam ʿushayrān, rāst, dūgāh, kurdī, chahārgāh, nawā, ḥusaynī]

Descending: [ḥusaynī, nawā, chahārgāh, kurdī, dūgāh, rāst, ʿajam ʿushayrān]

* maqām ṣabā būselīk:

Ascending: [dūgāh, segāh, chahārgāh, ḥijāz, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām ʿajam būselīk:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām ḥijāz būselīk:

Ascending: [dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām awj būselīk:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām nawā būselīk:

Ascending: [dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām bayyāt būselīk:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām ḥusaynī būselīk:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām shahnāz būselīk:

Ascending: [dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, ʿajam, shahnāz]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām iṣfahān būselīk:

Ascending: [dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām māhūr būselīk:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, nīm māhūr, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, nīm būselīk, dūgāh]

* maqām ʿajam kurdī:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh]

* maqām muḥayyar kurdī:

Ascending: [dūgāh, segāh, chahārgāh, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh]

* maqām ṣabā kurdī:

Ascending: [dūgāh, segāh, chahārgāh, ḥijāz, ḥusaynī, ʿajam, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh]

* maqām nawā kurdī:

Ascending: [dūgāh, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, awj, kurdān]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh]

* maqām ḥiṣār kurdī:

Ascending: [dūgāh, nīm būselīk, chahārgāh, ḥiṣār, ḥusaynī, ʿajam, shahnāz]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh]

* maqām shahnāz kurdī:

Ascending: [dūgāh, kurdī, ḥijāz, nawā, ḥusaynī, ʿajam, shahnāz]

Descending: [kurdān, ʿajam, ḥusaynī, nawā, chahārgāh, kurdī, dūgāh]

* maqām ʿanbar afshān:

Ascending: [yegāh, ʿajam ʿushayrān, ʿirāq, rāst, dūgāh, kurdī, chahārgāh, nawā, ḥiṣār, nīm māhūr]

Descending: [ʿajam, ḥiṣār, nawā, chahārgāh, kurdī, dūgāh, rāst, ʿirāq, ʿajam ʿushayrān, yegāh]

* maqām nawrūz sulṭānī:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam]

Descending: [nīm māhūr, ḥiṣār, nawā, chahārgāh, kurdī, dūgāh, rāst]

* maqām shahr nāz:

Ascending: [ʿushayrān, ʿirāq, rāst, dūgāh, segāh, chahārgāh, nawā]

Descending: [nawā, chahārgāh, segāh, dūgāh, rāst, ʿirāq, ʿushayrān]

* maqām banjegāh:

Ascending: [rāst, dūgāh, segāh, chahārgāh, nawā, ḥusaynī, ʿajam]

Descending: [ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst]

* maqām banjegāh 2:

Ascending: [rāst, kurdī, nīm būselīk, nīm ḥijāz, nawā, ḥusaynī, ʿajam, kurdān, muḥayyar]

Descending: [muḥayyar, kurdān, ʿajam, ḥusaynī, nawā, nīm ḥijāz, nīm būselīk, kurdī, rāst]

* maqām nāz:

Ascending: [rāst, dūgāh, segāh, chahārgāh, ḥijāz, ḥusaynī, ʿajam]

Descending: [ʿajam, ḥusaynī, nawā, chahārgāh, segāh, dūgāh, rāst]

I think next we should replace all the perdes/note names with pitches or intervals and do some analysis.

There are 35 note names among the ascending and descending forms of the maqamat:

[awj, buzurk, būselīk/ʿushshāq, chahārgāh, dūgāh, jawāb nīm būselīk, jawāb ḥijāz, kurdān, kurdī, muḥayyar, māhūr, māhūrān, nawā, nīm būselīk, nīm kawasht, nīm māhūr, nīm ʿajam, nīm ḥijāz, qarār ḥiṣār, rāst, saham/ramal tūtī, segāh, shahnāz, sunbuleh/zawāl, tīk ḥiṣār, yegāh, zīrgūleh, ʿajam, ʿajam ʿushayrān, ʿirāq, ʿushayrān, ḥijāz, ḥiṣār, ḥusaynī, ṣabā]

...

What Are Intervals?

I've written most of the content of my microtonal music theory textbook, and now I have to go back edit things until they're clear, informative, and enjoyable to read. I thought that my chapter on Intervals And Tuning Systems was the next one to fix, so I started rewriting it in my head. Unfortunately, the chapter actually starts out pretty strong. So I'm not sure what to do with this text. I might find some other place to work it in. Right now, I just don't want to lose it.

---

What are intervals? This shouldn't a big mystery; they're standard objects of western music theory, but lots of people think about them incorrectly, especially in the microtonal music community.

I'm going to give you a complicated but fairly complete definition of intervals and then we'll spend the rest of the chapter understanding it in detail.

Intervals are vectors abstracted from the prime factorization of frequency ratios. They are the natural domain in which we perform most operations of musical composition. They exist in a one-to-one correspondence with pitches of sheet music like "C#3", and they naturally represent the signed distance between pitches. They have musically significant names like "perfect fifth" and "minor seventh" which can be calculated from their vector coordinates, and these names tell us things about their consonance, how they participate in scales and chords, and how they transform into one another through standard operations like inversion and augmentation. Intervals are also the objects which tuning systems act on, i.e. tune, to produce frequencies and frequency ratios. Finally, intervals are a psycho-acoustically convenient representation of sound combination which allow independent aspects of musical objects to be manipulated independently, and allow dependent aspects of musical objects to be manipulated consistently.

Intervals, if you haven't figured out from the preceding paragraph, are not the same as frequency ratios, and they're not the same as "numbers of steps" in 12 tone equal temperament or other equal temperaments. The microtonal theorists who don't understand this are constantly saying nonsensical things, like that they have changed a frequency ratio into another one, or made two different ratios equal - as though rational numbers like 7/4 and 8/5 were clay in their hands to be molded and mixed. If this book achieves just one thing, I hope that it corrects the language of microtonal music theory to be free of arithmetical errors, simply by teaching the standard western music theory of intervals - and a small extension of this theory for representing music which is non-standard in the West.

...

Indian Music

It's time I learn about Indian music. Hindustani? Carnatic? Shrutis? Let's go.

Here's what I think I know. The basical musical notes are called swaras. Their solfege goes "Sa Ri/Re Ga Ma Pa Dha Ni Sa". They're short for "Shadja, Rishabh, Gandhar, Madhyam, Pancham, Dhaivat, Nishad" in North India, or those words with an additional "-am" in south India. I don't know why "Re" is an option as an abbreviation for "Rishabh", but I'd say it's a more common abbreviation than "Ri".

The scales are called ragas. They're tuned in 5-limit just intonation.

When you sing a raga in solfege, you sing the Ga for the third scale degree whether it's a major third or a minor third. Carnatic music distinguishes textually at least between Ga1, a minor third, and Ga2, a major third. Here are some options for each swara:

(P1 # 1/1) :: Sa

(Grm2 # 256/243) or (m2 # 16/15) :: Re1

(M2 # 10/9) or (AcM2 # 9/8) :: Re2

(Grm3 # 32/27) or (m3 # 6/5) :: Ga1

(M3 # 5/4) or (AcM3 # 81/64) :: Ga2

(P4 # 4/3) or (Ac4 # 27/20) :: Ma1

(AcA4 # 45/32) or (AcAcA4 # 729/512) :: Ma2

(P5 # 3/2) :: Pa

(Grm6 # 128/81) or (m6 # 8/5) :: Dha1

(M6 # 5/3) or (AcM6 # 27/16) :: Dha2

(Grm7 # 16/9) or (m7 # 9/5) :: Ni1

(M7 # 15/8) or (AcM7 # 243/128) :: Ni2

You can see that usually "1" means minor and "2" means major. The only time we break this pattern is with the fourth scale degree, Ma, for which "1" means perfect and "2"  means augmented.

With only one option for ^1 (=Sa) and for ^5 (=Pa), we get 22 options all together. I've sometimes seen (Gr5 # 40/27 @ 680c) discussed in texts on indian scale intonation - I think "mentioned in Bharata's "Natya Shastra" but not used in modern Indian music" is probably a concise explanation of that.

I've also seen a notation system which gives three options each for Ri, Ga, Dha, Ni, but then equates one of each set of three options to another interval. I think the system is basically this:

S  ~ P1 or perfect unison, 

R1 ~ m2 or minor second, 

R2 ~ M2 or major second, 

R3 ~ A2 or augmented second,

G1 ~ d3 or diminished third,

G2 ~ m3 or minor third,

G3 ~ M3 or major third,

M1 ~ P4 or perfect fourth,

M2 ~ A4 or augmented fourth,

P  ~ P5 or perfect fifth

D1 ~ m6 or minor sixth

D2 ~ M6 or major sixth

D3 ~ A6 or augmented sixth

N1 ~ d7 or diminished seventh

N2 ~ m7 or minor seventh

N3 ~ M7 or major seventh

Even though there are 16 lines in this table, it's more like 12 distinct sound levels because they recognize these equivalences:

Ri2 = Ga1 :: m2 ~ d3

Ri3 = Ga2 :: A2 ~ m3

Dha2 = Ni1 :: M6 ~ d7

Dha3 = Ni2 :: A6 ~ m7

I don't like this system at all. In addition to not distinguishing between differences of Ac1 (the options in the previous system), it doesn't distinguish between intervals separated by diminished 2nds, i.e. different letter names. So it's just 12-TET. And it doesn't even use the same numbers as the previous system. They could have done 0 for diminished, 1 for minor, 2 for major, 3 for augmented. Or something. Let's not talk of it again.

The 22 notes from the previous sytem, all the 5-limit options, are called shrutis. There are supposedly some different accounts of the shrutis, but I think the above is the most widely accepted. I have trouble finding differing accounts at least. Sometimes you'll see long names for each individual shruti. I've seen enough disagreement that I decided to just use my own interval names for now, but I think I'll figrue it out and give fairly standard long names for shrutis from both Carnatic and Hindustani music shortly.

...

Some old Indian music theorists talked like the 22 shrutis were equally spaced - 9/8 is a distance of 4 shrutis, 4/3 is a distance of  9 shrutis, 3/2 is a distance of 13 shrutis. This is weird, but actually consistent with a 22-EDO (or 44-EDO or 66-EDO) interpretation. In fact, if you tune all 22-shrutis in 22-EDO, you just get a list of ascending integers. 

P1: 0\22

Grm2: 1\22

m2: 2\22

M2: 3\22

AcM2: 4\22

Grm3: 5\22

m3: 6\22

M3: 7\22

AcM3: 8\22

P4: 9\22

Ac4: 10\22

AcA4: 11\22

AcAcA4: 12\22

P5: 13\22

Grm6: 14\22

m6: 15\22

M6: 16\22

AcM6: 17\22

Grm7: 18\22

m7: 19\22

M7: 20\22

AcM7: 21\22

P8: 22\22

People don't use any of those EDOs for indian music these days, if they ever did. And they might have? But not now. We'll come back to this.

I think it's exciting that the Chinese guqin and the indian shrutis are both 5-limit; in addition to some 5-limit just intonation efforts in the west, there are multiple independent well developed 5-limit composition systems in this world. If you were ever not sure what to do with yourself in 5-limit, or if you weren't sure of the importance of 5-limit just intonation to humankind, just look around for inspiration. It's everywhere.

The full gamut of possible microtones is made of just three relative intervals:

     [Ac1, A1, Grm2] # [81/80, 25/24, 256/243]

I'm not sure of the  tidiest way to represent the relative intervals, but I think this shows some of the regularity:

[P1 (Grm2)

Grm2 (Ac1) m2 (A1) M2 (Ac1) AcM2 (Grm2) 

Grm3 (Ac1) m3 (A1) M3 (Ac1) AcM3 (Grm2) 

P4 (Ac1) Ac4 (A1) AcA4 (Ac1) AcAcA4 (Grm2) 

P5 (Grm2) 

Grm6 (Ac1) m6 (A1) M6 (Ac1) AcM6 (Grm2)

Grm7 (Ac1) m7 (A1) M7 (Ac1) AcM7 (Grm2) 

P8]

I'd also like to note that the AcAcA4, while it might look like the weirdest interval of the bunch, is actually just the 5-limit/rank-3 name the Pythagorean A4.

Ragas are sometimes separated into two tetrachords - the purvanga ("first part") from Sa to Ma, and the uttaranga ("second part") from Pa to high Sa.

A raga has an ascending form, "arohana", and a descending form, "avarohana". Often the same. A raga has a primary melodic note, "vadi", and a secondary melodic note, "samvadi", which is usually P4/P5 away from vadi.

Not all ragas have 7 notes. Often a note is skipped. The skipped note is called varjya, ("avoided, excluded, forbidden"). I think it's correct to describe skipped scale degrees as varjya, but also a varjya note might tell you to avoid one option for a scale degree when another one is present in the scale - e.g. don't ever play a minor third in melodic ornaments for a certain raga that contains a major third.

The raga called Mohanam is pentatonic, and it skips ^4 and ^7, i.e. Ma and Ni, in both ascending and descending forms. Perhaps we could call these varjya swaras (skipped scale degrees) in contrast to varjyra shrutis (forbidden notes). 

A raga will also often have an associated melodic phrase, a pakad, which helps people to identify it.

The cyclic permuation of a scale to get a new mode is called Graha Bhedam in Carnatic music or murchhana in Hindustani music.

The primary ragas of Carnatic music are called Melakarta, and there are 72 of them. I don't think they're all used - they just form the full combinatoric space of 7 note scales with certain nice properties. Other Carnatic ragas are considered to be derived from the primary ones, and are called Janya ragas. I believe that Carnatic music has pretty well settled into a finite closed set of ragas at this point, possibly as a consequence of detailed codification, like the 72 melakarta raga system. 

Somewhat similarly to the 72 melakarta ragas of Carnatic music, Hindustiani music has Thaats, which are like families of Ragas. Hindustani ragas are definitely not a closed set, but we can still look the most popular ones.

Let's look at some scales.

I learned about five Hindustanti ragas from the authors of the ShrutiSense program, or at least Rajarshi Ghosh (the code repository is in his name). Here are their shruti names:

P1: Sa

Grm2: Re1

m2: Re1_

M2: Re2

AcM2: Re2_

Grm3: Ga1

m3: Ga1_

M3: Ga2

AcM3: Ga2_

P4: Ma1

Ac4: Ma1_

AcA4: Ma2

AcAcA4: Ma2_

P5: Pa

Grm6: Dha1

m6: Dha1_

M6: Dha2

AcM6: Dha2_

Grm7: Ni1

m7: Ni1_

M7: Ni2

AcM7: Ni2_

P8: Sa_

Some of the intervals get an underscore if they're a syntonic comma off from a more ?common? interval. Also the octave gets an underscore. The interval with a 3-limit just tuning is the more common / unadorned option when the interval has a minor sonority and the interval with a 5-limit tuning is the more common / unadorned option when the interval has a major sonority.

All five ragas from the ShrutiSense authors have the same ascending and descending forms. We'll first look at the ragas Yaman and Kalyan. They have identical scales:

    [Sa, Re2, Ga2, Ma2, Pa, Dha2, Ni2, Sa_]

which is

    [P1, AcM2, M3, AcA4, P5, M6, M7, P8] # [1/1, 9/8, 5/4, 45/32, 3/2, 5/3, 15/8, 2/1]

They also have the same vadi or primary melodic note, namely Ga2 ~ M3, and the same samvadi of Ni2 ~ M7. And since

    M3 + P5 = M7

that looks fine. The two ragas also have the same avoid-note / forbidden-tone / varjya shruti, namely Ma1 ~ P4. The shruti Ma1 isn't in the scale, but they want you to be sure you don't play it even a little bit in melodic ornaments.

These two ragas, it seems, only differ in their distinguishing melodic motif, their pakad. Here's how the ShrutiSense authors share pakads for ragas:

Yaman pakad: [[Ni2, Re2, Ga2], [Ma2, Pa, Dha2]]

Kalyan pakad: [[Sa, Re2, Ga2, Ma2], [Pa, Ma2, Ga2]]

Those don't quite look like melodies to me - the notes don't have duration, and I don't know why they're bracketed that way. But supposedly those two lines hold the key for disambiguating these two ragas.

Let's look at raga Bilaval next. Its scale is simply a 5-limit major scale:

[Sa, Re2, Ga2, Ma1, Pa, Dha2, Ni2, Sa_]

or

[P1, M2, M3, P4, P5, M6, M7, P8]

Its vadi is Sa ~ P1, its samvadi is Pa ~ P5. It has no varjya to avoid. Its pakad is

    [[Sa, Re2, Ga2], [Pa, Dha2, Ni2]]

Nice. At some point I'll listen to all the pakads and find out what structure they possess, if any.

Next let's look at raga Khamaaj. Here is its scale:

    [Sa, Re2, Ga2, Ma1, Pa, Dha2, Ni1, Sa_]

or 

    [P1, M2, M3, P4, P5, M6, Grm7, P8]

The vaid is Pa ~ P5, the samvadi is Sa ~ P1. The varjya to avoid is Ni2 ~ M7. And the pakad is

    [[Sa, Ga2, Ma1, Pa], [Pa, Dha2, Ni1]]

.

Finally here is raga Bhairavi. Its scale is

[Sa, Re1, Ga1, Ma1, Pa, Dha1, Ni1, Sa_]

or

[P1, Grm2, Grm3, P4, P5, Grm6, Grm7, P8]

The vadi is Ma1 ~ P4, the samvadi is Sa ~ P1, there is no varjya, and the pakad is

[[Sa, Re1, Ga1], [Ma1, Pa, Dha1]]

You've heard that before, right? Classic raga Bhairavi pakad.

I've seen other ragas described in other sources, but at the level of 12-TET swaras, not at the level of shrutis. I'm going to keep looking.

...

Here's some more data from Dinesh S. Thakur in "The Notion of Twenty-Two Shrutis". He has his own shruti notation: 

S: 1/1

R11: 256/243

R12: 16/15

R21: 10/9

R22: 9/8

G11: 32/27

G12: 6/5

G21: 5/4

G22: 81/64

M11: 4/3

M12: 27/20

M21: 45/32

M22: 729/512

P: 3/2

D11: 128/81

D12: 8/5

D21: 5/3

D22: 27/16

N11: 16/9

N12: 9/5

N21: 15/8

N22: 243/128

Using this, he describes two pentatonic ragas, namely raga Bhoop and raga Deskar.

Bhoop: [S, R21, G21, P, D21, S']

Deskar: [S, R22, G22, P, D22, S']

These are

    Bhoop: [P1, M2, M3, P5, M6, P8]

    Deskar: [P1, AcM2, AcM3, P5, AcM6, P8]

Nice. These are just 5-limit and 3-limit versions of the major pentatonic scale. Easy.

He also decsribes raga Todi in 12-EDO, and then tries to infer the shrutis from knowing that ^2 should be its lower variant, R11, and then assuming that notes of the scale are related by factors of 3/2 and 4/3 as much as possible. This is interesting. I'm not sure that it's right, but here's what he came up with:

    [S, R11, G11, M21, D11, N21, S']

 That's a six note scale, but he says P is also used sometimes. But keeping with the six note scale, we get these intervals:

    [P1, Grm2, Grm3, AcA4, Grm6, M7, P8]

I don't think he's very confident in this, but it's something.

...

Vidyadhar Oke of 22shruti.com describes lots of ragas in term of shrutis. He has his own notation:

S = 1/1

r1 = 256/243

r2 = 16/15

R1 = 10/9

R2 = 9/8

g1 = 32/27

g2 = 6/5

G1 = 5/4

G2 = 81/64

M1 = 4/3

M2 = 27/20

m1 = 45/32

m2 = 729/512

P = 3/2

d1 = 128/81

d2 = 8/5

D1 = 5/3

D2 = 27/16

n1 = 16/19

n2 = 9/5

N1 = 15/8

N2 = 243/128

Upper and lower case letters, just one number. I like this fine.

He describes these on the page "Topic 5":

Raga Bhoop: [S, R1, G1, P, D1]

Raga Bageshri: [S, R1, g1, m1, P, D1, n1]

Raga Darabari: [S, R1, g1, M1, P, d1, n1]

Raga Bhairav: [S, r1, G1, M1, P, d1, N1]

Raga Saraswati: [S, R2, m1, P, D2, n2]

On the page "Topic 53", he describes these hindustani 100 ragas. Why does he have 100 when other people have 2 to 5? I don't know. Maybe he made them all up. Maybe he's just that good. From his writing, I wouldn't guess that he's all that good, but he does have those 100 ragas. Let's dive in. I started by trascribing all of them, but quickly saw how many were 4 or 5 note scales and got disinterested. I'm going to focus on more complete ragas.

1. Raga Abhogi: [S, R1, g1, M1, D1]

2. Raga Adana: [S, R2, g2, M2, P, d2, n2]

3. Raga Ahirabhairav: [S, G1, M1, P, D1, n1] // He also describes 4. Ahirabhairav as having a larger set of swaras: [S, r2, G1, M1, P, D1, n1].

4. Raga Amritavrshini: [S, G1, m1, P, n1]

5. Raga Arunakouns: [S, G1, M1, N1]

6. Raga Bageshri: [S, R1, M1, P, D1, n1]

7. Raga Bageshrikouns: [S, M1, D1, n1] // More swaras: [S, g1, M1, D1, n1].

8. Raga Bahar: [S, R2, M1, P, D1, N1] // More swaras: [S, R2, G1, M1, P, D1, n1, N1]. Both n1 and N1, yes.

9. Raga Bairagi: [S, r2, M1, n1]

10. Raga Barawa: [S, R1, G1, M1, P, D1, n1] // More swaras: [S, R1, g1, G1, M1, P, D1, n1]. This looks a little fake. He lists g1 and then G1, but those aren't in increasing order - g1 is higher than G1.

11. Raga Basant:

12. Raga Basantbukhari: 

13. Raga Bhairav:

14. Raga Bhairavi: [S, R2, g2, M2, P, d2, n2]

15. Raga Bhatiyar:

16. Raga Bheemapalas:

17. Raga Bihag: [S, R2, G1, M1, P, D1, N1]

18. Raga Bihagada: [S, R2, G1, M1, P, D1, N1]

19. Raga Bhinnakouns: 

20: Raga Bhinnashadja:

21: Raga Bhoop: [S, R1, G1, P, D1]

22: Raga Bhoopal Todi: [S, r2, g2, P, d2]

23: Raga Bibhas:

24: Raga Bilashkhani Todi: [S, r2, g2, M1, P, d2, n2]

25: Raga Bilawal: [S, R2, G1, M1, P, D1, N1]

26: Raga Brindavani Sarang:

27: Raga Champakali: [S, R2, G1, m1, P, d2]

28: Raga Chandrakouns:

29: Raga Charukeshi: [S, R2, G1, M1, P]

30: Raga Chhayanata: [S, R2, G1, M1, P, D1, N1]

31: Raga Darabari: [S, R1, M1, P, n1]

32: Raga Desh: [S, R2, G1, M1, P, D1, N1]

33: Raga Deshakar: 

34: Raga Dhani: 

35: Raga Durga:

36: Raga Garudadhwani: [S, R2, G1, M1, P, D1]

37: Raga Gorakha Kalyan: [S, R1, M1, D1, n1]

38: Raga Gouda Malhar: [S, R2, G1, M1, P, D1, N1]

39: Raga Gujari Todi: [S, r1, g1, m2, d1, N2]

40: Raga Gunakouns: [S, R2, G1, M1, P]

41: Raga Gunakri: [S, r2, M1, P, d2]

42: Raga Hamir: [S, R2, G1, m1, P, d2, N1]

43: Raga Hansadhwani: [S, R2, G1, P, N1]

44: Raga Hindol:

45: Raga Janasammohinini: [S, R1, G1, P, D1, n1]

46: Raga Jayajayavanti: [S, R2, G1, M1, P, D1, N1]

47: Raga Jayat: [S, G1, P, D2]

48: Raga Jog:

49: Raga Jogakouns:

50: Raga Jogiya

51: Raga Jounapuri: [S, R2, g2, M2, P, d2, n2]

52: Raga Kafi: [S, R2, M1, P, D1]

53: Raga Kalavati:

54: Raga Kalingada:

55: Raga Kamod: [S, R2, G1, m1, P, D2, N1]

56: Raga Kedar: [S, R2, G1, m1, P, D2, N1]

57: Raga Keeravani: 

58: Raga Khamaj: [S, R1, G1, M1, P, D1, N1]

59: Raga Kolahas: 

60: Raga Lalat: 

61: Raga Madhamat Saranga: 

62: Raga Madhukouns: 

63: Raga Madhuvanti: [S, R2, m1, P, D1, N1]

64: Raga Malakouns: [S, g2, M1, d2, n1]

65: Raga Malhar: [S, R2, M1, P, D1, N1]

66: Raga Mand: [S, R2, G1, P, D2, N1]

67: Raga Marawa: 

68: Raga Marubihag: [S, R2, G1, m1, P, D2, N1]

69: Raga Multani: [S, r2, g2, m2]

70: Raga Nand: [S, R2, G1, m1, P, D2, N1]

71: Raga Nata Bhairav: [S, R2, G1, M1, P, N1]

72: Raga Nayaki Kanada: [S, R2, g2, M2, P, n2]

73: Raga Paraj: [S, G1, P, N1]

74: Raga Patadeep: [S, R2, m1, P, D2, N1]

75: Raga Parameshwari: [S, g1, M1, D1, n1]

76: Raga Pooriya: [S, G1, D1, N1]

77: Raga Pooriyadhanashree: [S, G1, P, N1]

78: Raga Poorvi: [S, G1, M1, P, N1]

79: Raga Rageshri: [S, R1, G1, M1, D1, n1]

80: Raga Rajakalyan: [S, R2, G1, m1, D1, N1]

81: Raga Ramadasi Malhar: [S, R2, g1, G1, M1, P, D1, n1, N1] // Both g1 and G1, both n1 and N1. Pretty crazy.

82: Raga Ramakali: [S, G1, M1, P, D1, N1]

83: Raga Salagavarali: [S, r2, g2, P, n2]

84: Raga Saraswati: [S, R2, m1, P, D2]

85: Raga Shahana Kanada: [S, R1, M1, P, D1, n1]

86: Raga Shankara: [S, G1, P, D1, N1]

87: Raga Shree: [S, r2, G2, m2, d2, N2]

88: Raga Sohani: [S, G1, D1, N1]

89: Raga Soora Malhar: [S, R2, G1, M1, P, D1, N1]

90: Raga Sorath: [S, R2, M1, P, D1, N1]

91: Raga Shivaranjani: [S, R2, g2, P]

92: Raga Shuddha Kalyan: [S, R2, G2, m1, P, D2, N1]

93: Raga Shuddha Saranga: [S, R2, m2, P, D2, N1]

94: Raga Shyama Kalyan: [S, R2, G1, m1, P, D2, N1]

95: Raga Tilakakamod: [S, R2, G1, M1, P, D1, N1]

96: Raga Tilanga: [S, R2, G1, M1, P, N1]

97: Raga Todi: [S, r1, g1, m2, d1, N2]

98: Raga Yaman: [S, R2, G1, m1, P, D2, N1]

99: Raga Yaman Kalyan: [S, R2, G1, m1, P, D2, N1]

100: Raga Zinzhoti: [S, R1, G1, M1, P, D1, n1]

Nice.

Let's look at only the full 7-note scales. There are a lot of repetitions:

[P1, AcM2, AcM3, AcA4, P5, AcM6, M7] _ Shuddha Kalyan

[P1, AcM2, M3, AcA4, P5, AcM6, M7] _ Kamod

[P1, AcM2, M3, AcA4, P5, AcM6, M7] _ Kedar

[P1, AcM2, M3, AcA4, P5, AcM6, M7] _ Marubihag

[P1, AcM2, M3, AcA4, P5, AcM6, M7] _ Nand

[P1, AcM2, M3, AcA4, P5, AcM6, M7] _ Shyama Kalyan

[P1, AcM2, M3, AcA4, P5, AcM6, M7] _ Yaman

[P1, AcM2, M3, AcA4, P5, AcM6, M7] _ Yaman Kalyan

[P1, AcM2, M3, AcA4, P5, m6, M7] _ Hamir

[P1, AcM2, M3, P4, P5, M6, M7] _ Bihag

[P1, AcM2, M3, P4, P5, M6, M7] _ Bihagada

[P1, AcM2, M3, P4, P5, M6, M7] _ Bilawal

[P1, AcM2, M3, P4, P5, M6, M7] _ Chhayanata

[P1, AcM2, M3, P4, P5, M6, M7] _ Desh

[P1, AcM2, M3, P4, P5, M6, M7] _ Gouda Malhar

[P1, AcM2, M3, P4, P5, M6, M7] _ Jayajayavanti

[P1, AcM2, M3, P4, P5, M6, M7] _ Soora Malhar

[P1, AcM2, M3, P4, P5, M6, M7] _ Tilakakamod

[P1, AcM2, m3, Ac4, P5, m6, m7] _ Adana

[P1, AcM2, m3, Ac4, P5, m6, m7] _ Bhairavi

[P1, AcM2, m3, Ac4, P5, m6, m7] _ Jounapuri

[P1, M2, M3, P4, P5, M6, Grm7] _ Barawa

[P1, M2, M3, P4, P5, M6, Grm7] _ Zinzhoti

[P1, M2, M3, P4, P5, M6, M7] _ Khamaj

[P1, m2, m3, P4, P5, m6, m7] _ Bilashkhani Todi

There are only 8 distinct scales if we look at them this way, but maybe they have different vadis, samvadis, varjyras, pakads. There's an Ionian and a Phrygian mode, no Aeolian. That's interesting.

It's entirely possible I have some transcription errors, but I'd think that would tend to create more scales, not a mere 8 distinct ones.

...

His Raga Bageshri from the first set of 5 ragas doesn't match his Bageshri from the set of 100 ragas. And his Darabari doesn't match itself. And his Bhairav doesn't match itself. Starting to regret transcribing so much data from this guy. Maybe there would be more agreement if I transcribed his swaras instead of his shrutis. But shrutis are supposed to be more precise than swaras. Why would I do that? Why do some ragas have more swaras than shrutis in his writing?

...

Okay, I have a few ideas of how to proceed. 

    1) Look at Bharata's "Natya Shastra" for information about ancient ragas. He used shrutis, so these should be microtonal. 

    2) Look at 12-TET data about ragas and compare it to Vidyadhar Oke's data. Maybe it will show that his shrutis or his swaras are not as terrible as they seem. 

    3) Just keep looking for sources that describe 2 to 5 ragas at a time in terms of shrutis and hope that I can get a picture of indian music at that rate.

...

I was reading about texts like Natya Shastra and needed a little break. I decided to check if the Manuel Op de Coul's list of musical modes on the Huygens Fokker website had some ragas. It has tons, and they're specifed at the level of shrutis. Like with all the modes on that list, I don't know who authored them or where they get their ideas, but they're often quite good when they're historic / ethnographic. Let's have a look.

First the modes are described as coming from this set of frequency ratios: [1/1, 256/243, 16/15, 10/9, 9/8, 32/27, 6/5, 5/4, 81/64, 4/3, 27/20, 45/32, 729/512 (or 64/45), 3/2, 128/81, 8/5, 5/3, 27/16, 16/9, 9/5, 15/8, 243/128]. The only thing to notice here is the 64/45 option. This is the just tuning for the grave diminished fifth, Grd5, and it's the octave complement of the acute augmented fourth that we all know and love from other shruti texts, 45/32. I'm not going to use 64/45 for a bunch of reasons. 

    First, it's tuned by 22-EDO to 11 steps, not 12 like 729/512. So it's at least in the wrong place on this list. 

    Second, I've never heard of anyone using it in shruti analysis. I've seen 7/5 as a tritone in "‘Yati’ – Decorative mathematical patterns in Carnatic music" by Srividhya Balaji, 2020. I've seen 40/27 mentioned in discussions of Bharata's "Natya Shastra". Give me a historic reference or a famous ethnographer or at least a guy with an Indian name who I can cite.

    Third, 64/45 is a kind of altered 5th interval, and Indian music only has the pure fifth at Pa. To be fair, 40/27 from Bharata's "Natya Shastra" is also an altered fifth interval, but I'm not using that in my analysis of modern ragas either. So there.

    Fourth, I wouldn't know when to use it in preference to the ratios which are more standard.

Anyway, I don't like that suggestion of a ratio, but I still have a lot of hope for the modes. They're all written like this:

    "Raga Deskar": [3, 4, 6, 3, 6],

To decode that, we take a running sum and then use the results as indices in the frequency ratio list. If the scales were in 22-EDO, you could also think of them as relative steps in the scale. But we're not doing that yet. So let's accumulate steps, figure out frequency ratio references, figure out justly associated intervals, and look at a whole bug of ragas (and thats and murchhanas and gramas).

Here we go:

[P1, AcM2, AcM3, AcA4, P5, AcM6, M7, P8]: Murchhana Asvakranta

[P1, AcM2, AcM3, AcAcA4, P5, AcM6, AcM7, P8]: Raga Yaman

[P1, AcM2, Grm3, P4, P5, Grm6, Grm7, P8]: Raga Jaunpuri

[P1, AcM2, Grm3, m3, P4, P5, Grm6, m6, m7, P8]: Raga Darbari Kanada

[P1, AcM2, M3, AcA4, P5, AcM6, M7, P8]: Murchhana Sauviri, Kalyan That

[P1, AcM2, M3, P4, AcA4, P5, M6, M7, P8]: Raga Suddha Kalyan

[P1, AcM2, M3, P4, AcAcA4, P5, AcM6, AcM7, P8]: Raga Bihag

[P1, AcM2, M3, P4, AcAcA4, P5, AcM6, M7, P8]: Raga Gaud Sarang

[P1, AcM2, M3, P4, AcAcA4, P5, M6, AcM7, P8]: Raga Yaman Kalyan

[P1, AcM2, M3, P4, AcAcA4, P5, M6, Grm7, AcM7, P8]: Raga Chayanat

[P1, AcM2, M3, P4, P5, AcM6, Grm7, P8]: Khamaj That

[P1, AcM2, M3, P4, P5, AcM6, M7, P8]: Shadja Grama, Murchhana Uttaramandra, Suddha Swara Saptaka

[P1, AcM2, M3, P4, P5, M6, Grm7, AcM7, P8]: Raga Khamaj

[P1, AcM2, M3, P4, P5, M6, Grm7, P8]: Murchhana Suddhasadja, Raga Harikambhoji, Palaiyazh

[P1, AcM2, M3, P4, P5, M6, M7, P8]: Madhyama Grama, Bilaval That, Murchhana Suddhamadhya

[P1, AcM2, M3, P4, P5, M6, P8]: Raga Kambhoji

[P1, AcM2, M3, P5, AcM6, P8]: Raga Bhupali

[P1, AcM2, M3, P5, M7, P8]: Raga Hamsadhvani

[P1, AcM2, P4, P5, AcM6, P8]: Raga Durga

[P1, AcM2, m3, Ac4, P5, M6, m7, P8]: Gandhaara Grama (Narada der. sa-grama)

[P1, AcM2, m3, Ac4, P5, m6, m7, P8]: Gandhaara Grama (Narada der. ma-grama), Murchhana Pauravi

[P1, AcM2, m3, AcA4, P5, AcM6, M7, P8]: Raga Madhuvanti, Ambika

[P1, AcM2, m3, AcM3, P4, P5, AcM6, m7, AcM7, P8]: Raga Ramdasi Malhar

[P1, AcM2, m3, P4, P5, AcM6, m7, AcM7, P8]: Raga Mian Ki Malhar

[P1, AcM2, m3, P4, P5, AcM6, m7, P8]: Raga Kharaharapriya, Bhimpalasi

[P1, AcM2, m3, P4, P5, m6, AcM6, m7, P8]: Raga Anandabhairavi

[P1, AcM2, m3, P4, P5, m6, Grm7, P8]: Asavari That

[P1, AcM2, m3, P4, P5, m6, m7, P8]: Gandhaara Grama (Damodara), Raga Darbari, Darbari Kanada

[P1, Grm2, Grm3, AcA4, Grm6, AcM7, P8]: Raga Gurjari Todi

[P1, Grm2, Grm3, AcAcA4, P5, Grm6, AcM7, P8]: Todi That

[P1, Grm2, Grm3, AcAcA4, P5, Grm6, M7, P8]: Raga Varali

[P1, Grm2, Grm3, P4, P5, Grm6, AcM7, P8]: Raga Rampurmat Pilu

[P1, Grm2, Grm3, P4, P5, Grm6, Grm7, P8]: Raga Bilashkhani Todi

[P1, Grm2, Grm3, P4, P5, Grm6, m7, P8]: Raga Asavari

[P1, Grm2, M3, P4, Ac4, P5, Grm6, M7, P8]: Raga Ramkali

[P1, Grm2, M3, P4, AcA4, Grm6, AcM7, P8]: Raga Lalita

[P1, Grm2, M3, P4, P5, Grm6, AcM7, P8]: Bhairav That

[P1, Grm2, M3, P4, P5, Grm6, M6, M7, P8]: Raga Saurashtra

[P1, Grm2, M3, P5, M6, P8]: Raga Vibhas (marva)

[P1, M2, Grm3, P4, AcAcA4, Grm6, Grm7, P8]: Gandhaara Grama (Sarngadeva der. ma-grama)

[P1, M2, Grm3, P4, AcAcA4, Grm6, Grm7, P8]: Murchhana Uttarayata [17]

[P1, M2, Grm3, P4, AcAcA4, M6, Grm7, P8]: Murchhana Kalopanata [4]

[P1, M2, Grm3, P4, AcAcA4, m6, Grm7, P8]: Gandhaara Grama (Sarngadeva der. sa-grama)

[P1, M2, Grm3, P4, P5, M6, Grm7, P8]: Murchhana Abhirudgata, Kafi That, Raga Bageshri

[P1, M2, Grm3, P4, P5, m6, M6, Grm7, P8]: Raga Mukhari

[P1, M2, Grm3, m3, M3, P4, AcAcA4, P5, M6, Grm7, m7, M7, P8]: Old Indian gamut

[P1, M2, M3, P4, P5, M6, Grm7, P8]: Murchhana Hrishyaka

[P1, M2, M3, P4, P5, M6, M7, P8]: Raga Jogiya

[P1, M2, M3, P5, M6, P8]: Raga Deskar

[P1, M2, P4, P5, M6, P8]: Raga Suddha Malhar

[P1, M3, P4, P5, Grm7, M7, P8]: Raga Tilang

[P1, m2, AcM2, m3, M3, P4, AcA4, P5, m6, AcM6, m7, M7, P8]: Modern Indian gamut

[P1, m2, Grm3, P4, P5, m6, Grm7, P8]: Raga Kanakangi

[P1, m2, M3, AcA4, P5, AcM6, M7, P8]: Raga Marva

[P1, m2, M3, AcAcA4, P5, M6, M7, P8]: Raga Puriya Kalyan

[P1, m2, M3, AcAcA4, P5, m6, M7, P8]: Purvi That, Raga Shri

[P1, m2, M3, P4, AcAcA4, P5, M6, M7, P8]: Raga Bhatiyar

[P1, m2, M3, P5, m6, M7, P8]: Raga Bauli

[P1, m2, P4, P5, Grm6, P8]: Raga Saveri

[P1, m2, m3, Ac4, P5, m6, m7, P8]: Gandhaara Grama (Popley), Murchhana Matsarikrita

[P1, m2, m3, AcAcA4, P5, Grm6, AcM7, P8]: Raga Multani

[P1, m2, m3, P4, AcA4, m6, Grm7, P8]: Murchhana Margavi [20]

[P1, m2, m3, P4, AcA4, m6, m7, P8]: Murchhana Rajani [20]

[P1, m2, m3, P4, AcAcA4, m6, m7, P8]: Gandhaara Grama (Somanatha)

[P1, m2, m3, P4, P5, m6, m7, P8]: Murchhana Harinasva, Bhairavi That

[P1, m2, m3, P5, m6, P8]: Raga Bhoop

[P1, m3, P4, P5, m6, M7, P8]: Raga Takka

[P1, m3, P4, m6, Grm7, P8]: Raga Malkauns

There are sixty eight lines here, and some of them are associated with more than one scale.

Let's learn about some of these scales. We said before than a murchhana is a mode of another raga in hindustani music - which ragas are these murchhanas modes of? Do the Thats have similarities to each other, or differences from the ragas? Why do some of the scales have numbers in brackets, like [17], [20], [4]? How many of these are Hindustani, how many are Carnatic, and how many ancient enough to be neither? When these modes have the same names as modes described by other sources, how closely do they agree?

One mode from Manuel Op de Coul / Huygens-Fokker has "(Popley)" in its name, so that gives us one hint about sources. It's probably Herbet Popley who wrote "The Music of India" in 1921. Fortunately that one has been digitized and archived online.

Another mode is credited to Damodara. Presumably this is Damodara Misra/Chatura Damodara Pandita who wrote "Sangita Darpana" around 1625 CE.

Another is attributed to Somanatha. Presumably the same Somanatha who wrote the Raga-Vibodha analyzing Carnatic music around 1610 AD.

I've got some reading to do if I want to catch up.

...

I started reading! The Music Of Indian by Popley is very good. I only had to scroll to page 52 to get some data about scales. Here's what I've learned so far.

The two foundational scales in the Natya Sastra were Shadja-grama and Madhyama-grama, or Sa-grama and Ma-grama for short.  The Sa-grama goes

    [4, 3, 2, 4, 4, 3, 2] : [0, 4, 7, 9, 13, 17, 20, 22]

i.e.

    [P1, AcM2, M3, P4, P5, AcM6, M7, P8]

The Ma-grama differs in having a sharpened fourth:

    [4 3 4 2 4 3 2] : [0, 4, 7, 11, 13, 17, 20, 22]

i.e.

    [P1, AcM2, M3, AcA4, P5, AcM6, M7, P8]

Each of these has seven modes. Let's construct these ourselves. Here are 7 modes of Sa-grama, all distinct:

1: [P1, AcM2, M3, P4, P5, AcM6, M7]

2: [P1, M2, Grm3, P4, P5, M6, Grm7]

3: [P1, m2, m3, Ac4, P5, m6, m7]

4: [P1, AcM2, AcM3, AcA4, P5, AcM6, M7]

5: [P1, AcM2, M3, P4, P5, M6, Grm7]

6: [P1, M2, Grm3, P4, Gr5, Grm6, Grm7]

7: [P1, m2, m3, P4, Grd5, m6, m7]

And here are the 7 modes of Ma-grama, all distinct from each other and from the 7 modes of Sa-grama:

1: [P1, AcM2, M3, AcA4, P5, AcM6, M7]

2: [P1, M2, M3, P4, P5, M6, Grm7]

3: [P1, AcM2, m3, Ac4, P5, m6, m7]

4: [P1, m2, m3, P4, Grd5, m6, Grm7]

5: [P1, AcM2, M3, P4, P5, M6, M7]

6: [P1, M2, Grm3, P4, Gr5, M6, Grm7]

7: [P1, m2, m3, P4, P5, m6, m7]

Among these 14 modes, we have two notes that are not found in the standard modern set of shrutis: Ma-grama mode 6 has a Gr5, justly tuned to 40/27. We've heard before that that would show up. Nice. Also mode 7 of Sa-grama dn mode 4 of Ma-grama have Grd5, justly tuned to 64/45, which was mentioned as a possibility in the Huygens Fokker data. Pretty cool.

A Murchhana scale is a modal rotation of a grama. I constructed them by hand, but they also exist in the Manuel Op de Coul / Huygens-Fokker data. They are represented here in relative shrutis: 

Sa-grama modes:

^1: [4, 3, 2, 4, 4, 3, 2] _ Murchhana Uttaramandra = Sa-grama

^2: [3, 2, 4, 4, 3, 2, 4] _ Murchhana Abhirudgata

^3: [2, 4, 4, 3, 2, 4, 3] _ Murchhana Matsarikrita

^4: [4, 4, 3, 2, 4, 3, 2] _ Murchhana Asvakranta

^5: [4, 3, 2, 4, 3, 2, 4] _ Murchhana Suddhasadja

^6: [3, 2, 4, 3, 2, 4, 4] _ Murchhana Uttarayata

^7: [2, 4, 3, 2, 4, 4, 3] _ Murchhana Rajani

Ma-grama modes:

^1: [4, 3, 2, 4, 3, 4, 2]: Murchhana Suddhamadhya = Ma-grama

^2: [3, 2, 4, 3, 4, 2, 4]: Murchhana Kalopanata

^3: [2, 4, 3, 4, 2, 4, 3]: Murchhana Harinasva

^4: [4, 3, 4, 2, 4, 3, 2]: Murchhana Sauviri

^5: [3, 4, 2, 4, 3, 2, 4]: Murchhana Hrishyaka

^6: [4, 2, 4, 3, 2, 4, 3]: Murchhana Pauravi

^7: [2, 4, 3, 2, 4, 3, 4]: Murchhana Margavi

Now, in 12-TET, these 14 scales become 7 distinct scales - the major scale and its modes. So there isn't a huge amount of variety above. If you can't hear a syntonic comma, poor thing, they'll all sound like western music. In particular, mode 1 of Sa-grama sounds like mode 5 of Ma-grama, and then the correspondences move around the circle, 2 with 6, 3 with 7, et cetera. But even if you're comma deaf, poor thing, it's still nice intellectually to have a bunch of historically important 5-limit just intonation scales, don't you think? I think it's nice.

I've read that there were actually 18 jatis, 7 based on Sa-grama and 11 based on Ma-grama. I'm excited to learn how the extra jatis are formed.

After describing Sa-grama and Ma-grama, Popley next describes raga Bilaval as the core modern Hindustani raga, and raga Mukhari (or Kanakangi) as the core Carnatic scale. He also says that the first is a major scale and the second is a minor scale.

Bilaval: [4, 3, 2, 4, 3, 4, 2] 

Kanakangi: [2, 3, 4, 4, 2, 3, 4]

After seeing how cyclic permutations of Sa-grama and Ma-grama produce intervals that aren't found in the standard modern gamut of shrutis, I'm a little wary of looking at a scale in terms of shruti "steps" and replacing them with gamut tones - that procedure wouldn't give us the correct modes of Sa-grama and Ma-grama, so why should it give us the correct intervals here?

Fundamentally, if we want to take the gamut as fundamental, then we can't have exact cyclic permutation of scales. And if we want to rotate scales, then we can't have that particular gamut which gives only one option per step of 22-EDO. So which is more fundamental and which one should budge? I don't know.

Anyway, the step patterns for the two ragas above match the data from Huygens Fokker, so we've already found a possible detempering of them, restricted to the modern gamut. And that's not so bad.

I don't work with 22-EDO much, so I looked up its properties. Its canonical definition over rank-3 interval space leads to it tempering out GrA1, justly tuned to 250/243, and the Grd2, justly tuned to 2048/2025. So, uh, if we think of the shruti system as a 5-limit detempering of 22-EDO, then we shouldn't be shocked to find pairs of intervals that differ by GrA1 or Grd2 being treated identically. I guess. I'm not sure that really tells me anything of value.

Oh, 22-EDO is tunes the 3rd harmonic 7 cents sharp, and the 5th harmonic 5 cents flat. Pretty good.

...

The rest of Popley details many modern Ragas, but not at the level of shrutis. I think it's effectively 12-EDO. I don't think there's any method we can come up with which will detemper each 12-EDO scale to a single 5-limit scale which is correct in the Indian system, since e.g. the sa-grama and ma-grama modes tempered down to the same set of 7 modes, so those 7 modes each have two valid detemperings.

Sa-grama and Ma-grama both have only [AcM2, M2, and m2] as relative intervals. It would be nice if we could use that as a constraint in detempering.

If we make scales out of [AcM2, M2, m2] as relative degrees, and we require that every scale degree is separated from another one by one of [P8, P5, M3, m3] # [2/1, 3/2, 4/3, 5/4, 6/5], and we also have to hit P5 and P8 exactly, then there are only 38 ideal theoretical ragas:

[P1, AcM2, AcM3, Ac4, P5, AcM6, M7, P8]

[P1, AcM2, AcM3, Ac4, P5, AcM6, m7, P8]

[P1, AcM2, AcM3, AcA4, P5, AcM6, M7, P8]

[P1, AcM2, AcM3, AcA4, P5, AcM6, m7, P8]

[P1, AcM2, M3, AcA4, P5, AcM6, M7, P8]

[P1, AcM2, M3, AcA4, P5, AcM6, m7, P8]

[P1, AcM2, M3, AcA4, P5, M6, M7, P8]

[P1, AcM2, M3, AcA4, P5, m6, m7, P8]

[P1, AcM2, M3, P4, P5, AcM6, M7, P8]

[P1, AcM2, M3, P4, P5, AcM6, m7, P8]

[P1, AcM2, M3, P4, P5, M6, Grm7, P8]

[P1, AcM2, M3, P4, P5, M6, M7, P8]

[P1, AcM2, M3, P4, P5, m6, Grm7, P8]

[P1, AcM2, M3, P4, P5, m6, m7, P8]

[P1, AcM2, m3, Ac4, P5, AcM6, M7, P8]

[P1, AcM2, m3, Ac4, P5, AcM6, m7, P8]

[P1, AcM2, m3, Ac4, P5, M6, M7, P8]

[P1, AcM2, m3, Ac4, P5, m6, m7, P8]

[P1, AcM2, m3, P4, P5, AcM6, M7, P8]

[P1, AcM2, m3, P4, P5, AcM6, m7, P8]

[P1, AcM2, m3, P4, P5, M6, Grm7, P8]

[P1, AcM2, m3, P4, P5, M6, M7, P8]

[P1, AcM2, m3, P4, P5, m6, Grm7, P8]

[P1, AcM2, m3, P4, P5, m6, m7, P8]

[P1, M2, Grm3, P4, P5, M6, Grm7, P8]

[P1, M2, Grm3, P4, P5, m6, Grm7, P8]

[P1, M2, M3, AcA4, P5, M6, M7, P8]

[P1, M2, M3, P4, P5, M6, Grm7, P8]

[P1, M2, M3, P4, P5, M6, M7, P8]

[P1, M2, M3, P4, P5, m6, Grm7, P8]

[P1, M2, M3, P4, P5, m6, m7, P8]

[P1, m2, Grm3, P4, P5, M6, Grm7, P8]

[P1, m2, Grm3, P4, P5, m6, Grm7, P8]

[P1, m2, m3, Ac4, P5, m6, m7, P8]

[P1, m2, m3, P4, P5, M6, Grm7, P8]

[P1, m2, m3, P4, P5, M6, M7, P8]

[P1, m2, m3, P4, P5, m6, Grm7, P8]

[P1, m2, m3, P4, P5, m6, m7, P8]

Not all the modes of Sa-grama and Ma-grama were self-consonant in this way, but that's okay. Removing modes of Sa-grama and Ma-grama, there are 28 new ideal theoretical ragas here.

The full set of 38, if we remove cyclic permutations, can be reduced to 10 theoretical ideal ragas:

[P1, AcM2, M3, P4, P5, AcM6, M7, P8]

[P1, AcM2, M3, AcA4, P5, AcM6, M7, P8]

[P1, M2, M3, P4, P5, M6, M7, P8]

[P1, AcM2, AcM3, Ac4, P5, AcM6, M7, P8]

[P1, M2, M3, AcA4, P5, M6, M7, P8]

[P1, AcM2, m3, P4, P5, AcM6, M7, P8]

[P1, AcM2, m3, P4, P5, M6, M7, P8]

[P1, m2, m3, P4, P5, M6, M7, P8]

[P1, AcM2, m3, Ac4, P5, AcM6, M7, P8]

[P1, AcM2, m3, Ac4, P5, M6, M7, P8]

I might have normally selected the lexicographically least scale from all the cyclic permuations for the representative member, but I noticed that each cyclic equivalence class had just one self-consonant scale with a M7, and since Sa-grama, Ma-grama, and the western 5-limit just intonation major scale all have M7, it seemed a natural choice to use that one as the type-species. I didn't try to select for it, but this set of 10 scales happens to have no intervals with a grave minor quality, like Grm3 or Grm7 (though their rotations do).

None of that is real Indian music theory, I just thought it was interesting. If you want to detemper a 12-TET raga, and you have nothing else to go on, you could do worse than finding an option among the set of 38 theoretical ragas (if any of the set of 38 theoretical ragas tempers down to your scale).

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Okay, time to read more primary and secondary sources.

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Oh! John Stephens argues forcefully in "The Microtones of Bharata’s Natyashastra" that many authors misinterpret shrutis as being above assocaited svaras, but that Bharata's text only makes sense if you interpret the shrutis as being attached below associated shrutis. When I say forcefully, I don't mean angrily - I mean this guy knows his stuff.

Thus sa-grama is

    [3, 2, 4, 4, 3, 2, 4]

not

    [4, 3, 2, 4, 4, 3, 2]

I did use the latter form of Sa-grama, but I also used all of its modes, so that doesn't really change the set of scales I've looked at. The form of sa-grama reccomended by Stephens is the same as "Murchhana Abhirudgata, Kafi That, Raga Bageshri" from the Huygens-Fokker data.

Stephens gives ma-grama as 

    [3, 2, 4, 3, 4, 2, 4]

and contrasts it with an incorrect version presented by (Kolinski, Hornbostel, and Fox-Strangways):

    [4, 3, 2, 3, 5, 3, 2]

This has a 5\22 interval and looks crazy. The ma-grama I used before at least was a cyclic permuation of the one from Stephens:

    [4, 3, 4, 2, 4, 3, 2]

I kind of believe him. I should track the details of his arguments against scale data more closely. Until I've done that, I'm going to use the previous definitions of the gramas that I got from Popley. They seem to also match the Huygens Fokker data.

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I'm going back to the Huygens-Fokker data for  a while. Lots of the scales there have multiple names. I'm going to separate them out so that we can look at them in separate families, as we already did with the Murchhanas.

Let's start with the foundational scales, the gramas. Huygens-Fokker gives us one Sa-grama, one Ma-grama, and and 7 different Ga-gramas.

[4, 3, 2, 4, 4, 3, 2]: Shadja Grama

[4, 3, 2, 4, 3, 4, 2]: Madhyama Grama

[2, 4, 3, 3, 3, 4, 3]: Gandhaara Grama (Somanatha)

[2, 4, 4, 3, 2, 4, 3]: Gandhaara Grama (Popley)

[3, 2, 4, 3, 2, 4, 4]: Gandhaara Grama (Sarngadeva der. ma-grama)

[3, 2, 4, 3, 3, 3, 4]: Gandhaara Grama (Sarngadeva der. sa-grama)

[4, 2, 3, 4, 2, 4, 3]: Gandhaara Grama (Damodara)

[4, 2, 4, 3, 2, 4, 3]: Gandhaara Grama (Narada der. ma-grama)

[4, 2, 4, 3, 3, 3, 3]: Gandhaara Grama (Narada der. sa-grama)

Ga-grama was a fairly ancient scale, but was first described in a text written after the Natya Sastra (which describes Sa-grama and Ma-grama). I think most scholars would say that the precise form of Ga-grama has been lost to history, though people still make guesses about its form enough that we have 7 different possible version of it above. I think "der." in the parenthetical comments means "derived", e.g. "An author named Naranda derived this version of the Ga-grama from the Sa-grama".

Let's look at the Thats next. Lots of modern sources give lip service to the ancient concept of shrutis but then just describe scales in what seemst to be 12-EDO, but Thats/Thaats are a modern collection of scales in Hindustanti music, so it's exciting to see modern indian scales described in shrutis. A few words about Thaats from Wikipedia:

"The modern thaat system was created by Vishnu Narayan Bhatkhande (1860–1936), an influential musicologist in the field of classical music in the early decades of the twentieth century. Bhatkhande modelled his system after the Carnatic melakarta classification, devised around 1640 by the musicologist Vidwan Venkatamakhin"

His research led him to a system of thirty-two thaats, each named after a prominent raga associated with it. Out of those thirty-two thaats, more than a dozen thaats were popular during his time; however, he chose to highlight only ten such thaats.

The Huygens-Fokker data doesn't exactly have 10 thaats in terms of shrutis / the 5-limit gamut. It has 9 of the 10 thaats of Bhatkhande, and then it's missing Marwa/Marva. However there is a Raga Marva described in terms of shrutis / the 5-limit gamut. Let's assume that they're the same for now.

[4, 2, 3, 4, 2, 3, 4]: Asavari That

[2, 4, 3, 4, 2, 4, 3]: Bhairavi That = Ma-grama mode ^3.

[4, 3, 2, 4, 3, 4, 2]: Bilaval That = Ma-grama.

[3, 2, 4, 4, 3, 2, 4]: Kafi That = Sa-grama mode ^2.

[4, 3, 4, 2, 4, 3, 2]: Kalyan That = Ma-grama mode ^4.

[1, 6, 2, 4, 1, 7, 1]: Bhairav That

[4, 3, 2, 4, 4, 1, 4]: Khamaj That

[2, 5, 4, 2, 4, 3, 2]: Raga Marva (Marva That?)

[2, 5, 5, 1, 2, 5, 2]: Purvi That

[1, 4, 7, 1, 1, 7, 1]: Todi That

These are cool, right? The old scales were all made of [2, 3, 4] as relative numbers of shrutis / steps of 22-EDO, but now we have all of [1, 2, 3, 4, 5, 6, 7]. The first five Thats above are still made out of [2, 3, 4]\22, and the second group of five contains the spicy ones. One shruti is (or can be detempered to) a Pythagorean minor second, justly tuned to 256/243, and the 7 shruti interval is most readily identified with a 5-limit major third, 5/4. They're not actually all that spicy intervallically, they're just a little more varied than the ancient modes.

But wait! When we gave an intervallic description of e.g. Todi That before (by accumulating shruti steps from the Huygens-Fokker data, using these as indices into the 5-limit gamut of frequency ratios, and then writing in the intervals justly associated with those ratios), the scale progressed by 2nd intervals / alphabetically. So the 7-shruti intervals can't be major thirds! Because thirds aren't seconds. Let's look at both absolute and relative intervals for the Thats, shall we?

Asavari That: [AcM2, m2, M2, AcM2, m2, M2, AcM2]

Bhairavi That: [m2, AcM2, M2, AcM2, m2, AcM2, M2]

Bilaval That: [AcM2, M2, m2, AcM2, M2, AcM2, m2]

Kafi That: [M2, m2, AcM2, AcM2, M2, m2, AcM2]

Kalyan That: [AcM2, M2, AcM2, m2, AcM2, M2, m2]

Bhairav That: [Grm2, AcAcA2, m2, AcM2, Grm2, AcAcAcA2, Grm2]

Khamaj That: [AcM2, M2, m2, AcM2, AcM2, Grm2, AcM2]

Raga Marva: [m2, AcA2, AcM2, m2, AcM2, M2, m2]

Purvi That: [m2, AcA2, AcAcM2, Grm2, m2, AcA2, m2]

Todi That: [Grm2, AcM2, AcAcAcA2, Grm2, Grm2, AcAcAcA2, Grm2]

There are some pretty crazy intervals in here. In addition to Grm2, we have these additions:

5\22: AcA2 # 75/64

5\22: AcAcM2 # 729/640

6\22: AcAcA2 # 1215/1024

7\22: AcAcAcA2 # 19683/16384

Seems a little suspicious, right? Let's see how we can fix this nonsense.

If we just look at the 12-EDO pitches for the Thaats, we get this:

Asavari: [C, D, Eb, F, G, Ab, Bb, C]

Bhairav: [C, Db, E, F, G, Ab, B, C]

Bhairavi: [C, Db, Eb, F, G, Ab, Bb, C]

Bilaval: [C, D, E, F, G, A, B, C]

Kafi: [C, D, Eb, F, G, A, Bb, C]

Kalyan: [C, D, E, F#, G, A, B, C]

Khamaj: [C, D, E, F, G, A, Bb, C]

Marva: [C, Db, E, F#, G, A, B, C]

Purvi: [C, Db, E, F#, G, Ab, B, C]

Todi: [C, Db, Eb, F#, G, Ab, B, C]

I don't think that tells us anything though.

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